The Age of Alternative Logics

Acknowledgments.- 1. Introduction: Alternative Logics and Classical Concerns J. van Benthem.- Part I Proof, Knowledge and Computation. 2. Epistemic Models, Logical Monotony and Substructural Logics M. Cozic. 3. Semantics as Based on Inference J. Peregrin. 4. Effectiveness S. Shapiro. 5. Does Godel's Incompleteness Theorem Prove thatTruth Transcends Proof? J. Vidal-Rosset. 6. Transpositions H. Visser.- Part II Truth Values Beyond Bivalence.- 7. Many-Valued and Kripke Semantics J.-Y. Beziau. 8. The Logic of Complementarity N. C. A. da Costa, D. Krause. 9. Semantics for Naive Set Theory in Many-Valued Logics T. Libert.- Part III Category-Theoretic Structures. 10. Continuity and Logical Completeness. An Application of Sheaf Theory and Topoi S. Awodey. 11. What is Categorical Structuralism? G. Hellman. 12. Category Theory as a Framework for an in re Interpretation of Mathematical Structuralism E. Landry. 13. Categories, Sets and the Nature of Mathematical Entities J.-P. Marquis.- Part IV Independence, Evaluation Games and Imperfect Information. 14. Truth, Negation and Other Basic Notions of Logic J. Hintikka. 15. Signalling in IF Games: A Tricky Business T. M.V. Janssen, F. Dechesne. 16. Independence-Friendly Logic and Games of Incomplete Information A.-V. Pietarinen. 17. IF and Epistemic Action Logic M. Rebuschi.- Part V Dialogue and Pragmatics. 18. Naturalizing Dialogic Pragmatics G. Heinzmann. 19. Logic as a Tool of Science Versus Logic as a Scientific Subject K. Lorenz. 20. Non-Normal Dialogics for a WonderfulWorld and More S. Rahman.- Part VI Appendices. A: Louis Joly as a Platonist Painter? Roger Pouivet.- Index.

[1]  M. Theunissen.  The other , 1984 .

[2]  A. Turing.  On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[3]  Steve Awodey.  An Answer to Hellman's Question: ‘Does Category Theory Provide a Framework for Mathematical Structuralism?’† , 2004 .

[4]  Jaakko Hintikka,et al.  Negation in Logic and in Natural Language , 2002 .

[5]  H KruijswijkJansen.  We are using... , 1992 .

[6]  Olivier Esser.  On the Consistency of a Positive Theory , 1999, Math. Log. Q..

[7]  Elaine Landry,et al.  Category Theory: The Language of Mathematics , 1999, Philosophy of Science.

[8]  K. Dosen,et al.  Models for normal intuitionistic modal logics , 1984 .

[9]  Jouko A. Väänänen,et al.  Second-Order Logic and Foundations of Mathematics , 2001, Bulletin of Symbolic Logic.

[10]  Thoralf Skolem.  Studies on the axiom of comprehension , 1963, Notre Dame J. Formal Log..

[11]  Alfred Tarski,et al.  Der Wahrheitsbegriff in den formalisierten Sprachen , 1935 .

[12]  B R Greene,et al.  String theory. , 1994, Proceedings of the National Academy of Sciences of the United States of America.

[13]  A. Heyting,et al.  Intuitionism: An introduction , 1956 .

[14]  Jaakko Hintikka,et al.  New Foundations for Mathematical Theories , 1998 .

[15]  John C. Baez.  An Introduction to n-Categories , 1997, Category Theory and Computer Science.

[16]  J. Milnor.  Games Against Nature , 1951 .

[17]  Berthold-Georg Englert,et al.  The Duality in Matter and Light , 1994 .

[18]  R. Courant,et al.  What Is Mathematics , 1943 .

[19]  A. Church.  An Unsolvable Problem of Elementary Number Theory , 1936 .

[20]  John MacFarlane.  The Logic of Confusion , 2007 .

[21]  Noam Chomsky.  Knowledge of Language , 1986 .

[22]  Yogi Berra,et al.  When You Come to a Fork in the Road, Take It! , 2001 .

[23]  David Maccallum,et al.  Quantum Mechanics: Historical Contingency and the Copenhagen Hegemony , 1996 .

