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A System of Logic, Ratiocinative and Inductive/Footnotes


   1 In the later editions of Archbishop Whately's "Logic," he states his
     meaning to be, not that "rules" for the ascertainment of truths by
     inductive investigation can not be laid down, or that they may not
     be "of eminent service," but that they "must always be comparatively
     vague and general, and incapable of being built up into a regular
     demonstrative theory like that of the Syllogism." (Book iv., ch.
     iv., § 3.) And he observes, that to devise a system for this
     purpose, capable of being "brought into a scientific form," would be
     an achievement which "he must be more sanguine than scientific who
     expects." (Book iv., ch. ii., § 4.) To effect this, however, being
     the express object of the portion of the present work which treats
     of Induction, the words in the text are no overstatement of the
     difference of opinion between Archbishop Whately and me on the
   2 Now forming a chapter in his volume on "The Philosophy of
   3 Archbishop Whately.
   4 I use these terms indiscriminately, because, for the purpose in
     view, there is no need for making any distinction between them. But
     metaphysicians usually restrict the name Intuition to the direct
     knowledge we are supposed to have of things external to our minds,
     and Consciousness to our knowledge of our own mental phenomena.
   5 This important theory has of late been called in question by a
     writer of deserved reputation, Mr. Samuel Bailey; but I do not
     conceive that the grounds on which it has been admitted as an
     established doctrine for a century past, have been at all shaken by
     that gentleman's objections. I have elsewhere said what appeared to
     me necessary in reply to his arguments. (Westminster Review for
     October, 1842; reprinted in "Dissertations and Discussions," vol.
   6 The view taken in the text, of the definition and purpose of Logic,
     stands in marked opposition to that of the school of philosophy
     which, in this country, is represented by the writings of Sir
     William Hamilton and of his numerous pupils. Logic, as this school
     conceives it, is "the Science of the Formal Laws of Thought;" a
     definition framed for the express purpose of excluding, as
     irrelevant to Logic, whatever relates to Belief and Disbelief, or to
     the pursuit of truth as such, and restricting the science to that
     very limited portion of its total province, which has reference to
     the conditions, not of Truth, but of Consistency. What I have
     thought it useful to say in opposition to this limitation of the
     field of Logic, has been said at some length in a separate work,
     first published in 1865, and entitled "An Examination of Sir William
     Hamilton's Philosophy, and of the Principal Philosophical Questions
     discussed in his Writings." For the purposes of the present
     Treatise, I am content that the justification of the larger
     extension which I give to the domain of the science, should rest on
     the sequel of the Treatise itself. Some remarks on the relation
     which the Logic of Consistency bears to the Logic of Truth, and on
     the place which that particular part occupies in the whole to which
     it belongs, will be found in the present volume (Book II., chap.
     iii., § 9).
   7 Computation or Logic, chap. ii.
   8 In the original "had, or had not." These last words, as involving
     a subtlety foreign to our present purpose, I have forborne to quote.
   9 Vide infra, note at the end of § 3, book ii., chap. ii.
  10 Notare, to mark; connotare, to mark along with; to mark one
     thing with or in addition to another.
  11 Archbishop Whately, who, in the later editions of his _Elements of
     Logic_, aided in reviving the important distinction treated of in
     the text, proposes the term "Attributive" as a substitute for
     "Connotative" (p. 22, 9th edit.). The expression is, in itself,
     appropriate; but as it has not the advantage of being connected with
     any verb, of so markedly distinctive a character as "to connote," it
     is not, I think, fitted to supply the place of the word Connotative
     in scientific use.
  12 A writer who entitles his book _Philosophy; or, the Science of
     Truth_, charges me in his very first page (referring at the foot of
     it to this passage) with asserting that general names have
     properly no signification. And he repeats this statement many times
     in the course of his volume, with comments, not at all flattering,
     thereon. It is well to be now and then reminded to how great a
     length perverse misquotation (for, strange as it appears, I do not
     believe that the writer is dishonest) can sometimes go. It is a
     warning to readers when they see an author accused, with volume and
     page referred to, and the apparent guarantee of inverted commas, of
     maintaining something more than commonly absurd, not to give
     implicit credence to the assertion without verifying the reference.
  13 "Take the familiar term Stone. It is applied to mineral and rocky
     materials, to the kernels of fruit, to the accumulations in the
     gall-bladder and in the kidney; while it is refused to polished
     minerals (called gems), to rocks that have the cleavage suited for
     roofing (slates), and to baked clay (bricks). It occurs in the
     designation of the magnetic oxide of iron (loadstone), and not in
     speaking of other metallic ores. Such a term is wholly unfit for
     accurate reasoning, unless hedged round on every occasion by other
     phrases; as building stone, precious stone, gall-stone, etc.
     Moreover, the methods of definition are baffled for want of
     sufficient community to ground upon. There is no quality uniformly
     present in the cases where it is applied, and uniformly absent where
     it is not applied; hence the definer would have to employ largely
     the license of striking off existing applications, and taking in new
     ones."--BAIN, Logic, ii., 172.
  14 Before quitting the subject of connotative names, it is proper to
     observe, that the first writer who, in our times, has adopted from
     the schoolmen the word to connote, Mr. James Mill, in his
     Analysis of the Phenomena of the Human Mind, employs it in a
     signification different from that in which it is here used. He uses
     the word in a sense co-extensive with its etymology, applying it to
     every case in which a name, while pointing directly to one thing
     (which is consequently termed its signification), includes also a
     tacit reference to some other thing. In the case considered in the
     text, that of concrete general names, his language and mine are the
     converse of one another. Considering (very justly) the signification
     of the name to lie in the attribute, he speaks of the word as
     noting the attribute, and connoting the things possessing the
     attribute. And he describes abstract names as being properly
     concrete names with their connotation dropped; whereas, in my view,
     it is the denotation which would be said to be dropped, what was
     previously connoted becoming the whole signification.
     In adopting a phraseology at variance with that which so high an
     authority, and one which I am less likely than any other person to
     undervalue, has deliberately sanctioned, I have been influenced by
     the urgent necessity for a term exclusively appropriated to express
     the manner in which a concrete general name serves to mark the
     attributes which are involved in its signification. This necessity
     can scarcely be felt in its full force by any one who has not found
     by experience how vain is the attempt to communicate clear ideas on
     the philosophy of language without such a word. It is hardly an
     exaggeration to say, that some of the most prevalent of the errors
     with which logic has been infected, and a large part of the
     cloudiness and confusion of ideas which have enveloped it, would, in
     all probability, have been avoided, if a term had been in common use
     to express exactly what I have signified by the term to connote. And
     the schoolmen, to whom we are indebted for the greater part of our
     logical language, gave us this also, and in this very sense. For
     though some of their general expressions countenance the use of the
     word in the more extensive and vague acceptation in which it is
     taken by Mr. Mill, yet when they had to define it specifically as a
     technical term, and to fix its meaning as such, with that admirable
     precision which always characterizes their definitions, they clearly
     explained that nothing was said to be connoted except forms, which
     word may generally, in their writings, be understood as synonymous
     with attributes.
     Now, if the word to connote, so well suited to the purpose to
     which they applied it, be diverted from that purpose by being taken
     to fulfill another, for which it does not seem to me to be at all
     required; I am unable to find any expression to replace it, but such
     as are commonly employed in a sense so much more general, that it
     would be useless attempting to associate them peculiarly with this
     precise idea. Such are the words, to involve, to imply, etc. By
     employing these, I should fail of attaining the object for which
     alone the name is needed, namely, to distinguish this particular
     kind of involving and implying from all other kinds, and to assure
     to it the degree of habitual attention which its importance demands.
  15 Professor Bain (Logic, i., 56) thinks that negative names are not
     names of all things whatever except those denoted by the correlative
     positive name, but only for all things of some particular class:
     not-white, for instance, he deems not to be a name for every thing
     in nature except white things, but only for every colored thing
     other than white. In this case, however, as in all others, the test
     of what a name denotes is what it can be predicated of: and we can
     certainly predicate of a sound, or a smell, that it is not white.
     The affirmation and the negation of the same attribute can not but
     divide the whole field of predication between them.
  16 Or rather, all objects except itself and the percipient mind; for,
     as we shall see hereafter, to ascribe any attribute to an object,
     necessarily implies a mind to perceive it.
     The simple and clear explanation given in the text, of relation and
     relative names, a subject so long the opprobrium of metaphysics, was
     given (as far as I know) for the first time, by Mr. James Mill, in
     his Analysis of the Phenomena of the Human Mind.
  17 On the preceding passage Professor Bain remarks (Logic, i., 265):
     "The Categories do not seem to have been intended as a
     classification of Namable Things, in the sense of 'an enumeration of
     all kinds of Things which are capable of being made predicates, or
     of having any thing predicated of them.' They seem to have been
     rather intended as a generalization of predicates; an analysis of
     the final import of predication. Viewed in this light, they are not
     open to the objections offered by Mr. Mill. The proper question to
     ask is not--In what Category are we to place sensations or other
     feelings or states of mind? but, Under what Categories can we
     predicate regarding states of mind? Take, for example, Hope. When we
     say that it is a state of mind, we predicate Substance: we may also
     describe how great it is (Quantity), what is the quality of it,
     pleasurable or painful (Quality), what it has reference to
     (Relation). Aristotle seems to have framed the Categories on the
     plan--Here is an individual; what is the final analysis of all that
     we can predicate about him?"
     This is doubtless a true statement of the leading idea in the
     classification. The Category οὐσία was certainly understood by
     Aristotle to be a general name for all possible answers to the
     question Quid sit? when asked respecting a concrete individual; as
     the other Categories are names comprehending all possible answers to
     the questions Quantum sit? Quale sit? etc. In Aristotle's
     conception, therefore, the Categories may not have been a
     classification of Things; but they were soon converted into one by
     his Scholastic followers, who certainly regarded and treated them as
     a classification of Things, and carried them out as such, dividing
     down the Category Substance as a naturalist might do, into the
     different classes of physical or metaphysical objects as
     distinguished from attributes, and the other Categories into the
     principal varieties of quantity, quality, relation, etc. It is,
     therefore, a just subject of complaint against them, that they had
     no Category of Feeling. Feeling is assuredly predicable as a summum
     genus, of every particular kind of feeling, for instance, as in Mr.
     Bain's example, of Hope: but it can not be brought within any of the
     Categories as interpreted either by Aristotle or by his followers.
  18 Philosophy of the Inductive Sciences, vol. i., p. 40.
  19 Discussions on Philosophy, etc. Appendix I., pp. 643, 644.
  20 It is to be regretted that Sir William Hamilton, though he often
     strenuously insists on this doctrine, and though, in the passage
     quoted, he states it with a comprehensiveness and force which leave
     nothing to be desired, did not consistently adhere to his own
     doctrine, but maintained along with it opinions with which it is
     utterly irreconcilable. See the third and other chapters of _An
     Examination of Sir William Hamilton's Philosophy_.
  21 "Nous savons qu'il existe quelque chose hors de nous, parceque nous
     ne pouvons expliquer nos perceptions sans les rattacher à des causes
     distinctes de nous mêmes; nous savons de plus que ces causes, dont
     nous ne connaissons pas d'ailleurs l'essence, produisent les effets
     les plus variables, les plus divers, et même les plus contraires,
     selon qu'elles rencontrent telle nature ou telle disposition du
     sujet. Mais savons-nous quelque chose de plus? et même, vu le
     caractère indéterminé des causes que nous concevons dans les corps,
     y a-t-il quelque chose de plus à savoir? Y a-t-il lieu de nous
     enquérir si nous percevons les choses telles qu'elles sont? Non
     évidemment.... Je ne dis pas que le problème est insoluble, _je dis
     qu'il est absurde et enferme une contradiction. Nous ne savons pas
     ce que ces causes sont en elles-mêmes_, et la raison nous défend de
     chercher à le connaître: mais il est bien évident à priori,
     qu'_elles ne sont pas en elles-mêmes ce qu'elles sont par rapport à
     nous_, puisque la présence du sujet modifie nécessairement leur
     action. Supprimez tout sujet sentant, il est certain que ces causes
     agiraient encore puisqu'elles continueraient d'exister; mais elles
     agiraient autrement; elles seraient encore des qualités et des
     propriétés, mais qui ne ressembleraient à rien de ce que nous
     connaissons. Le feu ne manifesterait plus aucune des propriétés que
     nous lui connaissons: que serait-il? C'est ce que nous ne saurons
     jamais. _C'est d'ailleurs peut-être un problème qui ne répugne pas
     seulement à la nature de notre esprit, mais à l'essence même des
     choses._ Quand même en effet on supprimerait par le pensée tous les
     sujets sentants, il faudrait encore admettre que nul corps ne
     manifesterait ses propriétés autrement qu'en relation avec un sujet
     quelconque, et dans ce cas _ses propriétés ne seraient encore que
     relatives_: en sorte qu'il me paraît fort raisonnable d'admettre que
     les propriétés déterminées des corps n'existent pas indépendamment
     d'un sujet quelconque, et que quand on demande si les propriétés de
     la matiere sont telles que nous les percevons, il faudrait voir
     auparavant si elles sont en tant que déterminées, et dans quel sens
     il est vrai de dire qu'elles sont."--_Cours d'Histoire de la
     Philosophie Morale au 18me siècle_, 8me leçon.
  22 An attempt, indeed, has been made by Reid and others, to establish
     that although some of the properties we ascribe to objects exist
     only in our sensations, others exist in the things themselves, being
     such as can not possibly be copies of any impression upon the
     senses; and they ask, from what sensations our notions of extension
     and figure have been derived? The gauntlet thrown down by Reid was
     taken up by Brown, who, applying greater powers of analysis than had
     previously been applied to the notions of extension and figure,
     pointed out that the sensations from which those notions are
     derived, are sensations of touch, combined with sensations of a
     class previously too little adverted to by metaphysicians, those
     which have their seat in our muscular frame. His analysis, which was
     adopted and followed up by James Mill, has been further and greatly
     improved upon in Professor Bain's profound work, _The Senses and the
     Intellect_, and in the chapters on "Perception" of a work of eminent
     analytic power, Mr. Herbert Spencer's Principles of Psychology.
     On this point M. Cousin may again be cited in favor of the better
     doctrine. M. Cousin recognizes, in opposition to Reid, the essential
     subjectivity of our conceptions of what are called the primary
     qualities of matter, as extension, solidity, etc., equally with
     those of color, heat, and the remainder of the so-called secondary
     qualities.--Cours, ut supra, 9me leçon.
  23 This doctrine, which is the most complete form of the philosophical
     theory known as the Relativity of Human Knowledge, has, since the
     recent revival in this country of an active interest in metaphysical
     speculation, been the subject of a greatly increased amount of
     discussion and controversy; and dissentients have manifested
     themselves in considerably greater number than I had any knowledge
     of when the passage in the text was written. The doctrine has been
     attacked from two sides. Some thinkers, among whom are the late
     Professor Ferrier, in his Institutes of Metaphysic, and Professor
     John Grote, in his Exploratio Philosophica, appear to deny
     altogether the reality of Noumena, or Things in themselves--of an
     unknowable substratum or support for the sensations which we
     experience, and which, according to the theory, constitute all our
     knowledge of an external world. It seems to me, however, that in
     Professor Grote's case at least, the denial of Noumena is only
     apparent, and that he does not essentially differ from the other
     class of objectors, including Mr. Bailey in his valuable _Letters on
     the Philosophy of the Human Mind_, and (in spite of the striking
     passage quoted in the text) also Sir William Hamilton, who contend
     for a direct knowledge by the human mind of more than the
     sensations--of certain attributes or properties as they exist not in
     us, but in the Things themselves.
     With the first of these opinions, that which denies Noumena, I have,
     as a metaphysician, no quarrel; but, whether it be true or false, it
     is irrelevant to Logic. And since all the forms of language are in
     contradiction to it, nothing but confusion could result from its
     unnecessary introduction into a treatise, every essential doctrine
     of which could stand equally well with the opposite and accredited
     opinion. The other and rival doctrine, that of a direct perception
     or intuitive knowledge of the outward object as it is in itself,
     considered as distinct from the sensations we receive from it, is of
     far greater practical moment. But even this question, depending on
     the nature and laws of Intuitive Knowledge, is not within the
     province of Logic. For the grounds of my own opinion concerning it,
     I must content myself with referring to a work already mentioned--_An
     Examination of Sir William Hamilton's Philosophy_; several chapters
     of which are devoted to a full discussion of the questions and
     theories relating to the supposed direct perception of external
  24 Professor Bain (Logic, i., 49) defines attributes as "points of
     community among classes." This definition expresses well one point
     of view, but is liable to the objection that it applies only to the
     attributes of classes; though an object, unique in its kind, may be
     said to have attributes. Moreover, the definition is not ultimate,
     since the points of community themselves admit of, and require,
     further analysis; and Mr. Bain does analyze them into resemblances
     in the sensations, or other states of consciousness excited by the
  25 Analysis of the Human Mind, i., 126 et seq.
  26 Logic, i., 85.
  27 Instead of Universal and Particular as applied to propositions,
     Professor Bain proposes (Logic, i., 81) the terms Total and
     Partial; reserving the former pair of terms for their inductive
     meaning, "the contrast between a general proposition and the
     particulars or individuals that we derive it from." This change in
     nomenclature would be attended with the further advantage, that
     Singular propositions, which in the Syllogism follow the same rules
     as Universal, would be included along with them in the same class,
     that of Total predications. It is not the Subject's denoting many
     things or only one, that is of importance in reasoning, it is that
     the assertion is made of the whole or a part only of what the
     Subject denotes. The words Universal and Particular, however, are so
     familiar and so well understood in both the senses mentioned by Mr.
     Bain, that the double meaning does not produce any material
  28 It may, however, be considered as equivalent to a universal
     proposition with a different predicate, viz.: "All wine is good
     quâ wine," or "is good in respect of the qualities which
     constitute it wine."
  29 Logic, i., 82.
  30 Dr. Whewell (Philosophy of Discovery, p. 242) questions this
     statement, and asks, "Are we to say that a mole can not dig the
     ground, except he has an idea of the ground, and of the snout and
     paws with which he digs it?" I do not know what passes in a mole's
     mind, nor what amount of mental apprehension may or may not
     accompany his instinctive actions. But a human being does not use a
     spade by instinct; and he certainly could not use it unless he had
     knowledge of a spade, and of the earth which he uses it upon.
  31 Professor Bain remarks, in qualification of the statement in the
     text (Logic, i., 50), that the word Class has two meanings; "the
     class definite, and the class indefinite. The class definite is an
     enumeration of actual individuals, as the Peers of the Realm, the
     oceans of the globe, the known planets.... The class indefinite is
     unenumerated. Such classes are stars, planets, gold-bearing rocks,
     men, poets, virtuous.... In this last acceptation of the word, class
     name and general name are identical. The class name denotes an
     indefinite number of individuals, and connotes the points of
     community or likeness."
     The theory controverted in the text, tacitly supposes all classes to
     be definite. I have assumed them to be indefinite; because, for
     the purposes of Logic, definite classes, as such, are almost
     useless; though often serviceable as means of abridged expression.
     (Vide infra, book iii., chap. ii.)
  32 "From hence also this may be deduced, that the first truths were
     arbitrarily made by those that first of all imposed names upon
     things, or received them from the imposition of others. For it is
     true (for example) that man is a living creature, but it is for
     this reason, that it pleased men to impose both these names on the
     same thing."--Computation or Logic, chap. iii., sect. 8.
  33 "Men are subject to err not only in affirming and denying, but also
     in perception, and in silent cogitation.... Tacit errors, or the
     errors of sense and cogitation, are made by passing from one
     imagination to the imagination of another different thing; or by
     feigning that to be past, or future, which never was, nor ever shall
     be; as when by seeing the image of the sun in water, we imagine the
     sun itself to be there; or by seeing swords, that there has been, or
     shall be, fighting, because it used to be so for the most part; or
     when from promises we feign the mind of the promiser to be such and
     such; or, lastly, when from any sign we vainly imagine something to
     be signified which is not. And errors of this sort are common to all
     things that have sense."--Computation or Logic, chap. v., sect. 1.
  34 Chap. iii., sect 3.
  35 To the preceding statement it has been objected, that "we naturally
     construe the subject of a proposition in its extension, and the
     predicate (which therefore may be an adjective) in its intension
     (connotation): and that consequently co-existence of attributes does
     not, any more than the opposite theory of equation of groups,
     correspond with the living processes of thought and language." I
     acknowledge the distinction here drawn, which, indeed, I had myself
     laid down and exemplified a few pages back (p. 77). But though it is
     true that we naturally "construe the subject of a proposition in its
     extension," this extension, or in other words, the extent of the
     class denoted by the name, is not apprehended or indicated directly.
     It is both apprehended and indicated solely through the attributes.
     In the "living processes of thought and language" the extension,
     though in this case really thought of (which in the case of the
     predicate it is not), is thought of only through the medium of what
     my acute and courteous critic terms the "intension."
     For further illustrations of this subject, see _Examination of Sir
     William Hamilton's Philosophy_, chap. xxii.
