Journal Name: Apeiron Issue: Ahead of print.

In De Interpretatione 6-9, Aristotle considers three logical principles: the principle of bivalence, the law of excluded middle, and the rule of contradictory pairs (according to which of any contradictory pair of statements, exactly one is true and the other false). Surprisingly, Aristotle accepts none of these without qualification. I offer a coherent interpretation of these chapters as a whole, while focusing special attention on two sorts of statements that are of particular interest to Aristotle: universal statements not made universally (...) and future particular statements. With respect to the former, I argue that Aristotle takes them to be indeterminate and so to violate the rule of contradictory pairs. With respect to the latter, the subject of the much discussed ninth chapter, I argue that the rule of contradictory pairs, and not the principle of bivalence, is the focus of Aristotle's refutation. Nevertheless, Aristotle rejects bivalence for future particular statements. (shrink)

In view of Alexander of Aphrodisias’s and Porphyry’s respective positions on the issue, I discuss whether logos apophantikos is to be defined, as DI 4 seems to imply, by its being true or false or rather, as DI 5 seems to imply, by its representing the ontological combination/separation of substrate and attribute through the logical combination/separation of subject and predicate.

In chapter 9 of De Interpretatione, Aristotle offers a defense of free will against the threat of fatalism. According to the traditional interpretation, Aristotle concedes the validity of the fatalist's arguments and then proceeds to reject the Principle of Bivalence in order to avoid the fatalist's conclusion. Assuming that the traditional interpretation is right on this point, it remains to be seen why Aristotle felt compelled to reject such an intuitive semantic principle rather than challenge the fatalist's inference from truth (...) to necessity. The answer, I contend, lies in Aristotle's theory of truth and truthmakers. (shrink)

In De interpretatione 9, Aristotle argues against the fatalist view that if statements about future contingent singular events (e.g. ‘There will be a sea battle tomorrow,’ ‘There will not be a sea battle tomorrow’) are already true or false, then the events to which those statements refer will necessarily occur or necessarily not occur. Scholars have generally held that, to refute this argument, Aristotle allows that future contingent statements are exempt from either the principle of bivalence, or the law of (...) excluded middle. This paper offers a new interpretation of Aristotle’s refutation of fatalism. According to this interpretation, each member of a pair of contradictory future contingent statements, in virtue of expressing modal necessity, is simply false. (shrink)