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E-raamat: Logics and Falsifications: A New Perspective on Constructivist Semantics

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  • Sari: Trends in Logic 40
  • Ilmumisaeg: 07-Jan-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319052069
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  • Formaat: PDF+DRM
  • Sari: Trends in Logic 40
  • Ilmumisaeg: 07-Jan-2015
  • Kirjastus: Springer International Publishing AG
  • Keel: eng
  • ISBN-13: 9783319052069

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This volume examines the concept of falsification as a central notion of semantic theories and its effects on logical laws. The point of departure is the general constructivist line of argument that Michael Dummett has offered over the last decades. From there, the author examines the ways in which falsifications can enter into a constructivist semantics, displays the full spectrum of options, and discusses the logical systems most suitable to each one of them. While the idea of introducing falsifications into the semantic account is Dummett's own, the many ways in which falsificationism departs quite radically from verificationism are here spelled out in detail for the first time.

The volume is divided into three large parts. The first part provides important background information about Dummetts program, intuitionism and logics with gaps and gluts. The second part is devoted to the introduction of falsifications into the constructive account and shows that there is more than one way in which one can do this. The third part details the logical effects of these various moves. In the end, the book shows that the constructive path may branch in different directions: towards intuitionistic logic, dual intuitionistic logic and several variations of Nelson logics. The author argues that, on balance, the latter are the more promising routes to take.

















"Kapsners book is the first detailed investigation of how to incorporate the notion of falsification into

formal logic. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes."

Graham Priest, Graduate Center, City University of New York and University of Melbourne

Arvustused

The book is nicely organized every chapter is equipped with an introductory chapter overview and a chapter summary. This greatly facilitates reading. (Yaroslav Shramko, zbMATH 1436.03004, 2020)

The book presents an interesting study of phenomena which were previously rarely considered together, namely constructivism and paraconsistency. It is clearly written with many (perhaps too many) abstracts and summaries which will help one see the forest, not only the trees. It may well be of interest for students of constructivism (not limited to mathematics) and paraconsistency. (Andrzej B. Indrzejczak, Mathematical Reviews, March, 2017) 

Andreas Kapsners Logics and Falsifications is unique with respect to the detail and thoroughness of its examination of the formal and philosophical dimensionsof falsification. ... Kapsners work succeeds at providing a philosophically coherent framework robust enough to stand on its own while providing a natural and compelling elaboration on Dummettian themes. Given the recent increase in attention paid to the notion of falsification, Logics and Falsifications will undoubtedly serve as a significant resource to scholars working in these areas. (Thomas Macaulay Ferguson, dialectica, Vol. 70 (1), March, 2016)

Logics and Falsifications should be read by anyone interested in the connections between formal logic and the philosophy of language, and it is highly recommended to those looking for well-entrenched philosophical motivations for non-classical logics, especially when it comes to paracompleteness and paraconsistency. (Henrique Antunes, Logic and Logical Philosophy, July, 2015)

