Humanitext Reader

Aristotle · Topics §6.7

Degrees of Intensity, Disjunction, and Definition Substitution

Passage 65 of 94 · Greek

Summary

The chapter discusses topics concerning whether degrees of intensity apply consistently to both the defined term and its definition, the logical contradictions that arise from disjunctive definitions, and the method of checking for discrepancies by substituting definitions for the names of genera and differences.

§6.7Σκεπτέον δὲ καὶ εἰ καθ᾿ ἕτερόν τι μᾶλλον λέγεται τὸ ὁρισθὲν ἢ κατὰ τὸν ἀποδοθέντα λόγον, οἷον εἰ ἡ δικαιοσύνη δύναμις τοῦ ἴσου διανεμητική.
One must also examine if the defined term is said to be such more in virtue of something else than in virtue of the rendered definition; for example, if justice is "a power of distributing what is equal".
Δίκαιος γὰρ μᾶλλον ὁ προαιρούμενος τὸ ἴσον διανεῖμαι τοῦ δυναμένου, ὥστ᾿ οὐκ ἂν εἴη ἡ δικαιοσύνη δύναμις τοῦ ἴσου διανεμητική· καὶ γὰρ δίκαιος εἴη ἂν μάλιστα ὁ δυνάμενος μάλιστα τὸ ἴσον διανεῖμαι.
For a just person is one who chooses to distribute what is equal, rather than one who is able to do so, so that justice would not be a power of distributing what is equal; for the one who is most able to distribute what is equal would be the most just.
Ἔτι εἰ τὸ μὲν πρᾶγμα δέχεται τὸ μᾶλλον, τὸ δὲ κατὰ τὸν λόγον ἀποδοθὲν μὴ δέχεται, ἢ ἀνάπαλιν τὸ μὲν κατὰ τὸν λόγον ἀποδοθὲν δέχεται, τὸ δὲ πρᾶγμα μή.
Moreover, if the thing itself admits of "the more", but what is rendered in the definition does not, or conversely, if what is rendered in the definition admits of it, but the thing does not.
Δεῖ γὰρ ἀμφότερα δέχεσθαι ἢ μηδέτερον, εἴπερ δὴ ταὐτόν ἐστι τὸ κατὰ τὸν λόγον ἀποδοθὲν τῷ πράγματι.
For both must admit of it, or neither, if indeed what is rendered in the definition is the same as the thing.
Ἔτι εἰ δέχεται μὲν ἀμφότερα τὸ μᾶλλον, μὴ ἅμα δὲ τὴν ἐπίδοσιν ἀμφότερα λαμβάνει, οἷον εἰ ὁ ἔρως ἐπιθυμία συνουσίας ἐστίν·
Moreover, if both admit of "the more", but both do not receive the increase at the same time; for example, if love is "a desire for intercourse".
ὁ γὰρ μᾶλλον ἐρῶν οὐ μᾶλλον ἐπιθυμεῖ τῆς συνουσίας, ὥστ᾿ οὐχ ἅμα ἀμφότερα τὸ μᾶλλον ἐπιδέχεται· ἔδει δέ γε, εἴπερ ταὐτὸν ἦν.
For he who loves more does not desire intercourse more, so that both do not admit of "the more" at the same time; yet they ought to, if indeed they were the same.
Ἔτι εἰ δύο τινῶν προτεθέντων, καθ᾿ οὗ τὸ πρᾶγμα μᾶλλον λέγεται, τὸ κατὰ τὸν λόγον ἧττον λέγεται, οἷον εἰ τὸ πῦρ ἐστὶ σῶμα τὸ λεπτομερέστατον·
Moreover, if when two things are proposed, that of which the thing is more said, has what is according to the definition less said of it; for example, if fire is "the most subtle body".
πῦρ μὲν γὰρ μᾶλλον ἡ φλόξ ἐστι τοῦ φωτός, σῶμα δὲ τὸ λεπτομερέστατον ἧττον φλὸξ τοῦ φωτός· ἔδει δ᾿ ἀμφότερα μᾶλλον τῷ αὐτῷ ὑπάρχειν, εἴπερ ταὐτὰ ἦν.
For flame is more fire than light is, but flame is less "the most subtle body" than light is; yet both ought to belong more to the same thing, if indeed they were the same.
Πάλιν εἰ τὸ μὲν ὁμοίως ἀμφοτέροις ὑπάρχει τοῖς προτεθεῖσι, τὸ δ᾿ ἕτερον μὴ ὁμοίως ἀμφοτέροις, ἀλλὰ τῷ ἑτέρῳ μᾶλλον.
Again, if one of them belongs equally to both the proposed things, but the other does not belong equally to both, but more to one of them.
Ἔτι ἐὰν πρὸς δύο τὸν ὁρισμὸν ἀποδῷ καθ᾿ ἑκάτερον, οἷον τὸ καλὸν τὸ δι᾿ ὄψεως ἢ τὸ δι᾿ ἀκοῆς ἡδύ, καὶ τὸ ὂν τὸ δυνατὸν παθεῖν ἢ ποιῆσαι·
Moreover, if he should render the definition in relation to two things, disjunctively for each; for example, if the beautiful is "that which is pleasant through sight or through hearing", and being is "that which is capable of acting or being acted upon".
ἅμα γὰρ ταὐτὸν καλόν τε καὶ οὐ καλὸν ἔσται, ὁμοίως δὲ καὶ ὄν τε καὶ οὐκ ὄν.
For then the same thing will be at once beautiful and not beautiful, and likewise both being and non-being.
Τὸ γὰρ δι᾿ ἀκοῆς ἡδὺ ταὐτὸν τῷ καλῷ ἔσται, ὥστε τὸ μὴ ἡδὺ δι᾿ ἀκοῆς τῷ μὴ καλῷ ταὐτόν· τοῖς γὰρ αὐτοῖς καὶ τὰ ἀντικείμενα ταὐτά, ἀντίκειται δὲ τῷ μὲν καλῷ τὸ οὐ καλόν, τῷ δὲ δι᾿ ἀκοῆς ἡδεῖ τὸ οὐχ ἡδὺ δι᾿ ἀκοῆς.
For "what is pleasant through hearing" will be the same as the beautiful, so that "what is not pleasant through hearing" will be the same as "not beautiful"; for to the same things their opposites are also the same, and the opposite of the beautiful is the "not beautiful", and of "what is pleasant through hearing" is "what is not pleasant through hearing".
Δῆλον οὖν ὅτι ταὐτὸν τὸ οὐχ ἡδὺ δι᾿ ἀκοῆς τῷ οὐ καλῷ.
It is clear, therefore, that "what is not pleasant through hearing" is the same as "not beautiful".
Εἰ οὖν τι ἐστὶ δι᾿ ὄψεως μὲν ἡδὺ δι᾿ ἀκοῆς δὲ μή, καλόν τε καὶ οὐ καλὸν ἔσται.
If, then, something is pleasant through sight but not through hearing, it will be both beautiful and not beautiful.
Ὁμοίως δὲ δείξομεν καὶ διότι ταὐτὸν ὄν τε καὶ οὐκ ὄν ἐστιν.
In the same way we shall also show that being and non-being are the same.
Ἔτι καὶ τῶν γενῶν καὶ τῶν διαφορῶν καὶ τῶν ἄλλων ἁπάντων τῶν ἐν τοῖς ὁρισμοῖς ἀποδιδομένων λόγους ἀντὶ τῶν ὀνομάτων ποιοῦντα σκοπεῖν εἴ τι διαφωνεῖ.
Moreover, one should substitute definitions for the names of the genera, differences, and all other things rendered in the definitions, and examine if there is any discrepancy.

