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020 _a9783031664526
_9978-3-031-66452-6
024 7 _a10.1007/978-3-031-66452-6
_2doi
050 4 _aB808.5.A-Z
072 7 _aHPCF5
_2bicssc
072 7 _aPHI039000
_2bisacsh
072 7 _aQDHR9
_2thema
100 1 _aCarrara, Massimiliano.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982420
245 1 0 _aArbitrary Reference in Logic and Mathematics
_h[electronic resource] /
_cby Massimiliano Carrara, Enrico Martino.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXI, 95 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,
_x2542-8292 ;
_v490
505 0 _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.
520 _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.
650 0 _aAnalysis (Philosophy).
_971325
650 0 _aMathematical logic.
_966195
650 0 _aLinguistics.
650 0 _aMathematics
_xPhilosophy.
_969649
650 0 _aLogic.
_970674
650 1 4 _aAnalytic Philosophy.
_971326
650 2 4 _aMathematical Logic and Foundations.
_966198
650 2 4 _aLinguistics.
650 2 4 _aPhilosophy of Mathematics.
_969650
650 2 4 _aLogic.
_970674
700 1 _aMartino, Enrico.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_982421
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031664519
776 0 8 _iPrinted edition:
_z9783031664533
776 0 8 _iPrinted edition:
_z9783031664540
830 0 _aSynthese Library, Studies in Epistemology, Logic, Methodology, and Philosophy of Science,
_x2542-8292 ;
_v490
_972350
856 4 0 _uhttps://doi.org/10.1007/978-3-031-66452-6
912 _aZDB-2-REP
912 _aZDB-2-SXPR
999 _c62503
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