A N A A N A 791 Morgan," who tells that a friend had constructed about 800 on his name, specimens of which are given in his Budget of Paradoxes, p. 82. The pseudonyms adopted by authors are often transposed forms, more or less exact, of their names; thus " Calvinus" becomes " Alcuinus;" " Francois Rabelais," " Alcofribas Nasier;" " Bryan Waller Proctor," "Barry Cornwall, poet;" "Henry Rogers," "R E. H. Greyson," &c. It is to be noted that the last two are impure anagrams, an "r" being left out in both cases. " Telliamed," a simple reversal, is the title of a well-known work by " De Maillet." The most remarkable pseudonym of this class is the name " Voltaire," which the celebrated philosopher assumed instead of his family name, " Francois Marie Arouet," and which is now generally allowed to be an anagram of "Arouet, l.j.," that is, Arouet the younger. Perhaps the only practical use to which anagrams have been turned is to be found in the transpositions in which some of the astronomers of the 17th century embodied their discoveries, with the design apparently of avoiding the risk that, while they were engaged in further verifica tion, the credit of what they had found out might be claimed by others. Thus Galileo announced Jhis discovery that Venus had phases like the moon in the form, " Hcec immat^tra a me jam frustra leguntur oy," that is, " Cynthia; figuras (Ktindatur Mater Amorum." ANAHUAC, the name of the great central plateau of Mexico, lying between 15 and 30 N. lat., and 95 and 110 W. long., at an elevation of from 6000 to 9000 feet above the sea. Anahuac comprises three-fourths of the territory of Mexico, including the capital ; and although much of its surface is level, many lofty mountains rise out of the table-land, the highest of which is Popocatepetl (17,720 feet), an active volcano. The name Anahuac is also used to designate a much less extensive part of the table-land, as well as that portion of the Rocky Mountains which lies to the south of 40 N". lat. The word itself is said to signify " near the water " in the old Mexican lan~ gunge, and seems to have been at one time the name of several other places in the ancient empire of Mexico. ANALOGY is the name in logic for a mode of real or material inference, proceeding upon the resemblance be tween particulars : speaking generally, it is that process whereby, from the known agreement of two or more things in certain respects, we infer agreement in some other point known to be present in one or more, but not known to be present in the other or others. It was signalised already by Aristotle under the different name of Example (-Trapd- Seiy/ia), the word Analogy (dvaXoyia) having with him the special sense of mathematical proportion or resemblance (equality) of ratios. The earliest use of the name in its current logical sense is to be found apparently in Galen. While, in popular language, the word has come to be vaguely used as a synonym for resemblance, the logical authorities, though having generally the same kind of inference in view, are by no means agreed as to its exact nature and ground. It has chiefly to be distinguished from the related process of Induction, in their conception of which logicians are notoriously at variance. (See INDUCTION.) Aristotle, distinguishing Syllogism and Induction as passing the one from whole to part (any part), and the other from part (all the parts) to whole, notes under each a loose or rhetorical form Enthymeme under Syllogism, and Paradigm, or Example, under Induction. Thus, to give his own instance, it is an inference by way of example if a war to come of Athens against Thebes is condemned because a past war of Thebes against Phocis is known to have been disastrous. Here the reason ing, which may be said to pass from part to part, is resolved by Aristotle as compounded of an imperfect in duction and a syllogism ; the particular case of Thebes against Phocis started from being first inductively widened into Avar between neighbours generally, and the particular case of Athens against Thebes arrived at being then drawn out by regular syllogism from that major. Example, or, to speak of it by its later name, the inference from analogy, is thus presented by Aristotle as directly related to induc tion : it differs from an imperfect induction what is now often called real or material induction from particulars incompletely enumerated only in having its conclusion particular instead of general, and its datum singular in stead of plural. Kant and his followers, while maintaining a relation between induction and analogy, mark the difference other wise than Aristotle. By induction, it is said, we seek to prove that some attribute belongs (or not) to all the mem bers of a class, because it belongs (or not) to many of that class ; by analogy, that all the attributes of a thing belong (or not) to another thing, because many of the attributes belong (or not) to this other. In this country Sir William Hamilton has adopted this view (Lectures on Logic, vol. ii. pp. 165-174), though he differs from Kant in understand ing it only of the process called applied or modified induc tion, not of the pure form of reasoning from all the parts to the whole, which, in the manner of Aristotle, he puts on a level with pure syllogistic deduction. The relation and difference of the two processes may be formulated in the short expressions : One in many, therefore one in all (Induction) ; Many in one, therefore all in one (Analogy). For instance, it would be an analogical inference to con clude that a disease corresponding in many symptoms with those observed in typhus corresponds in all, or, in other words, is typhus ; whereas it would be an induction to infer that a particular symptom appearing in a number of typhus patients will appear in all. The view of Kant and Hamilton does not reach below the surface of the matter, if it can be maintained at all. In the first of the examples just given the inference might well be a good induction, all depending upon the kind of symptoms that are made the ground of the conclusion ; on the other hand, the second might be a case of mere analogy, not to be called induction. Neither, again, is Aristotle s view satisfactory, which practically makes the difference to depend upon the mere quantity of the conclusion, worked out as particular for analogy by appending to the induc tion involved a syllogism of application. Since the univer sal always carries with it the particular, and cannot be affirmed unless the particular can, the two processes be come to all intents and purposes one and the same. If the particular or analogical conclusion is justifiable, it is because there was ground for a good induction (only not of the pure sort) ; if there was no ground for a good induction, then, upon Aristotle s resolution, there can be no ground for the particular inference either. Should it be said, indeed, that the peculiarity of the case lies not so much in the conclusion, as in the start being made from one particular instance, whence the process gets its name Example, that undoubtedly will distinguish it from any thing that can seriously be called induction ; but then what becomes of the resolution that Aristotle makes of it ? That resolution can be upheld only at the cost of the character of the inductive process. The logician who has done most to elaborate the theory of real or material induction, John Stuart Mill, has also been able to give an interpretation of analogy, which, without in the least severing its connection with induction, leaves it as a process for which a distinct name is neces sary. According to him, the two kinds of argument, while homogeneous in the type of their inference, which holds
for Jill reasoning from experience, namely, that things
