By Alexander of Aphrodisias, Ian Mueller
The statement of Alexander of Aphrodisias on Aristotle's Prior Analytics 1.8-22 is the most historic remark, via the 'greatest' commentator, at the chapters of the Prior Analytics during which Aristotle invented modal common sense - the common sense of propositions approximately what's invaluable or contingent (possible). during this quantity, which covers chapters 1.8-13, Alexander of Aphrodisias reaches the bankruptcy during which Aristotle discusses the thought of contingency. additionally incorporated during this quantity is Alexander's remark on that a part of Prior Analytics 1.17 and is the reason the conversion of contingent propositions (the remainder of 1.17 is integrated within the moment quantity of Mueller's translation).
Aristotle additionally invented the syllogism, a method of argument concerning premises and a end. Modal propositions may be deployed in syllogism, and within the chapters integrated during this quantity Aristotle discusses syllogisms which includes useful propositions in addition to the extra arguable ones containing one beneficial and one non-modal premiss. The dialogue of syllogisms containing contingent propositions is reserved for quantity 2.
In each one quantity, Ian Mueller offers a accomplished rationalization of Alexander's remark on modal good judgment as a complete
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Extra info for Alexander of Aphrodisias: On Aristotle Prior Analytics: 1.8-13
9. , pp. 26-7. We have followed them in rendering antikeimenon ‘opposite’ and enantios ‘contrary’, saving antiphasis and antiphatikos for ‘contradictory’. g. 195,18-22, 237,29-32) Alexander uses antikeimenon as a general term of which contraries and contradictories are species. , in representations of reductio proofs, he uses antikeimenon to refer to the contradictory of a proposition. The reader is well advised to learn the equivalences expressed by a and b, since both Alexander and Aristotle by and large take them for granted.
He rejects all forms with two particulars at 38b35-7. He tacitly rejects OA_2(NC_) and OE_2(NC_). Third-figure (Chapter 22) Direct reductions (cf. ) Waste cases justifiable by transformationc rules AE_3(NC‘C’) NEC(AaC) CON(BeC) NEC (AiB)? ) CON(AoB) (40b8-12)6 CONu(AoB) (not discussed) CONu(AoB) (not discussed) Rejected Cases *AE_3(CN_) *IE_3(CN_) CON(AaC) NEC(BeC) CON(AiC) NEC(BeC) (40a35-8) (40b8-12) These two rejections imply rejection of their equivalents, EE_3(CN_) and OE_3(CN_). Aristotle tacitly rejects AO_3(CN_), EO_3(CN_), and all third-figure N+C combinations with two particular premisses.
Ix) And what holds contingently (endekhomenôs) of some or will hold of some is the opposite of what holds of none by necessity. (36,7-25) We propose the following interpretation of Alexander’s argument: Aristotle takes for granted that NEC(XeY) is equivalent to ‘It is contingent that XiY’ (i). Hence (ii) he assumes NEC(BeA) and infers ‘It is contingent that (BiA)’ and so (v) either BiA or it is contingent that B will hold of A at some time. But (iv) at the time BiA holds, AiB holds by II-conversionu.
Alexander of Aphrodisias: On Aristotle Prior Analytics: 1.8-13 by Alexander of Aphrodisias, Ian Mueller