Introduzione alla Logica Formale by Armando Plebe

By Armando Plebe

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For since s o m e t h i n g impossible was shown to follow t h r o u g h a syllogism w h e n the opposite of t h i s is hypothesized, t h i s was posited because t h e hypothesis was done away w i t h a n d i t is necessary t h a t one or the other be t r u e . T h i s is w h a t is m e a n t b y 'because of t h e contradictory '. B u t i f i n the case of reductio ad impossibile t h e syllogism y i e l d i n g t h e falsehood is direct, t h a t is, categorical, a n d reaches i t s conclusion t h r o u g h one of the three figures, t h e n syllogisms t h r o u g h i m p o s s i b i l i t y , w h i c h are a p a r t of syllogisms from a hypothesis, w i l l also be i n t h e three figures.

22. I t is at this point that Aristotle switches to using letters to stand for propositions as well as terms (and for items i n geometric proofs). 23. Aristotle also mentions the case where A or B is justified inductively, but says nothing specifically about that case. 24. On the themata see Frede (1974), 172-96. 1 do not discuss most of 44a38-b24, which is of less significance. 26. Here I use the schematic arrangement described by Alexander starting at 301,17. Aristotle first introduces the letters at 44al2 (304,31).

46b28-37; cf. 338,29-339,28) The r e m a i n i n g criticisms relate to the fact t h a t division is supposed to provide the basis for p r o v i n g definitions: (v) I f t h i s is t r u e t h e n the method cannot provide proofs for accidents, propria, and genera, the other three provables of the Topics. (46b27-8; cf. 338,11-19) (vi) D i v i s i o n cannot show t h a t a conclusion is necessary, as a definition ought to be. ) (vii) I n the Posterior Analytics i t is shown t h a t one cannot prove a definition.

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