By Dieter Probst, Peter Schuster

This e-book presents the reader with learn bobbing up from the Humboldt-Kolleg 'Proof' held in Bern in fall 2013, which collected major specialists actively concerned with the idea that 'proof' in philosophy, arithmetic and computing device technology. This quantity goals to do justice to the breadth and intensity of the topic and provides correct present conceptions and technical advances that includes 'proof' in these fields.

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A~ro~ev 'tl 'tIDV uno 'to r] "53 of which P and R both hold, and deduce an i-proposition: even a comment on an Aristotelian use of ,tt -rIDV but a paraphrase of Aristotle's Et yap -rtVt, otov -rif! Pr,102,31), (Nor ought we to presume here that the word I1EPO~ excludes non-singulars, even though Philoponus does go on to speak of a singular: Socrates. J.. J. ) Philoponus, indeed, quite often uses -rt to refer to a plural subject. B] , It would seem, then, that Philoponus, like Alexander, could read the -rt in -rt 'tt'tIDV (x) as either singular or plural (see above, note 44), 51 -rif!

55, and p. 123, n. 98. ' 'tiP. l'tCx is different from the relation 'is said oC Both these other relations ('inheres in' and 'said of') are discussed at Cat.! a2329. As Furth argues, these two metaphysically-loaded expressions are "indifferently expressed" by the locution 'is predicated of' (see Furtb (1988), pp. 9-40, especially p. 10). 24b26-8]. See also Mignucci (1965a), pp. 224-233. 25 The signatures for the equivalences I shall use in this chapter are mnemonics, cuing on the first letter of the Greek phrases involved.

5, n. 31. It would seem then that Bochenski has little ground for his guess that it was Theophrastus who criticized Aristotle for using conversion of i-propositions in his proof of e-conversion. 25al4-17 (see Bochenski (1947), p. 55 and Bames et al (1991), 87, n. 19). But it is quite possible that Theophrastus's writings regarding the Prior Analytics were an independent presentation of the syllogistic--in "simpler" terms perhaps. 25al4-17 at all. U'ttKiilv 1tEP1. oU 'tOU cru~~(livov'to~ Ihix 'to ~'i~w yiVEcr9(lt ltpo'tacrEOlv ~llliEltOlIi' e1V(lt yvropt~OV 'to El( 'tiilv ~i~EOlV cruv(ly6~£vov.