  36 Professor Bain, in his Logic (i., 256), excludes Existence from
     the list, considering it as a mere name. All propositions, he says,
     which predicate mere existence "are more or less abbreviated, or
     elliptical: when fully expressed they fall under either co-existence
     or succession. When we say there exists a conspiracy for a
     particular purpose, we mean that at the present time a body of men
     have formed themselves into a society for a particular object; which
     is a complex affirmation, resolvable into propositions of
     co-existence and succession (as causation). The assertion that the
     dodo does not exist, points to the fact that this animal, once known
     in a certain place, has disappeared or become extinct; is no longer
     associated with the locality: all which may be better stated without
     the use of the verb 'exist.' There is a debated question--Does an
     ether exist? but the concrete form would be this--'Are heat and light
     and other radiant influences propagated by an ethereal medium
     diffused in space;' which is a proposition of causation. In like
     manner the question of the Existence of a Deity can not be discussed
     in that form. It is properly a question as to the First Cause of
     the Universe, and as to the continued exertion of that Cause in
     providential superintendence." (i., 407.)
     Mr. Bain thinks it "fictitious and unmeaning language" to carry up
     the classification of Nature to one summum genus, Being, or that
     which Exists; since nothing can be perceived or apprehended but by
     way of contrast with something else (of which important truth, under
     the name of Law of Relativity, he has been in our time the principal
     expounder and champion), and we have no other class to oppose to
     Being, or fact to contrast with Existence.
     I accept fully Mr. Bain's Law of Relativity, but I do not understand
     by it that to enable us to apprehend or be conscious of any fact, it
     is necessary that we should contrast it with some other positive
     fact. The antithesis necessary to consciousness need not, I
     conceive, be an antithesis between two positives; it may be between
     one positive and its negative. Hobbes was undoubtedly right when he
     said that a single sensation indefinitely prolonged would cease to
     be felt at all; but simple intermission, without other change, would
     restore it to consciousness. In order to be conscious of heat, it is
     not necessary that we should pass to it from cold; it suffices that
     we should pass to it from a state of no sensation, or from a
     sensation of some other kind. The relative opposite of Being,
     considered as a summum genus, is Nonentity, or Nothing; and we have,
     now and then, occasion to consider and discuss things merely in
     contrast with Nonentity.
     I grant that the decision of questions of Existence usually if not
     always depends on a previous question of either Causation or
     Co-existence. But Existence is nevertheless a different thing from
     Causation or Co-existence, and can be predicated apart from them.
     The meaning of the abstract name Existence, and the connotation of
     the concrete name Being, consist, like the meaning of all other
     names, in sensations or states of consciousness: their peculiarity
     is that to exist, is to excite, or be capable of exciting, any
     sensations or states of consciousness: no matter what, but it is
     indispensable that there should be some. It was from overlooking
     this that Hegel, finding that Being is an abstraction reached by
     thinking away all particular attributes, arrived at the
     self-contradictory proposition on which he founded all his
     philosophy, that Being is the same as Nothing. It is really the name
     of Something, taken in the most comprehensive sense of the word.
  37 Book iv., chap. vii.
  38 Logic, i., 103-105.
  39 The doctrines which prevented the real meaning of Essences from
     being understood, had not assumed so settled a shape in the time of
     Aristotle and his immediate followers, as was afterward given to
     them by the Realists of the Middle Ages. Aristotle himself (in his
     Treatise on the Categories) expressly denies that the δεύτεραι οὔσιαι, or Substantiæ Secundæ, inhere in a subject. They are only, he says, predicated of it.
  40 The always acute and often profound author of _An Outline of
     Sematology_ (Mr. B. H. Smart) justly says, "Locke will be much more
     intelligible, if, in the majority of places, we substitute 'the
     knowledge of' for what he calls 'the Idea of' " (p. 10). Among the
     many criticisms on Locke's use of the word Idea, this is the one
     which, as it appears to me, most nearly hits the mark; and I quote
     it for the additional reason that it precisely expresses the point
     of difference respecting the import of Propositions, between my view
     and what I have spoken of as the Conceptualist view of them. Where a
     Conceptualist says that a name or a proposition expresses our Idea
     of a thing, I should generally say (instead of our Idea) our
     Knowledge, or Belief, concerning the thing itself.
  41 This distinction corresponds to that which is drawn by Kant and
     other metaphysicians between what they term analytic and
     synthetic, judgments; the former being those which can be evolved
     from the meaning of the terms used.
  42 If we allow a differentia to what is not really a species. For the
     distinction of Kinds, in the sense explained by us, not being in any
     way applicable to attributes, it of course follows that although
     attributes may be put into classes, those classes can be admitted to
     be genera or species only by courtesy.
  43 Professor Bain, in his Logic, takes a peculiar view of Definition.
     He holds (i., 71) with the present work, that "the definition in its
     full import, is the sum of all the properties connoted by the name;
     it exhausts the meaning of a word." But he regards the meaning of a
     general name as including, not indeed all the common properties of
     the class named, but all of them that are ultimate properties, not
     resolvable into one another. "The enumeration of the attributes of
     oxygen, of gold, of man, should be an enumeration of the final (so
     far as can be made out), the underivable, powers or functions of
     each," and nothing less than this is a complete Definition (i., 75).
     An independent property, not derivable from other properties, even
     if previously unknown, yet as soon as discovered becomes, according
     to him, part of the meaning of the term, and should be included in
     the definition. "When we are told that diamond, which we know to be
     a transparent, glittering, hard, and high-priced substance, is
     composed of carbon, and is combustible, we must put these additional
     properties on the same level as the rest; to us they are henceforth
     connoted by the name" (i., 73). Consequently the propositions that
     diamond is composed of carbon, and that it is combustible, are
     regarded by Mr. Bain as merely verbal propositions. He carries this
     doctrine so far as to say that unless mortality can be shown to be a
     consequence of the ultimate laws of animal organization, mortality
     is connoted by man, and "Man is Mortal" is a merely verbal
     proposition. And one of the peculiarities (I think a disadvantageous
     peculiarity) of his able and valuable treatise, is the large number
     of propositions requiring proof, and learned by experience, which,
     in conformity with this doctrine, he considers as not real, but
     verbal, propositions.
     The objection I have to this language is that it confounds, or at
     least confuses, a much more important distinction than that which it
     draws. The only reason for dividing Propositions into real and
     verbal, is in order to discriminate propositions which convey
     information about facts, from those which do not. A proposition
     which affirms that an object has a given attribute, while
     designating the object by a name which already signifies the
     attribute, adds no information to that which was already possessed
     by all who understood the name. But when this is said, it is implied
     that, by the signification of a name, is meant the signification
     attached to it in the common usage of life. I can not think we ought
     to say that the meaning of a word includes matters of fact which are
     unknown to every person who uses the word unless he has learned them
     by special study of a particular department of Nature; or that
     because a few persons are aware of these matters of fact, the
     affirmation of them is a proposition conveying no information. I
     hold that (special scientific connotation apart) a name means, or
     connotes, only the properties which it is a mark of in the general
     mind; and that in the case of any additional properties, however
     uniformly found to accompany these, it remains possible that a thing
     which did not possess the properties might still be thought entitled
     to the name. Ruminant, according to Mr. Bain's use of language,
     connotes cloven-hoofed, since the two properties are always found
     together, and no connection has ever been discovered between them:
     but ruminant does not mean cloven-hoofed; and were an animal to be
     discovered which chews the cud, but has its feet undivided, I
     venture to say that it would still be called ruminant.
  44 In the fuller discussion which Archbishop Whately has given to this
     subject in his later editions, he almost ceases to regard the
     definitions of names and those of things as, in any important sense,
     distinct. He seems (9th ed., p. 145) to limit the notion of a Real
     Definition to one which "explains any thing more of the nature of
     the thing than is implied in the name;" (including under the word
     "implied," not only what the name connotes, but every thing which
     can be deduced by reasoning from the attributes connoted). Even
     this, as he adds, is usually called not a Definition, but a
     Description; and (as it seems to me) rightly so called. A
     Description, I conceive, can only be ranked among Definitions, when
     taken (as in the case of the zoological definition of man) to
     fulfill the true office of a Definition, by declaring the
     connotation given to a word in some special use, as a term of
     science or art: which special connotation of course would not be
     expressed by the proper definition of the word in its ordinary
     Mr. De Morgan, exactly reversing the doctrine of Archbishop Whately,
     understands by a Real Definition one which contains less than the
     Nominal Definition, provided only that what it contains is
     sufficient for distinction. "By real definition I mean such an
     explanation of the word, be it the whole of the meaning or only
     part, as will be sufficient to separate the things contained under
     that word from all others. Thus the following, I believe, is a
     complete definition of an elephant: An animal which naturally drinks
     by drawing the water into its nose, and then spurting it into its
     mouth."--Formal Logic, p. 36. Mr. De Morgan's general proposition
     and his example are at variance; for the peculiar mode of drinking
     of the elephant certainly forms no part of the meaning of the word
     elephant. It could not be said, because a person happened to be
     ignorant of this property, that he did not know what an elephant
  45 In the only attempt which, so far as I know, has been made to refute
     the preceding argumentation, it is maintained that in the first form
     of the syllogism,
     A dragon is a thing which breathes flame,
     A dragon is a serpent,
     Therefore some serpent or serpents breathe flame,
     "there is just as much truth in the conclusion as there is in the
     premises, or rather, no more in the latter than in the former. If
     the general name serpent includes both real and imaginary serpents,
     there is no falsity in the conclusion; if not, there is falsity in
     the minor premise."
     Let us, then, try to set out the syllogism on the hypothesis that
     the name serpent includes imaginary serpents. We shall find that it
     is now necessary to alter the predicates; for it can not be asserted
     that an imaginary creature breathes flame; in predicating of it such
     a fact, we assert by the most positive implication that it is real,
     and not imaginary. The conclusion must run thus, "Some serpent or
     serpents either do or are imagined to breathe flame." And to prove
     this conclusion by the instance of dragons, the premises must be, A
     dragon is imagined as breathing flame. A dragon is a (real or
     imaginary) serpent: from which it undoubtedly follows, that there
     are serpents which are imagined to breathe flame; but the major
     premise is not a definition, nor part of a definition; which is all
     that I am concerned to prove.
     Let us now examine the other assertion--that if the word serpent
     stands for none but real serpents, the minor premise (a dragon is a
     serpent) is false. This is exactly what I have myself said of the
     premise, considered as a statement of fact: but it is not false as
     part of the definition of a dragon; and since the premises, or one
     of them, must be false (the conclusion being so), the real premise
     can not be the definition, which is true, but the statement of fact,
     which is false.
  46 "Few people" (I have said in another place) "have reflected how
     great a knowledge of Things is required to enable a man to affirm
     that any given argument turns wholly upon words. There is, perhaps,
     not one of the leading terms of philosophy which is not used in
     almost innumerable shades of meaning, to express ideas more or less
     widely different from one another. Between two of these ideas a
     sagacious and penetrating mind will discern, as it were intuitively,
     an unobvious link of connection, upon which, though perhaps unable
     to give a logical account of it, he will found a perfectly valid
     argument, which his critic, not having so keen an insight into the
     Things, will mistake for a fallacy turning on the double meaning of
     a term. And the greater the genius of him who thus safely leaps over
     the chasm, the greater will probably be the crowing and vainglory of
     the mere logician, who, hobbling after him, evinces his own superior
     wisdom by pausing on its brink, and giving up as desperate his
     proper business of bridging it over."
  47 The different cases of Equipollency, or "Equivalent Propositional
     Forms," are set forth with some fullness in Professor Bain's
     Logic. One of the commonest of these changes of expression, that
     from affirming a proposition to denying its negative, or _vicè
     versa_, Mr. Bain designates, very happily, by the name Obversion.
  48 As Sir William Hamilton has pointed out, "Some A is not B" may also
     be converted in the following form: "No B is some A." Some men are
     not negroes; therefore, No negroes are some men (e.g.,
  49 Contraries:
     All  A is B
     No   A is B
     Some A is B
     Some A is not B
     All  A is B
     Some A is not B
     Also contradictories:
     No A is B
     Some A is B
     Respectively subalternate:
     All  A is B and No A is B
     Some A is B and Some A is not B
  50 Professor Bain denies the claim of Singular Propositions to be
     classed, for the purposes of ratiocination, with Universal; though
     they come within the designation which he himself proposes as an
     equivalent for Universal, that of Total. He would even, to use his
     own expression, banish them entirely from the syllogism. He takes as
     an example,
     Socrates is wise,
     Socrates is poor, therefore
     Some poor men are wise,
     or more properly (as he observes) "one poor man is wise." "Now, if
     wise, poor, and a man, are attributes belonging to the meaning of
     the word Socrates, there is then no march of reasoning at all. We
     have given in Socrates, inter alia, the facts wise, poor, and a
     man, and we merely repeat the concurrence which is selected from the
     whole aggregate of properties making up the whole, Socrates. The
     case is one under the head 'Greater and Less Connotation' in
     Equivalent Propositional Forms, or Immediate Inference.
     "But the example in this form does not do justice to the syllogism
     of singulars. We must suppose both propositions to be real, the
     predicates being in no way involved in the subject. Thus
     Socrates was the master of Plato,
     Socrates fought at Delium,
     The master of Plato fought at Delium.
     "It may fairly be doubted whether the transitions, in this instance,
     are any thing more than equivalent forms. For the proposition
     'Socrates was the master of Plato and fought at Delium,' compounded
     out of the two premises, is obviously nothing more than a
     grammatical abbreviation. No one can say that there is here any
     change of meaning, or any thing beyond a verbal modification of the
     original form. The next step is, 'The master of Plato fought at
     Delium,' which is the previous statement cut down by the omission of
     Socrates. It contents itself with reproducing a part of the meaning,
     or saying less than had been previously said. The full equivalent of
     the affirmation is, 'The master of Plato fought at Delium, and the
     master of Plato was Socrates:' the new form omits the last piece of
     information, and gives only the first. Now, we never consider that
     we have made a real inference, a step in advance, when we repeat
     less than we are entitled to say, or drop from a complex statement
     some portion not desired at the moment. Such an operation keeps
     strictly within the domain of equivalence, or Immediate Inference.
     In no way, therefore, can a syllogism with two singular premises be
     viewed as a genuine syllogistic or deductive inference." (Logic,
     i., 159.)
     The first argument, as will have been seen, rests upon the
     supposition that the name Socrates has a meaning; that man, wise,
     and poor, are parts of this meaning; and that by predicating them of
     Socrates we convey no information; a view of the signification of
     names which, for reasons already given (Note to § 4 of the chapter
     on Definition, supra, pp. 110, 111.), I can not admit, and which,
     as applied to the class of names which Socrates belongs to, is at
     war with Mr. Bain's own definition of a Proper Name (i., 148), "a
     single meaningless mark or designation appropriated to the thing."
     Such names, Mr. Bain proceeded to say, do not necessarily indicate
     even human beings: much less then does the name Socrates include the
     meaning of wise or poor. Otherwise it would follow that if Socrates
     had grown rich, or had lost his mental faculties by illness, he
     would no longer have been called Socrates.
     The second part of Mr. Bain's argument, in which he contends that
     even when the premises convey real information, the conclusion is
     merely the premises with a part left out, is applicable, if at all,
     as much to universal propositions as to singular. In every syllogism
     the conclusion contains less than is asserted in the two premises
     taken together. Suppose the syllogism to be
     All bees are intelligent,
     All bees are insects, therefore
     Some insects are intelligent:
     one might use the same liberty taken by Mr. Bain, of joining
     together the two premises as if they were one--"All bees are insects
     and intelligent"--and might say that in omitting the middle term
     bees we make no real inference, but merely reproduce part of what
     had been previously said. Mr. Bain's is really an objection to the
     syllogism itself, or at all events to the third figure: it has no
     special applicability to singular propositions.
  51 His conclusions are, "The first figure is suited to the discovery or
     proof of the properties of a thing; the second to the discovery or
     proof of the distinctions between things; the third to the discovery
     or proof of instances and exceptions; the fourth to the discovery,
     or exclusion, of the different species of a genus." The reference of
     syllogisms in the last three figures to the _dictum de omni et
     nullo_ is, in Lambert's opinion, strained and unnatural: to each of
     the three belongs, according to him, a separate axiom, co-ordinate
     and of equal authority with that dictum, and to which he gives the
     names of dictum de diverso for the second figure, _dictum de
     exemplo for the third, and dictum de reciproco_ for the fourth.
     See part i., or Dianoiologie, chap, iv., § 229 et seqq. Mr.
     Bailey (Theory of Reasoning, 2d ed., pp. 70-74) takes a similar
     view of the subject.
  52 Since this chapter was written, two treatises have appeared (or
     rather a treatise and a fragment of a treatise), which aim at a
     further improvement in the theory of the forms of ratiocination: Mr.
     De Morgan's "Formal Logic; or, the Calculus of Inference, Necessary
     and Probable;" and the "New Analytic of Logical Forms," attached as
     an Appendix to Sir William Hamilton's Discussions on Philosophy,
     and at greater length, to his posthumous Lectures on Logic.
     In Mr. De Morgan's volume--abounding, in its more popular parts, with
     valuable observations felicitously expressed--the principal feature
     of originality is an attempt to bring within strict technical rules
     the cases in which a conclusion can be drawn from premises of a form
     usually classed as particular. Mr. De Morgan observes, very justly,
     that from the premises most Bs are Cs, most Bs are As, it may be
     concluded with certainty that some As are Cs, since two portions of
     the class B, each of them comprising more than half, must
     necessarily in part consist of the same individuals. Following out
     this line of thought, it is equally evident that if we knew exactly
     what proportion the "most" in each of the premises bear to the
     entire class B, we could increase in a corresponding degree the
     definiteness of the conclusion. Thus if 60 per cent. of B are
     included in C, and 70 per cent. in A, 30 per cent. at least must be
     common to both; in other words, the number of As which are Cs, and
     of Cs which are As, must be at least equal to 30 per cent. of the
     class B. Proceeding on this conception of "numerically definite
     propositions," and extending it to such forms as these:--"45 Xs (or
     more) are each of them one of 70 Ys," or "45 Xs (or more) are no one
     of them to be found among 70 Ys," and examining what inferences
     admit of being drawn from the various combinations which may be made
     of premises of this description, Mr. De Morgan establishes universal
     formulæ for such inferences; creating for that purpose not only a
     new technical language, but a formidable array of symbols analogous
     to those of algebra.
     Since it is undeniable that inferences, in the cases examined by Mr.
     De Morgan, can legitimately be drawn, and that the ordinary theory
     takes no account of them, I will not say that it was not worth while
     to show in detail how these also could be reduced to formulæ as
     rigorous as those of Aristotle. What Mr. De Morgan has done was
     worth doing once (perhaps more than once, as a school exercise); but
     I question if its results are worth studying and mastering for any
     practical purpose. The practical use of technical forms of reasoning
     is to bar out fallacies: but the fallacies which require to be
     guarded against in ratiocination properly so called, arise from the
     incautious use of the common forms of language; and the logician
     must track the fallacy into that territory, instead of waiting for
     it on a territory of his own. While he remains among propositions
     which have acquired the numerical precision of the Calculus of
     Probabilities, the enemy is left in possession of the only ground on
     which he can be formidable. And since the propositions (short of
     universal) on which a thinker has to depend, either for purposes of
     speculation or of practice, do not, except in a few peculiar cases,
     admit of any numerical precision; common reasoning can not be
     translated into Mr. De Morgan's forms, which therefore can not serve
     any purpose as a test of it.
     Sir William Hamilton's theory of the "quantification of the
     predicate" may be described as follows:
     "Logically" (I quote his words) "we ought to take into account the
     quantity, always understood in thought, but usually, for manifest
     reasons, elided in its expression, not only of the subject, but also
     of the predicate of a judgment." All A is B, is equivalent to all A
     is some B. No A is B, to No A is any B. Some A is B, is
     tantamount to some A is some B. Some A is not B, to Some A is _not
     any_ B. As in these forms of assertion the predicate is exactly
     co-extensive with the subject, they all admit of simple conversion;
     and by this we obtain two additional forms--Some B is all A, and No
     B is some A. We may also make the assertion All A is all B, which
     will be true if the classes A and B are exactly co-extensive. The
     last three forms, though conveying real assertions, have no place in
     the ordinary classification of Propositions. All propositions, then,
     being supposed to be translated into this language, and written each
     in that one of the preceding forms which answers to its
     signification, there emerges a new set of syllogistic rules,
     materially different from the common ones. A general view of the
     points of difference may be given in the words of Sir W. Hamilton
     (Discussions, 2d ed., p. 651):
     "The revocation of the two terms of a Proposition to their true
     relation; a proposition being always an equation of its subject
     and its predicate.
     "The consequent reduction of the Conversion of Propositions from
     three species to one--that of Simple Conversion.
     "The reduction of all the General Laws of Categorical Syllogisms
     to a single Canon.
     "The evolution from that one canon of all the Species and varieties
     of Syllogisms.
     "The abrogation of all the Special Laws of Syllogism.
     "A demonstration of the exclusive possibility of Three Syllogistic
     Figures; and (on new grounds) the scientific and final abolition of
     the Fourth.
     "A manifestation that Figure is an unessential variation in
     syllogistic form; and the consequent absurdity of Reducing the
     syllogisms of the other figures to the first.
     "An enouncement of one Organic Principle for each Figure.
     "A determination of the true number of the Legitimate Moods; with
     "Their amplification in number (thirty-six);
     "Their numerical equality under all the figures; and
     "Their relative equivalence, or virtual identity, throughout every
     schematic difference.
     "That, in the second and third figures, the extremes holding both
     the same relation to the middle term, there is not, as in the first,
     an opposition and subordination between a term major and a term
     minor, mutually containing and contained, in the counter wholes of
     Extension and Comprehension.
     "Consequently, in the second and third figures, there is no
     determinate major and minor premises, and there are two indifferent
     conclusions: whereas in the first the premises are determinate, and
     there is a single proximate conclusion."
