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Aristotle · Prior Analytics §2.2.9-2.2.10

Three Types of Definition and Their Relation to Demonstration

Passage 114 of 123 · Greek

Summary

The text distinguishes the knowledge of 'what it is' between immediate principles without another cause and mediated things with another cause, then presents three types of definition (nominal, causal, and the conclusion of a demonstration) to summarize the relationship between definition and demonstration.

§2.2.9Ἔστι δὲ τῶν μὲν ἕτερόν τι αἴτιον, τῶν δʼ οὐκ ἔστιν.
Now, for some things there is another cause, and for others there is not.
ὥστε δῆλον ὅτι καὶ τῶν τί ἐστι τὰ μὲν ἄμεσα καὶ ἀρχαί εἰσιν, ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ ἢ ἄλλον τρόπον φανερὰ ποιῆσαι (ὅπερ ὁ ἀριθμητικὸς ποιεῖ· καὶ γὰρ τί ἐστι τὴν μονάδα ὑποτίθεται, καὶ ὅτι ἔστιν)·
Hence, it is clear that also among 'what they are' some are immediate and are principles, which must be assumed both to exist and to be what they are, or made manifest in some other way (just as the arithmetician does; for he assumes both what the unit is and that it exists).
τῶν δʼ ἐχόντων μέσον, καὶ ὥν ἔστι τι ἕτερον αἴτιον τῆς οὐσίας, ἔστι διʼ ἀποδείξεως, ὥσπερ εἴπομεν, δηλῶσαι, μὴ τὸ τί ἐστιν ἀποδεικνύντας.
But for those things that have a middle term, and of whose essence there is some other cause, it is possible, as we said, to make them manifest through demonstration, though without demonstrating 'what they are'.
§2.2.10Ὁρισμὸς δʼ ἐπειδὴ λέγεται εἶναι λόγος τοῦ τί ἐστι, φανερὸν ὅτι ὁ μέν τις ἔσται λόγος τοῦ τί σημαίνει τὸ ὅνομμα ἢ λόγος ἕτερος ὀνοματώδης, οἶον τί σηᾳᾳμαίνει τρίγωνον.
Since definition is said to be an account of 'what a thing is', it is manifest that one kind of definition will be an account of what the name means, or another name-like account, such as what 'triangle' means.
ὅπερ ἔχοντες ὅτι ἔστι, ζητοῦμεν διὰ τί ἔστιν· χαλεπὸν δʼ οὅτως ἐστὶ λαβεῖν ἃ μὴ σμεν ὅτι ἔστιν.
Having that this exists, we seek why it exists; but it is difficult in this way to grasp things which we do not know to exist.
ἡ δʼ αἰτα εἴρηται πρότερον τῆς χαλεπότητος, ὅτι οὐδʼ εἰ ἔστιν ἢ μὴ ἴσμεν, ἀλλʼ ἢ κατὰ συμβεβηκός. (λόγος δʼ ἐἶς ἐστὶ διχῶς. ὁ μὲν συνδέσμῳ, ὥσπερ ἡ Ἰλιάς, ὁ δὲ τῷ ἕν καθʼ ἑνὸς δηλοῦν μὴ κατὰ συμβεβηκός. ) Ἐἷς μὲν δὴ ὅρος ἐστὶν ὅρου ὁ εἰρημένος, ἄλλος δʼ ἐστὶν ὅρος λόγος ὁ δηῳλῶν διὰ τί ἔστιν.
And the cause of this difficulty has been stated before, namely, that we do not even know whether they exist or not, but only accidentally. (An account is 'one' in two ways: one by conjunction, like the Iliad, and the other by showing one thing of one thing, not accidentally.) One definition of definition, then, is the one mentioned, and another definition is an account that makes manifest why a thing exists.
ὥστε ὁ μὲν πρότερος σημαίνει μέν, δείκνυσι δʼ οὔ, ὁ δʼ ὕστερος φανερόν ὅτι ἔσται οἷον ἄποδειξις τοῦ τί ἐστι, τῇ θέσει διαφέρων τῆς ἀποδείξεως.
Consequently, the former means indeed, but does not show; whereas the latter is manifest that it will be as it were a demonstration of 'what it is', differing from demonstration in its arrangement.
διαφέρει γὰρ εὐπεῖν διὰ τί βροντ καὶ τί ἐστι βροντή· ἐρεῖ γὰρ οὕτω μὲν διότι ἀποσβέννυται τὸ πῦρ ἐν τοῖς νέφεσιʼʼ τί δʼ ἐστὶ βροντή;
For it differs to state why it thunders and what thunder is; for in the former case one will say "because the fire is extinguished in the clouds," while in the latter, "what is thunder?
φόρος ἀποσβεννυμένου πυρός ἐν νέφεσιν. ὥστε ὁ αὐτὸς λόγος ἄλλον τρόπον λέγεται, καὶ δὶ μὲν ἀπόδειξις συνεχής, ὡδὶ δὲ ὁρισμός. (ἔτι ἐστὶν ὅρος βροντῆς ψόφος ἐν νέφεσι· τοῦτο δʼ ἐστὶ τῆς τοῦ τί ἐστιν ἀποδείξεως συμτπέρασμα. ) ὁ δὲ τῶν ἀμέσων ὁρισμὸς θέσις ἐστὶ τοῦ τί ἐστιν ἀναπόδεικτος.
A sound of extinguished fire in the clouds." Thus, the same account is stated in another way: in this way it is a continuous demonstration, and in that way a definition. (Further, a definition of thunder is 'a sound in the clouds'; and this is the conclusion of the demonstration of 'what it is'.) On the other hand, the definition of immediate things is an indemonstrable thesis of 'what it is'.
Ἔστιν ἄρα ὁρισμός εἷς μὲν λόγος τοῦ τί ἐστιν ἀναπόδεικτος, εἶς δὲ συλλογισμός τοῦ τί ἐστι, πτώσει διαφέρων τῆς ἀποδείξεως, τρίτος δὲ τῆς τοῦ τί ἐστιν ἀποδείξεως συμτπέρασμα.
Therefore, definition is, in one way, an indemonstrable account of 'what a thing is'; in another way, a syllogism of 'what it is', differing from demonstration in grammatical formulation; and in a third way, the conclusion of the demonstration of 'what it is'.
φανερὸν οὖν ἐκ τῶν εἰρημέναων καὶ πῶς ἔστι τοῦ τί ἐστιν ἀπόδειξις καὶ πῶς οὐκ ἔστι, καὶ τίνων ἔστι καὶ τίνων οὐκ ἔστιν, ἔτι δʼ ὁρισμὸς ποσαχῶς τε λέγεται καὶ πῶς τὸ τί ἐστι δείκνυσι καὶ πῶς οὔ, καὶ τίνων ἔστι καὶ τίνων οὔ, ἔτι δὲ τπρὸς ἀπόδειξιν πῶς ἔχει, καὶ πῶς ἐνδέχεται τοῦ αὐτοῦ εἶναι καὶ πῶς οὐκ ἐνδέχεται.
It is manifest, therefore, from what has been said, both how there is a demonstration of 'what it is' and how there is not, and of what things there is and of what there is not; and further, in how many ways definition is said, and how it shows 'what it is' and how it does not, and of what things there is and of what there is not; and further, how it stands in relation to demonstration, and how it is possible for both to belong to the same thing, and how it is not possible.

