Commentary Aristotle Posterior Analytics
Lecture 37
Whether universal demonstration is stronger than particular demonstration
a12. Since demonstrations may be either commensurately universal or particular, and either affirmative or negative; the question arises, which form is the better? And the same question may be put in regard to so-called ‘direct’ demonstration and reductio ad impossibile.
a17. Let us first examine the commensurately universal and the particular forms, and when we have cleared up this problem proceed to discuss ‘direct’ demonstration and reductio ad impossibile.
a20. The following considerations might lead some minds to prefer particular demonstration. (1) The superior demonstration is the demonstration which gives us greater knowledge (for this is the ideal of demonstration), and we have greater knowledge of a particular individual when we know it in itself than when we know it through something else; e.g., we know Coriscus the musician better when we know that Coriscus is musical than when we know only that man is musical, and a like argument holds in all other cases. But commensurately universal demonstration, instead of proving that the subject itself actually is x, proves only that something else is x—e.g., in attempting to prove that isosceles is x, it proves not that isosceles but only that triangle is x—whereas particular demonstration proves that the subject itself is x. The demonstration, then, that a subject, as such, possesses an attribute is superior. If this is so, and if the particular rather than the commensurately universal forms demonstrates, particular demonstration is superior.
a31. (2) The universal has not a separate being over against groups of singulars. Demonstration nevertheless creates the opinion that its function is conditioned by something like this—some separate entity belonging to the real world; that, for instance, of triangle or of figure or number, over against particular triangles, figures, and numbers. But demonstration which touches the real and will not mislead is superior to that which moves among unrealities and is delusory. Now, commensurately universal demonstration is of the latter kind: if we engage in it we find ourselves reasoning after a fashion well illustrated by the argument that the proportionate is what answers to the definition of some entity which is neither line, number, solid, nor plane, but a proportionate apart from all these. Since, then, such a proof is characteristically commensurate and universal, and less touches reality than does particular demonstration, and creates a false opinion, it will follow that commensurate and universal is inferior to particular demonstration.
b4. We may retort thus. (1) The first argument applies no more to commensurate and universal than to particular demonstration. If equality to two right angles is attributable to its subject not qua isosceles but qua triangle, he who knows that isosceles possesses that attribute knows the subject as qua itself possessing the attribute, to a less degree than he who knows that triangle has that attribute. To sum up the whole matter: if a subject is proved to possess qua triangle an attribute which it does not in fact possess qua triangle, that is not demonstration: but if it does possess it qua triangle the rule applies that the greater knowledge is his who knows the subject as possessing its attribute qua that in virtue of which it actually does possess it. Since, then, triangle is the wider term, and there is one identical definition of triangle—that is, the term is not equivocal—and since equality to two right angles belongs to all triangles, it is isosceles qua triangle and not triangle qua isosceles which has its angles so related. It follows that he who knows a connexion universally has greater knowledge of it as it in fact is than he who knows the particular; and the inference is that commensurate and universal is superior to particular demonstration.
b15. (2) If there is a single identical definition—that is, if the commensurate universal is unequivocal — then the universal will possess being not less but more than some of the particulars, inasmuch as it is universals which comprise the imperishable, particulars that tend to perish.
b18. (3) Because the universal has a single meaning, we are not therefore compelled to suppose that in these examples it has being as a substance apart from its particulars — any more than we need make a similar supposition in the other cases of unequivocal universal predication, viz. where the predicate signifies not substance but quality, essential relatedness, or action. If such a supposition is entertained, the blame rests not with the demonstration but with the hearer.
Since demonstrations may be. After determining about the demonstrative syllogism, the Philosopher now treats of the comparison of demonstrations one to another.
And because science is caused by demonstration, his treatment is divided into two parts.
In the first he treats of the comparison of demonstrations.
In the second of the comparison of sciences, at: the science which is knowledge (87a31; [356]).
First, he raises a doubt concerning the comparison of demonstrations.
Second, he lays down the order of procedure, at: let us first examine (85a17; [325]).
Third, he deals with the doubts raised, at: the following considerations (85a20; [326]).
