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We focus in this paper on some meta-level ontological distinctions among unary predicates, like those between concepts and assertional properties. Three are the main contributions of this work, mostly based on a revisitation of philosophical (and linguistic) literature in the perspective of knowledge representation. The first is a formal notion of ontological commitment, based on a modal logic endowed with mereological and topological primitives. The second is a formal account of Strawson's distinction between sortal and non-sortal predicates. Assertional properties like red belong to the latter category, while the former category is further refined by distinguishing substantial predicates (corresponding to types like person ) from non-substantial predicates (corresponding to roles like student ). The third technical contribution is definition of countability which exploits the topological notion of connection to capture the intended semantics of unary predicates.

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.

This chapter argues against predicative analyses of plurality, which force plurals into the familiar mould of singular logic by turning an apparently plural term standing for several objects into a singular predicate standing for a concept or property. Michael Dummett enlists support from Fregean semantics in favour of a predicative analysis, but his arguments do not stand up, either as exegesis of Frege or on their own merits. As well as facing difficulties in eliminating plural content, predicative analyses are sunk by the equivocity objection: they misrepresent single English predicates as equivocal, by treating the predicate differently according as it combines with singular or plural arguments. Although George Boolos does not offer a predicative analysis, it is argued that his second-order treatment of plurals is also sunk by the equivocity objection. And Ian Rumfitt fails in his attempt to avoid the objection by modifying Boolos's scheme.

Contro una proposta deflazionista sul rapporto fra credenza e verità