     This doctrine, like that of Mr. De Morgan previously noticed, is a
     real addition to the syllogistic theory; and has moreover this
     advantage over Mr. De Morgan's "numerically definite Syllogism,"
     that the forms it supplies are really available as a test of the
     correctness of ratiocination; since propositions in the common form
     may always have their predicates quantified, and so be made amenable
     to Sir W. Hamilton's rules. Considered, however, as a contribution
     to the Science of Logic, that is, to the analysis of the mental
     processes concerned in reasoning, the new doctrine appears to me, I
     confess, not merely superfluous, but erroneous; since the form in
     which it clothes propositions does not, like the ordinary form,
     express what is in the mind of the speaker when he enunciates the
     proposition. I can not think Sir William Hamilton right in
     maintaining that the quantity of the predicate is "always understood
     in thought." It is implied, but is not present to the mind of the
     person who asserts the proposition. The quantification of the
     predicate, instead of being a means of bringing out more clearly the
     meaning of the proposition, actually leads the mind out of the
     proposition, into another order of ideas. For when we say, All men
     are mortal, we simply mean to affirm the attribute mortality of all
     men; without thinking at all of the class mortal in the concrete,
     or troubling ourselves about whether it contains any other beings or
     not. It is only for some artificial purpose that we ever look at the
     proposition in the aspect in which the predicate also is thought of
     as a class-name, either including the subject only, or the subject
     and something more. (See above, p. 77, 78.)
     For a fuller discussion of this subject, see the twenty-second
     chapter of a work already referred to, "An Examination of Sir
     William Hamilton's Philosophy."
  53 Mr. Herbert Spencer (Principles of Psychology, pp. 125-7), though
     his theory of the syllogism coincides with all that is essential of
     mine, thinks it a logical fallacy to present the two axioms in the
     text, as the regulating principles of syllogism. He charges me with
     falling into the error pointed out by Archbishop Whately and myself,
     of confounding exact likeness with literal identity; and maintains,
     that we ought not to say that Socrates possesses the same
     attributes which are connoted by the word Man, but only that he
     possesses attributes exactly like them: according to which
     phraseology, Socrates, and the attribute mortality, are not two
     things co-existing with the same thing, as the axiom asserts, but
     two things coexisting with two different things.
     The question between Mr. Spencer and me is merely one of language;
     for neither of us (if I understand Mr. Spencer's opinions rightly)
     believes an attribute to be a real thing, possessed of objective
     existence; we believe it to be a particular mode of naming our
     sensations, or our expectations of sensation, when looked at in
     their relation to an external object which excites them. The
     question raised by Mr. Spencer does not, therefore, concern the
     properties of any really existing thing, but the comparative
     appropriateness, for philosophical purposes, of two different modes
     of using a name. Considered in this point of view, the phraseology I
     have employed, which is that commonly used by philosophers, seems to
     me to be the best. Mr. Spencer is of opinion that because Socrates
     and Alcibiades are not the same man, the attribute which constitutes
     them men should not be called the same attribute; that because the
     humanity of one man and that of another express themselves to our
     senses not by the same individual sensations but by sensations
     exactly alike, humanity ought to be regarded as a different
     attribute in every different man. But on this showing, the humanity
     even of any one man should be considered as different attributes now
     and half an hour hence; for the sensations by which it will then
     manifest itself to my organs will not be a continuation of my
     present sensations, but a repetition of them; fresh sensations, not
     identical with, but only exactly like the present. If every general
     conception, instead of being "the One in the Many," were considered
     to be as many different conceptions as there are things to which it
     is applicable, there would be no such thing as general language. A
     name would have no general meaning if man connoted one thing when
     predicated of John, and another, though closely resembling, thing
     when predicated of William. Accordingly a recent pamphlet asserts
     the impossibility of general knowledge on this precise ground.
     The meaning of any general name is some outward or inward
     phenomenon, consisting, in the last resort, of feelings; and these
     feelings, if their continuity is for an instant broken, are no
     longer the same feelings, in the sense of individual identity. What,
     then, is the common something which gives a meaning to the general
     name? Mr. Spencer can only say, it is the similarity of the
     feelings; and I rejoin, the attribute is precisely that similarity.
     The names of attributes are in their ultimate analysis names for the
     resemblances of our sensations (or other feelings). Every general
     name, whether abstract or concrete, denotes or connotes one or more
     of those resemblances. It will not, probably, be denied, that if a
     hundred sensations are undistinguishably alike, their resemblance
     ought to be spoken of as one resemblance, and not a hundred
     resemblances which merely resemble one another. The things
     compared are many, but the something common to all of them must be
     conceived as one, just as the name is conceived as one, though
     corresponding to numerically different sensations of sound each time
     it is pronounced. The general term man does not connote the
     sensations derived once from one man, which, once gone, can no more
     occur again than the same flash of lightning. It connotes the
     general type of the sensations derived always from all men, and the
     power (always thought of as one) of producing sensations of that
     type. And the axiom might be thus worded: Two types of sensation
     each of which co-exists with a third type, co-exist with another; or
     Two powers each of which co-exists with a third power co-exist
     with one another.
     Mr. Spencer has misunderstood me in another particular. He supposes
     that the co-existence spoken of in the axiom, of two things with the
     same third thing, means simultaneousness in time. The co-existence
     meant is that of being jointly attributes of the same subject. The
     attribute of being born without teeth, and the attribute of having
     thirty-two teeth in mature age, are in this sense co-existent, both
     being attributes of man, though ex vi termini never of the same
     man at the same time.
  54 Supra, p. 93.
  55 Professor Bain (Logic, i., 157) considers the axiom (or rather
     axioms) here proposed as a substitute for the dictum de omni, to
     possess certain advantages, but to be "unworkable as a basis of the
     syllogism. The fatal defect consists in this, that it is ill-adapted
     to bring out the difference between total and partial coincidence of
     terms, the observation of which is the essential precaution in
     syllogizing correctly. If all the terms were co-extensive, the axiom
     would flow on admirably; A carries B, all B and none but B; B
     carries C in the same manner; at once A carries C, without
     limitation or reserve. But in point of fact, we know that while A
     carries B, other things carry B also; whence a process of limitation
     is required, in transferring A to C through B. A (in common with
     other things) carries B; B (in common with other things) carries C;
     whence A (in common with other things) carries C. The axiom provides
     no means of making this limitation; if we were to follow A
     literally, we should be led to suppose A and C co-extensive: for
     such is the only obvious meaning of 'the attribute A coincides with
     the attribute C.' "
     It is certainly possible that a careless learner here and there may
     suppose that if A carries B, it follows that B carries A. But if any
     one is so incautious as to commit this mistake, the very earliest
     lesson in the logic of inference, the Conversion of propositions,
     will correct it. The first of the two forms in which I have stated
     the axiom, is in some degree open to Mr. Bain's criticism: when B is
     said to co-exist with A (it must be by a lapsus calami that Mr.
     Bain uses the word coincide), it is possible, in the absence of
     warning, to suppose the meaning to be that the two things are only
     found together. But this misinterpretation is excluded by the other,
     or practical, form of the maxim; Nota notoe est nota rei ipsius. No
     one would be in any danger of inferring that because a is a mark
     of b, b can never exist without a; that because being in a
     confirmed consumption is a mark of being about to die, no one dies
     who is not in a consumption; that because being coal is a mark of
     having come out of the earth, nothing can come out of the earth
     except coal. Ordinary knowledge of English seems a sufficient
     protection against these mistakes, since in speaking of a mark of
     any thing we are never understood as implying reciprocity.
     A more fundamental objection is stated by Mr. Bain in a subsequent
     passage (p. 158). "The axiom does not accommodate itself to the type
     of Deductive Reasoning as contrasted with Induction--the application
     of a general principle to a special case. Any thing that fails to
     make prominent this circumstance is not adapted as a foundation for
     the syllogism." But though it may be proper to limit the term
     Deduction to the application of a general principle to a special
     case, it has never been held that Ratiocination or Syllogism is
     subject to the same limitation; and the adoption of it would exclude
     a great amount of valid and conclusive syllogistic reasoning.
     Moreover, if the dictum de omni makes prominent the fact of the
     application of a general principle to a particular case, the axiom I
     propose makes prominent the condition which alone makes that
     application a real inference.
     I conclude, therefore, that both forms have their value, and their
     place in Logic. The dictum de omni should be retained as the
     fundamental axiom of the logic of mere consistency, often called
     Formal Logic; nor have I ever quarreled with the use of it in that
     character, nor proposed to banish it from treatises on Formal Logic.
     But the other is the proper axiom for the logic of the pursuit of
     truth by way of Deduction; and the recognition of it can alone show
     how it is possible that deductive reasoning can be a road to truth.
  56 Logic, p. 239 (9th ed.).
  57 It is hardly necessary to say, that I am not contending for any such
     absurdity as that we actually "ought to have known" and considered
     the case of every individual man, past, present, and future, before
     affirming that all men are mortal: although this interpretation has
     been, strangely enough, put upon the preceding observations. There
     is no difference between me and Archbishop Whately, or any other
     defender of the syllogism, on the practical part of the matter; I am
     only pointing out an inconsistency in the logical theory of it, as
     conceived by almost all writers. I do not say that a person who
     affirmed, before the Duke of Wellington was born, that all men are
     mortal, knew that the Duke of Wellington was mortal; but I do say
     that he asserted it; and I ask for an explanation of the apparent
     logical fallacy, of adducing in proof of the Duke of Wellington's
     mortality, a general statement which presupposes it. Finding no
     sufficient resolution of this difficulty in any of the writers on
     Logic, I have attempted to supply one.
  58 The language of ratiocination would, I think, be brought into closer
     agreement with the real nature of the process, if the general
     propositions employed in reasoning, instead of being in the form All
     men are mortal, or Every man is mortal, were expressed in the form
     Any man is mortal. This mode of expression, exhibiting as the type
     of all reasoning from experience "The men A, B, C, etc., are so and
     so, therefore any man is so and so," would much better manifest
     the true idea--that inductive reasoning is always, at bottom,
     inference from particulars to particulars, and that the whole
     function of general propositions in reasoning, is to vouch for the
     legitimacy of such inferences.
  59 Review of Quetelet on Probabilities, Essays, p. 367.
  60 Philosophy of Discovery, p. 289.
  61 Theory of Reasoning, chap. iv., to which I may refer for an able
     statement and enforcement of the grounds of the doctrine.
  62 On a recent careful reperusal of Berkeley's whole works, I have been
     unable to find this doctrine in them. Sir John Herschel probably
     meant that it is implied in Berkeley's argument against abstract
     ideas. But I can not find that Berkeley saw the implication, or had
     ever asked himself what bearing his argument had on the theory of
     the syllogism. Still less can I admit that the doctrine is (as has
     been affirmed by one of my ablest and most candid critics) "among
     the standing marks of what is called the empirical philosophy."
  63 Logic, book iv., chap. i., sect. 1.
  64 See the important chapter on Belief, in Professor Bain's great
     treatise, The Emotions and the Will, pp. 581-4.
  65 A writer in the "British Quarterly Review" (August, 1846), in a
     review of this treatise, endeavors to show that there is no _petitio
     principii_ in the syllogism, by denying that the proposition, All
     men are mortal, asserts or assumes that Socrates is mortal. In
     support of this denial, he argues that we may, and in fact do, admit
     the general proposition that all men are mortal, without having
     particularly examined the case of Socrates, and even without knowing
     whether the individual so named is a man or something else. But this
     of course was never denied. That we can and do draw conclusions
     concerning cases specifically unknown to us, is the datum from which
     all who discuss this subject must set out. The question is, in what
     terms the evidence, or ground, on which we draw these conclusions,
     may best be designated--whether it is most correct to say, that the
     unknown case is proved by known cases, or that it is proved by a
     general proposition including both sets of cases, the unknown and
     the known? I contend for the former mode of expression. I hold it an
     abuse of language to say, that the proof that Socrates is mortal, is
     that all men are mortal. Turn it in what way we will, this seems to
     me to be asserting that a thing is the proof of itself. Whoever
     pronounces the words, All men are mortal, has affirmed that Socrates
     is mortal, though he may never have heard of Socrates; for since
     Socrates, whether known to be so or not, really is a man, he is
     included in the words, All men, and in every assertion of which they
     are the subject. If the reviewer does not see that there is a
     difficulty here, I can only advise him to reconsider the subject
     until he does: after which he will be a better judge of the success
     or failure of an attempt to remove the difficulty. That he had
     reflected very little on the point when he wrote his remarks, is
     shown by his oversight respecting the dictum de omni et nullo. He
     acknowledges that this maxim as commonly expressed--"Whatever is true
     of a class, is true of every thing included in the class," is a mere
     identical proposition, since the class is nothing but the things
     included in it. But he thinks this defect would be cured by wording
     the maxim thus--"Whatever is true of a class, is true of every thing
     which can be shown to be a member of the class:" as if a thing
     could "be shown" to be a member of the class without being one. If a
     class means the sum of all the things included in the class, the
     things which can "be shown" to be included in it are part of the
     sum, and the dictum is as much an identical proposition with
     respect to them as to the rest. One would almost imagine that, in
     the reviewer's opinion, things are not members of a class until they
     are called up publicly to take their place in it--that so long, in
     fact, as Socrates is not known to be a man, he is not a man, and
     any assertion which can be made concerning men does not at all
     regard him, nor is affected as to its truth or falsity by any thing
     in which he is concerned.
     The difference between the reviewer's theory and mine may be thus
     stated. Both admit that when we say, All men are mortal, we make an
     assertion reaching beyond the sphere of our knowledge of individual
     cases; and that when a new individual, Socrates, is brought within
     the field of our knowledge by means of the minor premise, we learn
     that we have already made an assertion respecting Socrates without
     knowing it: our own general formula being, to that extent, for the
     first time interpreted to us. But according to the reviewer's
     theory, the smaller assertion is proved by the larger: while I
     contend, that both assertions are proved together, by the same
     evidence, namely, the grounds of experience on which the general
     assertion was made, and by which it must be justified.
     The reviewer says, that if the major premise included the
     conclusion, "we should be able to affirm the conclusion without the
     intervention of the minor premise; but every one sees that that is
     impossible." A similar argument is urged by Mr. De Morgan (_Formal
     Logic_, p. 259): "The whole objection tacitly assumes the
     superfluity of the minor; that is, tacitly assumes we know Socrates
     (Mr. De Morgan says 'Plato,' but to prevent confusion I have kept to
     my own exemplum.) to be a man as soon as we know him to be
     Socrates." The objection would be well grounded if the assertion
     that the major premise includes the conclusion, meant that it
     individually specifies all it includes. As, however, the only
     indication it gives is a description by marks, we have still to
     compare any new individual with the marks; and to show that this
     comparison has been made, is the office of the minor. But since, by
     supposition, the new individual has the marks, whether we have
     ascertained him to have them or not; if we have affirmed the major
     premise, we have asserted him to be mortal. Now my position is that
     this assertion can not be a necessary part of the argument. It can
     not be a necessary condition of reasoning that we should begin by
     making an assertion, which is afterward to be employed in proving a
     part of itself. I can conceive only one way out of this difficulty,
     viz., that what really forms the proof is the other part of the
     assertion: the portion of it, the truth of which has been
     ascertained previously: and that the unproved part is bound up in
     one formula with the proved part in mere anticipation, and as a
     memorandum of the nature of the conclusions which we are prepared to
     With respect to the minor premise in its formal shape, the minor as
     it stands in the syllogism, predicating of Socrates a definite class
     name, I readily admit that it is no more a necessary part of
     reasoning than the major. When there is a major, doing its work by
     means of a class name, minors are needed to interpret it: but
     reasoning can be carried on without either the one or the other.
     They are not the conditions of reasoning, but a precaution against
     erroneous reasoning. The only minor premise necessary to reasoning
     in the example under consideration, is, Socrates is like A, B, C,
     and the other individuals who are known to have died. And this is
     the only universal type of that step in the reasoning process which
     is represented by the minor. Experience, however, of the uncertainty
     of this loose mode of inference, teaches the expediency of
     determining beforehand what kind of likeness to the cases
     observed, is necessary to bring an unobserved case within the same
     predicate; and the answer to this question is the major. The minor
     then identifies the precise kind of likeness possessed by Socrates,
     as being the kind required by the formula. Thus the syllogistic
     major and the syllogistic minor start into existence together, and
     are called forth by the same exigency. When we conclude from
     personal experience without referring to any record--to any general
     theorems, either written, or traditional, or mentally registered by
     ourselves as conclusions of our own drawing--we do not use, in our
     thoughts, either a major or a minor, such as the syllogism puts into
     words. When, however, we revise this rough inference from
     particulars to particulars, and substitute a careful one, the
     revision consists in selecting two syllogistic premises. But this
     neither alters nor adds to the evidence we had before; it only puts
     us in a better position for judging whether our inference from
     particulars to particulars is well grounded.
  66 Infra, book iii., chap. ii.
  67 Infra, book iii., ch. iv., § 3, and elsewhere.
  68 It is justly remarked by Professor Bain (Logic, ii., 134) that the
     word Hypothesis is here used in a somewhat peculiar sense. An
     hypothesis, in science, usually means a supposition not proved to be
     true, but surmised to be so, because if true it would account for
     certain known facts; and the final result of the speculation may be
     to prove its truth. The hypotheses spoken of in the text are of a
     different character; they are known not to be literally true, while
     as much of them as is true is not hypothetical, but certain. The two
     cases, however, resemble in the circumstance that in both we reason,
     not from a truth, but from an assumption, and the truth therefore of
     the conclusions is conditional, not categorical. This suffices to
     justify, in point of logical propriety, Stewart's use of the term.
     It is of course needful to bear in mind that the hypothetical
     element in the definitions of geometry is the assumption that what
     is very nearly true is exactly so. This unreal exactitude might be
     called a fiction, as properly as an hypothesis; but that
     appellation, still more than the other, would fail to point out the
     close relation which exists between the fictitious point or line and
     the points and lines of which we have experience.
  69 Mechanical Euclid, pp. 149 et seqq.
  70 We might, it is true, insert this property into the definition of
     parallel lines, framing the definition so as to require, both that
     when produced indefinitely they shall never meet, and also that any
     straight line which intersects one of them shall, if prolonged, meet
     the other. But by doing this we by no means get rid of the
     assumption; we are still obliged to take for granted the geometrical
     truth, that all straight lines in the same plane, which have the
     former of these properties, have also the latter. For if it were
     possible that they should not, that is, if any straight lines in the
     same plane, other than those which are parallel according to the
     definition, had the property of never meeting although indefinitely
     produced, the demonstrations of the subsequent portions of the
     theory of parallels could not be maintained.
  71 Some persons find themselves prevented from believing that the
     axiom, Two straight lines can not inclose a space, could ever become
     known to us through experience, by a difficulty which may be stated
     as follows: If the straight lines spoken of are those contemplated
     in the definition--lines absolutely without breadth and absolutely
     straight--that such are incapable of inclosing a space is not proved
     by experience, for lines such as these do not present themselves in
     our experience. If, on the other hand, the lines meant are such
     straight lines as we do meet with in experience, lines straight
     enough for practical purposes, but in reality slightly zigzag, and
     with some, however trifling, breadth; as applied to these lines the
     axiom is not true, for two of them may, and sometimes do, inclose a
     small portion of space. In neither case, therefore, does experience
     prove the axiom.
     Those who employ this argument to show that geometrical axioms can
     not be proved by induction, show themselves unfamiliar with a common
     and perfectly valid mode of inductive proof; proof by approximation.
     Though experience furnishes us with no lines so unimpeachably
     straight that two of them are incapable of inclosing the smallest
     space, it presents us with gradations of lines possessing less and
     less either of breadth or of flexure, of which series the straight
     line of the definition is the ideal limit. And observation shows
     that just as much, and as nearly, as the straight lines of
     experience approximate to having no breadth or flexure, so much and
     so nearly does the space-inclosing power of any two of them approach
     to zero. The inference that if they had no breadth or flexure at
     all, they would inclose no space at all, is a correct inductive
     inference from these facts, conformable to one of the four Inductive
     Methods hereinafter characterized, the Method of Concomitant
     Variations; of which the mathematical Doctrine of Limits presents
     the extreme case.
  72 Whewell's History of Scientific Ideas, i., 140.
  73 Dr. Whewell (Philosophy of Discovery, p. 289) thinks it
     unreasonable to contend that we know by experience, that our idea of
     a line exactly resembles a real line. "It does not appear," he says,
     "how we can compare our ideas with the realities, since we know the
     realities only by our ideas." We know the realities by our
     sensations. Dr. Whewell surely does not hold the "doctrine of
     perception by means of ideas," which Reid gave himself so much
     trouble to refute. If Dr. Whewell doubts whether we compare our
     ideas with the corresponding sensations, and assume that they
     resemble, let me ask on what evidence do we judge that a portrait of
     a person not present is like the original. Surely because it is like
     our idea, or mental image of the person, and because our idea is
     like the man himself.