Notes

  1. p.375καὶ γὰρ δίκαιος εἴη ἂν μάλιστα ὁ δυνάμενος μάλιστα τὸ ἴσον διανεῖμαι — The potential optative with ἄν (εἴη ἂν) is used here to present a reductio ad absurdum resulting from the incorrect definition: 'for [if justice were a power,] the one most able to distribute what is equal would be the most just' (which is absurd, since justice depends on choice/intention, not mere capacity).
  2. p.375σῶμα δὲ τὸ λεπτομερέστατον ἧττον φλὸξ τοῦ φωτός — 'τοῦ φωτός' is a genitive of comparison governed by the comparative adverb 'ἧττον' (less). The subject is 'ἡ φλόξ' (flame), meaning 'flame is less "the most subtle body" than light is' (since light is more subtle than flame).
  3. p.375τοῖς γὰρ αὐτοῖς καὶ τὰ ἀντικείμενα ταὐτά — There is an ellipsis of the copula (either ἐστίν or εἶναι). The phrase asserts a logical rule: 'for to things that are the same (τοῖς αὐτοῖς, dative of relation/reference), their opposites (τὰ ἀντικείμενα) are also the same (ταὐτά, predicate adjective)'. That is, if A = B, then non-A = non-B.

Cite this passage

Aristotle, Topics §6.7. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg044.humanitext-grc1:6.7

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