He says therefore first (85a12) that demonstration is divided in three ways: for in one way it is divided into universal and particular; in another way into categorical and privative, that is, affirmative and negative; in a third way into that which demonstrates ostensively and that which leads to the impossible. In each division, therefore, the question arises as to which is the stronger.
Then, at: let us first examine the commensurately (85a17) he shows what order should be followed.
He says that the comparison of universal to particular demonstration should be treated first. And when this has been done, we shall speak of demonstrations which demonstrate something affirmatively and of those which demonstrate to the impossible, namely, whether the affirmative is stronger and whether the demonstration to the impossible is stronger.
Then, at: the following considerations (85a20) he deals with the problems he has proposed.
First, of the comparison of the particular with the universal.
Second, of the comparison of the affirmative with the negative, at: that affirmative demonstration (86a32; [340]).
Third, of the comparison of the ostensive with that which leads to the impossible, at: since affirmative demonstration (87a1; [349]).
Concerning the first he does three things.
First, he proposes reasons to show that the particular demonstration is more powerful than the universal.
Second, he solves them, at: we may retort thus (85b4; [329]).
Third, he gives reasons to the contrary, at: demonstration is syllogism (85b22; [332]).
In regard to the first he sets forth three reasons, remarking that in virtue of these reasons to be set down forthwith, it will perhaps seem to some that a particular demonstration is of more value than a universal one.
The first reason (85a20) is this: That demonstration is stronger through which we know best in a scientific way. (And he proves it on the ground that the strength of a demonstration consists in knowing in a scientific way. For the most that a thing can do is called its strength: for the strength of a man able to carry 100 pounds is not that he can carry ten but that he can carry 100, which is the limit of his power, as it is stated in On the Heavens I. Now, the most that a demonstration can do is to cause scientific knowledge; consequently, that is the strength of a demonstration. But a thing is more perfect to the extent that it attains the strength appropriate to it, as is clear from Physics VII. Hence this proposition is quite evident, namely, that the better a demonstration causes scientific knowledge, the stronger it is). (He assumes that we know a thing better when we know it according to itself than when we know it according to something else: thus we know more in regard to Coriscus when we know that Coriscus is a musician than when we merely know that some man is a musician). And this proposition is true, absolutely speaking, because that which is per se is always prior to and the cause of that which is through something else, as it is stated in Physics VIII. From these facts the conclusion is gathered that a demonstration which makes one know something according to itself is stronger than one which makes one know something according to something else. But a universal demonstration demonstrates and makes one know something not according to itself, but according to something else, namely, according to the universal, as that a triangle with two equal sides, that is, an isosceles, has three, not because it is isosceles but because it is a triangle. A particular demonstration, on the other hand, demonstrates about a particular thing according to itself. Hence according to this it follows that a particular demonstration is stronger than a universal.
Then, at: the universal has not a separate being (85a31) he gives a second reason.
It is this. The universal is not something apart from singulars, as was proved in Metaphysics VII. But a universal demonstration leads one to think, from the very manner of its demonstration, that the universal is something, that is, a certain nature in the realm of beings: for example, when it demonstrates something of triangle apart from particular triangles, and of figure apart from particular figures, and of number apart from particular numbers. To these two propositions he adds two others: to the first one, which stated that the universal is not something apart from the singulars, he adds this proposition, namely, that a demonstration concerned with being is stronger than one concerned with non-being. But to the second proposition, which stated that a universal demonstration leads one to think that a universal is something existing as a real nature, he adds another proposition, namely, that a demonstration which does not cause error is stronger than one which leads to error. Then he shows that one is led into error on account of a universal demonstration, because one who proceeds according to a universal demonstration demonstrates concerning some universal as of some analogue, that is, as of something common which is referred to many things proportionally, as though there existed something common which is neither a line nor a number nor a solid, that is, a body, nor a plane, that is, a surface, but something apart from these, that is, a universal quantity; or something owing to them, that is, something which must be posited, if they are to have the formality of quantity. Thus, therefore, in virtue of two middles, equivalent as it were to two arguments, he concludes to one conclusion, saying that if the universal demonstration is as described, that is, is less an entity than the particular, and more likely to create a false opinion than the particular, it follows from these two middles that the universal ranks lower than the particular.
