[68] Analyt. Post. I. xxiii. p. 84, b. 37: καὶ ὥσπερ ἐν τοῖς ἄλλοις ἡ ἀρχὴ ἁπλοῦν, τοῦτο δ’ οὐ ταὐτὸ πανταχοῦ, ἀλλ’ ἐν βαρεῖ μὲν μνᾶ, ἐν δὲ μέλει δίεσις, ἄλλο δ’ ἐν ἄλλῳ, οὕτως ἐν συλλογισμῷ τὸ ἓν πρότασις ἄμεσος, ἐν δ’ ἀποδείξει καὶ ἐπιστήμῃ ὁ νοῦς.
[69] Ibid. b. 35-p. 85, a. 1.
Having thus, in the long preceding reasoning, sought to prove that all demonstration must take its departure from primary undemonstrable principia — from some premisses, affirmative and negative, which are directly true in themselves, and not demonstrable through any middle term or intervening propositions, Aristotle now passes to a different enquiry. We have some demonstrations in which the conclusion is Particular, others in which it is Universal: again, some Affirmative, some Negative, Which of the two, in each of these alternatives, is the best? We have also demonstrations Direct or Ostensive, and demonstrations Indirect or by way of Reductio ad Absurdum. Which of these two is the best? Both questions appear to have been subjected to debate by contemporary philosophers.[70]
[70] Ibid. xxiv. p. 85, a. 13-18. ἀμφισβητεῖται ποτέρα βελτίων· ὡς δ’ αὕτως καὶ περὶ τῆς ἀποδεικνύναι λεγομένης καὶ τῆς εἰς τὸ ἀδύνατον ἀγούσης ἀποδείξεως.
Aristotle discusses these points dialectically (as indeed he points out in the Topica that the comparison of two things generally, as to better and worse, falls under the varieties of dialectical enquiry[71]), first stating and next refuting the arguments on the weaker side. Some persons may think (he says) that demonstration of the Particular is better than demonstration of the Universal: first, because it conducts to fuller cognition of that which the thing is in itself, and not merely that which it is quatenus member of a class; secondly, because demonstrations of the Universal are apt to generate an illusory belief, that the Universal is a distinct reality apart from and independent of all its particulars (i.e., that figure in general has a real existence apart from all particular figures, and number in general apart from all particular numbers, &c.), while demonstrations of the Particular do not lead to any such illusion.[72]
[71] Aristot. Topic. III. i. p. 116, a. 1, seq.
[72] Analyt. Post. I. xxiv. p. 85, a. 20-b. 3. Themistius, pp. 58-59, Spengel: οὐ γὰρ ὁμώνυμον τὸ καθόλου ἐστίν, οὐδὲ φωνὴ μόνον, ἀλλ’ ὑπόστασις, οὐ χωριστὴ μὲν ὥσπερ οὐδὲ τὰ συμβεβηκότα, ἐναργῶς δ’ οὖν ἐμφαινομένη τοῖς πράγμασιν. The Scholastic doctrine of Universalia in re is here expressed very clearly by Themistius.
To these arguments Aristotle replies:— 1. It is not correct to say that cognition of the Particular is more complete, or bears more upon real existence, than cognition of the Universal. The reverse would be nearer to the truth. To know that the isosceles, quatenus triangle, has its three angles equal to two right angles, is more complete cognition than knowing simply that the isosceles has its three angles equal to two right angles. 2. If the Universal be not an equivocal term — if it represents one property and one definition common to many particulars, it then has a real existence as much or more than any one or any number of the particulars. For all these particulars are perishable, but the class is imperishable. 3. He who believes that the universal term has one meaning in all the particulars, need not necessarily believe that it has any meaning apart from all particulars; he need not believe this about Quiddity, any more than he believes it about Quality or Quantity. Or if he does believe so, it is his own individual mistake, not imputable to the demonstration. 4. We have shown that a complete demonstration is one in which the middle term is the cause or reason of the conclusion. Now the Universal is most of the nature of Cause; for it represents the First Essence or the Per Se, and is therefore its own cause, or has no other cause behind it. The demonstration of the Universal has thus more of the Cause or the Why, and is therefore better than the demonstration of the Particular. 5. In the Final Cause or End of action, there is always some ultimate end for the sake of which the intermediate ends are pursued, and which, as it is better than they, yields, when it is known, the only complete explanation of the action. So it is also with the Formal Cause: there is one highest form which contains the Why of the subordinate forms, and the knowledge of which is therefore better; as when, for example, the exterior angles of a given isosceles triangle are seen to be equal to four right angles, not because it is isosceles or triangle, but because it is a rectilineal figure. 6. Particulars, as such, fall into infinity of number, and are thus unknowable; the Universal tends towards oneness and simplicity, and is thus essentially knowable, more fully demonstrable than the infinity of particulars. The demonstration thereof is therefore better. 7. It is also better, on another ground; for he that knows the Universal does in a certain sense know also the Particular;[73] but he that knows the Particular cannot be said in any sense to know the Universal. 8. The principium or perfection of cognition is to be found in the immediate proposition, true per se. When we demonstrate, and thus employ a middle term, the nearer the middle term approaches to that principium, the better the demonstration is. The demonstration of the Universal is thus better and more accurate than that of the Particular.[74]
[73] Compare Analyt. Post. I. i. p. 71, a. 25; also Metaphys. A. p. 981, a. 12.
[74] Analyt. Post. I. xxiv. p. 85, b. 4-p. 86, a. 21. Schol. p. 233, b. 6: ὁμοίως δὲ ὄντων γνωρίμων, ἡ δι’ ἐλαττόνων μέσων αἱρετωτέρα· μᾶλλον γὰρ ἐγγυτέρω τῆς τοῦ νοῦ ἐνεργείας.