One semantic and two syntactic decision procedures are given for determining the validity of Aristotelian assertoric and apodeictic syllogisms. Results are obtained by using the Aristotelian deductions that necessarily have an even number of premises.

What is a problem? What is problematic about any problem whatsoever, philosophical or otherwise? As the origin of assertion and apodeiction, the problematic suspends the categories of necessity and contingency, possibility and impossibility. And it is this suspension that is the essence of the problem, which is why it is so suspenseful. But then, how is the problem problematic? Only if what is suspended neither comes to presence, nor simply goes out into absence, that is, if the suspension continues, which (...) continues the problem. But what is problematic about suspension? As a consideration of language shows, the problem of suspension is the problem of implication. If being, for example, is merely implied, neither present nor absent, then it is the suspension of both, at least insofar as it is problematic. And this not only says something about language; rather, it has ontological implications as well — it speaks of being, and the being of anything whatsoever. For if being is implied, if that is the problem of being, it is because being is an implication. Then the being of things like problems is implied as well; or being is in things by implication. But what does it mean for being to be neither presence nor absence, but an implication? It means that being is implied in a way that is problematic — before it is necessary, or even possible. For being’s way of being is characterized by suspension — which has implications for thinking and speaking about being, and about things like problems, even about anything whatsoever. And this has implications for what being implies, namely, unity and time and aspect. (shrink)

A semantics is presented for Storrs McCall's separate axiomatizations of Aristotle's accepted and rejected polysyllogisms. The polysyllogisms under discussion are made up of either assertoric or apodeictic propositions. The semantics is given by associating a property with a pair of sets: one set consists of things having the property essentially and the other of things having it accidentally. A completeness proof and a semantic decision procedure are given.

Fred's semantics for McCall's syntactic presentation of Aristotle's assertoric and apodeictic syllogistic is altered to free it from Thom's objections that it is unAristotelian. The altered semantics rejects Baroco-XLL and Bocardo-LXL, which Thom says Aristotle should have accepted. Aristotle's proofs that use ecthesis are formalized by using singular sentences. With one exception the (acceptance) axioms for McCall's system L-X-M are derivable. Formal proofs are shown to be sound.