Muu info

"Shouldn't the notion of falsification be just as central to constructivist semantics as the notion of verification is? And if so: does this entail that traditional intuitionistic logic ought to be replaced by an alternative system of constructivist logic? I recommend this monograph to everyone with an interest in these questions and in semantic antirealism and paraconsistent logic more generally." (Hannes Leitgeb, Professor, Chair and Head of the Munich Center for Mathematical Philosophy, Ludwig-Maximilians-University Munchen, March 2014) "Verification is a concept of central importance in the last 100 years of philosophy, and has been made the corner-stone of notable formal logics, such as intuitionist logic. The dual notion of falsification has also been of central importance; but how to incorporate it into formal logic in the same way has been little investigated. The same is true of the natural thought that verification and falsification should be treated on a par with each other. Kapsner's book is the first detailed investigation of these possibilities. It investigates the variety of techniques that may be put into play here, and discusses the pros and cons of each. This is a fascinating logico-philosophical investigation, which will interest non-classical logicians of all stripes." (Graham Priest, Distinguished Professor, Graduate Center, City University of New York, March 2014)
1 Introduction
1(10)
1.1 Analytical Table of Contents
2(5)
1.2 Symbols and Abbreviations
7(4)
Part I Background
2 Constructivism
11(20)
2.1
Chapter Overview
11(1)
2.2 Constructivism
11(2)
2.3 Language, Logic, Metaphysics
13(2)
2.4 Decidability
15(2)
2.5 Undecidability, Bivalence, and the Law of Excluded Middle
17(2)
2.6 Where to Start?
19(1)
2.7 Truth Conditions
20(1)
2.8 Meaning as Use
20(2)
2.9 Correct Assertibility or Truth?
22(2)
2.10 Meaning Theory, Theory of Meaning and Semantic Theory
24(2)
2.11 Revisionism versus Eclecticism
26(2)
2.12 Metaphysical Conclusions
28(1)
2.13
Chapter Summary
29(2)
3 Intuitionism
31(26)
3.1
Chapter Overview
31(1)
3.2 Brouwer's Philosophy of Mathematics
31(1)
3.3 Constructive Mathematics
32(1)
3.4 The Axiomatization of Intuitionistic Logic
33(1)
3.5 Various Semantics
33(1)
3.6 The BHK Interpretation
34(5)
3.6.1 Correctness and Explosion
38(1)
3.7 Kripke Semantics
39(8)
3.7.1 Logical Constants
42(1)
3.7.2 Logical Consequence
43(1)
3.7.3 Kripke Semantics and the BHK Interpretation
44(3)
3.8 Tensed or Untensed Provability?
47(7)
3.8.1 Untensed Provability
48(1)
3.8.2 Tensed Provability
49(1)
3.8.3 Varieties of Tensed Provability
50(3)
3.8.4 The Meaning of the Value 1
53(1)
3.9
Chapter Summary
54(3)
4 Gaps, Gluts and Paraconsistency
57(28)
4.1
Chapter Overview
57(1)
4.2 Relevant Logic
58(1)
4.3 First Degree Entailment
59(5)
4.3.1 Designated Values
61(1)
4.3.2 Thinking Computers
62(2)
4.4 Exactly True Logic
64(2)
4.5 LP and K3
66(1)
4.6 Uses of Gaps
67(2)
4.6.1 Presupposition Failure
67(2)
4.7 Designated Values, Assertoric Content and Ingredient Sense
69(2)
4.8 Motivations for Paraconsistency
71(1)
4.9 Dialetheism
72(1)
4.10 Expressing the Law of Non-Contradiction
73(2)
4.11 The Law of Non-Contradiction, Bivalence, and Duality
75(1)
4.12 Analetheism
76(1)
4.13
Chapter Summary
77(8)
Part II Falsifications
5 From Proofs to Verifications and on to Falsifications
85(20)
5.1
Chapter Overview
85(3)
5.2 Stage I: Pure Verificationism
88(3)
5.3 Stage II: Expanded Verificationism
91(5)
5.3.1 Intuitionistic Logic?
92(4)
5.4 Stage III: Hybrid Strategies
96(3)
5.5 Stages IV and V: Expanded and Pure Falsificationism
99(2)
5.6 Hybrid Strategies Again
101(1)
5.7
Chapter Summary
102(3)
6 Falsificationism
105(20)
6.1
Chapter Overview
105(1)
6.2 The Centrality of Incorrectness
106(2)
6.3 Retracting, Surprising, and Misleading
108(1)
6.4 What is a Falsification?
109(1)
6.5 Correct Assertibility as Unfalsifiability
110(2)
6.6 Example I: Legal Trials
112(1)
6.7 Example II: Faultless Disagreement
113(5)
6.7.1 General Strategies and Their Problems
113(2)
6.7.2 Unfalsifiability and Analetheism
115(1)
6.7.3 Agreeing to Differ
116(1)
6.7.4 Falsificationism About Taste
117(1)
6.8 Correctness and Truth
118(2)
6.9 The Uncertain Truth Conditions of Conditionals
120(1)
6.10 Falsificationistic Systems of Logic
121(1)
6.11
Chapter Summary
121(4)
Part III Logics
7 Stage Five: Pure Falsificationism and Dual Intuitionistic Logic
125(20)
7.1
Chapter Overview
125(1)
7.2 Dummett's Falsificationistic Logic
126(1)
7.3 Falsificationistic Semantics
127(1)
7.3.1 Rumfitt's "Safe Assertibility"
127(1)
7.4 Kripke Semantics for Dual Intuitionistic Logic
128(6)
7.4.1 Kripke Semantics: The Basic Setup
129(3)
7.4.2 The Connectives
132(2)
7.5 Some Characteristic Features of DIL
134(3)
7.5.1 Paraconsistency
135(2)
7.6 A BHK-Style Interpretation
137(7)
7.6.1 Conjunction and Disjunction
137(1)
7.6.2 The Conditional
137(5)
7.6.3 Co-implication
142(1)
7.6.4 Negation
143(1)
7.7
Chapter Summary
144(1)
8 Stage Two: Expanded Verificationism and the Logic N3
145(18)
8.1
Chapter Overview
145(1)
8.2 BHK Interpretation
146(1)
8.3 Kripke Semantics
147(3)
8.3.1 The Connectives
149(1)
8.4 Do We Want Gluts?
150(3)
8.5 Features of the Logic N3
153(6)
8.5.1 Some Attempts to Get Contraposition Back
155(2)
8.5.2 Embracing Contraposition Failure
157(2)
8.6 Toggle Negation Versus Intuitionistic Negation
159(3)
8.7
Chapter Summary
162(1)
9 Stage Four: Expanded Falsificationism and the Logic N3f
163(12)
9.1
Chapter Overview
163(1)
9.2 Falsificationistic Nelson Logics
164(3)
9.3 Incoherence
167(5)
9.3.1 Getting Rid of Incoherence
170(2)
9.4 Safe Assertibility Reconsidered
172(1)
9.5
Chapter Summary
173(2)
10 Stage Three: Hybrid Strategies
175(22)
10.1
Chapter Overview
175(2)
10.2 Dummett on Hybrid Strategies
177(3)
10.2.1 Gappy Semantics
177(1)
10.2.2 Dummett Against In/Correctness Gaps
177(3)
10.3 CV&IF: Additional Effects
180(1)
10.4 Verificationism and Falsificationism Again (with Additional Effects)
181(1)
10.5 A Tripartite Setup
182(2)
10.6 Unifying the Account
184(1)
10.7 Burden of Proof Distribution
185(5)
10.7.1 Taking the BoP Outside of Legal Discourse
186(1)
10.7.2 The BoP in the Conversational Score
187(2)
10.7.3 Summing Up the BoP Strategy
189(1)
10.8 Hybrid Consequence
190(2)
10.9 Whatever Happened to Truth?
192(1)
10.10
Chapter Summary
193(4)
Part IV Summary
11 Summary
197(6)
11.1 Resume
197(2)
11.2 What is Constructivity?
199(4)
Appendix A Characteristics of Some of the Logics 203(2)
Appendix B Tableaux for N3, N3f, NAND, NAND f and Hybrid Consequence 205(6)
References 211(4)
Index 215
Andreas Kapsner is currently postdoctoral researcher at the Munich Center of Mathematical Philosophy. He received his PhD from the University of Barcelona in 2011, and his doctoral dissertation was awarded the Beth Dissertation Prize in 2012. His main research fields are the philosophy of logic and the philosophy of language, but he is also working on Asian philosophy, political philosophy and narrative theory.