Chapter XXIV: Whether Universal or Particular Demonstration is superiorEdit
- It may be supposed that particular demonstration is superior to universal: Because (1) It gives knowledge of the things in themselves. (2) The universal is a nonentity, and has no existence outside the particulars. But knowledge of the universal is really more extensive than knowledge of the particular. The universal has not a separate existence, but resembles other abstractions like Quality or Relation. It alone gives the Cause; it cannot end in an unknowable infinity; it gives knowledge of more things than of the one under consideration. It contains the particular potentially, and ends in Understanding, not, like the particular, in Sensation.
Since one sort of demonstration is universal and another particular, one affirmative and the other negative, the question is raised as to which is superior. A similar doubt attaches to the method of direct demonstration and of that which proceeds by reduction to the impossible. First then let us consider the universal and particular demonstration, and when we have explained that point we may consider direct and indirect demonstration. Some may perhaps regard the particular method as superior in virtue of the following considerations. If that demonstration which gives us more scientific knowledge be superior (for to produce that is the function of demonstration), if further we have more scientific knowledge of each thing when we know it essentially than when we know it through something else (e.g. we know better about the musician Coriscus, when we know the fact that Coriscus is musical than when we know that ‘man’ is musical, and so in other instances); if, thirdly, universal demonstration prove that something else, not merely the thing in question, is what it is (e.g. prove that the angles of an isosceles triangle are equal to two right angles, not because it is isosceles but because it is a triangle), while particular demonstration shews that the thing itself and not something else possesses the quality in question; if, in short, essential demonstration be of a superior kind and particular demonstration be more essential than universal, then particular demonstration would seem to be the superior. Further, they would argue, no universal can exist outside the particulars, while universal demonstration produces the impression that there is some independent universal in connection with the thing demonstrated, and that a natural quality of this kind exists in real objects (e.g. that there is a universal triangle outside particular triangles, and a universal figure outside particular figures, and a universal number outside particular numbers); and demonstration which is concerned with the existing is superior to that which is concerned with the non-existing, and that which leads to no errors to that which does. Now universal demonstration is of the latter kind, since the method adopted is cumulative, as e.g. in the demonstration of analogy, that ‘what is not in line, number, solid or plane is the universal of analogy.’ Since then universal demonstration is of this character, and since it is less concerned with existence than is particular demonstration, and since it may produce wrong opinions, it would seem to be inferior to particular demonstration. But is not this last argument favourable rather to universal than to particular demonstration? If the quality of having its angles equal to two right angles belong to a figure, not because it is isosceles but because it is triangle, he who only knows that it is isosceles knows less than he who knows it to be a triangle. Strictly speaking when this quality is proved to inhere in isosceles triangle, but not as a result of that figure being a triangle, the proof is not a demonstration at all. If however the proof be effected in the manner mentioned, one who knows everything in the light of its particular essential qualities has superior knowledge of it. If triangle has a wider denotation than isosceles triangle, and if the word ‘triangle’ is not equivocal and the same idea underlies all triangles, and if further the quality of having its angles equal to two right angles belongs to every triangle, then an isosceles triangle does not possess this quality because it is isosceles but because it is a triangle.
Consequently one who knows the universal has a higher knowledge of the thing’s essential qualities than one who knows the particular. Thus universal demonstration is superior to particular. Further, if the universal be one and unambiguous, the universal will exist in no less a degree than the particulars, but actually in a greater degree, in that the universal possesses only imperishable qualities while the particulars are more liable to perish. Moreover there is no necessity for supposing that the universal is anything outside the particulars because it expresses a unity, any more than that those categories have independent existence which signify, not substances, but qualities, relations or actions. If, in fact, it be supposed that the universal has a separate existence, it is not the demonstration which is to be blamed, but the listener who misunderstands it.
Moreover if demonstration be a syllogism proving the cause and reason of a thing, the universal contains the cause to a higher degree, for that which is an essential attribute of a thing is its own cause. Now the universal is primary and is therefore the cause of the attribute. Hence universal demonstration is superior for it gives a better proof of the cause and reason.
Further we pursue our search for the cause of a thing until, and think that we have learned it when, we see nothing else which can be regarded as the cause, whether it be in the region of becoming or being. This last must be the end and goal of our enquiry. Take the question, ‘for what reason did he come?’ ‘To receive the money, and this in order to pay his debt, and that again in order not to act unjustly.’ If we proceed in this way, when we find that a thing has happened on no other account and for no other reason than the fact we have attained to, we say that ‘he came’ or ‘it is, or becomes owing to this ultimate cause,’ and that we have then learned most completely why he came. But if the same happens with regard to all causes and all reasons, and if our knowledge is most complete when we know the ultimate cause, then in other cases also we have most complete knowledge of a thing when its existence is not merely the result of the existence of something else. When therefore we know that the external angles of a figure are equal to four right angles because it is isosceles, there remains the question ‘why have isosceles figures this quality?’ The reason of this is that they are triangles, and the reason why triangles possess this quality is that they are rectlinear figures. If this latter fact be not caused by something else, we have then the most complete knowledge of it, and have then attained to the universal. Hence universal demonstration is superior.
Further, the more a demonstration partakes of the nature of the particular, the larger is the indefinite element which it contains. In so far as things are indefinite they are unknowable, in so far as they are definite they are knowable. Hence things are more knowable the greater the universal element they contain, less knowable the greater the particular element. Demonstration is applicable in a higher degree to things which are more capable of demonstration, and corresponds in definiteness to the definiteness of its objects. Consequently that demonstration which is the more universal is superior, since it is demonstration in a higher sense. Moreover, that demonstration which brings one knowledge of other things as well as of the single object of study is preferable to that which gives information about the latter alone; and one who has a universal demonstration knows the particular as well, while one who knows the particular does not know the universal. Hence universal demonstration is superior from this point of view also.
We may also consider the following point. To prove more universally is to use for the proof a middle term which is nearer to the elementary law; now that which is nearest to this law is the ultimate, and so the ultimate must be identical with the elementary principle. If then the demonstration which is derived from the elementary principle be more exact than that which is not, that which is more nearly derived from it must be more exact than that which is more remote. Now the former has the larger universal element. Hence from this point of view the universal is superior. E.g. If one had to prove that A is predicable of D; the middle terms are B and C, B being the more universal. Then the demonstration based on B is more universal.
Some, however, of the arguments here used are merely dialectical, and the best proof that the universal demonstration is the superior may be derived from the fact that when we possess the major premise we in a manner know the minor also and possess it potentially. E.g. If we know that every triangle has its angles equal to two right angles, we know in a manner, or potentially, that an isosceles figure has this property, even if we do not know that an isosceles figure is a triangle. On the other hand one who possesses this minor premise, does not in any way know the universal, either potentially or actually. The universal too belongs to pure thought, while the particular is finally referable to acts of sensation. This may suffice to shew that universal demonstration is superior to particular.