[81] Analyt. Post. I. xxvii. p. 87, a. 31-37. Themistius, Paraphras. p. 60, ed. Speng.: κατ’ ἄλλον δὲ (τρόπον), ἐὰν ἡ μὲν περὶ ὑποκείμενά τινα καὶ αἰσθητὰ πραγματεύηται, ἡ δὲ περὶ νοητὰ καὶ καθόλου.
Philoponus illustrates this (Schol. p. 235, b. 41, Br.): οἷον τὰ Θεοδοσίου σφαιρικὰ ἀκριβέστερά ἐστιν ἐπιστήμῃ τῆς τῶν Αὐτολύκου περὶ κινουμένης σφαίρας. &c.
[82] Analyt. Post. I. xxviii. p. 87, a. 38-b. 5. Themistius, p. 61: δῆλον δὲ τοῦτο γίνεται προϊοῦσιν ἐπὶ τὰς ἀναποδείκτους ἀρχάς· αὗται γὰρ εἰ μηδεμίαν ἔχοιεν συγγένειαν, ἕτεραι αἱ ἐπιστῆμαι.
[83] Analyt. Post. I. xxix. p. 87, b. 5-18. Aristotle gives an example to illustrate this general doctrine: ἥδεσθαι, τὸ κινεῖσθαι, τὸ ἠρεμίζεσθαι, τὸ μεταβάλλειν. As he includes these terms and this subject among the topics for demonstration, it is difficult to see where he would draw a distinct line between topics for Demonstration and topics for Dialectic.
There cannot be demonstrative cognition of fortuitous events,[84] for all demonstration is either of the necessary or of the customary. Nor can there be demonstrative cognition through sensible perception. For though by sense we perceive a thing as such and such (through its sensible qualities), yet we perceive it inevitably as hoc aliquid, hic, et nunc. But the Universal cannot be perceived by sense; for it is neither hic nor nunc, but semper et ubique.[85] Now demonstrations are all accomplished by means of the Universal, and demonstrative cognition cannot therefore be had through sensible perception. If the equality of the three angles of a triangle to two right angles were a fact directly perceivable by sense, we should still have looked out for a demonstration thereof: we should have no proper scientific cognition of it (though some persons contend for this): for sensible perception gives us only particular cases, and Cognition or Science proper comes only through knowing the Universal.[86] If, being on the surface of the moon, we had on any one occasion seen the earth between us and the sun, we could not have known from that single observation that such interposition is the cause universally of eclipses. We cannot directly by sense perceive the Universal, though sense is the principium of the Universal. By multiplied observation of sensible particulars, we can hunt out and elicit the Universal, enunciate it clearly and separately, and make it serve for demonstration.[87] The Universal is precious, because it reveals the Cause or διότι, and is therefore more precious, not merely than sensible observation, but also than intellectual conception of the ὅτι only, where the Cause or διότι lies apart, and is derived from a higher genus. Respecting First Principles or Summa Genera, we must speak elsewhere.[88] It is clear, therefore, that no demonstrable matter can be known, properly speaking, from direct perception of sense; though there are cases in which nothing but the impossibility of direct observation drives us upon seeking for demonstration. Whenever we can get an adequate number of sensible observations, we can generalize the fact; and in some instances we may perhaps not seek for any demonstrative knowledge (i.e. to explain it by any higher principle). If we could see the pores in glass and the light passing through them, we should learn through many such observations why combustion arises on the farther side of the glass; each of our observations would have been separate and individual, but we should by intellect generalize the result that all the cases fall under the same law.[89]
[84] Analyt. Post. I. xxx. p. 87, b. 19-27.
[85] Ibid. xxxi. p. 87, b. 28: εἰ γὰρ καὶ ἔστιν ἡ αἴσθησις τοῦ τοιοῦδε καὶ μὴ τοῦδέ τινος, ἀλλ’ αἰσθάνεσθαί γε ἀναγκαῖον τόδε τι καὶ ποῦ καὶ νῦν.
[86] Ibid. b. 35: δῆλον ὅτι καὶ εἰ ἦν αἰσθάνεσθαι τὸ τρίγωνον ὅτι δυσὶν ὀρθαῖς ἴσας ἔχει τὰς γωνίας, ἐζητοῦμεν ἂν ἀπόδειξιν, καὶ οὐχ (ὥσπερ φασί τινες) ἠπιστάμεθα· αἰσθάνεσθαι μὲν γὰρ ἀνάγκη καθ’ ἕκαστον, ἡ δ’ ἐπιστήμη τῷ τὸ καθόλου γνωρίζειν ἐστίν.
Euclid, in the 20th Proposition of his first Book, demonstrates that any two sides of a triangle are together greater than the third side. According to Proklus, the Epikureans derided the demonstration of such a point as absurd; and it seems that some contemporaries of Aristotle argued in a similar way, judging by the phrase ὥσπερ φασί τινες.
[87] Analyt. Post. I. xxxi. p. 88, a. 2: οὐ μὴν ἀλλ’ ἐκ τοῦ θεωρεῖν τοῦτο πολλάκις συμβαῖνον, τὸ καθόλου ἂν θηρεύσαντες ἀπόδειξιν εἴχομεν· ἐκ γὰρ τῶν καθ’ ἕκαστα πλειόνων τὸ καθόλου δῆλον. Themistius, p. 62, Sp.: ἀρχὴ μὲν γὰρ ἀποδείξεως αἴσθησις, καὶ τὸ καθόλου ἐννοοῦμεν διὰ τὸ πολλάκις αἰσθέσθαι.