Aristotle · Topics §5.6#2

Properties from Affirmation, Negation, and Coordinates

Passage 51 of 94 · Greek

Summary

The author explains the topics based on affirmations and negations (both in predicates and the subjects themselves), showing that attempts to establish a property of negation from that of affirmation are false, and then presents the topic of co-divided coordinates using virtues as examples.

§5.6#2Δεύτερον δ᾿ ἐκ τῶν κατηγορουμένων ἢ μὴ κατηγορουμένων, καὶ καθ᾿ ὧν κατηγορεῖται ἢ μὴ κατηγορεῖται, ἀνασκευάζοντα μὲν εἰ ἡ φάσις τῆς φάσεως μή ἐστιν ἴδιον· οὐδὲ γὰρ ἡ ἀπόφασις τῆς ἀποφάσεως ἔσται ἴδιον.

Secondly, from predicates or non-predicates, and from those of which they are predicated or not predicated. For refuting, if the affirmation is not the property of the affirmation; for then neither will the negation be the property of the negation.

Κἂν εἰ δ᾿ ἡ ἀπόφασις τῆς ἀποφάσεως μή ἐστιν ἴδιον, οὐδ᾿ ἡ φάσις τῆς φάσεως ἔσται ἴδιον.

And if the negation is not the property of the negation, neither will the affirmation be the property of the affirmation.

Οἷον ἐπεὶ οὐκ ἔστι τοῦ ἀνθρώπου ἴδιον τὸ ζῷον, οὐδ᾿ ἂν τοῦ μὴ ἀνθρώπου εἴη ἴδιον τὸ μὴ ζῷον.

For instance, since animal is not the property of man, neither would non-animal be the property of non-man.

Κἂν εἰ δὲ τοῦ μὴ ἀνθρώπου φαίνηται μὴ ἴδιον τὸ μὴ ζῷον, οὐδὲ τοῦ ἀνθρώπου ἔσται ἴδιον τὸ ζῷον.

And if non-animal should appear not to be the property of non-man, neither will animal be the property of man.

Κατασκευάζοντα δ᾿ εἰ τῆς φάσεως ἡ φάσις ἐστὶν ἴδιον· καὶ γὰρ τῆς ἀποφάσεως ἡ ἀπόφασις ἔσται ἴδιον.

And for establishing, if the affirmation is the property of the affirmation; for then the negation will also be the property of the negation.

Κἂν εἰ δὲ τῆς ἀποφάσεως ἡ ἀπόφασίς ἐστιν ἴδιον, καὶ ἡ φάσις τῆς φάσεως ἔσται ἴδιον.

And if the negation is the property of the negation, the affirmation will also be the property of the affirmation.

Οἷον ἐπεὶ τοῦ μὴ ζῴου ἴδιόν ἐστι τὸ μὴ ζῆν, εἴη ἂν τοῦ ζῴου ἴδιον τὸ ζῆν· κἂν εἰ δὲ τοῦ ζῴου φαίνηται ἴδιον τὸ ζῆν, καὶ τοῦ μὴ ζῴου φανεῖται ἴδιον τὸ μὴ ζῆν.

For instance, since not living is the property of non-animal, living would be the property of animal; and if living should appear to be the property of animal, not living will also appear to be the property of non-animal.

Τρίτον δὲ ἐξ αὐτῶν τῶν ὑποκειμένων ἀνασκευάζοντα μὲν εἰ τὸ ἀποδεδομένον ἴδιον τῆς φάσεώς ἐστιν ἴδιον· οὐ γὰρ ἔσται τὸ αὐτὸ καὶ τῆς ἀποφάσεως ἴδιον.

Thirdly, from the subjects themselves. For refuting, if the assigned property is the property of the affirmation; for the same will not also be the property of the negation.

Κἂν εἰ δὲ τῆς ἀποφάσεως ἴδιον τὸ ἀποδοθέν, οὐκ ἔσται τῆς φάσεως ἴδιον.

And if what is assigned is the property of the negation, it will not be the property of the affirmation.

Οἷον ἐπεὶ τοῦ ζῴου ἴδιον τὸ ἔμψυχον, οὐκ ἂν εἴη τοῦ μὴ ζῴου ἴδιον τὸ ἔμψυχον.

For instance, since animate is the property of animal, animate would not be the property of non-animal.

Κατασκευάζοντα δὲ εἰ τὸ ἀποδοθὲν μὴ τῆς φάσεως ἴδιον, εἴη ἂν τῆς ἀποφάσεως.

