Essentialism is, on the one hand, anchored with considerable firmness in a common sense picture of the world. On the other hand, it was dismissed for logico-philosophical reasons by a scientifically minded theorist like Quine. ``New essentialists'' like Kripke did engage in very profitable theorizing on an essentialist basis, but made no significant effort to investigate the prospects of imparting to an essentialist metaphysics a solid foundation within a scientific world view. These foundational prospects are the concern of the article. (...) – The investigation is guided by two ideas which are elaborated within a proof theoretical framework in the course of the article. First, being an essential F (where ``F'' represents a predicate) is linked with a lifelong possession of the property signified by ``F'' (but there is something more in it). Second, a special kind of necessity is involved in (true) predications of essential F-ness; it should be capable, like possibly all kinds of necessity, of being spelt out, in the final analysis, in terms of the provability of appropriate propositions in appropriate theoretical systems. In outlining the relevant axiomatic bases, the article draws on an early paper by E. Hirsch on individuation and essence. (shrink)

Aristotle's explanation of what is said ‘of every’ and ‘of none’ has been interpreted either as involving individuals, or as regarding exclusively universal terms. I claim that Alexander of Aphrodisias endorsed this latter interpretation of the dictum de omni et de nullo. This interpretation affects our understanding of Alexander's syllogistic: as a matter of fact, Alexander maintained that the dictum de omni et de nullo is one of the core principles of syllogistic.

The question as to what makes a perfect Aristotelian syllogism a perfect one has long been discussed by Aristotelian scholars. G. Patzig was the first to point the way to a correct answer: it is the evidence of the logical necessity that is the special feature of perfect syllogisms. Patzig moreover claimed that the evidence of a perfect syllogism can be seen for Barbara in the transitivity of the a-relation. However, this explanation would give Barbara a different status over the (...) other three first figure syllogisms. I argue that, taking into account the role of the being-contained-as-in-a-whole formulation, transitivity can be seen to be present in all four first figure syllogisms. Using this wording will put the negation sign with the predicate, similar to the notation in modern predicate calculus. (shrink)