Notes

  1. p.168ἃ καὶ εἶναι καὶ τί ἐστιν ὑποθέσθαι δεῖ — The antecedent of the relative pronoun ἃ is ἄμεσα καὶ ἀρχαί. Since these are immediate first principles (essences) without another cause, it is necessary to assume (ὑποθέσθαι, infinitive depending on δεῖ) both their existence (εἶναι) and their essence (τί ἐστιν).
  2. 94aτῇ θέσει διαφέρων τῆς ἀποδείξεως — Meaning 'differing from demonstration in its arrangement'. As shown in the subsequent examples, demonstration and definition contain the same constituent elements (causal relations) but differ in the order of presentation or grammatical connection (whether as a continuous proof or a single definition sentence; θέσις here refers to 'placement' or 'arrangement').
  3. 94aπτώσει διαφέρων τῆς ἀποδείξεως — While πτῶσις generally refers to grammatical 'case' or 'inflection', here it means the 'grammatical reformulation' or 'modification' of logical propositions. It refers to the change in formulation from the 'why' form (διότι...) to the 'what' (definitional) form (e.g., noun phrases).

Cite this passage

Aristotle, Prior Analytics §2.2.9-2.2.10. Humanitext Reader, https://reader.humanitext.ai/en/text/urn:cts:greekLit:tlg0086.tlg001.humanitext-grc2:2.2.9-2.2.10

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