     Dr. Whewell also says, that it does not appear why this resemblance
     of ideas to the sensations of which they are copies, should be
     spoken of as if it were a peculiarity of one class of ideas, those
     of space. My reply is, that I do not so speak of it. The peculiarity
     I contend for is only one of degree. All our ideas of sensation of
     course resemble the corresponding sensations, but they do so with
     very different degrees of exactness and of reliability. No one, I
     presume, can recall in imagination a color or an odor with the same
     distinctness and accuracy with which almost every one can mentally
     reproduce an image of a straight line or a triangle. To the extent,
     however, of their capabilities of accuracy, our recollections of
     colors or of odors may serve as subjects of experimentation, as well
     as those of lines and spaces, and may yield conclusions which will
     be true of their external prototypes. A person in whom, either from
     natural gift or from cultivation, the impressions of color were
     peculiarly vivid and distinct, if asked which of two blue flowers
     was of the darkest tinge, though he might never have compared the
     two, or even looked at them together, might be able to give a
     confident answer on the faith of his distinct recollection of the
     colors; that is, he might examine his mental pictures, and find
     there a property of the outward objects. But in hardly any case
     except that of simple geometrical forms, could this be done by
     mankind generally, with a degree of assurance equal to that which is
     given by a contemplation of the objects themselves. Persons differ
     most widely in the precision of their recollection, even of forms:
     one person, when he has looked any one in the face for half a
     minute, can draw an accurate likeness of him from memory; another
     may have seen him every day for six months, and hardly know whether
     his nose is long or short. But every body has a perfectly distinct
     mental image of a straight line, a circle, or a rectangle. And every
     one concludes confidently from these mental images to the
     corresponding outward things. The truth is, that we may, and
     continually do, study nature in our recollections, when the objects
     themselves are absent; and in the case of geometrical forms we can
     perfectly, but in most other cases only imperfectly, trust our
  74 Logic, i., 222.
  75 Ibid., 226.
  76 History of Scientific Ideas, i., 65-67.
  77 Ibid., i., 60.
  78 Ibid., 58, 59.
  79 "If all mankind had spoken one language, we can not doubt that there
     would have been a powerful, perhaps a universal, school of
     philosophers, who would have believed in the inherent connection
     between names and things, who would have taken the sound man to be
     the mode of agitating the air which is essentially communicative of
     the ideas of reason, cookery, bipedality, etc."--De Morgan, _Formal
     Logic_, p. 246.
  80 It would be difficult to name a man more remarkable at once for the
     greatness and the wide range of his mental accomplishments, than
     Leibnitz. Yet this eminent man gave as a reason for rejecting
     Newton's scheme of the solar system, that God could not make a
     body revolve round a distant centre, unless either by some impelling
     mechanism, or by miracle: "Tout ce qui n'est pas explicable," says
     he in a letter to the Abbé Conti, "par la nature des créatures, est
     miraculeux. Il ne suffit pas de dire: Dieu a fait une telle loi de
     nature; donc la chose est naturelle. Il faut que la loi soit
     exécutable par les natures des créatures. Si Dien donnait cette loi,
     par exemple, à un corps libre, de tourner à l'entour d'un certain
     centre, _il faudrait ou qu'il y joignît d'autres corps qui par leur
     impulsion l'obligeassent de rester toujours dans son orbite
     circulaire, ou qu'il mît un ange à ses trousses, ou enfin il
     faudrait qu'il y concourût extraordinairement_; car naturellement il
     s'écartera par la tangente."--Works of Leibnitz, ed. Dutens, iii.,
  81 Novum Organum Renovatum, pp. 32, 33.
  82 History of Scientific Ideas, i., 264.
  83 Ibid., i., 263.
  84 Ibid., 240.
  85 Hist. Scientific Ideas, ii., 25, 26.
  86 Phil. of Disc., p. 339.
  87 Phil. of Disc., p. 338.
  88 Ibid., p. 463.
  89 Phil. of Disc., pp. 472, 473.
  90 The Quarterly Review for June, 1841, contained an article of great
     ability on Dr. Whewell's two great works (since acknowledged and
     reprinted in Sir John Herschel's Essays) which maintains, on the
     subject of axioms, the doctrine advanced in the text, that they are
     generalizations from experience, and supports that opinion by a line
     of argument strikingly coinciding with mine. When I state that the
     whole of the present chapter (except the last four pages, added in
     the fifth edition) was written before I had seen the article (the
     greater part, indeed, before it was published), it is not my object
     to occupy the reader's attention with a matter so unimportant as the
     degree of originality which may or may not belong to any portion of
     my own speculations, but to obtain for an opinion which is opposed
     to reigning doctrines, the recommendation derived from a striking
     concurrence of sentiment between two inquirers entirely independent
     of one another. I embrace the opportunity of citing from a writer of
     the extensive acquirements in physical and metaphysical knowledge
     and the capacity of systematic thought which the article evinces,
     passages so remarkably in unison with my own views as the following:
     "The truths of geometry are summed up and embodied in its
     definitions and axioms.... Let us turn to the axioms, and what do we
     find? A string of propositions concerning magnitude in the abstract,
     which are equally true of space, time, force, number, and every
     other magnitude susceptible of aggregation and subdivision. Such
     propositions, where they are not mere definitions, as some of them
     are, carry their inductive origin on the face of their
     enunciation.... Those which declare that two straight lines can not
     inclose a space, and that two straight lines which cut one another
     can not both be parallel to a third, are in reality the only ones
     which express characteristic properties of space, and these it will
     be worth while to consider more nearly. Now the only clear notion we
     can form of straightness is uniformity of direction, for space in
     its ultimate analysis is nothing but an assemblage of distances and
     directions. And (not to dwell on the notion of continued
     contemplation, i.e., mental experience, as included in the very
     idea of uniformity; nor on that of transfer of the contemplating
     being from point to point, and of experience, during such transfer,
     of the homogeneity of the interval passed over) we can not even
     propose the proposition in an intelligible form to any one whose
     experience ever since he was born has not assured him of the fact.
     The unity of direction, or that we can not march from a given point
     by more than one path direct to the same object, is matter of
     practical experience long before it can by possibility become matter
     of abstract thought. _We can not attempt mentally to exemplify the
     conditions of the assertion in an imaginary case opposed to it,
     without violating our habitual recollection of this experience, and
     defacing our mental picture of space as grounded on it._ What but
     experience, we may ask, can possibly assure us of the homogeneity of
     the parts of distance, time, force, and measurable aggregates in
     general, on which the truth of the other axioms depends? As regards
     the latter axiom, after what has been said it must be clear that the
     very same course of remarks equally applies to its case, and that
     its truth is quite as much forced on the mind as that of the former
     by daily and hourly experience, ... _including always, be it
     observed, in our notion of experience, that which is gained by
     contemplation of the inward picture which the mind forms to itself
     in any proposed case, or which it arbitrarily selects as an
     example--such picture, in virtue of the extreme simplicity of these
     primary relations, being called up by the imagination with as much
     vividness and clearness as could be done by any external impression,
     which is the only meaning we can attach to the word intuition, as
     applied to such relations_."
     And again, of the axioms of mechanics: "As we admit no such
     propositions, other than as truths inductively collected from
     observation, even in geometry itself, it can hardly be expected
     that, in a science of obviously contingent relations, we should
     acquiesce in a contrary view. Let us take one of these axioms and
     examine its evidence: for instance, that equal forces
     perpendicularly applied at the opposite ends of equal arms of a
     straight lever will balance each other. What but experience, we may
     ask, in the first place, can possibly inform us that a force so
     applied will have any tendency to turn the lever on its centre at
     all? or that force can be so transmitted along a rigid line
     perpendicular to its direction, as to act elsewhere in space than
     along its own line of action? Surely this is so far from being
     self-evident that it has even a paradoxical appearance, which is
     only to be removed by giving our lever thickness, material
     composition, and molecular powers. Again, we conclude, that the two
     forces, being equal and applied under precisely similar
     circumstances, must, if they exert any effort at all to turn the
     lever, exert equal and opposite efforts: but what a priori
     reasoning can possibly assure us that they do act under precisely
     similar circumstances? that points which differ in place are
     similarly circumstanced as regards the exertion of force? that
     universal space may not have relations to universal force--or, at all
     events, that the organization of the material universe may not be
     such as to place that portion of space occupied by it in such
     relations to the forces exerted in it, as may invalidate the
     absolute similarity of circumstances assumed? Or we may argue, what
     have we to do with the notion of angular movement in the lever at
     all? The case is one of rest, and of quiescent destruction of force
     by force. Now how is this destruction effected? Assuredly by the
     counter-pressure which supports the fulcrum. But would not this
     destruction equally arise, and by the same amount of counteracting
     force, if each force simply pressed its own half of the lever
     against the fulcrum? And what can assure us that it is not so,
     except removal of one or other force, and consequent tilting of the
     lever? The other fundamental axiom of statics, that the pressure on
     the point of support is the sum of the weights ... is merely a
     scientific transformation and more refined mode of stating a coarse
     and obvious result of universal experience, viz., that the weight of
     a rigid body is the same, handle it or suspend it in what position
     or by what point we will, and that whatever sustains it sustains its
     total weight. Assuredly, as Mr. Whewell justly remarks, 'No one
     probably ever made a trial for the purpose of showing that the
     pressure on the support is equal to the sum of the weights.' ... But
     it is precisely because in every action of his life from earliest
     infancy he has been continually making the trial, and seeing it made
     by every other living being about him, that he never dreams of
     staking its result on one additional attempt made with scientific
     accuracy. This would be as if a man should resolve to decide by
     experiment whether his eyes were useful for the purpose of seeing,
     by hermetically sealing himself up for half an hour in a metal
     On the "paradox of universal propositions obtained by experience,"
     the same writer says: "If there be necessary and universal truths
     expressible in propositions of axiomatic simplicity and obviousness,
     and having for their subject-matter the elements of all our
     experience and all our knowledge, surely these are the truths which,
     if experience suggest to us any truths at all, it ought to suggest
     most readily, clearly, and unceasingly. If it were a truth,
     universal and necessary, that a net is spread over the whole surface
     of every planetary globe, we should not travel far on our own
     without getting entangled in its meshes, and making the necessity of
     some means of extrication an axiom of locomotion.... There is,
     therefore, nothing paradoxical, but the reverse, in our being led by
     observation to a recognition of such truths, as general
     propositions, co-extensive at least with all human experience. That
     they pervade all the objects of experience, must insure their
     continual suggestion by experience; that they are true, must
     insure that consistency of suggestion, that iteration of
     uncontradicted assertion, which commands implicit assent, and
     removes all occasion of exception; that they are simple, and admit
     of no misunderstanding, must secure their admission by every mind."
     "A truth, necessary and universal, relative to any object of our
     knowledge, must verify itself in every instance where that object is
     before our contemplation, and if at the same time it be simple and
     intelligible, its verification must be obvious. _The sentiment of
     such a truth can not, therefore, but be present to our minds
     whenever that object is contemplated, and must therefore make a part
     of the mental picture or idea of that object which we may on any
     occasion summon before our imagination.... All propositions,
     therefore, become not only untrue but inconceivable_, if ... axioms
     be violated in their enunciation."
     Another eminent mathematician had previously sanctioned by his
     authority the doctrine of the origin of geometrical axioms in
     experience. "Geometry is thus founded likewise on observation; but
     of a kind so familiar and obvious, that the primary notions which it
     furnishes might seem intuitive."--Sir John Leslie, quoted by Sir
     William Hamilton, Discourses, etc., p. 272.
  91 Principles of Psychology.
  92 Mr. Spencer is mistaken in supposing me to claim any peculiar
     "necessity" for this axiom as compared with others. I have corrected
     the expressions which led him into that misapprehension of my
  93 Mr. Spencer, in recently returning to the subject (Principles of
     Psychology, new edition, chap. xii.: "The Test of Relative
     Validity"), makes two answers to the preceding remarks. One is:
     "Were an argument formed by repeating the same proposition over and
     over again, it would be true that any intrinsic fallibility of the
     postulate would not make the conclusion more untrustworthy than the
     first step. But an argument consists of unlike propositions. Now,
     since Mr. Mill's criticism on the Universal Postulate is that in
     some cases, which he names, it has proved to be an untrustworthy
     test; it follows that in any argument consisting of heterogeneous
     propositions, there is a risk, increasing as the number of
     propositions increases, that some one of them belongs to this class
     of cases, and is wrongly accepted because of the inconceivableness
     of its negation."
     No doubt: but this supposes new premises to be taken in. The point
     we are discussing is the fallibility not of the premises, but of the
     reasoning, as distinguished from the premises. Now the validity of
     the reasoning depends always upon the same axiom, repeated (in
     thought) "over and over again," viz., that whatever has a mark, has
     what it is a mark of. Even, therefore, on the assumption that this
     axiom rests ultimately on the Universal Postulate, and that, the
     Postulate not being wholly trustworthy, the axiom may be one of the
     cases of its failure; all the risk there is of this is incurred at
     the very first step of the reasoning, and is not added to, however
     long may be the series of subsequent steps.
     I am here arguing, of course, from Mr. Spencer's point of view. From
     my own the case is still clearer; for, in my view, the truth that
     whatever has a mark has what it is a mark of, is wholly trustworthy,
     and derives none of its evidence from so very untrustworthy a test
     as the inconceivability of the negative.
     Mr. Spencer's second answer is valid up to a certain point; it is,
     that every prolongation of the process involves additional chances
     of casual error, from carelessness in the reasoning operation. This
     is an important consideration in the private speculations of an
     individual reasoner; and even with respect to mankind at large, it
     must be admitted that, though mere oversights in the syllogistic
     process, like errors of addition in an account, are special to the
     individual, and seldom escape detection, confusion of thought
     produced (for example) by ambiguous terms has led whole nations or
     ages to accept fallacious reasoning as valid. But this very fact
     points to causes of error so much more dangerous than the mere
     length of the process, as quite to vitiate the doctrine that the
     "test of the relative validities of conflicting conclusions" is the
     number of times the fundamental postulate is involved. On the
     contrary, the subjects on which the trains of reasoning are longest,
     and the assumption, therefore, oftenest repeated, are in general
     those which are best fortified against the really formidable causes
     of fallacy; as in the example already given of mathematics.
  94 Mr. Spencer makes a distinction between conceiving myself looking
     into darkness, and conceiving that I am then and there looking
     into darkness. To me it seems that this change of the expression to
     the form I am, just marks the transition from conception to
     belief, and that the phrase "to conceive that I am," or "that any
     thing is," is not consistent with using the word conceive in its
     rigorous sense.
  95 I have myself accepted the contest, and fought it out on this
     battle-ground, in the eleventh chapter of _An Examination of Sir
     William Hamilton's Philosophy._
  96 Chap. xi.
  97 In one of the three cases, Mr. Spencer, to my no small surprise,
     thinks that the belief of mankind "can not be rightly said to have
     undergone" the change I allege. Mr. Spencer himself still thinks we
     are unable to conceive gravitation acting through empty space. "If
     an astronomer avowed that he could conceive gravitative force as
     exercised through space absolutely void, my private opinion would be
     that he mistook the nature of conception. Conception implies
     representation. Here the elements of the representation are the two
     bodies and an agency by which either affects the other. To conceive
     this agency is to represent it in some terms derived from our
     experiences--that is, from our sensations. As this agency gives us no
     sensations, we are obliged (if we try to conceive it) to use symbols
     idealized from our sensations--imponderable units forming a medium."
     If Mr. Spencer means that the action of gravitation gives us no
     sensations, the assertion is one than which I have not seen, in the
     writings of philosophers, many more startling. What other sensation
     do we need than the sensation of one body moving toward another?
     "The elements of the representation" are not two bodies and an
     "agency," but two bodies and an effect; viz., the fact of their
     approaching one another. If we are able to conceive a vacuum, is
     there any difficulty in conceiving a body falling to the earth
     through it?
  98 Discussions, etc., 2d ed., p. 624.
  99 Professor Bain (Logic, i., 16) identifies the Principle of
     Contradiction with his Law of Relativity, viz., that "every thing
     that can be thought of, every affirmation that can be made, has an
     opposite or counter notion or affirmation;" a proposition which is
     one of the general results of the whole body of human experience.
     For further considerations respecting the axioms of Contradiction
     and Excluded Middle, see the twenty-first chapter of _An Examination
     of Sir William Hamilton's Philosophy_.
 100 Dr. Whewell thinks it improper to apply the term Induction to any
     operation not terminating in the establishment of a general truth.
     Induction, he says (Philosophy of Discovery, p. 245), "is not the
     same thing as experience and observation. Induction is experience or
     observation consciously looked at in a general form. This
     consciousness and generality are necessary parts of that knowledge
     which is science." And he objects (p. 241) to the mode in which the
     word Induction is employed in this work, as an undue extension of
     that term "not only to the cases in which the general induction is
     consciously applied to a particular instance, but to the cases in
     which the particular instance is dealt with by means of experience
     in that rude sense in which experience can be asserted of brutes,
     and in which of course we can in no way imagine that the law is
     possessed or understood as a general proposition." This use of the
     term he deems a "confusion of knowledge with practical tendencies."
     I disclaim, as strongly as Dr. Whewell can do, the application of
     such terms as induction, inference, or reasoning, to operations
     performed by mere instinct, that is, from an animal impulse, without
     the exertion of any intelligence. But I perceive no ground for
     confining the use of those terms to cases in which the inference is
     drawn in the forms and with the precautions required by scientific
     propriety. To the idea of Science, an express recognition and
     distinct apprehension of general laws as such, is essential: but
     nine-tenths of the conclusions drawn from experience in the course
     of practical life, are drawn without any such recognition: they are
     direct inferences from known cases, to a case supposed to be
     similar. I have endeavored to show that this is not only as
     legitimate an operation, but substantially the same operation, as
     that of ascending from known cases to a general proposition; except
     that the latter process has one great security for correctness which
     the former does not possess. In science, the inference must
     necessarily pass through the intermediate stage of a general
     proposition, because Science wants its conclusions for record, and
     not for instantaneous use. But the inferences drawn for the guidance
     of practical affairs, by persons who would often be quite incapable
     of expressing in unexceptionable terms the corresponding
     generalizations, may and frequently do exhibit intellectual powers
     quite equal to any which have ever been displayed in science; and if
     these inferences are not inductive, what are they? The limitation
     imposed on the term by Dr. Whewell seems perfectly arbitrary;
     neither justified by any fundamental distinction between what he
     includes and what he desires to exclude, nor sanctioned by usage, at
     least from the time of Reid and Stewart, the principal legislators
     (as far as the English language is concerned) of modern metaphysical
 101 Supra, p. 145.
 102 Novum Organum Renovatum, pp. 72, 73.
 103 Novum Organum Renovatum, p. 32.
 104 Cours de Philosophie Positive, vol. ii., p. 202.
 105 Dr. Whewell, in his reply, contests the distinction here drawn, and
     maintains, that not only different descriptions, but different
     explanations of a phenomenon, may all be true. Of the three theories
     respecting the motions of the heavenly bodies, he says (_Philosophy
     of Discovery_, p. 231): "Undoubtedly all these explanations may be
     true and consistent with each other, and would be so if each had
     been followed out so as to show in what manner it could be made
     consistent with the facts. And this was, in reality, in a great
     measure done. The doctrine that the heavenly bodies were moved by
     vortices was successfully modified, so that it came to coincide in
     its results with the doctrine of an inverse-quadratic centripetal
     force.... When this point was reached, the vortex was merely a
     machinery, well or ill devised, for producing such a centripetal
     force, and therefore did not contradict the doctrine of a
     centripetal force. Newton himself does not appear to have been
     averse to explaining gravity by impulse. So little is it true that
     if one theory be true the other must be false. The attempt to
     explain gravity by the impulse of streams of particles flowing
     through the universe in all directions, which I have mentioned in
     the Philosophy, is so far from being inconsistent with the
     Newtonian theory, that it is founded entirely upon it. And even with
     regard to the doctrine, that the heavenly bodies move by an inherent
     virtue; if this doctrine had been maintained in any such way that it
     was brought to agree with the facts, the inherent virtue must have
     had its laws determined; and then it would have been found that the
     virtue had a reference to the central body; and so, the 'inherent
     virtue' must have coincided in its effect with the Newtonian force;
     and then, the two explanations would agree, except so far as the
     word 'inherent' was concerned. And if such a part of an earlier
     theory as this word inherent indicates, is found to be untenable,
     it is of course rejected in the transition to later and more exact
     theories, in Inductions of this kind, as well as in what Mr. Mill
     calls Descriptions. There is, therefore, still no validity
     discoverable in the distinction which Mr. Mill attempts to draw
     between descriptions like Kepler's law of elliptical orbits, and
     other examples of induction."
     If the doctrine of vortices had meant, not that vortices existed,
     but only that the planets moved in the same manner as if they had
     been whirled by vortices; if the hypothesis had been merely a mode
     of representing the facts, not an attempt to account for them; if,
     in short, it had been only a Description; it would, no doubt, have
     been reconcilable with the Newtonian theory. The vortices, however,
     were not a mere aid to conceiving the motions of the planets, but a
     supposed physical agent, actively impelling them; a material fact,
     which might be true or not true, but could not be both true and not
     true. According to Descartes's theory it was true, according to
     Newton's it was not true. Dr. Whewell probably means that since the
     phrases, centripetal and projectile force, do not declare the nature
     but only the direction of the forces, the Newtonian theory does not
     absolutely contradict any hypothesis which may be framed respecting
     the mode of their production. The Newtonian theory, regarded as a
     mere description of the planetary motions, does not; but the
     Newtonian theory as an explanation of them does. For in what does
     the explanation consist? In ascribing those motions to a general law
     which obtains between all particles of matter, and in identifying
     this with the law by which bodies fall to the ground. If the planets
     are kept in their orbits by a force which draws the particles
     composing them toward every other particle of matter in the solar
     system, they are not kept in those orbits by the impulsive force of
     certain streams of matter which whirl them round. The one
     explanation absolutely excludes the other. Either the planets are
     not moved by vortices, or they do not move by a law common to all
     matter. It is impossible that both opinions can be true. As well
     might it be said that there is no contradiction between the
     assertions, that a man died because somebody killed him, and that he
     died a natural death.