Then, at: we may retort thus (85b4) he solves these reasons in order.
First, he solves the first one, saying that the first, that is, the ground on which the first reason rests, is no different in the universal than in the particular, because in both cases we find something which is according to itself and something according to something else. And he shows that something which is according to itself is found in the universal. For “to have three angles equal to two right angles” does not belong to isosceles according to itself, that is, precisely as isosceles, but according as it is a triangle. Consequently, one who knows that a certain triangle, namely, the isosceles, “has three,” has less knowledge of that which is per se than if he knew that a triangle “has three.” And it must be admitted universally that if there be any characteristic which does not belong to triangle as triangle, but that characteristic is nevertheless demonstrated of it, the demonstration will not be true. But if it is in it precisely as it is a triangle, then by knowing it in a universal way of triangle precisely as of triangle, he has a more perfect knowledge. From these facts, therefore, he concludes a conditional statement in whose antecedent three things are placed: one is that “triangle” is in more things than isosceles is; the second is that “triangle” is predicated of isosceles and of those others according to the same formality and not equivocally; the third is that “having three angles equal to two right angles” is present in every triangle. With these three suppositions, the consequent is that “the having of three” does not belong to triangle precisely as it is isosceles, but vice versa.
Now the first two were put in the antecedent on the ground that if “triangle” were not the wider term or if it were predicated equivocally of its several inferiors, it would not be compared to “isosceles” as universal to particular. But he added the third, because if “having three” did not belong to every triangle, it would not belong to isosceles precisely as triangle, but in virtue of being a certain triangle; just as the characteristic of “having three” does not belong to every figure precisely as figure, but because it is a certain figure which is a triangle.
From these statements, therefore, he concludes to the opposite of that which the objection presupposed, namely, he concludes that one who knows in the universal knows the thing per se and as such in a better way than one who knows in the particular. And from this he further concludes his chief proposition, namely, that universal demonstration is stronger than particular.
Then, at: if there is a single identical definition (85b15) he answers the second reason.
He says that if the universal is predicated of several according to one formality and not equivocally, the universal, so far as its formality is concerned, that is, so far as science and demonstration are concerned, will not be less of an entity than the particular, but more. For the incorruptible is more a being than the corruptible; but the formality of a universal is incorruptible, whereas particulars are corruptible, in that they are subject to corruption as to their individual principles, although not as to the formality of the species, which is common to all and conserved through generation. And so in regard to that which pertains to their formality, the universals are beings to a higher degree than particulars. Nevertheless, in regard to natural subsistence the particulars, which are called the first and chief substances, have more being.
Then, at: because the universal has (85b18) he answers the third reason.
He says that although in propositions or demonstrations that are universal, something which is one according to itself, say “triangle,” is signified, nevertheless there is no need for anyone to suppose on this account that “triangle” is some one thing apart from the many, any more than there is need in the case of things which do not signify substance but some genus of accident (when we signify them absolutely, as when we say “whiteness” or “fatherhood”), to suppose that such things exist apart from the substance. For the intellect is able to understand one of the things which are joined in reality without actually thinking of some other one; yet the intellect is not false. Thus, if something white is musical, I am able to think of the white and attribute something to it and demonstrate something of it, say, that it disperses the vision, without adverting at all to musical. However, if one were to understand that the white one is not musical, then the intellect would be false. And so when we say or understand that whiteness is a color, no mention being made of the subject, we are saying something true. But it would be false, were we to say that the whiteness which is a color is not in a subject. In like fashion, when we say that every man is an animal, we are speaking truly, even though no particular man is mentioned. But it would be false were we to say that man is “an animal existing apart from particular men.” Now, if this is so, then demonstration is not the cause of the false opinion according to which someone supposes that the universal is some thing outside the singulars, but it is rather the hearer who understands incorrectly. Hence this does not detract at all from universal demonstration.