April 18, 2009

Quote of the Day: Aristotle on the Law of Contradiction

βεβαιοτάτη δ᾽ ἀρχὴ πασῶν περὶ ἣν διαψευσθῆναι ἀδύνατον ... ἣν γὰρ ἀναγκαῖον ἔχειν τὸν ὁτιοῦν ξυνιέντα τῶν ὄντων, τοῦτο οὐχ ὑπόθεσις ... τίς δ᾽ ἔστιν αὕτη, μετὰ ταῦτα λέγωμεν. τὸ γὰρ αὐτὸ ἅμα ὑπάρχειν τε καὶ μὴ ὑπάρχειν ἀδύνατον τῷ αὐτῷ καὶ κατὰ τὸ αὐτό (καὶ ὅσα ἄλλα προσδιορισαίμεθ᾽ ἄν, ἔστω προσδιωρισμένα πρὸς τὰς λογικὰς δυσχερείας)
...
ἡμεῖς δὲ νῦν εἰλήφαμεν ὡς ἀδυνάτου ὄντος ἅμα εἶναι καὶ μὴ εἶναι, καὶ διὰ τούτου ἐδείξαμεν ὅτι βεβαιοτάτη αὕτη τῶν ἀρχῶν πασῶν. ἀξιοῦσι δὴ καὶ τοῦτο ἀποδεικνύναι τινὲς δι᾽ ἀπαιδευσίαν: ἔστι γὰρ ἀπαιδευσία τὸ μὴ γιγνώσκειν τίνων δεῖ ζητεῖν ἀπόδειξιν καὶ τίνων οὐ δεῖ: ὅλως μὲν γὰρ ἁπάντων ἀδύνατον ἀπόδειξιν εἶναι (εἰς ἄπειρον γὰρ ἂν βαδίζοι, ὥστε μηδ᾽ οὕτως εἶναι ἀπόδειξιν), εἰ δέ τινων μὴ δεῖ ζητεῖν ἀπόδειξιν, τίνα ἀξιοῦσιν εἶναι μᾶλλον τοιαύτην ἀρχὴν οὐκ ἂν ἔχοιεν εἰπεῖν. ἔστι δ᾽ ἀποδεῖξαι ἐλεγκτικῶς καὶ περὶ τούτου ὅτι ἀδύνατον, ἂν μόνον τι λέγῃ ὁ ἀμφισβητῶν: ἂν δὲ μηθέν, γελοῖον τὸ ζητεῖν λόγον πρὸς τὸν μηθενὸς ἔχοντα λόγον, ᾗ μὴ ἔχει: ὅμοιος γὰρ φυτῷ ὁ τοιοῦτος ᾗ τοιοῦτος ἤδη.


The most certain principle of all [is one] it is impossible to be mistaken about ... A [principle] one must have in order to understand any being whatsoever - this is not a [mere] hypothesis! ... Next we will state what this principle is: it is impossible for the same thing at the same time to exist and not to exist in the same [subject] and in the same respect (and however many other [qualifications] we [previously] defined, let them be defined [here] on account of the logical difficulties).
...
But we now have accepted that it is impossible for a being to be and not be at the same time, and we showed that this was the most certain of all principles. In fact, some people, because [they are] uneducated, think that even this ought to be proven. [Someone who] doesn't know that it is necessary to prove some things and not others is uneducated. After all, it is completely impossible for every [claim] to have a proof, since then [every proof] would have to be infinitely long. As a result, there wouldn't be any proofs at all. If, on the other hand, some things don't need to be proven, these people have not said what [principles] they consider worthy [of this status] instead of the sort of principle [described above]. It is, [however,] possible to prove by reduction [to performative contradiction] that this is impossible, if the doubter makes any use of reason; but if he doesn't [use reason] it is ridiculous to reason with someone who himself lacks reason. This sort of person, insofar as he is indeed this sort of person, is like a plant.

     - Aristotle, Metaphysics 1005b-1006a (my translation)

Indeed, some people (Aristotle has relativists and radical skeptics in mind) just can't be reasoned with. Trying to argue with this sort of person is just as pointless as (and more frustrating than) trying to argue with your houseplants.

Posted by Kenny at April 18, 2009 9:14 PM
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