Arbitrary Reference in Logic and Mathematics
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Beschreibung
This book develops a new approach to plural arbitrary reference and examines mereology, including considering four theses on the alleged innocence of mereology. The authors have advanced the notion of plural arbitrary reference in terms of idealized plural acts of choice, performed by a suitable team of agents. In the first part of the book, readers will discover a revision of Boolosʼ interpretation of second order logic in terms of plural quantification and a sketched structuralist reconstruction of second-order arithmetic based on the axiom of infinite, a la Dedekind, as the unique non-logical axiom. The work goes on to analyse the pros and cons of the new interpretation, also with respect to Linneboʼs objections to the thesis that second order logic is genuine logic. A theory of concepts that can be labelled as a theory of logical concepts is expounded.
In the second part of the book, the authors consider grounding megethology on plural arbitrary reference and argue that the arguments for the ontological innocence of mereology are not conclusive and that – for a certain use of mereology – a thesis of innocence, similar to that of plural arbitrary reference, is defensible. The work proposes a virtual theory of mereology in which the role of individuals is played by plural choices of atoms.
This considered work will appeal to scholars from branches of analytic philosophy, logic and the philosophy of mathematics in particular.
Examines the application of plural arbitrary reference in logic and philosophy of mathematics Develops a theory of concepts that can be labelled as a theory of logical concepts Considers grounding megethology on plural arbitrary reference
Autor*in
Massimiliano Carrara
Themen in »Arbitrary Reference in Logic and Mathematics«
Arbitrary reference Plural reference Second order logic Plural quantification Logicality of second order logic Mereology Megethology Plural acts of choice logic plural arbitrary reference philosophy plural arbitrary reference mathematics plural aribitrary reference Boolos second order logic Boolos plural quantification structuralist second-order arithmetic Linnebo logic