[24]  Marcelo Tsuji.  Many-Valued Logics and Suszko's Thesis Revisited , 1998, Stud Logica.

[25]  Solomon Feferman,et al.  Categorical Foundations and Foundations of Category Theory , 1977 .

[26]  Moh Shaw-Kwei.  Logical Paradoxes for Many-Valued Systems , 1954, J. Symb. Log..

[27]  Jacques Dubucs,et al.  Feasibility In Logic , 2002, Synthese.

[28]  Colin McLarty,et al.  Exploring Categorical Structuralism , 2004 .

[29]  Jean-Yves Girard,et al.  Linear logic: its syntax and semantics , 1995 .

[30]  V. Umansky,et al.  Dephasing in electron interference by a ‘which-path’ detector , 1998, Nature.

[31]  Roman Suszko,et al.  The Fregean Axiom and Polish mathematical logic in the 1920s , 1977 .

[32]  Thomas Jech,et al.  About the Axiom of Choice , 1973 .

[33]  John L. Bell,et al.  Category Theory and the Foundations of Mathematics* , 1981, The British Journal for the Philosophy of Science.

[34]  Roland Hinnion,et al.  Positive abstraction and extensionality , 2003, Journal of Symbolic Logic.

[35]  Jean-Pierre Marquis,et al.  Category theory and the foundations of mathematics: Philosophical excavations , 1995, Synthese.

[36]  Mara Beller,et al.  The birth of Bohr's complementarity: The context and the dialogues , 1992 .

[37]  Irvin D. Rutman,et al.  Remains to be seen. , 1995 .

[38]  Ralph Kopperman,et al.  Continuity Spaces: Reconciling Domains and Metric Spaces , 1997, Theor. Comput. Sci..

[39]  Heinrich Wansing,et al.  A general possible worlds framework for reasoning about knowledge and belief , 1990, Stud Logica.

[40]  Dale Gottlieb.  No Entity Without Identity , 1978 .

[41]  J. Lambek,et al.  Introduction to higher order categorical logic , 1986 .

[42]  Robert Burn.  The genesis of mathematical structures , 2003 .

[43]  J. Hintikka,et al.  Game-Theoretical Semantics , 1997 .

[44]  S. Kleene.  General recursive functions of natural numbers , 1936 .

[45]  Michael Makkai,et al.  Towards a Categorical Foundation of Mathematics , 1995, Logic Colloquium.

[46]  Jean-Yves Béziau,et al.  Théorie de la valuation , 1994 .

[47]  R. Carnap.  Empiricism, semantics and ontology , 1984 .

[48]  Willard Van Orman Quine,et al.  Philosophy of Logic. , 1988 .

[49]  Otávio Bueno,et al.  Paraconsistency: Towards a tentative interpretation , 2001 .

[50]  Jean-Yves Béziau,et al.  What is many-valued logic? , 1997, Proceedings 1997 27th International Symposium on Multiple- Valued Logic.

[51]  Jaakko Hintikka,et al.  No scope for scope , 1998 .

[52]  A. Troelstra.  Constructivism in mathematics , 1988 .

[53]  F. W. Lawvere.  Cohesive Toposes and Cantor's 'lauter Einsen' , 1994 .

[54]  Michael Batanin,et al.  Monoidal Globular Categories As a Natural Environment for the Theory of Weakn-Categories☆ , 1998 .

[55]  F. W. Lawvere.  Variable Quantities and Variable Structures in Topoi , 1976 .

[56]  E. Landry.  Logicism, Structuralism and Objectivity , 2001 .

[57]  Niels Bohr,et al.  Atomic Theory and the Description of Nature , 1934 .

[58]  Colin McLarty,et al.  Numbers Can Be Just What They Have To , 1993 .

[59]  Nicholas Bourbaki,et al.  The Architecture of Mathematics , 1950 .

[60]  J. Hintikka,et al.  Tarski’s Guilty Secret: Compositionality , 1999 .

[61]  Roland Hinnion.  Naive Set Theory with Extensionality in Partial Logic and in Paradoxical Logic , 1994, Notre Dame J. Formal Log..

[62]  Niels Bohr,et al.  Causality and Complementarity , 1937, Philosophy of Science.

