03801nam a22005175i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001500153072001800168072002300186072001700209100008400226245011600310250001800426264007500444300003200519336002600551337002600577338003600603347002400639490011200663505041100775520146101186650002702647650002402674650001702698650002902715650001102744650002502755650004002780650001702820650003102837650001102868700007802879710003402957773002602991776003603017776003603053776003603089830011203125856004603237978-3-031-66452-6DE-He21320251030112855.0cr nn 008mamaa240816s2024    sz |    s    |||| 0|eng d  a97830316645267 a10.1007/978-3-031-66452-62doi 4aB808.5.A-Z 7aHPCF52bicssc 7aPHI0390002bisacsh 7aQDHR92thema1 aCarrara, Massimiliano.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut10aArbitrary Reference in Logic and Mathematicsh[electronic resource] /cby Massimiliano Carrara, Enrico Martino.  a1st ed. 2024. 1aCham :bSpringer International Publishing :bImprint: Springer,c2024.  aXI, 95 p.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,x2542-8292 ;v4900 aPreface -- 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.  aThis 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. 0aAnalysis (Philosophy). 0aMathematical logic. 0aLinguistics. 0aMathematicsxPhilosophy. 0aLogic.14aAnalytic Philosophy.24aMathematical Logic and Foundations.24aLinguistics.24aPhilosophy of Mathematics.24aLogic.1 aMartino, Enrico.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303166451908iPrinted edition:z978303166453308iPrinted edition:z9783031664540 0aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,x2542-8292 ;v49040uhttps://doi.org/10.1007/978-3-031-66452-6