Search

This note disambiguates the predicate ‘is an unknowable event’ and shows how Transparent Intensional Logic interprets the sentences “Agent a is calculating the final decimal of π” and “Agent a has calculated the final decimal of π”. The knowability paradox is used to set the stage.

In Parts of Classes David Lewis attempts to draw a sharp contrast between mereology and set theory and he tries to assimilate mereology to logic. For him, like logic but unlike set theory, mereology is “ontologically innocent”. In mereology, given certain objects, no further ontological commitment is required for the existence of their sum. On the contrary, by accepting set theory, given certain objects, a further commitment is required for the existence of the set of them. The latter – unlike the sum of the given objects – seems to be an abstract entity whose existence is not directly entailed by the existence of the objects themselves. The argument for the innocence of mereology is grounded on the thesis of composition as identity. In our paper we argue that: (T1) arguments for the ontological innocence of mereology are not conclusive. (T2) Some arguments against the ontological innocence of mereology show a certain ambiguity in the innocence thesis itself. (T3) The innocence thesis seems to depend on a general conception of the nature of objects and on how the notion of ontological commitment is understood. Specifically, we think that the thesis is the manifesto of a realistic conception of parts and sums. (T4) Quine‟s notorious criticism of the set-theoretical interpretation of second order logic seems to be reproducible against Lewis‟defence of mereology. To the purpose we construct a mereological model of a substantive fragment of set theory, adequate to ground the set-theoretical semantics of second order logic.

Aim of the paper is to make some steps towards a formal characterization of identity criteria. First of all, we analyse some logical requirements identity criteria are supposed to satisfy and observe that some commonly used identity criteria fail to meet some of them. We focus in particular on the equivalence requirement. We consider then the proposals which have been given so far and aimed at providing logical adequacy to non-equivalent identity conditions. To this purpose, we analyse Williamson’s and De Clerq and Horsten’s treatment of identity criteria. We expand their formal framework, characterizing identity conditions in terms of contexts and levels of granularity too.