[63]  Robert Goldblatt.  Mathematical modal logic: A view of its evolution , 2003, J. Appl. Log..

[64]  Jean-Yves Girard,et al.  Linear Logic , 1987, Theor. Comput. Sci..

[65]  Furio Honsell,et al.  Processes and Hyperuniverses , 1994, MFCS.

[66]  Emmy Noether.  Idealtheorie in Ringbereichen , 1921 .

[67]  Newton C. A. da Costa,et al.  On the theory of inconsistent formal systems , 1974, Notre Dame J. Formal Log..

[68]  G. Hellman,et al.  Pluralism and the Foundations of Mathematics , 2006 .

[69]  Jaakko Hintikka,et al.  On the Epistemology of Game-Theoretical Semantics , 2003 .

[70]  Anton Zeilinger,et al.  Experimental verification of the Heisenberg uncertainty principle for fullerene molecules , 2001, quant-ph/0105061.

[71]  R. Morrow,et al.  Foundations of Quantum Mechanics , 1968 .

[72]  M. de Rijke,et al.  Modal Logic , 2001, Cambridge Tracts in Theoretical Computer Science.

[73]  Mitsuhiro Okada.  An Introduction to Linear Logic: Expressiveness and Phase Semantics , 1998 .

[74]  W. Carnielli,et al.  A Taxonomy of C-systems , 2001 .

[75]  Pierre Teilhard de Chardin,et al.  Let Me Explain , 1970 .

[76]  Leon Henkin,et al.  Completeness in the theory of types , 1950, Journal of Symbolic Logic.

[77]  Horst Herrlich,et al.  Category theory , 1979 .

[78]  J. Bell,et al.  From absolute to local mathematics , 1986, Synthese.

[79]  Jan Łukasiewicz,et al.  A System of Modal Logic , 1953 .

[80]  Mark Saaltink.  Relational semantics , 1985, SOEN.

[81]  J. Hintikka.  Knowledge and belief , 1962 .

[82]  C. McLarty.  The Uses and Abuses of the History of Topos Theory , 1990, The British Journal for the Philosophy of Science.

[83]  Brandon Seyferth.  Here it is , 2001 .

[84]  Saul A. Kripke,et al.  Outline of a Theory of Truth , 1975 .

[85]  C. Hartshorne,et al.  Collected Papers of Charles Sanders Peirce , 1935, Nature.

[86]  Martin Strauss.  Mathematics as Logical Syntax — A Method to Formalize the Language of a Physical Theory , 1975 .

[87]  John Mayberry.  What is Required of a Foundation for Mathematics , 1994 .

[88]  Geoffrey Hellman,et al.  Three Varieties of Mathematical Structuralism , 2001 .

[89]  Martin D. Davis,et al.  Why Gödel Didn't Have Church's Thesis , 1982, Inf. Control..

[90]  Steven Awodey,et al.  Topological Completeness for Higher-Order Logic , 2000, J. Symb. Log..

[91]  Th. Skolem,et al.  A Set Theory Based on a Certain 3-Valued Logic. , 1960 .

[92]  Wilfried Sieg,et al.  Mechanical Procedures and Mathematical Experience , 1991 .

[93]  G. Kreisel.  Informal Rigour and Completeness Proofs , 1967 .

[94]  John McDowell,et al.  Truth-Value Gaps* , 1982 .

[95]  On a theorem of Feferman , 1980 .

[96]  F W Lawvere,et al.  AN ELEMENTARY THEORY OF THE CATEGORY OF SETS. , 1964, Proceedings of the National Academy of Sciences of the United States of America.

[97]  James Dugundji.  Note on a Property of Matrices for Lewis and Langford's Calculi of Propositions , 1940, J. Symb. Log..

[98]  Dov M. Gabbay,et al.  Grafting Modalities onto Substructural Implication Systems , 1997, Stud Logica.

[99]  Jaakko Hintikka,et al.  Post-Tarskian Truth , 2004, Synthese.

[100]  Richard B. White,et al.  The consistency of the axiom of comprehension in the infinite-valued predicate logic of Łukasiewicz , 1979, J. Philos. Log..

[101]  Jaakko Hintikka,et al.  Independence-friendly logic and axiomatic set theory , 2004, Ann. Pure Appl. Log..