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Aristotle's Two Modal Theses Again

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This paper offers an interpretation of the arguments Aristotle offers in Metaphysics 9.4, 1047b14-30, for the two modal theses

[1] if (if A is the case then B is the case) then (if A is possible then B is possible)

[2] if (if A is possible then B is possible) then (if A is the case then B is the case)

Aristotle's arguments for these theses have not typically impressed commentators. I offer two arguments which are relatively faithful to Aristotle's text. The arguments rest on the following pair of claims concerning conditionals and possibility respectively

[COND] 'if A then B' is true if and only if in any circumstances in which A obtains, B obtains also

[TEST] 'possibly A' is true in a range of circumstances C1 . . . Cn if and only if assuming A true in any Ci gives rise to no impossibilities, once any further required adjustments are taken into account

The arguments and the premises on which they rest are stated without formalisation of the theses [1] and [2]. The argument for [1] is a defensible and persuasive argument. The argument for [2] is invalid, though plausible. That is consistent with our differential verdicts on [1] and [2]. [2] appears to be false: the argument provided for [2] explains why Aristotle might nevertheless have asserted it. The aim of the paper is to justify a more positive verdict on Aristotle's arguments than is usual among commentators.

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