And for establishing, if what is assigned is not the property of the affirmation, it would be that of the negation.

Οὗτος δ᾿ ὁ τόπος ψευδής ἐστιν· φάσις γὰρ ἀποφάσεως καὶ ἀπόφασις φάσεως οὐκ ἔστιν ἴδιον.

But this topic is false; for an affirmation is not the property of a negation, and a negation is not the property of an affirmation.

Φάσις μὲν γὰρ ἀποφάσει οὐδ᾿ ὅλως ὑπάρχει, ἀπόφασις δὲ φάσει ὑπάρχει μέν, οὐχ ὡς ἴδιον δὲ ὑπάρχει.

For an affirmation does not belong to a negation at all, while a negation belongs to an affirmation, but does not belong as a property.

Ἔπειτα δ᾿ ἐκ τῶν ἀντιδιῃρημένων ἀνασκευάζοντα μὲν εἰ τῶν ἀντιδιῃρημένων μηδὲν μηδενὸς τῶν λοιπῶν ἀντιδιῃρημένων ἐστὶν ἴδιον· οὐδὲ γὰρ τὸ κείμενον ἔσται ἴδιον τούτου οὗ κεῖται ἴδιον.

Next, from co-divided coordinates. For refuting, if none of the co-divided coordinates is the property of any of the remaining co-divided coordinates; for then neither will the established property be the property of that of which it is established to be the property.

Οἷον ἐπεὶ ζῷον αἰσθητὸν οὐδενὸς τῶν ἄλλων θνητῶν ζῴων ἐστὶν ἴδιον, οὐκ ἂν εἴη τὸ ζῷον νοητὸν τοῦ θεοῦ ἴδιον.

For instance, since sensible animal is not the property of any of the other mortal animals, intelligible animal would not be the property of God.

Κατασκευάζοντα δ᾿ εἰ τῶν λοιπῶν τῶν ἀντιδιῃρημένων ὁτιοῦν ἐστὶν ἴδιον τούτων ἑκάστου τῶν ἀντιδιῃρημένων· καὶ γὰρ τὸ λοιπὸν ἔσται τούτου ἴδιον, οὗ κεῖται μὴ εἶναι ἴδιον.

And for establishing, if any of the remaining co-divided coordinates is the property of each of these co-divided coordinates; for then the remainder will be the property of this, of which it is established not to be the property.

Οἷον ἐπεὶ φρονήσεώς ἐστιν ἴδιον τὸ καθ᾿ αὑτὸ πεφυκέναι λογιστικοῦ ἀρετὴν εἶναι, καὶ τῶν ἄλλων ἀρετῶν οὕτως ἑκάστης λαμβανομένης, εἴη ἂν σωφροσύνης ἴδιον τὸ καθ᾿ αὑτὸ πεφυκέναι ἐπιθυμητικοῦ ἀρετὴν εἶναι.

For instance, since it is the property of wisdom to be by its own nature the virtue of the rational part, and so also for each of the other virtues if taken in this way, it would be the property of temperance to be by its own nature the virtue of the desiring part.

Notes

p.350εἰ ἡ φάσις τῆς φάσεως μή ἐστιν ἴδιον — Here, 'affirmation' (φάσις) and 'negation' (ἀπόφασις) refer to positive terms (e.g., 'man', 'animal') and negative terms (e.g., 'non-man', 'non-animal') rather than full propositions.
p.350εἰ τὸ ἀποδεδομένον ἴδιον τῆς φάσεώς ἐστιν ἴδιον — The subject 'the assigned property' (τὸ ἀποδεδομένον ἴδιον) is paired with the predicate 'property of the affirmation' (τῆς φάσεως ἴδιον). The first occurrence of ἴδιον refers to the candidate property being examined, while the second functions as a predicate.
p.350ἀπόφασις δὲ φάσει ὑπάρχει μέν, οὐχ ὡς ἴδιον δὲ ὑπάρχει — Explains that while a negative counter-concept (e.g., 'not inanimate') necessarily accompanies a positive concept (e.g., 'animate'), it does so as a trivial consequence and is not convertible, meaning it cannot count as a 'property' (ἴδιον) in the strict definition.
p.351τῶν ἀντιδιῃρημένων — Refers to co-divided coordinates or mutually exclusive members resulting from the division of the same genus. In this context, the virtues (wisdom, temperance) and the classification of animals (sensible, intelligible) serve as examples.

Cite this passage

Aristotle, Topics §5.6#2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg044.humanitext-grc1:5.6%232

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