[436] Topic. VIII. xii. p. 162, a. 35-b. 2.
On the other hand, your argument may deserve to be pronounced false on four distinct grounds:— (1) If your syllogism appears to prove the conclusion but does not really prove it, being then an eristic or contentious syllogism; (2) If the conclusion be good but not relevant to the thesis, which is most likely to happen where you employ Reductio ad Impossible; (3) If your conclusion though valid and even relevant, is not founded on the premisses and principia appropriate to the thesis; (4) If your premisses are false, even though the conclusion in itself may prove true, since it has already been said that a true conclusion may sometimes be obtained from false premisses.[437]
[437] Ibid. b. 3-15: ψευδὴς δὲ λόγος καλεῖται τετραχῶς, &c.
Falsehood in your argument will be rather your own fault than that of your argument, especially if you yourself are not aware of its falsehood. Indeed, there are some false arguments which are more valuable in Dialectic than many true ones; where, for example, from highly probable premisses you refute some recognized truth. Such an argument is sure to serve as a demonstration of other truths; at the very least, it shows that some one of the propositions concerned is altogether untrue.[438] On the other hand, if you prove a true conclusion by premisses false and improbable, your argument will be more worthless than many others in which the conclusion is false; from such premisses, indeed, the conclusion may well be really false.[439]
[438] Ibid. b. 16-22: τὸ μὲν οὖν ψευδῆ τὸν λόγον εἶναι τοῦ λέγοντος ἁμάρτημα μᾶλλον ἢ τοῦ λόγου, καὶ οὐδὲ τοῦ λέγοντος ἀεὶ τὸ ἁμάρτημα, ἀλλ’ ὅταν λανθάνῃ αὐτόν, ἐπεὶ καθ’ αὑτόν γε πολλῶν ἀληθῶν ἀποδεχόμεθα μᾶλλον, ἂν ἐξ ὅτι μάλιστα δοκούντων ἀναιρῇ τι τῶν ἀληθῶν· τοιοῦτος γὰρ ὢν ἑτέρων ἀληθῶν ἀπόδειξίς ἐστιν· δεῖ γὰρ τῶν κειμένων τι μὴ εἶναι παντελῶς, ὥστ’ ἔσται τούτου ἀπόδειξις.
[439] Ibid. b. 22-24.
In estimating the dialectical value of an argument, therefore, we must first look whether the conclusion is formally valid; next, whether the conclusion is true or false; lastly, what are the premisses from whence it is derived.[440] For, if it be derived from premisses false yet probable, it has logical or dialectical value; while, if derived from premisses true yet improbable, it has none.[441] If derived from premisses both false and improbable, it will of course be worthless; either absolutely in itself, or with reference to the thesis under debate.
[440] Ibid. b. 24: ὥστε δῆλον ὅτι πρώτη μὲν ἐπίσκεψις λόγου καθ’ αὑτὸν εἰ συμπεραίνεται, δευτέρα δὲ πότερον ἀληθὲς ἢ ψεῦδος· τρίτη δ’ ἐκ ποίων τινῶν.
[441] Topic. VIII. xii. p. 162, b. 27: εἰ μὲν γὰρ ἐκ ψευδῶν ἐνδόξων δέ, λογικός, εἰ δ’ ἐξ ὄντων μὲν ἀδόξων δέ, φαῦλος, &c.
Two faults of questioners in Dialectic are dealt with specially by Aristotle:— (1) Petitio Principii; (2) Petitio Contrariorum. He had touched upon both of them (in the Analytica Priora) as they concerned the demonstrative process, or the proving of truth: he now deals with them as they concern the dialectical process, or the setting out of opinions and probabilities.[442]