     So, again, the theory that the planets move by a virtue inherent in
     their celestial nature, is incompatible with either of the two
     others: either that of their being moved by vortices, or that which
     regards them as moving by a property which they have in common with
     the earth and all terrestrial bodies. Dr. Whewell says that the
     theory of an inherent virtue agrees with Newton's when the word
     inherent is left out, which of course it would be (he says) if
     "found to be untenable." But leave that out, and where is the
     theory? The word inherent is the theory. When that is omitted,
     there remains nothing except that the heavenly bodies move "by a
     virtue," i.e., by a power of some sort; or by virtue of their
     celestial nature, which directly contradicts the doctrine that
     terrestrial bodies fall by the same law.
     If Dr. Whewell is not yet satisfied, any other subject will serve
     equally well to test his doctrine. He will hardly say that there is
     no contradiction between the emission theory and the undulatory
     theory of light; or that there can be both one and two
     electricities; or that the hypothesis of the production of the
     higher organic forms by development from the lower, and the
     supposition of separate and successive acts of creation, are quite
     reconcilable; or that the theory that volcanoes are fed from a
     central fire, and the doctrines which ascribe them to chemical
     action at a comparatively small depth below the earth's surface, are
     consistent with one another, and all true as far as they go.
     If different explanations of the same fact can not both be true,
     still less, surely, can different predictions. Dr. Whewell quarrels
     (on what ground it is not necessary here to consider) with the
     example I had chosen on this point, and thinks an objection to an
     illustration a sufficient answer to a theory. Examples not liable to
     his objection are easily found, if the proposition that conflicting
     predictions can not both be true, can be made clearer by many
     examples. Suppose the phenomenon to be a newly-discovered comet, and
     that one astronomer predicts its return once in every 300
     years--another once in every 400: can they both be right? When
     Columbus predicted that by sailing constantly westward he should in
     time return to the point from which he set out, while others
     asserted that he could never do so except by turning back, were both
     he and his opponents true prophets? Were the predictions which
     foretold the wonders of railways and steamships, and those which
     averred that the Atlantic could never be crossed by steam
     navigation, nor a railway train propelled ten miles an hour, both
     (in Dr. Whewell's words) "true, and consistent with one another?"
     Dr. Whewell sees no distinction between holding contradictory
     opinions on a question of fact, and merely employing different
     analogies to facilitate the conception of the same fact. The case of
     different Inductions belongs to the former class, that of different
     Descriptions to the latter.
 106 Phil. of Discov., p. 256.
 107 Essays on the Pursuit of Truth.
 108 In the first edition a note was appended at this place, containing
     some criticism on Archbishop Whately's mode of conceiving the
     relation between Syllogism and Induction. In a subsequent issue of
     his Logic, the Archbishop made a reply to the criticism, which
     induced me to cancel part of the note, incorporating the remainder
     in the text. In a still later edition, the Archbishop observes in a
     tone of something like disapprobation, that the objections,
     "doubtless from their being fully answered and found untenable, were
     silently suppressed," and that hence he might appear to some of his
     readers to be combating a shadow. On this latter point, the
     Archbishop need give himself no uneasiness. His readers, I make bold
     to say, will fully credit his mere affirmation that the objections
     have actually been made.
     But as he seems to think that what he terms the suppression of the
     objections ought not to have been made "silently," I now break that
     silence, and state exactly what it is that I suppressed, and why. I
     suppressed that alone which might be regarded as personal criticism
     on the Archbishop. I had imputed to him the having omitted to ask
     himself a particular question. I found that he had asked himself the
     question, and could give it an answer consistent with his own
     theory. I had also, within the compass of a parenthesis, hazarded
     some remarks on certain general characteristics of Archbishop
     Whately as a philosopher. These remarks, though their tone, I hope,
     was neither disrespectful nor arrogant, I felt, on reconsideration,
     that I was hardly entitled to make; least of all, when the instance
     which I had regarded as an illustration of them, failed, as I now
     saw, to bear them out. The real matter at the bottom of the whole
     dispute, the different view we take of the function of the major
     premise, remains exactly where it was; and so far was I from
     thinking that my opinion had been fully "answered" and was
     "untenable," that in the same edition in which I canceled the note,
     I not only enforced the opinion by further arguments, but answered
     (though without naming him) those of the Archbishop.
     For not having made this statement before, I do not think it needful
     to apologize. It would be attaching very great importance to one's
     smallest sayings, to think a formal retractation requisite every
     time that one falls into an error. Nor is Archbishop Whately's
     well-earned fame of so tender a quality as to require that in
     withdrawing a slight criticism on him I should have been bound to
     offer a public amende for having made it.
 109 But though it is a condition of the validity of every induction that
     there be uniformity in the course of nature, it is not a necessary
     condition that the uniformity should pervade all nature. It is
     enough that it pervades the particular class of phenomena to which
     the induction relates. An induction concerning the motions of the
     planets, or the properties of the magnet, would not be vitiated
     though we were to suppose that wind and weather are the sport of
     chance, provided it be assumed that astronomical and magnetic
     phenomena are under the dominion of general laws. Otherwise the
     early experience of mankind would have rested on a very weak
     foundation; for in the infancy of science it could not be known that
     all phenomena are regular in their course.
     Neither would it be correct to say that every induction by which we
     infer any truth, implies the general fact of uniformity _as
     foreknown_, even in reference to the kind of phenomena concerned. It
     implies, either that this general fact is already known, or that
     we may now know it: as the conclusion, the Duke of Wellington is
     mortal, drawn from the instances A, B, and C, implies either that we
     have already concluded all men to be mortal, or that we are now
     entitled to do so from the same evidence. A vast amount of confusion
     and paralogism respecting the grounds of Induction would be
     dispelled by keeping in view these simple considerations.
 110 Infra, chap. xxi.
 111 Infra, chap. xxi., xxii.
 112 In strictness, wherever the present constitution of space exists;
     which we have ample reason to believe that it does in the region of
     the fixed stars.
 113 Dr. Whewell (Phil. of Discov., p. 246) will not allow these and
     similar erroneous judgments to be called inductions; inasmuch as
     such superstitious fancies "were not collected from the facts by
     seeking a law of their occurrence, but were suggested by an
     imagination of the anger of superior powers, shown by such
     deviations from the ordinary course of nature." I conceive the
     question to be, not in what manner these notions were at first
     suggested, but by what evidence they have, from time to time, been
     supposed to be substantiated. If the believers in these erroneous
     opinions had been put on their defense, they would have referred to
     experience: to the comet which preceded the assassination of Julius
     Cæsar, or to oracles and other prophecies known to have been
     fulfilled. It is by such appeals to facts that all analogous
     superstitions, even in our day, attempt to justify themselves; the
     supposed evidence of experience is necessary to their hold on the
     mind. I quite admit that the influence of such coincidences would
     not be what it is, if strength were not lent to it by an antecedent
     presumption; but this is not peculiar to such cases; preconceived
     notions of probability form part of the explanation of many other
     cases of belief on insufficient evidence. The a priori prejudice
     does not prevent the erroneous opinion from being sincerely regarded
     as a legitimate conclusion from experience; though it improperly
     predisposes the mind to that interpretation of experience.
     Thus much in defense of the sort of examples objected to. But it
     would be easy to produce instances, equally adapted to the purpose,
     and in which no antecedent prejudice is at all concerned. "For many
     ages," says Archbishop Whately, "all farmers and gardeners were
     firmly convinced--and convinced of their knowing it by
     experience--that the crops would never turn out good unless the seed
     were sown during the increase of the moon." This was induction, but
     bad induction; just as a vicious syllogism is reasoning, but bad
 114 The assertion, that any and every one of the conditions of a
     phenomenon may be and is, on some occasions and for some purposes,
     spoken of as the cause, has been disputed by an intelligent reviewer
     of this work in the Prospective Review (the predecessor of the
     justly esteemed National Review), who maintains that "we always
     apply the word cause rather to that element in the antecedents which
     exercises force, and which would tend at all times to produce
     the same or a similar effect to that which, under certain
     conditions, it would actually produce." And he says, that "every one
     would feel" the expression, that the cause of a surprise was the
     sentinel's being off his post, to be incorrect; but that the
     "allurement or force which drew him off his post, might be so
     called, because in doing so it removed a resisting power which would
     have prevented the surprise." I can not think that it would be wrong
     to say, that the event took place because the sentinel was absent,
     and yet right to say that it took place because he was bribed to be
     absent. Since the only direct effect of the bribe was his absence,
     the bribe could be called the remote cause of the surprise, only on
     the supposition that the absence was the proximate cause; nor does
     it seem to me that any one (who had not a theory to support) would
     use the one expression and reject the other.
     The reviewer observes, that when a person dies of poison, his
     possession of bodily organs is a necessary condition, but that no
     one would ever speak of it as the cause. I admit the fact; but I
     believe the reason to be, that the occasion could never arise for so
     speaking of it; for when in the inaccuracy of common discourse we
     are led to speak of some one condition of a phenomenon as its cause,
     the condition so spoken of is always one which it is at least
     possible that the hearer may require to be informed of. The
     possession of bodily organs is a known condition, and to give that
     as the answer, when asked the cause of a person's death, would not
     supply the information sought. Once conceive that a doubt could
     exist as to his having bodily organs, or that he were to be compared
     with some being who had them not, and cases may be imagined in which
     it might be said that his possession of them was the cause of his
     death. If Faust and Mephistopheles together took poison, it might be
     said that Faust died because he was a human being, and had a body,
     while Mephistopheles survived because he was a spirit.
     It is for the same reason that no one (as the reviewer remarks)
     "calls the cause of a leap, the muscles or sinews of the body,
     though they are necessary conditions; nor the cause of a
     self-sacrifice, the knowledge which was necessary for it; nor the
     cause of writing a book, that a man has time for it, which is a
     necessary condition." These conditions (besides that they are
     antecedent states, and not proximate antecedent events, and are
     therefore never the conditions in closest apparent proximity to the
     effect) are all of them so obviously implied, that it is hardly
     possible there should exist that necessity for insisting on them,
     which alone gives occasion for speaking of a single condition as if
     it were the cause. Wherever this necessity exists in regard to some
     one condition, and does not exist in regard to any other, I conceive
     that it is consistent with usage, when scientific accuracy is not
     aimed at, to apply the name cause to that one condition. If the only
     condition which can be supposed to be unknown is a negative
     condition, the negative condition may be spoken of as the cause. It
     might be said that a person died for want of medical advice: though
     this would not be likely to be said, unless the person was already
     understood to be ill, and in order to indicate that this negative
     circumstance was what made the illness fatal, and not the weakness
     of his constitution, or the original virulence of the disease. It
     might be said that a person was drowned because he could not swim;
     the positive condition, namely, that he fell into the water, being
     already implied in the word drowned. And here let me remark, that
     his falling into the water is in this case the only positive
     condition: all the conditions not expressly or virtually included in
     this (as that he could not swim, that nobody helped him, and so
     forth) are negative. Yet, if it were simply said that the cause of a
     man's death was falling into the water, there would be quite as
     great a sense of impropriety in the expression, as there would be if
     it were said that the cause was his inability to swim; because,
     though the one condition is positive and the other negative, it
     would be felt that neither of them was sufficient, without the
     other, to produce death.
     With regard to the assertion that nothing is termed the cause,
     except the element which exerts active force; I waive the question
     as to the meaning of active force, and accepting the phrase in its
     popular sense, I revert to a former example, and I ask, would it be
     more agreeable to custom to say that a man fell because his foot
     slipped in climbing a ladder, or that he fell because of his weight?
     for his weight, and not the motion of his foot, was the active force
     which determined his fall. If a person walking out in a frosty day,
     stumbled and fell, it might be said that he stumbled because the
     ground was slippery, or because he was not sufficiently careful: but
     few people, I suppose, would say, that he stumbled because he
     walked. Yet the only active force concerned was that which he
     exerted in walking: the others were mere negative conditions; but
     they happened to be the only ones which there could be any necessity
     to state; for he walked, most likely, in exactly his usual manner,
     and the negative conditions made all the difference. Again, if a
     person were asked why the army of Xerxes defeated that of Leonidas,
     he would probably say, because they were a thousand times the
     number; but I do not think he would say, it was because they fought,
     though that was the element of active force. To borrow another
     example, used by Mr. Grove and by Mr. Baden Powell, the opening of
     flood-gates is said to be the cause of the flow of water; yet the
     active force is exerted by the water itself, and opening the
     flood-gates merely supplies a negative condition. The reviewer adds,
     "There are some conditions absolutely passive, and yet absolutely
     necessary to physical phenomena, viz., the relations of space and
     time; and to these no one ever applies the word cause without being
     immediately arrested by those who hear him." Even from this
     statement I am compelled to dissent. Few persons would feel it
     incongruous to say (for example) that a secret became known because
     it was spoken of when A. B. was within hearing; which is a condition
     of space: or that the cause why one of two particular trees is
     taller than the other, is that it has been longer planted; which is
     a condition of time.
 115 There are a few exceptions; for there are some properties of objects
     which seem to be purely preventive; as the property of opaque
     bodies, by which they intercept the passage of light. This, as far
     as we are able to understand it, appears an instance not of one
     cause counteracting another by the same law whereby it produces its
     own effects, but of an agency which manifests itself in no other way
     than in defeating the effects of another agency. If we knew on what
     other relations to light, or on what peculiarities of structure,
     opacity depends, we might find that this is only an apparent, not a
     real, exception to the general proposition in the text. In any case
     it needs not affect the practical application. The formula which
     includes all the negative conditions of an effect in the single one
     of the absence of counteracting causes, is not violated by such
     cases as this; though, if all counteracting agencies were of this
     description, there would be no purpose served by employing the
 116 I mean by this expression, the ultimate laws of nature (whatever
     they may be) as distinguished from the derivative laws and from the
     collocations. The diurnal revolution of the earth (for example) is
     not a part of the constitution of things, because nothing can be so
     called which might possibly be terminated or altered by natural
 117 I use the words "straight line" for brevity and simplicity. In
     reality the line in question is not exactly straight, for, from the
     effect of refraction, we actually see the sun for a short interval
     during which the opaque mass of the earth is interposed in a direct
     line between the sun and our eyes; thus realizing, though but to a
     limited extent, the coveted desideratum of seeing round a corner.
 118 Second Burnett Prize Essay, by Principal Tulloch, p. 25.
 119 Letters on the Philosophy of the Human Mind, First Series, p. 219.
 120 Essays, pp. 206-208.
 121 To the universality which mankind are agreed in ascribing to the Law
     of Causation, there is one claim of exception, one disputed case,
     that of the Human Will; the determinations of which, a large class
     of metaphysicians are not willing to regard as following the causes
     called motives, according to as strict laws as those which they
     suppose to exist in the world of mere matter. This controverted
     point will undergo a special examination when we come to treat
     particularly of the Logic of the Moral Sciences (Book vi., chap. 2).
     In the mean time, I may remark that these metaphysicians, who, it
     must be observed, ground the main part of their objection on the
     supposed repugnance of the doctrine in question to our
     consciousness, seem to me to mistake the fact which consciousness
     testifies against. What is really in contradiction to consciousness,
     they would, I think, on strict self-examination, find to be, the
     application to human actions and volitions of the ideas involved in
     the common use of the term Necessity; which I agree with them in
     objecting to. But if they would consider that by saying that a
     person's actions necessarily follow from his character, all that
     is really meant (for no more is meant in any case whatever of
     causation) is that he invariably does act in conformity to his
     character, and that any one who thoroughly knew his character could
     certainly predict how he would act in any supposable case; they
     probably would not find this doctrine either contrary to their
     experience or revolting to their feelings. And no more than this is
     contended for by any one but an Asiatic fatalist.
 122 I believe, however, the accredited authorities do suppose that
     molecular motion, equivalent in amount to that which will be
     manifested in the combustion of the coal, is actually taking place
     during the whole of the long interval, if not in the coal, yet in
     the oxygen which will then combine with it. But how purely
     hypothetical this supposition is, need hardly be remarked; I venture
     to say, unnecessarily and extravagantly hypothetical.
 123 Lectures on Metaphysics, vol. ii., Lect. xxxix., pp. 391-2.
     I regret that I can not invoke the authority of Sir William Hamilton
     in favor of my own opinions on Causation, as I can against the
     particular theory which I am now combating. But that acute thinker
     has a theory of Causation peculiar to himself, which has never yet,
     as far as I know, been analytically examined, but which, I venture
     to think, admits of as complete refutation as any one of the false
     or insufficient psychological theories which strew the ground in
     such numbers under his potent metaphysical scythe. (Since examined
     and controverted in the sixteenth chapter of _An Examination of Sir
     William Hamilton's Philosophy_.)
 124 Unless we are to consider as such the following statement, by one of
     the writers quoted in the text: "In the case of mental exertion, the
     result to be accomplished is preconsidered or meditated, and is
     therefore known a priori, or before experience."--(Bowen's _Lowell
     Lectures on the Application of Metaphysical and Ethical Science to
     the Evidence of Religion_. Boston, 1849.) This is merely saying that
     when we will a thing we have an idea of it. But to have an idea of
     what we wish to happen, does not imply a prophetic knowledge that it
     will happen. Perhaps it will be said that the first time we
     exerted our will, when we had of course no experience of any of the
     powers residing in us, we nevertheless must already have known that
     we possessed them, since we can not will that which we do not
     believe to be in our power. But the impossibility is perhaps in the
     words only, and not in the facts; for we may desire what we do not
     know to be in our power; and finding by experience that our bodies
     move according to our desire, we may then, and only then, pass
     into the more complicated mental state which is termed will.
     After all, even if we had an instinctive knowledge that our actions
     would follow our will, this, as Brown remarks, would prove nothing
     as to the nature of Causation. Our knowing, previous to experience,
     that an antecedent will be followed by a certain consequent, would
     not prove the relation between them to be any thing more than
     antecedence and consequence.
 125 Reid's Essays on the Active Powers, Essay iv., chap. 3.
 126 Prospective Review for February, 1850.
 127 Vide supra, p. 178, note.
 128 Westminster Review for October, 1855.
 129 See the whole doctrine in Aristotle de Ánimâ, where the θρεπτικὲ ψυχὲ is treated as exactly equivalent to θρεπτικὲ δύναμις.
 130 It deserves notice that the parts of nature which Aristotle regards
     as representing evidence of design, are the Uniformities: the
     phenomena in so far as reducible to law. Τύχε and τὸ αὐτομάτον
     satisfy him as explanations of the variable element in phenomena,
     but their occurring according to a fixed rule can only, to his
     conceptions, be accounted for by an Intelligent Will. The common, or
     what may be called the instinctive, religious interpretation of
     nature, is the reverse of this. The events in which men
     spontaneously see the hand of a supernatural being, are those which
     can not, as they think, be reduced to a physical law. What they can
     distinctly connect with physical causes, and especially what they
     can predict, though of course ascribed to an Author of Nature, if
     they already recognize such an author, might be conceived, they
     think, to arise from a blind fatality, and in any case do not appear
     to them to bear so obviously the mark of a divine will. And this
     distinction has been countenanced by eminent writers on Natural
     Theology, in particular by Dr. Chalmers, who thinks that though
     design is present everywhere, the irresistible evidence of it is to
     be found not in the laws of nature but in the collocations,
     i.e., in the part of nature in which it is impossible to trace any
     law. A few properties of dead matter might, he thinks, conceivably
     account for the regular and invariable succession of effects and
     causes; but that the different kinds of matter have been so placed
     as to promote beneficent ends, is what he regards as the proof of a
     Divine Providence. Mr. Baden Powell, in his Essay entitled
     "Philosophy of Creation," has returned to the point of view of
     Aristotle and the ancients, and vigorously re-asserts the doctrine
     that the indication of design in the universe is not special
     adaptations, but Uniformity and Law, these being the evidences of
     mind, and not what appears to us to be a provision for our uses.
     While I decline to express any opinion here on this _vexata
     quæstio_, I ought not to mention Mr. Powell's volume without the
     acknowledgment due to the philosophic spirit which pervades
     generally the three Essays composing it, forming in the case of one
     of them (the "Unity of Worlds") an honorable contrast with the other
     dissertations, so far as they have come under my notice, which have
     appeared on either side of that controversy.
 131 In the words of Fontenelle, another celebrated Cartesian, "les
     philosophes aussi bien que le peuple avaient cru que l'âme et le
     corps agissaient réellement et physiquement l'un sur l'autre.
     Descartes vint, qui prouva que leur nature ne permettait point cette
     sorte de communication véritable, et qu'ils n'en pouvaient avoir
     qu'une apparente, dont Dieu était le Médiateur."--(_OEuvres de
     Fontenelle_, ed. 1767, tom. v., p. 534.)
 132 I omit, for simplicity, to take into account the effect, in this
     latter case, of the diminution of pressure, in diminishing the flow
     of water through the drain; which evidently in no way affects the
     truth or applicability of the principle, since when the two causes
     act simultaneously the conditions of that diminution of pressure do
     not arise.
 133 Professor Bain adds several other well-established chemical
     generalizations: "The laws that simple substances exhibit the
     strongest affinities; that compounds are more fusible than their
     elements; that combination tends to a lower state of matter from gas
     down to solid;" and some general propositions concerning the
     circumstances which facilitate or resist chemical combination.
     (Logic, ii., 254.)
 134 Professor Bain (Logic, ii., 39) points out a class of cases, other
     than that spoken of in the text, which he thinks must be regarded as
     an exception to the Composition of Causes. "Causes that merely make
     good the collocation for bringing a prime mover into action, or that
     release a potential force, do not follow any such rule. One man may
     direct a gun upon a fort as well as three: two sparks are not more
     effectual than one in exploding a barrel of gunpowder. In medicine
     there is a certain dose that answers the end; and adding to it does
     no more good."
