Humanitext Reader

Aristotle · Great Ethics §1.10.1-1.10.2

The Relation Between Principles and Their Consequences

Passage 12 of 71 · Greek

Summary

The author explains that in all natural generation as well as in geometrical deductions, the state of the starting principles determines the state of the subsequent results.

§1.10.1— ἔτι δ᾿ ἄν τις τοῦτο ἐναργέστερον καὶ ἐντεῦθεν ἴδοι.
— And one might see this even more clearly from the following.
πᾶσα γὰρ φύσις γεννητική ἐστιν οὐσίας τοιαύτης οἵα ἐστίν, οἷον τὰ φυτὰ καὶ τὰ ζῷα· ἀμφότερα γὰρ γεννητικά.
For every nature is generative of a substance such as itself, for example plants and animals; for both are generative.
γεννητικὰ δὲ ἐκ τῶν ἀρχῶν, οἷον τὸ δένδρον ἐκ τοῦ σπέρματος· αὕτη γάρ τις ἀρχή.
And they generate from principles, for example the tree from the seed; for this is a certain principle.
τὸ δὲ μετὰ τὰς ἀρχὰς οὕτως ἔχει· ὡς γὰρ ἂν ἔχωσιν αἱ ἀρχαί, οὕτως καὶ τὰ ἐκ τῶν ἀρχῶν ἔχει.
And that which is after the principles is in this state: for as the principles may be, so also are the things from the principles.
ἐναργέστερον δ᾿ ἔστι κατιδεῖν τοῦτο ἐν τοῖς κατὰ γεωμετρίαν.
And it is possible to perceive this more clearly in the matters of geometry.
§1.10.2καὶ γὰρ ἐκεῖ ἐπειδή τινες λαμβάνονται ἀρχαί, ὡς ἂν αἱ ἀρχαὶ ἔχωσιν, οὕτω καὶ τὰ μετὰ τὰς ἀρχάς, οἷον εἰ τὸ τρίγωνον δυσὶν ὀρθαῖς ἴσας ἔχει, τὸ δὲ τετράγωνον τένταρσιν, καὶ ὡς ἂν μεταβάλῃ τὸ τρίγωνον, οὕτωρ καὶ τὸ τετράγωνον συμμεταβάλλει (ἀντιστρέφει γὰρ), καὶ ἐὰν τὸ τετράγωνον μὴ ἔχῃ τέτταρον ὀρθαῖς ἴσας, οὐδὲ τὸ τρίγωνον ἕξει δυσὶν ὀρθαῖς ἴσας.
For there too, since certain principles are assumed, as the principles may be, so also are the things after the principles, for example, if the triangle has [angles] equal to two right angles, and the quadrangle to four, and as the triangle may change, so also the quadrangle changes with it (for they convert), and if the quadrangle does not have [angles] equal to four right angles, neither will the triangle have [angles] equal to two right angles.

Notes

  1. 1.10.1ἄν ... ἴδοι — Potential optative (optative with ἄν), expressing a possibility or a mild, polite assertion ('one might see').
  2. 1.10.1ὡς γὰρ ἂν ἔχωσιν — The relative adverb ὡς combined with the particle ἄν and the subjunctive ἔχωσιν (present subjunctive of ἔχω), forming a general conditional clause ('in whatever state the principles may be').
  3. 1.10.2δυσὶν ὀρθαῖς ἴσας — The adjective ἴσας (accusative feminine plural, 'equal') modifies an omitted noun 'angles' (γωνίας). The dative δυσὶν ὀρθαῖς ('to two right [angles]', with γωνίαις also omitted) depends on ἴσας. The phrase means '[has angles] equal to two right angles.'
  4. 1.10.2ἀντιστρέφει γάρ — The verb ἀντιστρέφω is used intransitively here, meaning 'to convert' or 'to be reciprocal'. It points to the logical conversion or mutual implication between the property of the triangle and that of the quadrangle.

Cite this passage

Aristotle, Great Ethics §1.10.1-1.10.2. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg022.humanitext-grc1:1.10.1-1.10.2

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