03447nam 2200457 450 991055939020332120221121133610.03-030-87548-2(MiAaPQ)EBC6951389(Au-PeEL)EBL6951389(CKB)21502463300041(EXLCZ)992150246330004120221121d2022 uy 0engurcnu||||||||txtrdacontentcrdamediacrrdacarrierOskar Becker, On the logic of modalities (1930) translation, commentary and analysis /Oskar Becker, translated by Stefania Centrone, Pierluigi MinariCham, Switzerland :Springer,[2022]©20221 online resource (167 pages)Synthese Library ;v.444Print version: Centrone, Stefania Oskar Becker, on the Logic of Modalities (1930): Translation, Commentary and Analysis Cham : Springer International Publishing AG,c2022 9783030875473 Includes bibliographical references and index.Intro -- Preface -- Preface -- Contents -- 1 Introduction -- 2 Part I of On the Logic of Modalities -- 2.1 The Conditional, or The Crows on the Roofs -- 2.2 The Decision Problem and Leibniz's Dream -- 2.3 Normal Modal Logics: a Quick Resumé -- 2.4 Lewis's S3 and Becker's Extensions -- 2.5 Lewis's Survey System S3 -- 2.6 Becker's Six Modalities System S3' -- 2.7 Becker's Ten Modalities System S3'' -- 2.8 Becker's Further ``Experiments'' -- 2.8.1 A Variant of S3' -- 2.8.2 A More Abstract Approach -- 2.9 Becker's Logical Accomplishments: An Assessment -- 3 Part II of On the Logic of Modalities -- 3.1 Introduction -- 3.2 On Edmund Husserl -- 3.2.1 Existence -- 3.2.2 Definiteness and Universal Arithmetic -- 3.2.3 ``To Be Grounded in the Essence of Something'' -- 3.3 On Cassirer and Brouwer -- 3.3.1 On the Object of Mathematics -- 3.3.2 Brouwer's Intuitionism -- 3.4 On Weyl -- 3.5 Oskar Becker on Cassirer -- 4 Oskar Becker: On the Logic of Modalities -- Preliminary Remark -- I. On the Rank Order and Reduction of Logical Modalities -- Introduction -- II. The Logical Interpretation of the Mathematical Intuitionism from the Standpoint of Modality -- Cassirer's Remark on Oskar Becker's Monograph Mathematical Existence172 -- 5 Appendix -- 5.1 Lewis's Axiomatizations of S3 -- 5.2 Lemmon-Style Axiomatization of S3 -- 5.3 Irreducible Modalities in S3 -- 5.4 Kripke-Style Semantics for S3 -- 5.5 Completeness Theorem(s) for S3 -- 5.5.1 Completeness of S3 with Respect to Mod2+ and Mod1* -- 5.5.2 Completeness of S3 with Respect to Mod3+ -- 5.6 Finite Model Property and Decidability of S3 -- 5.7 Modal Translation of IPC in S3 and Embeddings of S4 in S3 -- 5.8 Lewis's System S2 -- 5.9 Becker's ``Experiments'': A Technical Evaluation -- 5.9.1 The ``Variant'' Six Modalities System S3* -- 5.9.2 The Ten Modalities System S3'' -- 5.9.3 The System SM -- References.Author Index -- Subject Index.Synthese LibraryModality (Logic)Modality (Logic)160Becker Oskar1889-1964,54355Centrone StefaniaMinari PierluigiMiAaPQMiAaPQMiAaPQBOOK9910559390203321Oskar Becker, On the logic of modalities (1930)2966667UNINA