Abstract of the Ph.D. thesis.pdfVIP

Abstract of the Ph.D. thesis Francesco Belardinelli 27th December 2005 My Ph.D. thesis - entitled Quantified modal logic and the Ontology of physical objects - deals with logics and ontology. I wrote it under the supervision of prof. M. Mugnai (Scuola Normale Superiore), prof. A. Varzi (Columbia University), prof. G. Corsi (Universita? di Bologna) and prof. S. Ghilardi (Universita? di Milano). In the first part I analyse three semantical accounts for quantified modal logics, then in the second part I make use of the formal machinery developed thus far to formally compare ontological theories on persistence conditions of physical objects. Quantified modal logic - QML in short - has always had a strong philosophical appeal, since it first appeared in papers by Barcan Marcus ([1], [2], [3]), Hintikka ([14], [15]), Prior ([24], [25], [26]) and Kripe ([18], [19], [20]). As propositional modal logic, QML deals with major philosophical concepts: necessity and possibility, indi- vidual knowledge, obligation and permission. In addition QML has a special interest in individuals: we deal with actual and possible objects, existence, modal and tempo- ral properties, counterfactual situations, trans-world identity. These topics concern the most different fields in the philosophical investigation: ontology, epistemology, philosophy of science, ethics. In my opinion the development of quantified modal logic would provide an useful tool to philosophical analysis, in order to precisely define the concepts listed above. This is exactly my task in the first part of my Ph.D. thesis, in which I deal with three different semantical accounts for QML: Kripke semantics, the substantial interpretation, and counterpart semantics. In the first chapter I consider Kripke semantics, as presented by Corsi in [7]. I provide a general completeness proof for first-order modal calculi based both on Kripke’s theory of quantification and on free and classical logic. In particular I prove some original re