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Aristotle · Prior Analytics §1.2.15#1

Syllogisms from Opposite Premises in the First Two Figures

Passage 67 of 123 · Greek

Summary

This chunk examines the possibility of constructing a syllogism from opposite premises in the first and second figures. It demonstrates that while it is impossible in the first figure, it is possible in the second figure provided that the terms falling under the middle term are either identical or related as whole to part.

§1.2.15#1Ἐν ποίῳ δὲ σχήματι ἔστιν ἐξ ἀντικειμένων προτάσεων συλλογίσασθαι καὶ ἐν ποίῳ οὐκ ἔστιν, ὧδ’ ἔσται φανερόν.
In which figure it is possible to syllogize from opposite premises, and in which it is not, will be clear as follows.
λέγω δʼ ἀντικειμένας εἶναι προτάσεις κατὰ μὲν τὴν λέξιν τέτταρας, οἷον τὸ παντὶ τῷ οὐδενί, καὶ τὸ παντὶ τῷ οὐ παντί, καὶ τὸ τινὶ τῷ οὐδενί, καὶ τὸ τινὶ τῷ οὐ τινί, κατʼ ἀλήθειαν δὲ τρεῖς· τό γὰρ τινὶ τῷ οὐ τινὶ κατὰ τὴν λέξιν ἀντίκειται μόνον.
I say that premises are opposite in expression in four ways, as "all" to "none", "all" to "not all", "some" to "none", and "some" to "not some"; but in truth they are three, for "some" and "not some" are opposite only in expression.
τούτων δʼ ἐναντίας μὲν τὰς καθόλου, τὸ παντὶ τῷ μηδενὶ ὑπάρχειν, οἷον τὸ πᾶσαν ἐπιστήμην εἶναι σπουδαίαν τῷ· μηδεμίαν εἶναι σπουδαίαν, τὰς δʼ ἄλλας ἀντικειμένας.
And of these, the contraries are the universal ones, namely "belonging to all" to "belonging to none", such as "every science is excellent" to "no science is excellent"; and the others are opposites.
Ἐν μὲν οὖν τῷ πρώτῳ σχήματι οὐκ ἔστιν ἐξ ἀντικειμένων προτάσεων συλλογισμός, οὔτε καταφατικὸς οὔτε ἀποφατικός, καταφατικός μὲν ὅτι ἀμφοτέρας δεῖ καταφατικὰς εἶναι τὰς προτάσεις, αἱ δʼ ἀντικείμεναι φάσις καὶ ἀπόφασις, στερητικός δὲ ὅτι αἱ μὲν ἀντικείμεναι τὸ αὐτὸ τοῦ αὐτοῦ κατηγοροῦσι καὶ ἀπαρνοῦνται, τὸ δʼ ἐν τῷ πρώτῳ μέσον οὐ λέγεται κατʼ ἀμφοῖν, ἀλλʼ ἐκείνου μὲν ἄλλο ἀπαρνεῖται, αὐτὸ δὲ ἄλλου κατηγορεῖται· αὗται δʼ οὐκ ἀντίκεινται.
In the first figure, then, there is no syllogism from opposite premises, whether affirmative or negative: an affirmative one, because it is necessary for both premises to be affirmative, whereas opposite premises are an affirmation and a negation; and a negative one, because opposite premises predicate and deny the same of the same, but the middle in the first figure is not predicated of both, but something else is denied of it, while it is predicated of another; and these are not opposite.
Ἐν δὲ τῷ μέσῳ σχήματι καὶ ἐκ τῶν ἀντικειμένων καὶ ἐκ τῶν ἐναντίων ἐνδέχεται γίγνεσθαι συλλογισμόν.
But in the middle figure it is possible for a syllogism to arise both from opposites and from contraries.
ἔστω γὰρ ἀγαθὸν μὲν ἐφʼ οὗ Α, ἐπιστήμη δὲ ἐφʼ οὗ Β καὶ Γ. εἰ δὴ πᾶσαν ἐπιστήμην σπουδαίαν ἔλαβε καὶ μηδεμίαν, τὸ Α τῷ Β παντὶ ὑπάρχει καὶ τῷ οὐδενί, ὥστε τὸ Β τῷ Γ οὐδενί·
For let "good" be A, and "science" be B and Γ. If, then, one assumes that every science is excellent and that none is, A belongs to all B and to no [Γ]; so that B belongs to no Γ.
οὐδεμία ἄρα ἐπιστήμη ἐπιστήμη ἐστίν.
Therefore, no science is science.
ὁμοίως δὲ καὶ εἰ πᾶσαν λαβὼν σπουδαίαν τὴν ἰατρικὴν μὴ σπουδαίαν ἔλαβε· τῷ μὲν γὰρ Β παντὶ τὸ Α, τῷ δὲ Γ οὐδενί, ὥστε ἡ τὶς ἐπιστήμη οὐκ ἔσται ἐπιστήμη.
And similarly also if, having assumed every science to be excellent, one assumes medicine not to be excellent; for A belongs to all B, but to no Γ, so that a certain science will not be science.
καὶ εἰ τῷ μὲν Γ παντὶ τὸ Α, τῷ δὲ Β μηδενί, ἔστι δὲ τὸ μὲν Β ἐπιστήμη, τὸ δὲ Γ ἰατρική, τὸ δὲ ὑπόληψις· οὐδεμίαν γὰρ ἐπιστήμην ὑπόληψιν λαβὼν εἴληφε τινὰ εἶναι ὑπόληψιν.
And even if A belongs to all Γ, but to no B, and B is "science", Γ "medicine", and [A] "belief"; for having assumed no science to be belief, one has assumed some [science] to be belief.
διαφέρει δὲ τοῦ πάλαι τῷ ἐπὶ τῶν ὅρων ἀντιστρέφεσθαι· πρότερον μὲν γὰρ πρὸς τῷ Β, νῦν δὲ πρὸς τῷ Γ τὸ καταφατικόν.
And this differs from the previous case by the conversion in respect of the terms; for previously the affirmative was in relation to B, but now it is in relation to Γ.
καὶ ἂν ᾖ δὲ μὴ καθόλου ἡ ἑτέρα πρότασις, ὡσαύτως· ἀεὶ γὰρ τὸ μέσον ἐστὶν ὃ ἀπὸ θατέρου μὲν ἀποφατικῶς λέγεται, κατὰ θατέρου δὲ καταφατικῶς.
And even if one of the premises is not universal, it is the same; for the middle is always that which is denied of one and affirmed of the other.
ὥστʼ ἐνδέχεται τἀντικείμενα περαίνεσθαι, πλὴν οὐκ ἀεὶ οὐδὲ πάντως, ἀλλʼ ἐὰν οὕτως ἔχῃ τὰ ὑπὸ τὸ μέσον ὥστʼ ἢ ταὐτὰ εἶναι ἢ ὅλον πρὸς μέρος.
So that it is possible for opposites to be concluded, except not always nor in every way, but if the terms under the middle are so related as to be either the same or as whole to part.
ἄλλως δʼ ἀδύνατον· οὐ γὰρ ἔσονται οὐδαμῶς αἱ προτάσεις οὔτʼ ἐναντίαι οὔτʼ ἀντικείμεναι.
Otherwise it is impossible; for the premises will in no way be either contraries or opposites.

