[40] Soph. El. vi. p. 168, a. 19: ἔστι γὰρ ἅπαντας ἀναλῦσαι τοὺς λεχθέντας τρόπους εἰς τὸν τοῦ ἐλέγχου διορισμόν.
[41] Ibid. a. 35.
[42] Ibid. p. 169, b. 15.
In regard to two among the thirteen heads — Fallacia Accidentis and Fallacia Consequentis (which however ought properly to rank as only one head, since the second is merely a particular variety of the first) — Aristotle’s observations are remarkable. After having pointed out that a Syllogism embodying this fallacy will not be valid or conclusive (thus showing that it involves Ignoratio Elenchi), he affirms that even scientific men were often not aware of it, and conceived themselves to be really refuted by an unscientific opponent urging against them such an inconclusive syllogism. To take an example:— Every triangle has its three angles equal to two right angles; every triangle is a figure; therefore, every figure has its three angles equal to two right angles.[43] Here we have an invalid syllogism; for it is in the Third figure, and sins against the conditions of that figure, by exhibiting an universal affirmative conclusion: it is a syllogism properly concluding in Darapti, but with conclusion improperly generalized. Yet Aristotle intimates that a scientific geometer of his day, in argument with an unscientific opponent, would admit the conclusion to be well proved, not knowing how to point out where the fallacy lay: he would, if asked, grant the premisses necessary for constructing such a syllogism; and, even if not asked, would suppose that he had already granted them, or that they ought to be granted.[44]
[43] Ibid. p. 168, a. 40: οὐδ’ εἰ τὸ τρίγωνον δυοῖν ὀρθαῖν ἴσας ἔχει, συμβέβηκε δ’ αὐτῷ σχήματι εἶναι ἢ πρώτῳ ἢ ἀρχῇ, ὅτι σχῆμα ἢ ἀρχὴ ἢ πρῶτον τοῦτο.
Here we have Figure reckoned as an accident of Triangle. This is a specimen of Aristotle’s occasional laxity in employing the word συμβεβηκός. He commonly uses it as contrasted with essential, of which last term Mr. Poste says very justly (notes, p. 129):— “To complete the statement of Aristotle’s view, it should be added, that essential propositions are those whose predicate cannot be defined without naming the subject, or whose subject cannot be defined without naming the predicate.â€� Now figure is the genus to which triangle belongs, and triangle cannot be defined without naming its genus figure. But to include Genus as a predicable under the head of συμβεβηκός or Accident, is in marked opposition to Aristotle’s own doctrine elsewhere: see Topic. I. v. p. 102, b. 4; iv. p. 101, b. 17; Analyt. Post. I. ii. p. 71, b. 9; Metaphys. E. p. 1026, b. 32. It is a misfortune that Aristotle gave to this general head of Fallacy the misleading title of Fallacia Accidentia — παρὰ τὸ συμβεβηκός. When he gave this title, he probably had present to his mind only such examples as he indicates in Soph. El. v. p. 166, b. 32. Throughout the Topica and elsewhere, Genus is distinguished pointedly from συμβεβηκός, though examples occur occasionally in which the distinction is neglected. The two Fallacies called Accidentis and Consequentis, would both be more properly ranked under one common logical title — Supposed convertibility or interchangeableness between Subject and Predicate — εἰ τόδε ἀπὸ τοῦδε μὴ χωρίζεται, μηδ’ ἀπὸ θατέρου χωρίζεσθαι θάτερον (vii. p. 169, b. 8).
[44] Soph. El. vi. p. 168, b. 6: ἀλλὰ παρὰ τοῦτο καὶ οἱ τεχνῖται καὶ ὅλως οἱ ἐπιστήμονες ὑπὸ τῶν ἀνεπιστημόνων ἐλέγχονται· κατὰ συμβεβηκὸς γὰρ ποιοῦνται τοὺς συλλογισμοὺς πρὸς τοὺς εἰδότας· οἱ δ’ οὐ δυνάμενοι διαιρεῖν ἢ ἐρωτώμενοι διδόασιν ἢ οὐ δόντες οἴονται δεδωκέναι.
The passage affords us a curious insight into the intellectual grasp of the scientific men contemporary with Aristotle. Most of them were prepared to admit fallacious inferences (such as the above) which assumed the interchangeability of subject and predicate. They had paid little or no attention to the logical relations between one proposition and another, and between the two different terms of the same proposition. The differences of essential from accidental predication, and of each among the five Predicables from the others, must have been practically familiar to them, as to others, from the habit of correct speaking in detail; but they had not been called upon to consider correct speaking and reasoning in theory, nor to understand upon what conditions it depended whether the march of their argumentative discourse landed them in true or false results. And, if even the scientific men were thus unaware of logical fallacies, we may be sure that this must have been still more the case with unscientific men, of ordinary intelligence and education. Aristotle tells us here, in more than one passage, how widespread such illogical tendencies were: to fancy that two subjects which had one predicate the same must be the same with each other in all respects;[45] to understand each predicate applied to a subject as being itself an independent subject, implying a new Hoc Aliquid or Unum;[46] to treat the universal, not as a common epithet but, as a substantive and singular apart;[47] to use equivocal words or phrases, even the most wide and vague, without any attempt to discriminate their various meanings.[48] Such insensibility to the conditions of accurate reasoning prevailed alike among ordinary men and among the men of special science. A geometer would be imposed upon by the inconclusive syllogism stated in the last paragraph, which, as being founded on the Fallacia Accidentia (or interchangeability of subject and predicate), Aristotle numbers among Sophistical Refutations. Such a refutation, however, even when successful, would not at all prove that the geometer was deficient in knowledge of his own science;[49] for it would puzzle the really scientific man as well as the pretender.
[45] Soph. El. vi. p. 168, b. 31: τὰ γὰρ ἑνὶ ταὐτά, καὶ ἀλλήλοις ἀξιοῦμεν εἶναι ταὐτά. — vii. p. 169, b. 7: ἔτι καὶ ἐπὶ πολλῶν φαίνεται καὶ ἀξιοῦται οὕτως, εἰ τόδε ἀπὸ τοῦδε μὴ χωρίζεται, μηδ’ ἀπὸ θατέρου χωρίζεσθαι θάτερον.
[46] Ibid. vii. p. 169, a. 33: ὅτι πᾶν τὸ κατηγορούμενόν τινος ὑπολαμβάνομεν τόδε τι καὶ ὡς ἓν ὑπακούομεν· τῷ γὰρ ἑνὶ καὶ τῇ οὐσίᾳ μάλιστα δοκεῖ παρέπεσθαι τὸ τόδε τι καὶ τὸ ὄν.