The logic of concept expansion

The operation of developing a concept is a common procedure in mathematics and in natural science, but has traditionally seemed much less possible to philosophers and, especially, logicians. Meir Buzaglo's innovative study proposes a way of expanding logic to include the stretching of concepts, while modifying the principles which block this possibility. He offers stimulating discussions of the idea of conceptual expansion as a normative process, and of the relation of conceptual expansion to truth, meaning, reference, ontology and paradox, and analyzes the views of Kant, Wittgenstein, Godel, and others, paying especially close attention to Frege. His book will be of interest to a wide range of readers, from philosophers (of logic, mathematics, language, and science) to logicians, mathematicians, linguists, and cognitive scientists.

[1]  J. Hintikka III. Kantian intuitions , 1972 .

[2]  K. Gödel Philosophy of mathematics: What is Cantor's continuum problem? , 1984 .

[3]  P. Simons,et al.  Reviews-The Applicability of Mathematics as a Philosophical Problem , 1998 .

[4]  Paul Bachmann Zur Theorie der complexen Zahlen. , 1867 .

[5]  Saul A. Kripke,et al.  Wittgenstein on Rules and Private Language. , 1985 .

[6]  I. Lakatos,et al.  Proofs and Refutations: Frontmatter , 1976 .

[7]  Haragauri N. Gupta IX.—ON THE RULE OF EXISTENTIAL SPECIFICATION IN SYSTEMS OF NATURAL DEDUCTION , 1968 .

[8]  M. Dummett Frege: Philosophy of Language , 1973 .

[9]  Mark A. Wilson Frege: The Royal Road from Geometry , 1992 .

[10]  B. V. Fraassen Singular Terms, Truth-Value Gaps, and Free Logic , 1966 .

[11]  J. Hintikka Are Logical Truths Analytic , 1965 .

[12]  E. J. Lemmon QUANTIFIER RULES AND NATURAL DEDUCTION , 1961 .

[13]  Penelope Maddy,et al.  Realism in mathematics , 1991 .

[14]  Kit Fine,et al.  Reasoning with arbitrary objects , 1988 .

[15]  I. Lakatos PROOFS AND REFUTATIONS (I)*† , 1963, The British Journal for the Philosophy of Science.

[16]  George Peacock Report on the recent progress and present state of certain branches of analysis , 1833 .

[17]  L. Ahlfors Complex Analysis , 1979 .

[18]  Charles Parsons,et al.  Reason and Intuition* , 2000, Synthese.

[19]  Jaakko Hintikka,et al.  Kant on the Mathematical Method , 1967 .

[20]  W. Quine The ways of paradox, and other essays , 1966 .

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

[22]  George Boolos,et al.  IX—Saving Frege from Contradiction , 1987 .

[23]  Paul Benacerraf,et al.  Philosophy of mathematics: What numbers could not be , 1965 .

[24]  W. Rudin Real and complex analysis , 1968 .

[25]  E. R. Hedrick,et al.  Elementary Mathematics from an Advanced Standpoint. Arithmetic. Algebra. Analysis , 1933 .

[26]  R. Goodstein,et al.  Remarks on the Foundations of Mathematics , 1957, The Mathematical Gazette.

[27]  Hilary Putnam,et al.  RETHINKING MATHEMATICAL NECESSITY , 2002 .

[28]  M. Kline Mathematical Thought from Ancient to Modern Times , 1972 .

[29]  J. Gibson The perception of the visual world , 1951 .

[30]  J. Neumann,et al.  The Logic of Quantum Mechanics , 1936 .

[31]  Charles Parsons,et al.  X—Mathematical Intuition , 1980 .

[32]  L. Wittgenstein Tractatus Logico-Philosophicus , 2021, Nordic Wittgenstein Review.

[33]  Charles D. Parsons,et al.  Platonism and Mathematical Intuition in Kurt Gödel's Thought , 1995, Bulletin of Symbolic Logic.