     I am not sure that these cases are really exceptions. The law of
     Composition of Causes, I think, is really fulfilled, and the
     appearance to the contrary is produced by attending to the remote
     instead of the immediate effect of the causes. In the cases
     mentioned, the immediate effect of the causes in action is a
     collocation, and the duplication of the cause does double the
     quantity of collocation. Two men could raise the gun to the required
     angle twice as quickly as one, though one is enough. Two sparks put
     two sets of particles of the gunpowder into the state of intestine
     motion which makes them explode, though one is sufficient. It is the
     collocation itself that does not, by being doubled, always double
     the effect; because in many cases a certain collocation, once
     obtained, is all that is required for the production of the whole
     amount of effect which can be produced at all at the given time and
     place. Doubling the collocation with difference of time and place,
     as by pointing two guns, or exploding a second barrel after the
     first, does double the effect. This remark applies still more to Mr.
     Bain's third example, that of a double dose of medicine; for a
     double dose of an aperient does purge more violently, and a double
     dose of laudanum does produce longer and sounder sleep. But a double
     purging, or a double amount of narcotism, may have remote effects
     different in kind from the effect of the smaller amount, reducing
     the case to that of heteropathic laws, discussed in the text.
 135 Unless, indeed, the consequent was generated, not by the antecedent,
     but by the means employed to produce the antecedent. As, however,
     these means are under our power, there is so far a probability that
     they are also sufficiently within our knowledge to enable us to
     judge whether that could be the case or not.
 136 Discourse on the Study of Natural Philosophy, p. 179.
 137 For this speculation, as for many other of my scientific
     illustrations, I am indebted to Professor Bain, whose subsequent
     treatise on Logic abounds with apt illustrations of all the
     inductive methods.
 138 This view of the necessary co-existence of opposite excitements
     involves a great extension of the original doctrine of two
     electricities. The early theorists assumed that, when amber was
     rubbed, the amber was made positive and the rubber negative to the
     same degree; but it never occurred to them to suppose that the
     existence of the amber charge was dependent on an opposite charge in
     the bodies with which the amber was contiguous, while the existence
     of the negative charge on the rubber was equally dependent on a
     contrary state of the surfaces that might accidentally be confronted
     with it; that, in fact, in a case of electrical excitement by
     friction, four charges were the minimum that could exist. But this
     double electrical action is essentially implied in the explanation
     now universally adopted in regard to the phenomena of the common
     electric machine.
 139 Pp. 110, 111.
 140 Infra, book iv., chap. ii., On Abstraction.
 141 I must, however, remark, that this example, which seems to militate
     against the assertion we made of the comparative inapplicability of
     the Method of Difference to cases of pure observation, is really one
     of those exceptions which, according to a proverbial expression,
     prove the general rule. For in this case, in which Nature, in her
     experiment, seems to have imitated the type of the experiments made
     by man, she has only succeeded in producing the likeness of man's
     most imperfect experiments; namely, those in which, though he
     succeeds in producing the phenomenon, he does so by employing
     complex means, which he is unable perfectly to analyze, and can
     form, therefore, no sufficient judgment what portion of the effects
     may be due, not to the supposed cause, but to some unknown agency of
     the means by which that cause was produced. In the natural
     experiment which we are speaking of, the means used was the clearing
     off a canopy of clouds; and we certainly do not know sufficiently in
     what this process consists, or on what it depends, to be certain _a
     priori_ that it might not operate upon the deposition of dew
     independently of any thermometric effect at the earth's surface.
     Even, therefore, in a case so favorable as this to Nature's
     experimental talents, her experiment is of little value except in
     corroboration of a conclusion already attained through other means.
 142 In his subsequent work, Outlines of Astronomy (§ 570), Sir John
     Herschel suggests another possible explanation of the acceleration
     of the revolution of a comet.
 143 Discourse, pp. 156-8, and 171.
 144 Outlines of Astronomy, § 856.
 145 Philosophy of Discovery, pp. 263, 264.
 146 See, on this point, the second chapter of the present book.
 147 Ante, chap. vii., § 1.
 148 It seems hardly necessary to say that the word impinge, as a
     general term to express collision of forces, is here used by a
     figure of speech, and not as expressive of any theory respecting the
     nature of force.
 149 Essays on some Unsettled Questions of Political Economy, Essay V.
 150 It is justly remarked by Professor Bain, that though the Methods of
     Agreement and Difference are not applicable to these cases, they are
     not wholly inaccessible to the Method of Concomitant Variations. "If
     a cause happens to vary alone, the effect will also vary alone: a
     cause and effect may be thus singled out under the greatest
     complications. Thus, when the appetite for food increases with the
     cold, we have a strong evidence of connection between these two
     facts, although other circumstances may operate in the same
     direction. The assigning of the respective parts of the sun and moon
     in the action of the tides may be effected, to a certain degree of
     exactness, by the variations of the amount according to the
     positions of the two attractive bodies. By a series of experiments
     of Concomitant Variations, directed to ascertain the elimination of
     nitrogen from the human body under varieties of muscular exercise,
     Dr. Parkes obtained the remarkable conclusion, that a muscle grows
     during exercise, and loses bulk during the subsequent rest."
     (Logic, ii., 83.)
     It is, no doubt, often possible to single out the influencing causes
     from among a great number of mere concomitants, by noting what are
     the antecedents, a variation in which is followed by a variation in
     the effect. But when there are many influencing causes, no one of
     them greatly predominating over the rest, and especially when some
     of these are continually changing, it is scarcely ever possible to
     trace such a relation between the variations of the effect and those
     of any one cause as would enable us to assign to that cause its real
     share in the production of the effect.
 151 Bain's Logic, ii., 360.
 152 What is said in the text on the applicability of the experimental
     methods to resolve particular questions of medical treatment, does
     not detract from their efficacy in ascertaining the general laws of
     the animal or human system. The functions, for example, of the
     different classes of nerves have been discovered, and probably could
     only have been discovered, by experiments on living animals.
     Observation and experiment are the ultimate basis of all knowledge:
     from them we obtain the elementary laws of life, as we obtain all
     other elementary truths. It is in dealing with the complex
     combinations that the experimental methods are for the most part
     illusory, and the deductive mode of investigation must be invoked to
     disentangle the complexity.
 153 Professor Bain, though concurring generally in the views expressed
     in this chapter, seems to estimate more highly than I do the scope
     for specific experimental evidence in politics. (Logic, ii.,
     333-337.) There are, it is true, as he remarks (p. 336), some cases
     "when an agent suddenly introduced is almost instantaneously
     followed by some other changes, as when the announcement of a
     diplomatic rupture between two nations is followed the same day by a
     derangement of the money-market." But this experiment would be quite
     inconclusive merely as an experiment. It can only serve, as any
     experiment may, to verify the conclusion of a deduction. Unless we
     already knew by our knowledge of the motives which act on business
     men, that the prospect of war tends to derange the money-market,
     we should never have been able to prove a connection between the two
     facts, unless after having ascertained historically that the one
     followed the other in too great a number of instances to be
     consistent with their having been recorded with due precautions.
     Whoever has carefully examined any of the attempts continually made
     to prove economic doctrines by such a recital of instances, knows
     well how futile they are. It always turns out that the circumstances
     of scarcely any of the cases have been fully stated; and that cases,
     in equal or greater numbers, have been omitted which would have
     tended to an opposite conclusion.
 154 Vide Memoir by Thomas Graham, F.R.S., Master of the Mint, "On Liquid
     Diffusion applied to Analysis," in the Philosophical Transactions
     for 1862, reprinted in the Journal of the Chemical Society, and
     also separately as a pamphlet.
 155 It was an old generalization in surgery, that tight bandaging had a
     tendency to prevent or dissipate local inflammation. This sequence,
     being, in the progress of physiological knowledge, resolved into
     more general laws, led to the important surgical invention made by
     Dr. Arnott, the treatment of local inflammation and tumors by means
     of an equable pressure, produced by a bladder partially filled with
     air. The pressure, by keeping back the blood from the part, prevents
     the inflammation, or the tumor, from being nourished: in the case of
     inflammation, it removes the stimulus, which the organ is unfit to
     receive; in the case of tumors, by keeping back the nutritive fluid,
     it causes the absorption of matter to exceed the supply, and the
     diseased mass is gradually absorbed and disappears.
 156 Since acknowledged and reprinted in Mr. Martineau's Miscellanies.
 157 Dissertations and Discussions, vol. i., fourth paper.
 158 Written before the rise of the new views respecting the relation of
     heat to mechanical force; but confirmed rather than contradicted by
 159 As is well remarked by Professor Bain, in the very valuable chapter
     of his Logic which treats of this subject (ii., 121), "scientific
     explanation and inductive generalization being the same thing, the
     limits of Explanation are the limits of Induction," and "the limits
     to inductive generalization are the limits to the agreement or
     community of facts. Induction supposes similarity among phenomena;
     and when such similarity is discovered, it reduces the phenomena
     under a common statement. The similarity of terrestrial gravity to
     celestial attraction enables the two to be expressed as one
     phenomenon. The similarity between capillary attraction, solution,
     the operation of cements, etc., leads to their being regarded not as
     a plurality, but as a unity, a single causative link, the operation
     of a single agency.... If it be asked whether we can merge gravity
     itself in some still higher law, the answer must depend upon the
     facts. Are there any other forces, at present held distinct from
     gravity, that we may hope to make fraternize with it, so as to join
     in constituting a higher unity? Gravity is an attractive force; and
     another great attractive force is cohesion, or the force that binds
     together the atoms of solid matter. Might we, then, join these two
     in a still higher unity, expressed under a more comprehensive law?
     Certainly we might, but not to any advantage. The two kinds of force
     agree in the one point, attraction, but they agree in no other;
     indeed, in the manner of the attraction, they differ widely; so
     widely that we should have to state totally distinct laws for each.
     Gravity is common to all matter, and equal in amount in equal masses
     of matter, whatever be the kind; it follows the law of the diffusion
     of space from a point (the inverse square of the distance); it
     extends to distances unlimited; it is indestructible and invariable.
     Cohesion is special for each separate substance; it decreases
     according to distance much more rapidly than the inverse square,
     vanishing entirely at very small distances. Two such forces have not
     sufficient kindred to be generalized into one force; the
     generalization is only illusory; the statement of the difference
     would still make two forces; while the consideration of one would
     not in any way simplify the phenomena of the other, as happened in
     the generalization of gravity itself."
     To the impassable limit of the explanation of laws of nature, set
     forth in the text, must therefore be added a further limitation.
     Although, when the phenomena to be explained are not, in their own
     nature, generically distinct, the attempt to refer them to the same
     cause is scientifically legitimate; yet to the success of the
     attempt it is indispensable that the cause should be shown to be
     capable of producing them according to the same law. Otherwise the
     unity of cause is a mere guess, and the generalization only a
     nominal one, which, even if admitted, would not diminish the number
     of ultimate laws of nature.
 160 Cours de Philosophie Positive, ii., 656.
 161 Vide supra, book iii., chap. xi.
 162 Philosophy of Discovery, p. 185 et seq.
 163 Comte, Philosophie Positive, ii., 434-437.
 164 As an example of legitimate hypothesis according to the test here
     laid down, has been justly cited that of Broussais, who, proceeding
     on the very rational principle that every disease must originate in
     some definite part or other of the organism, boldly assumed that
     certain fevers, which not being known to be local were called
     constitutional, had their origin in the mucous membrane of the
     alimentary canal. The supposition was, indeed, as is now generally
     admitted, erroneous; but he was justified in making it, since by
     deducing the consequences of the supposition, and comparing them
     with the facts of those maladies, he might be certain of disproving
     his hypothesis if it was ill founded, and might expect that the
     comparison would materially aid him in framing another more
     conformable to the phenomena.
     The doctrine now universally received that the earth is a natural
     magnet, was originally an hypothesis of the celebrated Gilbert.
     Another hypothesis, to the legitimacy of which no objection can lie,
     and which is well calculated to light the path of scientific
     inquiry, is that suggested by several recent writers, that the brain
     is a voltaic pile, and that each of its pulsations is a discharge of
     electricity through the system. It has been remarked that the
     sensation felt by the hand from the beating of a brain, bears a
     strong resemblance to a voltaic shock. And the hypothesis, if
     followed to its consequences, might afford a plausible explanation
     of many physiological facts, while there is nothing to discourage
     the hope that we may in time sufficiently understand the conditions
     of voltaic phenomena to render the truth of the hypothesis amenable
     to observation and experiment.
     The attempt to localize, in different regions of the brain, the
     physical organs of our different mental faculties and propensities,
     was, on the part of its original author, a legitimate example of a
     scientific hypothesis; and we ought not, therefore, to blame him for
     the extremely slight grounds on which he often proceeded, in an
     operation which could only be tentative, though we may regret that
     materials barely sufficient for a first rude hypothesis should have
     been hastily worked up into the vain semblance of a science. If
     there be really a connection between the scale of mental endowments
     and the various degrees of complication in the cerebral system, the
     nature of that connection was in no other way so likely to be
     brought to light as by framing, in the first instance, an hypothesis
     similar to that of Gall. But the verification of any such hypothesis
     is attended, from the peculiar nature of the phenomena, with
     difficulties which phrenologists have not shown themselves even
     competent to appreciate, much less to overcome.
     Mr. Darwin's remarkable speculation on the Origin of Species is
     another unimpeachable example of a legitimate hypothesis. What he
     terms "natural selection" is not only a vera causa, but one proved
     to be capable of producing effects of the same kind with those which
     the hypothesis ascribes to it; the question of possibility is
     entirely one of degree. It is unreasonable to accuse Mr. Darwin (as
     has been done) of violating the rules of Induction. The rules of
     Induction are concerned with the conditions of Proof. Mr. Darwin has
     never pretended that his doctrine was proved. He was not bound by
     the rules of Induction, but by those of Hypothesis. And these last
     have seldom been more completely fulfilled. He has opened a path of
     inquiry full of promise, the results of which none can foresee. And
     is it not a wonderful feat of scientific knowledge and ingenuity to
     have rendered so bold a suggestion, which the first impulse of every
     one was to reject at once, admissible and discussible, even as a
 165 Whewell's Phil. of Discovery, pp. 275, 276.
 166 What has most contributed to accredit the hypothesis of a physical
     medium for the conveyance of light, is the certain fact that light
     travels (which can not be proved of gravitation); that its
     communication is not instantaneous, but requires time; and that it
     is intercepted (which gravitation is not) by intervening objects.
     These are analogies between its phenomena and those of the
     mechanical motion of a solid or fluid substance. But we are not
     entitled to assume that mechanical motion is the only power in
     nature capable of exhibiting those attributes.
 167 Phil. of Discovery, p. 274.
 168 P. 271.
 169 P. 251 and the whole of Appendix G.
 170 In Dr. Whewell's latest version of his theory (_Philosophy of
     Discovery_, p. 331) he makes a concession respecting the medium of
     the transmission of light, which, taken in conjunction with the rest
     of his doctrine on the subject, is not, I confess, very intelligible
     to me, but which goes far toward removing, if it does not actually
     remove, the whole of the difference between us. He is contending,
     against Sir William Hamilton, that all matter has weight. Sir
     William, in proof of the contrary, cited the luminiferous ether, and
     the calorific and electric fluids, "which," he said, "we can neither
     denude of their character of substance, nor clothe with the
     attribute of weight." "To which," continues Dr. Whewell, "my reply
     is, that precisely because I can not clothe these agents with the
     attribute of Weight, I do denude them of the character of
     Substance. They are not substances, but agencies. These Imponderable
     Agents are not properly called Imponderable Fluids. This I conceive
     that I have proved." Nothing can be more philosophical. But if the
     luminiferous ether is not matter, and fluid matter, too, what is the
     meaning of its undulations? Can an agency undulate? Can there be
     alternate motion forward and backward of the particles of an agency?
     And does not the whole mathematical theory of the undulations imply
     them to be material? Is it not a series of deductions from the known
     properties of elastic fluids? This opinion of Dr. Whewell reduces
     the undulations to a figure of speech, and the undulatory theory to
     the proposition which all must admit, that the transmission of light
     takes place according to laws which present a very striking and
     remarkable agreement with those of undulations. If Dr. Whewell is
     prepared to stand by this doctrine, I have no difference with him on
     the subject.
 171 Thus water, of which eight-ninths in weight are oxygen, dissolves
     most bodies which contain a high proportion of oxygen, such as all
     the nitrates (which have more oxygen than any others of the common
     salts), most of the sulphates, many of the carbonates, etc. Again,
     bodies largely composed of combustible elements, like hydrogen and
     carbon, are soluble in bodies of similar composition; resin, for
     instance, will dissolve in alcohol, tar in oil of turpentine. This
     empirical generalization is far from being universally true; no
     doubt because it is a remote, and therefore easily defeated, result
     of general laws too deep for us at present to penetrate; but it will
     probably in time suggest processes of inquiry, leading to the
     discovery of those laws.
 172 Or, according to Laplace's theory, the sun and the sun's rotation.
 173 Supra, book iii., chap. v., § 7.
 174 Supra, book iii., chap. x., § 2
 175 In the preceding discussion, the mean is spoken of as if it were
     exactly the same thing with the average. But the mean, for
     purposes of inductive inquiry, is not the average, or arithmetical
     mean, though in a familiar illustration of the theory the difference
     may be disregarded. If the deviations on one side of the average are
     much more numerous than those on the other (these last being fewer
     but greater), the effect due to the invariable cause, as distinct
     from the variable ones, will not coincide with the average, but will
     be either below or above the average, the deviation being toward the
     side on which the greatest number of the instances are found. This
     follows from a truth, ascertained both inductively and deductively,
     that small deviations from the true central point are greatly more
     frequent than large ones. The mathematical law is, "that the most
     probable determination of one or more invariable elements from
     observation is that in which the sum of the squares of the
     individual aberrations," or deviations, "_shall be the least
     possible_." See this principle stated, and its grounds popularly
     explained, by Sir John Herschel, in his review of Quetelet on
     Probabilities, Essays, p. 395 et seq.
 176 Essai Philosophique sur les Probabilités, fifth Paris edition, p.
 177 It even appears to me that the calculation of chances, where there
     are no data grounded either on special experience or on special
     inference, must, in an immense majority of cases, break down, from
     sheer impossibility of assigning any principle by which to be guided
     in setting out the list of possibilities. In the case of the colored
     balls we have no difficulty in making the enumeration, because we
     ourselves determine what the possibilities shall be. But suppose a
     case more analogous to those which occur in nature: instead of three
     colors, let there be in the box all possible colors, we being
     supposed ignorant of the comparative frequency with which different
     colors occur in nature, or in the productions of art. How is the
     list of cases to be made out? Is every distinct shade to count as a
     color? If so, is the test to be a common eye, or an educated eye--a
     painter's, for instance? On the answer to these questions would
     depend whether the chances against some particular color would be
     estimated at ten, twenty, or perhaps five hundred to one. While if
     we knew from experience that the particular color occurs on an
     average a certain number of times in every hundred or thousand, we
     should not require to know any thing either of the frequency or of
     the number of the other possibilities.
 178 Prospective Review for February, 1850.
 179 "If this be not so, why do we feel so much more probability added by
     the first instance than by any single subsequent instance? Why,
     except that the first instance gives us its possibility (a cause
     adequate to it), while every other only gives us the frequency of
     its conditions? If no reference to a cause be supposed, possibility
     would have no meaning; yet it is clear that, antecedent to its
     happening, we might have supposed the event impossible, i.e., have
     believed that there was no physical energy really existing in the
     world equal to producing it.... After the first time of happening,
     which is, then, more important to the whole probability than any
     other single instance (because proving the possibility), the
     number of times becomes important as an index to the intensity or
     extent of the cause, and its independence of any particular time. If
     we took the case of a tremendous leap, for instance, and wished to
     form an estimate of the probability of its succeeding a certain
     number of times; the first instance, by showing its possibility
     (before doubtful) is of the most importance; but every succeeding
     leap shows the power to be more perfectly under control, greater and
     more invariable, and so increases the probability; and no one would
     think of reasoning in this case straight from one instance to the
     next, without referring to the physical energy which each leap
     indicated. Is it not, then, clear that we do not ever" (let us
     rather say, that we do not in an advanced state of our knowledge)
     "conclude directly from the happening of an event to the probability
     of its happening again; but that we refer to the cause, regarding
     the past cases as an index to the cause, and the cause as our guide
     to the future?"--Ibid.
 180 The writer last quoted says that the valuation of chances by
     comparing the number of cases in which the event occurs with the
     number in which it does not occur, "would generally be wholly
     erroneous," and "is not the true theory of probability." It is at
     least that which forms the foundation of insurance, and of all those
     calculations of chances in the business of life which experience so
     abundantly verifies. The reason which the reviewer gives for
     rejecting the theory is, that it "would regard an event as certain
     which had hitherto never failed; which is exceedingly far from the
     truth, even for a very large number of constant successes." This is
     not a defect in a particular theory, but in any theory of chances.
     No principle of evaluation can provide for such a case as that which
     the reviewer supposes. If an event has never once failed, in a
     number of trials sufficient to eliminate chance, it really has all
     the certainty which can be given by an empirical law; it is
     certain during the continuance of the same collocation of causes
     which existed during the observations. If it ever fails, it is in
     consequence of some change in that collocation. Now, no theory of
     chances will enable us to infer the future probability of an event
     from the past, if the causes in operation, capable of influencing
     the event, have intermediately undergone a change.
