04188nam a22006015i 4500 978-3-031-66452-6 DE-He213 20251030112855.0 cr nn 008mamaa 240816s2024 sz | s |||| 0|eng d 9783031664526 978-3-031-66452-6 10.1007/978-3-031-66452-6 doi B808.5.A-Z HPCF5 bicssc PHI039000 bisacsh QDHR9 thema Carrara, Massimiliano. author. aut http://id.loc.gov/vocabulary/relators/aut 82420 Arbitrary Reference in Logic and Mathematics [electronic resource] / by Massimiliano Carrara, Enrico Martino. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XI, 95 p. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, 2542-8292 ; 490 Preface -- 1. On Arbitrary Reference -- 2. On Plural Arbitrary Reference -- 3. On Arbitrary Fictional Models -- 4. Second-Order Logic and Plural Arbitrary Reference -- 5. Logical Concepts and Plural Arbitrary Reference -- 6. Plural Arbitrary Reference and mereology -- 7. Grounding Megethology on Plural Arbitrary Reference -- 8. The Mereological foundation of Megethology -- 9. Final ruminations -- Index. 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. Analysis (Philosophy). 71325 Mathematical logic. 66195 Linguistics. Mathematics Philosophy. 69649 Logic. 70674 Analytic Philosophy. 71326 Mathematical Logic and Foundations. 66198 Linguistics. Philosophy of Mathematics. 69650 Logic. 70674 Martino, Enrico. author. aut http://id.loc.gov/vocabulary/relators/aut 82421 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031664519 Printed edition: 9783031664533 Printed edition: 9783031664540 Synthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science, 2542-8292 ; 490 72350 https://doi.org/10.1007/978-3-031-66452-6 ZDB-2-REP ZDB-2-SXPR 62503 62503