Quantified Modal Logic and Essentialism

Quine rejects quantified modal logic because it gives, among other things, rise to "Aristotelian essentialism", a metaphysical theory he considers to be quite indefensible. Essentialism is the theory that individuals (kinds) have some of their properties essentially, and roughly, quantified modal logic is the theory of the derivability of sentences like `All humans are necessarily rational` and so on from sets of such sentences. During the last 20-30 years essentialism was, despite Quine`s criticism, subject to notable reassessment. Moreover, the thesis is supported that modal syllogistic is a modern modal logic as well as the opposite one that it is not. As a consequence of the first, modal syllogistic might be reconstructed as a certain sub-theory of modal predicate logic, whereas the second shows that this will not do. Since modal syllogistic is in comparison with full modal predicate logic a relatively simple quantified modal logic, its simplicity facilitates, in our view, the investigation of the prospects of an essentialist foundation of quantified modal logic and makes their assessment easier. For, as well as modal syllogistic cannot cope with relations, essentialism also doesn`t deal primarily with essential relations. Thus, in this project, we investigate the questions to what extent such attempts to justify essentialism are successful, how modal syllogistic can be based on essentialism, and how the results of such an investigation might be carried over to an essentialist foundation of full modal predicate logic. In order to do this, above all the hitherto unclear relationship between modal syllogistic and modal predicate logic has to be determined, too. The latter amounts to a systematic comparison of two approaches of reconstructing modal syllogistic that differ tremendously from each other with respect to the presupposed concepts and methods. If it turns out that modal syllogistic can be reconstructed as a certain sub-theory of modal predicate logic, then an appropriate essentialist foundation of the first is also one of this sub-theory. But, if it cannot be reconstructed in that way, then at least some results of its essentialist foundation might be expected. Nevertheless, in this case, some conclusions might be drawn how that sub-theory corresponding to modal syllogistic might be based on essentialism in some way, too. In both cases an essentialist foundation of full modal predicate logic might be expected anyway because of the intended justification of the extensions of essentialism to cope with essential relations between individuals (kinds). A principal feature of such an essentialist foundation would be that it proceeds from time-logical concepts, but not from the notion of a possible world, thus, turning out to be a relevant alternative to common metaphysics of modalities (e.g. actualism vs. possibilism).

The main goals of the project are the development of a genuine Aristotelian semantics for a language of modal syllogistic and to verify as much as possible of the Aristotelian claims concerning the validity and non-validity, respectively, of his apodictic syllogisms in the framework of such a semantics. To this purpose the details of a theory of ecthesis (= exposition) are worked out as well as a theory of necessary set inclusion. It is demonstrated that modal syllogistic is not based on possible worlds semantics and, hence, that it is not a modal logic in the modern sense. Finally, a connection between Aristotelian essentialism and our theory of necessary set inclusion is investigated.