 181 Pp. 18, 19. The theorem is not stated by Laplace in the exact terms
     in which I have stated it; but the identity of import of the two
     modes of expression is easily demonstrable.
 182 For a fuller treatment of the many interesting questions raised by
     the theory of probabilities, I may now refer to a recent work by Mr.
     Venn, Fellow of Caius College, Cambridge, "The Logic of Chance;" one
     of the most thoughtful and philosophical treatises on any subject
     connected with Logic and Evidence which have been produced, to my
     knowledge, for many years. Some criticisms contained in it have been
     very useful to me in revising the corresponding chapters of the
     present work. In several of Mr. Venn's opinions, however, I do not
     agree. What these are will be obvious to any reader of Mr. Venn's
     work who is also a reader of this.
 183 Hartley's Observations on Man, vol. i., p. 16. The passage is not
     in Priestley's curtailed edition.
 184 I am happy to be able to quote the following excellent passage from
     Mr. Baden Powell's Essay on the Inductive Philosophy, in
     confirmation, both in regard to history and to doctrine, of the
     statement made in the text. Speaking of the "conviction of the
     universal and permanent uniformity of nature," Mr. Powell says (pp.
     "We may remark that this idea, in its proper extent, is by no means
     one of popular acceptance or natural growth. Just so far as the
     daily experience of every one goes, so far indeed he comes to
     embrace a certain persuasion of this kind, but merely to this
     limited extent, that what is going on around him at present, in his
     own narrow sphere of observation, will go on in like manner in
     future. The peasant believes that the sun which rose to-day will
     rise again to-morrow; that the seed put into the ground will be
     followed in due time by the harvest this year as it was last year,
     and the like; but has no notion of such inferences in subjects
     beyond his immediate observation. And it should be observed that
     each class of persons, in admitting this belief within the limited
     range of his own experience, though he doubt or deny it in every
     thing beyond, is, in fact, bearing unconscious testimony to its
     universal truth. Nor, again, is it only among the most ignorant
     that this limitation is put upon the truth. There is a very general
     propensity to believe that every thing beyond common experience, or
     especially ascertained laws of nature, is left to the dominion of
     chance or fate or arbitrary intervention; and even to object to any
     attempted explanation by physical causes, if conjecturally thrown
     out for an apparently unaccountable phenomenon.
     "The precise doctrine of the generalization of this idea of the
     uniformity of nature, so far from being obvious, natural, or
     intuitive, is utterly beyond the attainment of the many. In all the
     extent of its universality it is characteristic of the philosopher.
     It is clearly the result of philosophic cultivation and training,
     and by no means the spontaneous offspring of any primary principle
     naturally inherent in the mind, as some seem to believe. It is no
     mere vague persuasion taken up without examination, as a common
     prepossession to which we are always accustomed; on the contrary,
     all common prejudices and associations are against it. It is
     pre-eminently an acquired idea. It is not attained without deep
     study and reflection. The best informed philosopher is the man who
     most firmly believes it, even in opposition to received notions; its
     acceptance depends on the extent and profoundness of his inductive
 185 Supra, book iii., chap. iii., § 1
 186 It deserves remark, that these early generalizations did not, like
     scientific inductions, presuppose causation. What they did
     presuppose, was uniformity in physical facts. But the observers
     were as ready to presume uniformity in the co-existence of facts as
     in the sequences. On the other hand, they never thought of assuming
     that this uniformity was a principle pervading all nature: their
     generalizations did not imply that there was uniformity in every
     thing, but only that as much uniformity as existed within their
     observation, existed also beyond it. The induction, fire burns, does
     not require for its validity that all nature should observe uniform
     laws, but only that there should be uniformity in one particular
     class of natural phenomena; the effects of fire on the senses and on
     combustible substances. And uniformity to this extent was not
     assumed, anterior to the experience, but proved by the experience.
     The same observed instances which proved the narrower truth, proved
     as much of the wider one as corresponded to it. It is from losing
     sight of this fact, and considering the law of causation in its full
     extent as necessarily presupposed in the very earliest
     generalizations, that persons have been led into the belief that the
     law of causation is known a priori, and is not itself a conclusion
     from experience.
 187 Book ii., chap. iii.
 188 One of the most rising thinkers of the new generation in France, M.
     Taine (who has given, in the Revue des Deux Mondes, the most
     masterly analysis, at least in one point of view, ever made of the
     present work), though he rejects, on this and similar points of
     psychology, the intuition theory in its ordinary form, nevertheless
     assigns to the law of causation, and to some other of the most
     universal laws, that certainty beyond the bounds of human
     experience, which I have not been able to accord to them. He does
     this on the faith of our faculty of abstraction, in which he seems
     to recognize an independent source of evidence, not indeed
     disclosing truths not contained in our experience, but affording an
     assurance which experience can not give, of the universality of
     those which it does contain. By abstraction M. Taine seems to think
     that we are able, not merely to analyze that part of nature which we
     see, and exhibit apart the elements which pervade it, but to
     distinguish such of them as are elements of the system of nature
     considered as a whole, not incidents belonging to our limited
     terrestrial experience. I am not sure that I fully enter into M.
     Taine's meaning; but I confess I do not see how any mere abstract
     conception, elicited by our minds from our experience, can be
     evidence of an objective fact in universal Nature, beyond what the
     experience itself bears witness of; or how, in the process of
     interpreting in general language the testimony of experience, the
     limitations of the testimony itself can be cast off.
     Dr. Ward, in an able article in the Dublin Review for October,
     1871, contends that the uniformity of nature can not be proved from
     experience, but from "transcendental considerations" only, and that,
     consequently, all physical science would be deprived of its basis,
     if such transcendental proof were impossible.
     When physical science is said to depend on the assumption that the
     course of nature is invariable, all that is meant is that the
     conclusions of physical science are not known as absolute truths:
     the truth of them is conditional on the uniformity of the course
     of nature; and all that the most conclusive observations and
     experiments can prove, is that the result arrived at will be true
     if, and as long as, the present laws of nature are valid. But this
     is all the assurance we require for the guidance of our conduct. Dr.
     Ward himself does not think that his transcendental proofs make it
     practically greater; for he believes, as a Catholic, that the course
     of nature not only has been, but frequently and even daily is,
     suspended by supernatural intervention.
     But though this conditional conclusiveness of the evidence of
     experience, which is sufficient for the purposes of life, is all
     that I was necessarily concerned to prove, I have given reasons for
     thinking that the uniformity, as itself a part of experience, is
     sufficiently proved to justify undoubting reliance on it. This Dr.
     Ward contests, for the following reasons:
     First (p. 315), supposing it true that there has hitherto been no
     well authenticated case of a breach in the uniformity of nature;
     "the number of natural agents constantly at work is incalculably
     large; and the observed cases of uniformity in their action must be
     immeasurably fewer than one thousandth of the whole. Scientific men,
     we assume for the moment, have discovered that in a certain
     proportion of instances--immeasurably fewer than one thousandth of
     the whole--a certain fact has prevailed; the fact of uniformity; and
     they have not found a single instance in which that fact does not
     prevail. Are they justified, we ask, in inferring from these
     premises that the fact is universal? Surely the question answers
     itself. Let us make a very grotesque supposition, in which, however,
     the conclusion would really be tried according to the arguments
     adduced. In some desert of Africa there is an enormous connected
     edifice, surrounding some vast space, in which dwell certain
     reasonable beings, who are unable to leave the inclosure. In this
     edifice are more than a thousand chambers, which some years ago were
     entirely locked up, and the keys no one knew where. By constant
     diligence twenty-five keys have been found, out of the whole number;
     and the corresponding chambers, situated promiscuously throughout
     the edifice, have been opened. Each chamber, when examined, is found
     to be in the precise shape of a dodecahedron. Are the inhabitants
     justified on that account in holding with certitude that the
     remaining 975 chambers are built on the same plan?"
     Not with perfect certitude, but (if the chambers to which the keys
     have been found are really "situated promiscuously") with so high a
     degree of probability that they would be justified in acting upon
     the presumption until an exception appeared.
     Dr. Ward's argument, however, does not touch mine as it stands in
     the text. My argument is grounded on the fact that the uniformity of
     the course of nature as a whole, is constituted by the uniform
     sequences of special effects from special natural agencies; that the
     number of these natural agencies in the part of the universe known
     to us is not incalculable, nor even extremely great; that we have
     now reason to think that at least the far greater number of them, if
     not separately, at least in some of the combinations into which they
     enter, have been made sufficiently amenable to observation, to have
     enabled us actually to ascertain some of their fixed laws; and that
     this amount of experience justifies the same degree of assurance
     that the course of nature is uniform throughout, which we previously
     had of the uniformity of sequence among the phenomena best known to
     us. This view of the subject, if correct, destroys the force of Dr.
     Ward's first argument.
     His second argument is, that many or most persons, both scientific
     and unscientific, believe that there are well authenticated cases
     of breach in the uniformity of nature, namely, miracles. Neither
     does this consideration touch what I have said in the text. I admit
     no other uniformity in the events of nature than the law of
     Causation; and (as I have explained in the chapter of this volume
     which treats of the Grounds of Disbelief) a miracle is no exception
     to that law. In every case of alleged miracle, a new antecedent is
     affirmed to exist; a counteracting cause, namely, the volition of
     a supernatural being. To all, therefore, to whom beings with
     superhuman power over nature are a vera causa, a miracle is a
     case of the Law of Universal Causation, not a deviation from it.
     Dr. Ward's last, and as he says, strongest argument, is the familiar
     one of Reid, Stewart, and their followers--that whatever knowledge
     experience gives us of the past and present, it gives us none of the
     future. I confess that I see no force whatever in this argument.
     Wherein does a future fact differ from a present or a past fact,
     except in their merely momentary relation to the human beings at
     present in existence? The answer made by Priestley, in his
     Examination of Reid, seems to me sufficient, viz., that though we
     have had no experience of what is future, we have had abundant
     experience of what was future. The "leap in the dark" (as
     Professor Bain calls it) from the past to the future, is exactly as
     much in the dark and no more, as the leap from a past which we have
     personally observed, to a past which we have not. I agree with Mr.
     Bain in the opinion that the resemblance of what we have not
     experienced to what we have, is, by a law of our nature, presumed
     through the mere energy of the idea, before experience has proved
     it. This psychological truth, however, is not, as Dr. Ward when
     criticising Mr. Bain appears to think, inconsistent with the
     logical truth that experience does prove it. The proof comes after
     the presumption, and consists in its invariable verification by
     experience when the experience arrives. The fact which while it was
     future could not be observed, having as yet no existence, is always,
     when it becomes present and can be observed, found conformable to
     the past.
     Dr. M'Cosh maintains (Examination of Mr. J. S. Mill's Philosophy,
     p. 257) that the uniformity of the course of nature is a different
     thing from the law of causation; and while he allows that the former
     is only proved by a long continuance of experience, and that it is
     not inconceivable nor necessarily incredible that there may be
     worlds in which it does not prevail, he considers the law of
     causation to be known intuitively. There is, however, no other
     uniformity in the events of nature than that which arises from the
     law of causation: so long therefore as there remained any doubt that
     the course of nature was uniform throughout, at least when not
     modified by the intervention of a new (supernatural) cause, a doubt
     was necessarily implied, not indeed of the reality of causation, but
     of its universality. If the uniformity of the course of nature has
     any exceptions--if any events succeed one another without fixed
     laws--to that extent the law of causation fails; there are events
     which do not depend on causes.
 189 Book i., chap. vii.
 190 In some cases, a Kind is sufficiently identified by some one
     remarkable property: but most commonly several are required; each
     property considered singly, being a joint property of that and of
     other Kinds. The color and brightness of the diamond are common to
     it with the paste from which false diamonds are made; its octohedral
     form is common to it with alum, and magnetic iron ore; but the color
     and brightness and the form together, identify its Kind: that is,
     are a mark to us that it is combustible; that when burned it
     produces carbonic acid; that it can not be cut with any known
     substance; together with many other ascertained properties, and the
     fact that there exist an indefinite number still unascertained.
 191 This doctrine of course assumes that the allotropic forms of what is
     chemically the same substance are so many different Kinds; and such,
     in the sense in which the word Kind is used in this treatise, they
     really are.
 192 Professor Bain (Logic, ii., 13) mentions two empirical laws, which
     he considers to be, with the exception of the law connecting Gravity
     with Resistance to motion, "the two most widely operating laws as
     yet discovered whereby two distinct properties are conjoined
     throughout substances generally." The first is, "a law connecting
     Atomic Weight and Specific Heat by an inverse proportion. For equal
     weights of the simple bodies, the atomic weight multiplied by a
     number expressing the specific heat, gives a nearly uniform product.
     The products, for all the elements, are near the constant number 6."
     The other is a law which obtains "between the specific gravity of
     substances in the gaseous state, and the atomic weights. The
     relationship of the two numbers is in some instances equality; in
     other instances the one is a multiple of the other."
     Neither of these generalizations has the smallest appearance of
     being an ultimate law. They point unmistakably to higher laws. Since
     the heat necessary to raise to a given temperature the same weight
     of different substances (called their specific heat) is inversely as
     their atomic weight, that is, directly as the number of atoms in a
     given weight of the substance, it follows that a single atom of
     every substance requires the same amount of heat to raise it to a
     given temperature; a most interesting and important law, but a law
     of causation. The other law mentioned by Mr. Bain points to the
     conclusion, that in the gaseous state all substances contain, in the
     same space, the same number of atoms; which, as the gaseous state
     suspends all cohesive force, might naturally be expected, though it
     could not have been positively assumed. This law may also be a
     result of the mode of action of causes, namely, of molecular
     motions. The cases in which one of the numbers is not identical with
     the other, but a multiple of it, may be explained on the nowise
     unlikely supposition, that in our present estimate of the atomic
     weights of some substances, we mistake two, or three, atoms for one,
     or one for several.
 193 Dr. M'Cosh (p. 324 of his book) considers the laws of the chemical
     composition of bodies as not coming under the principle of
     Causation; and thinks it an omission in this work not to have
     provided special canons for their investigation and proof. But every
     case of chemical composition is, as I have explained, a case of
     causation. When it is said that water is composed of hydrogen and
     oxygen, the affirmation is that hydrogen and oxygen, by the action
     on one another which they exert under certain conditions, generate
     the properties of water. The Canons of Induction, therefore, as laid
     down in this treatise, are applicable to the case. Such special
     adaptations as the Inductive methods may require in their
     application to chemistry, or any other science, are a proper subject
     for any one who treats of the logic of the special sciences, as
     Professor Bain has done in the latter part of his work; but they do
     not appertain to General Logic.
     Dr. M'Cosh also complains (p. 325) that I have given no canons for
     those sciences in which "the end sought is not the discovery of
     Causes or of Composition, but of Classes; that is, Natural Classes."
     Such canons could be no other than the principles and rules of
     Natural Classification, which I certainly thought that I had
     expounded at considerable length. But this is far from the only
     instance in which Dr. M'Cosh does not appear to be aware of the
     contents of the books he is criticising.
 194 Mr. De Morgan, in his Formal Logic, makes the just remark, that
     from two such premises as Most A are B, and Most A are C, we may
     infer with certainty that some B are C. But this is the utmost limit
     of the conclusions which can be drawn from two approximate
     generalizations, when the precise degree of their approximation to
     universality is unknown or undefined.
 195 Rationale of Judicial Evidence, vol. iii., p. 224.
 196 The evaluation of the chances in this statement has been objected to
     by a mathematical friend. The correct mode, in his opinion, of
     setting out the possibilities is as follows. If the thing (let us
     call it T) which is both an A and a C, is a B, something is true
     which is only true twice in every thrice, and something else which
     is only true thrice in every four times. The first fact being true
     eight times in twelve, and the second being true six times in every
     eight, and consequently six times in those eight; both facts will be
     true only six times in twelve. On the other hand, if T, although it
     is both an A and a C, is not a B, something is true which is only
     true once in every thrice, and something else which is only true
     once in every four times. The former being true four times out of
     twelve, and the latter once in every four, and therefore once in
     those four; both are only true in one case out of twelve. So that T
     is a B six times in twelve, and T is not a B, only once: making the
     comparative probabilities, not eleven to one, as I had previously
     made them, but six to one.
     In the last edition I accepted this reasoning as conclusive. More
     attentive consideration, however, has convinced me that it contains
     a fallacy.
     The objector argues, that the fact of A's being a B is true eight
     times in twelve, and the fact of C's being a B six times in eight,
     and consequently six times in those eight; both facts, therefore,
     are true only six times in every twelve. That is, he concludes that
     because among As taken indiscriminately only eight out of twelve are
     Bs and the remaining four are not, it must equally hold that four
     out of twelve are not Bs when the twelve are taken from the select
     portion of As which are also Cs. And by this assumption he arrives
     at the strange result, that there are fewer Bs among things which
     are both As and Cs than there are among either As or Cs taken
     indiscriminately; so that a thing which has both chances of being a
     B, is less likely to be so than if it had only the one chance or
     only the other.
     The objector (as has been acutely remarked by another correspondent)
     applies to the problem under consideration, a mode of calculation
     only suited to the reverse problem. Had the question been--If two of
     every three Bs are As and three out of every four Bs are Cs, how
     many Bs will be both As and Cs, his reasoning would have been
     correct. For the Bs that are both As and Cs must be fewer than
     either the Bs that are As or the Bs that are Cs, and to find their
     number we must abate either of these numbers in the ratio due to the
     other. But when the problem is to find, not how many Bs are both As
     and Cs, but how many things that are both As and Cs are Bs, it is
     evident that among these the proportion of Bs must be not less, but
     greater, than among things which are only A, or among things which
     are only B.
     The true theory of the chances is best found by going back to the
     scientific grounds on which the proportions rest. The degree of
     frequency of a coincidence depends on, and is a measure of, the
     frequency, combined with the efficacy, of the causes in operation
     that are favorable to it. If out of every twelve As taken
     indiscriminately eight are Bs and four are not, it is implied that
     there are causes operating on A which tend to make it a B, and that
     these causes are sufficiently constant and sufficiently powerful to
     succeed in eight out of twelve cases, but fail in the remaining
     four. So if of twelve Cs, nine are Bs and three are not, there must
     be causes of the same tendency operating on C, which succeed in nine
     cases and fail in three. Now suppose twelve cases which are both As
     and Cs. The whole twelve are now under the operation of both sets of
     causes. One set is sufficient to prevail in eight of the twelve
     cases, the other in nine. The analysis of the cases shows that six
     of the twelve will be Bs through the operation of both sets of
     causes; two more in virtue of the causes operating on A; and three
     more through those operating on C, and that there will be only one
     case in which all the causes will be inoperative. The total number,
     therefore, which are Bs will be eleven in twelve, and the evaluation
     in the text is correct.
 197 Supra, book i., chap. v.
 198 Supra, book i., chap. v., § 1, and book ii., chap, v., § 5.
 199 The axiom, "Equals subtracted from equals leave equal differences,"
     may be demonstrated from the two axioms in the text. If A = a and
     B = b, A-B = a-b. For if not, let A-B = a-b+c. Then since B =
     b, adding equals to equals, A = a+c. But A = a. Therefore _a =
     a+c_, which is impossible.
     This proposition having been demonstrated, we may, by means of it,
     demonstrate the following: "If equals be added to unequals, the sums
     are unequal." If A = a and B not = b, A+B is not = a+b. For
     suppose it to be so. Then, since A = a and A+B = a+b,
     subtracting equals from equals, B = b; which is contrary to the
     So again, it may be proved that two things, one of which is equal
     and the other unequal to a third thing, are unequal to one another.
     If A = a and A not = B, neither is a = B. For suppose it to be
     equal. Then since A = a and a = B, and since things equal to the
     same thing are equal to one another A = B; which is contrary to the
 200 Geometers have usually preferred to define parallel lines by the
     property of being in the same plane and never meeting. This,
     however, has rendered it necessary for them to assume, as an
     additional axiom, some other property of parallel lines; and the
     unsatisfactory manner in which properties for that purpose have been
     selected by Euclid and others has always been deemed the opprobrium
     of elementary geometry. Even as a verbal definition, equidistance is
     a fitter property to characterize parallels by, since it is the
     attribute really involved in the signification of the name. If to be
     in the same plane and never to meet were all that is meant by being
     parallel, we should feel no incongruity in speaking of a curve as
     parallel to its asymptote. The meaning of parallel lines is, lines
     which pursue exactly the same direction, and which, therefore,
     neither draw nearer nor go farther from one another; a conception
     suggested at once by the contemplation of nature. That the lines
     will never meet is of course included in the more comprehensive
     proposition that they are everywhere equally distant. And that any
     straight lines which are in the same plane and not equidistant will
     certainly meet, may be demonstrated in the most rigorous manner from
     the fundamental property of straight lines assumed in the text,
     viz., that if they set out from the same point, they diverge more
     and more without limit.
 201 Philosophie Positive, iii., 414-416.
 202 See the two remarkable notes (A) and (F), appended to his _Inquiry
     into the Relation of Cause and Effect_.
 203 Supra, p. 413.
 204 A writer to whom I have several times referred, gives as the
     definition of an impossibility, that which there exists in the world
     no cause adequate to produce. This definition does not take in such
     impossibilities as these--that two and two should make five; that two
     straight lines should inclose a space; or that any thing should
     begin to exist without a cause. I can think of no definition of
     impossibility comprehensive enough to include all its varieties,
     except the one which I have given: viz., An impossibility is that,
     the truth of which would conflict with a complete induction, that
     is, with the most conclusive evidence which we possess of universal
     As to the reputed impossibilities which rest on no other grounds
     than our ignorance of any cause capable of producing the supposed
     effects; very few of them are certainly impossible, or permanently
     incredible. The facts of traveling seventy miles an hour, painless
     surgical operations, and conversing by instantaneous signals between
     London and New York, held a high place, not many years ago, among
     such impossibilities.