Notes

  1. 63b25κατὰ μὲν τὴν λέξιν — The expression κατὰ τὴν λέξιν ('in expression') is contrasted with κατʼ ἀλήθειαν ('in truth'). While verbally there are four pairs of opposites (universal affirmative/universal negative, universal affirmative/particular negative, particular affirmative/universal negative, and particular affirmative/particular negative), in logical reality 'some are' and 'some are not' can be true together (subcontraries) and thus do not constitute a true opposition, reducing the real oppositions to three.
  2. 63b36τὸ δʼ ἐν τῷ πρώτῳ μέσον — Explanation of the syntactic role of the middle term in the first figure. The middle (τὸ μέσον) is the subject of the clause, and the passage explains that it 'is not predicated of both (οὐ λέγεται κατʼ ἀμφοῖν)', but rather 'something else (ἄλλο, i.e., the major term) is denied of it (ἐκείνου), while it itself (αὐτό, i.e., the middle term) is predicated of another (ἄλλου, i.e., the minor term)'. Thus, the syntactical references of ἐκείνου and αὐτό must be carefully aligned with the middle term.
  3. 64a3τῷ οὐδενί — In the phrase καὶ τῷ οὐδενί ('and to none') following τὸ Α τῷ Β παντὶ ὑπάρχει ('A belongs to all B'), the dative object Γ (or the term representing Γ) is omitted. Based on the premise structure of the second figure (A-B, A-Γ) and the context where both B and Γ are set as 'science', the omitted term must be understood as Γ.
  4. 64a9εἴληφε τινὰ εἶναι ὑπόληψιν — The indefinite pronoun τινά (feminine accusative singular) refers to 'a certain science' or 'a certain thing (medicine)' and functions as the subject of the infinitive clause. While assuming the universal negative premise that A (belief) belongs to no B (science), because A belongs to all Γ (medicine) and medicine is a part of science, one has implicitly assumed (εἴληφε) that 'some science is belief', which is contradictory.

Cite this passage

Aristotle, Prior Analytics §1.2.15#1. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg001.humanitext-grc2:1.2.15%231

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