 205 Not, however, as might at first sight appear, 999 times as much. A
     complete analysis of the cases shows that (always assuming the
     veracity of the witness to be 9/10) in 10,000 drawings, the drawing
     of No. 79 will occur nine times, and be announced incorrectly once;
     the credibility, therefore, of the announcement of No. 79 is 9/10;
     while the drawing of a white ball will occur nine times, and be
     announced incorrectly 999 times. The credibility, therefore, of the
     announcement of white is 9/1008, and the ratio of the two 1008:10;
     the one announcement being thus only about a hundred times more
     credible than the other, instead of 999 times.
 206 Supra, book iii., chap. ii., § 3, 4, 5.
 207 Mr. Bailey has given the best statement of this theory. "The general
     name," he says, "raises up the image sometimes of one individual of
     the class formerly seen, sometimes of another, not unfrequently of
     many individuals in succession; and it sometimes suggests an image
     made up of elements from several different objects, by a latent
     process of which I am not conscious." (Letters on the Philosophy of
     the Human Mind, 1st series, letter 22.) But Mr. Bailey must allow
     that we carry on inductions and ratiocinations respecting the class,
     by means of this idea or conception of some one individual in it.
     This is all I require. The name of a class calls up some idea,
     through which we can, to all intents and purposes, think of the
     class as such, and not solely of an individual member of it.
 208 I have entered rather fully into this question in chap. xvii. of _An
     Examination of Sir William Hamilton's Philosophy_, headed "The
     Doctrine of Concepts or General Notions," which contains my last
     views on the subject.
 209 Other examples of inappropriate conceptions are given by Dr. Whewell
     (Phil. Ind. Sc. ii., 185) as follows: "Aristotle and his followers
     endeavored in vain to account for the mechanical relation of forces
     in the lever, by applying the inappropriate geometrical
     conceptions of the properties of the circle: they failed in
     explaining the form of the luminous spot made by the sun shining
     through a hole, because they applied the inappropriate conception
     of a circular quality in the sun's light: they speculated to no
     purpose about the elementary composition of bodies, because they
     assumed the inappropriate conception of likeness between the
     elements and the compound, instead of the genuine notion of elements
     merely determining the qualities of the compound." But in these
     cases there is more than an inappropriate conception; there is a
     false conception; one which has no prototype in nature, nothing
     corresponding to it in facts. This is evident in the last two
     examples, and is equally true in the first; the "properties of the
     circle" which were referred to, being purely fantastical. There is,
     therefore, an error beyond the wrong choice of a principle of
     generalization; there is a false assumption of matters of fact. The
     attempt is made to resolve certain laws of nature into a more
     general law, that law not being one which, though real, is
     inappropriate, but one wholly imaginary.
 210 Professor Bain.
 211 This sentence having been erroneously understood as if I had meant
     to assert that belief is nothing but an irresistible association, I
     think it necessary to observe that I express no theory respecting
     the ultimate analysis either of reasoning or of belief, two of the
     most obscure points in analytical psychology. I am speaking not of
     the powers themselves, but of the previous conditions necessary to
     enable those powers to exert themselves: of which conditions I am
     contending that language is not one, senses and association being
     sufficient without it. The irresistible association theory of
     belief, and the difficulties connected with the subject, have been
     discussed at length in the notes to the new edition of Mr. James
     Mill's Analysis of the Phenomena of the Human Mind.
 212 Mr. Bailey agrees with me in thinking that whenever "from something
     actually present to my senses, conjoined with past experience, I
     feel satisfied that something has happened, or will happen, or is
     happening, beyond the sphere of my personal observation," I may with
     strict propriety be said to reason: and of course to reason
     inductively, for demonstrative reasoning is excluded by the
     circumstances of the case. (The Theory of Reasoning, 2d ed., p.
 213 Novum Organum Renovatum, pp. 35-37.
 214 Novum Organum Renovatum, pp. 39, 40.
 215 P. 217, 4to edition.
 216 "E, ex, extra, extraneus, étranger, stranger."
     Another etymological example sometimes cited is the derivation of
     the English uncle from the Latin avus. It is scarcely possible
     for two words to bear fewer outward marks of relationship, yet there
     is but one step between them, avus, avunculus, uncle. So
     pilgrim, from ager: per agrum, peragrinus, peregrinus,
     pellegrino, pilgrim. Professor Bain gives some apt examples of
     these transitions of meaning. "The word 'damp' primarily signified
     moist, humid, wet. But the property is often accompanied with the
     feeling of cold or chilliness, and hence the idea of cold is
     strongly suggested by the word. This is not all. Proceeding upon the
     superadded meaning, we speak of damping a man's ardor, a metaphor
     where the cooling is the only circumstance concerned; we go on still
     further to designate the iron slide that shuts off the draft of a
     stove, 'the damper,' the primary meaning being now entirely dropped.
     'Dry,' in like manner, through signifying the absence of moisture,
     water, or liquidity, is applied to sulphuric acid containing water,
     although not thereby ceasing to be a moist, wet, or liquid
     substance." So in the phrases, dry sherry, or Champagne.
     " 'Street,' originally a paved way, with or without houses, has been
     extended to roads lined with houses, whether paved or unpaved.
     'Impertinent' signified at first irrelevant, alien to the purpose in
     hand: through which it has come to mean, meddling, intrusive,
     unmannerly, insolent." (Logic, ii., 173, 174.)
 217 Pp. 226, 227.
 218 Essays, p. 214.
 219 Essays, p. 215.
 220 Though no such evil consequences as take place in these instances
     are likely to arise from the modern freak of writing sanatory
     instead of sanitary, it deserves notice as a charming specimen of
     pedantry ingrafted upon ignorance. Those who thus undertake to
     correct the spelling of the classical English writers, are not aware
     that the meaning of sanatory, if there were such a word in the
     language, would have reference not to the preservation of health,
     but to the cure of disease.
 221 Historical Introduction, vol. i., pp. 66-68.
 222 History of Scientific Ideas, ii., 110, 111.
 223 History of Scientific Ideas, ii., 111-113.
 224 Nov. Org. Renov., pp. 286, 287.
 225 History of Scientific Ideas, ii., 120-122.
 226 Nov. Org. Renov., p. 274.
 227 Hist. Sc. Id., i. 133.
 228 Dr. Whewell, in his reply (Philosophy of Discovery, p. 270) says
     that he "stopped short of, or rather passed by, the doctrine of a
     series of organized beings," because he "thought it bad and narrow
     philosophy." If he did, it was evidently without understanding this
     form of the doctrine; for he proceeds to quote a passage from his
     "History," in which the doctrine he condemns is designated as that
     of "a mere linear progression in nature, which would place each
     genus in contact only with the preceding and succeeding ones." Now
     the series treated of in the text agrees with this linear
     progression in nothing whatever but in being a progression.
 229 Supra, p. 137.
 230 Vulgar Errors, book v., chap. 21.
 231 Pharmacologia, Historical Introduction, p. 16.
 232 The author of one of the Bridgewater Treatises has fallen, as it
     seems to me, into a similar fallacy when, after arguing in rather a
     curious way to prove that matter may exist without any of the known
     properties of matter, and may therefore be changeable, he concludes
     that it can not be eternal, because "eternal (passive) existence
     necessarily involves incapability of change." I believe it would be
     difficult to point out any other connection between the facts of
     eternity and unchangeableness, than a strong association between the
     two ideas. Most of the a priori arguments, both religious and
     anti-religious, on the origin of things, are fallacies drawn from
     the same source.
 233 Supra, book ii., chap. v., § 6, and chap. vii., § 1, 2, 3, 4. See
     also Examination of Sir William Hamilton's Philosophy, chap. vi.
     and elsewhere.
 234 It seems that this doctrine was, before the time I have mentioned,
     disputed by some thinkers. Dr. Ward mentions Scotus, Vasquez, Biel,
     Francis Lugo, and Valentia.
 235 I quote this passage from Playfair's celebrated _Dissertation on the
     Progress of Mathematical and Physical Science_.
 236 This statement I must now correct, as too unqualified. The maxim in
     question was maintained with full conviction by no less an authority
     than Sir William Hamilton. See my Examination, chap. xxiv.
 237 Nouveaux Essais sur l'Entendement Humain--Avant-propos. (OEuvres,
     Paris ed., 1842, vol. i., p. 19.)
 238 This doctrine also was accepted as true, and conclusions were
     grounded on it, by Sir William Hamilton. See Examination, chap.
 239 Not that of Leibnitz, but the principle commonly appealed to under
     that name by mathematicians.
 240 Dissertation, p. 27.
 241 Hist. Ind. Sc., Book i., chap. i.
 242 Novum Organum, Aph. 75.
 243 Supra, book iii., chap. vii., § 4.
 244 It is hardly needful to remark that nothing is here intended to be
     said against the possibility at some future period of making gold--by
     first discovering it to be a compound, and putting together its
     different elements or ingredients. But this is a totally different
     idea from that of the seekers of the grand arcanum.
 245 Pharmacologia, pp. 43-45.
 246 Vol. i., chap. 8.
 247 Nov. Org., Aph. 46.
 248 Playfair's Dissertation, sect. 4.
 249 Nov. Org. Renov., p. 61.
 250 Pharmacologia, p. 21.
 251 Pharmacologia, pp. 23, 24.
 252 Ibid., p. 28.
 253 Ibid., p. 62.
 254 Ibid., pp. 61, 62.
 255 Supra, p. 450.
 256 Elements of the Philosophy of the Mind, vol. ii., chap. 4, sect.
 257 "Thus Fourcroy," says Dr. Paris, "explained the operation of mercury
     by its specific gravity, and the advocates of this doctrine favored
     the general introduction of the preparations of iron, especially in
     scirrhus of the spleen or liver, upon the same hypothetical
     principle; for, say they, whatever is most forcible in removing the
     obstruction must be the most proper instrument of cure: such is
     steel, which, besides the attenuating power with which it is
     furnished, has still a greater force in this case from the gravity
     of its particles, which, being seven times specifically heavier than
     any vegetable, acts in proportion with a stronger impulse, and
     therefore is a more powerful deobstruent. This may be taken as a
     specimen of the style in which these mechanical physicians reasoned
     and practiced."--Pharmacologia, pp. 38, 39.
 258 Pharmacologia, pp. 39, 40.
 259 I quote from Dr. Whewell's Hist. Ind. Sc., 3d ed., i., 129.
 260 Hist. Ind. Sc., i., 52.
 261 Nov. Org., Aph. 60.
 262 "An advocate," says Mr. De Morgan (Formal Logic, p. 270), "is
     sometimes guilty of the argument _à dicto secundum quid ad dictum
     simpliciter_: it is his business to do for his client all that his
     client might honestly do for himself. Is not the word in italics
     frequently omitted? Might any man honestly try to do for himself
     all that counsel frequently try to do for him? We are often reminded
     of the two men who stole the leg of mutton; one could swear he had
     not got it, the other that he had not taken it. The counsel is doing
     his duty by his client, the client has left the matter to his
     counsel. Between the unexecuted intention of the client, and the
     unintended execution of the counsel, there may be a wrong done, and,
     if we are to believe the usual maxims, no wrong-doer."
     The same writer justly remarks (p. 251) that there is a converse
     fallacy, à dicto simpliciter ad dictum secundum quid, called by
     the scholastic logicians fallacia accidentis; and another which
     may be called _à dicto secundum quid ad dictum secundum alterum
     quid_ (p. 265). For apt instances of both, I must refer the reader
     to Mr. De Morgan's able chapter on Fallacies.
 263 An example of this fallacy is the popular error that strong drink
     must be a cause of strength. There is here fallacy within fallacy;
     for granting that the words "strong" and "strength" were not (as
     they are) applied in a totally different sense to fermented liquors
     and to the human body, there would still be involved the error of
     supposing that an effect must be like its cause; that the conditions
     of a phenomenon are likely to resemble the phenomenon itself; which
     we have already treated of as an a priori fallacy of the first
     rank. As well might it be supposed that a strong poison will make
     the person who takes it strong.
 264 In his later editions, Archbishop Whately confines the name of
     Petitio Principii "to those cases in which one of the premises
     either is manifestly the same in sense with the conclusion, or is
     actually proved from it, or is such as the persons you are
     addressing are not likely to know, or to admit, except as an
     inference from the conclusion; as, e.g., if any one should infer
     the authenticity of a certain history, from its recording such and
     such facts, the reality of which rests on the evidence of that
 265 No longer even a probable hypothesis, since the establishment of the
     atomic theory; it being now certain that the integral particles of
     different substances gravitate unequally. It is true that these
     particles, though real minima for the purposes of chemical
     combination, may not be the ultimate particles of the substance; and
     this doubt alone renders the hypothesis admissible, even as an
 266 Hist. Ind. Sc., i., 34.
 267 "And coxcombs vanquish Berkeley with a grin."
 268 Some arguments and explanations, supplementary to those in the text,
     will be found in _An Examination of Sir William Hamilton's
     Philosophy_, chap. xxvi.
 269 Supra, p. 424.
 270 When this chapter was written, Professor Bain had not yet published
     even the first part ("The Senses and the Intellect") of his profound
     Treatise on the Mind. In this the laws of association have been more
     comprehensively stated and more largely exemplified than by any
     previous writer; and the work, having been completed by the
     publication of "The Emotions and the Will," may now be referred to
     as incomparably the most complete analytical exposition of the
     mental phenomena, on the basis of a legitimate Induction, which has
     yet been produced. More recently still, Mr. Bain has joined with me
     in appending to a new edition of the "Analysis," notes intended to
     bring up the analytic science of Mind to its latest improvements.
     Many striking applications of the laws of association to the
     explanation of complex mental phenomena are also to be found in Mr.
     Herbert Spencer's "Principles of Psychology."
 271 In the case of the moral sentiments the place of direct experiment
     is to a considerable extent supplied by historical experience, and
     we are able to trace with a tolerable approach to certainty the
     particular associations by which those sentiments are engendered.
     This has been attempted, so far as respects the sentiment of
     justice, in a little work by the present author, entitled
 272 The most favorable cases for making such approximate generalizations
     are what may be termed collective instances; where we are
     fortunately enabled to see the whole class respecting which we are
     inquiring in action at once, and, from the qualities displayed by
     the collective body, are able to judge what must be the qualities of
     the majority of the individuals composing it. Thus the character of
     a nation is shown in its acts as a nation; not so much in the acts
     of its government, for those are much influenced by other causes;
     but in the current popular maxims, and other marks of the general
     direction of public opinion; in the character of the persons or
     writings that are held in permanent esteem or admiration; in laws
     and institutions, so far as they are the work of the nation itself,
     or are acknowledged and supported by it; and so forth. But even here
     there is a large margin of doubt and uncertainty. These things are
     liable to be influenced by many circumstances; they are partially
     determined by the distinctive qualities of that nation or body of
     persons, but partly also by external causes which would influence
     any other body of persons in the same manner. In order, therefore,
     to make the experiment really complete, we ought to be able to try
     it without variation upon other nations: to try how Englishmen would
     act or feel if placed in the same circumstances in which we have
     supposed Frenchmen to be placed; to apply, in short, the Method of
     Differences as well as that of Agreement. Now these experiments we
     can not try, nor even approximate to.
 273 "To which," says Dr. Whewell, "we may add, that it is certain, from
     the history of the subject, that in that case the hypothesis would
     never have been framed at all."
     Dr. Whewell (Philosophy of Discovery, pp. 277-282) defends Bacon's
     rule against the preceding strictures. But his defense consists only
     in asserting and exemplifying a proposition which I had myself
     stated, viz., that though the largest generalizations may be the
     earliest made, they are not at first seen in their entire
     generality, but acquire it by degrees, as they are found to explain
     one class after another of phenomena. The laws of motion, for
     example, were not known to extend to the celestial regions, until
     the motions of the celestial bodies had been deduced from them.
     This, however, does not in any way affect the fact, that the middle
     principles of astronomy, the central force, for example, and the law
     of the inverse square, could not have been discovered, if the laws
     of motion, which are so much more universal, had not been known
     first. On Bacon's system of step-by-step generalization, it would be
     impossible in any science to ascend higher than the empirical laws;
     a remark which Dr. Whewell's own Inductive Tables, referred to by
     him in support of his argument, amply bear out.
 274 Supra, page 317 to the end of the chapter.
 275 Biographia Literaria, i., 214.
 276 Supra, p. 321.
 277 Essays on some Unsettled Questions of Political Economy, pp.
 278 The quotations in this paragraph are from a paper written by the
     author, and published in a periodical in 1834.
 279 Cours de Philosophie Positive, iv., 325-29.
 280 Since reprinted entire in Dissertations and Discussions, as the
     concluding paper of the first volume.
 281 Written and first published in 1840.
 282 This great generalization is often unfavorably criticised (as by Dr.
     Whewell, for instance) under a misapprehension of its real import.
     The doctrine, that the theological explanation of phenomena belongs
     only to the infancy of our knowledge of them, ought not to be
     construed as if it was equivalent to the assertion, that mankind, as
     their knowledge advances, will necessarily cease to believe in any
     kind of theology. This was M. Comte's opinion; but it is by no means
     implied in his fundamental theorem. All that is implied is, that in
     an advanced state of human knowledge, no other Ruler of the World
     will be acknowledged than one who rules by universal laws, and does
     not at all, or does not unless in very peculiar cases, produce
     events by special interpositions. Originally all natural events were
     ascribed to such interpositions. At present every educated person
     rejects this explanation in regard to all classes of phenomena of
     which the laws have been fully ascertained; though some have not yet
     reached the point of referring all phenomena to the idea of Law, but
     believe that rain and sunshine, famine and pestilence, victory and
     defeat, death and life, are issues which the Creator does not leave
     to the operation of his general laws, but reserves to be decided by
     express acts of volition. M. Comte's theory is the negation of this
     Dr. Whewell equally misunderstands M. Comte's doctrine respecting
     the second or metaphysical stage of speculation. M. Comte did not
     mean that "discussions concerning ideas" are limited to an early
     stage of inquiry, and cease when science enters into the positive
     stage. (Philosophy of Discovery, pp. 226 et seq.) In all M.
     Comte's speculations as much stress is laid on the process of
     clearing up our conceptions as on the ascertainment of facts. When
     M. Comte speaks of the metaphysical stage of speculation, he means
     the stage in which men speak of "Nature" and other abstractions as
     if they were active forces, producing effects; when Nature is said
     to do this, or forbid that; when Nature's horror of a vacuum,
     Nature's non-admission of a break, Nature's vis medicatrix, were
     offered as explanations of phenomena; when the qualities of things
     were mistaken for real entities dwelling in the things; when the
     phenomena of living bodies were thought to be accounted for by being
     referred to a "vital force;" when, in short, the abstract names of
     phenomena were mistaken for the causes of their existence. In this
     sense of the word it can not be reasonably denied that the
     metaphysical explanation of phenomena, equally with the theological,
     gives way before the advance of real science.
     That the final, or positive stage, as conceived by M. Comte, has
     been equally misunderstood, and that, notwithstanding some
     expressions open to just criticism, M. Comte never dreamed of
     denying the legitimacy of inquiry into all causes which are
     accessible to human investigation, I have pointed out in a former
 283 Buckle's History of Civilization, i., 30.
 284 I have been assured by an intimate friend of Mr. Buckle that he
     would not have withheld his assent from these remarks, and that he
     never intended to affirm or imply that mankind are not progressive
     in their moral as well as in their intellectual qualities. "In
     dealing with his problem, he availed himself of the artifice
     resorted to by the Political Economist, who leaves out of
     consideration the generous and benevolent sentiments, and founds his
     science on the proposition that mankind are actuated by acquisitive
     propensities alone," not because such is the fact, but because it is
     necessary to begin by treating the principal influence as if it was
     the sole one, and make the due corrections afterward. "He desired to
     make abstraction of the intellect as the determining and dynamical
     element of the progression, eliminating the more dependent set of
     conditions, and treating the more active one as if it were an
     entirely independent variable."
     The same friend of Mr. Buckle states that when he used expressions
     which seemed to exaggerate the influence of general at the expense
     of special causes, and especially at the expense of the influence of
     individual minds, Mr. Buckle really intended no more than to affirm
     emphatically that the greatest men can not effect great changes in
     human affairs unless the general mind has been in some considerable
     degree prepared for them by the general circumstances of the age; a
     truth which, of course, no one thinks of denying. And there
     certainly are passages in Mr. Buckle's writings which speak of the
     influence exercised by great individual intellects in as strong
     terms as could be desired.
 285 Essay on Dryden, in Miscellaneous Writings, i., 186.
 286 In the Cornhill Magazine for June and July, 1861.
 287 It is almost superfluous to observe, that there is another meaning
     of the word Art, in which it may be said to denote the poetical
     department or aspect of things in general, in contradistinction to
     the scientific. In the text, the word is used in its older, and I
     hope, not yet obsolete sense.
 288 Professor Bain and others call the selection from the truths of
     science made for the purposes of an art, a Practical Science, and
     confine the name Art to the actual rules.
 289 The word Teleology is also, but inconveniently and improperly,
     employed by some writers as a name for the attempt to explain the
     phenomena of the universe from final causes.
 290 For an express discussion and vindication of this principle, see the
     little volume entitled "Utilitarianism."