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  1. Home
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  3. The Logic of Concept Expansion
  • Cited by 4
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
2001
Online ISBN:
9780511487460
DOI:
https://doi.org/10.1017/CBO9780511487460
Subjects:
Area Studies, Logic, History, European Studies, Philosophy, Russian and East European History
Information

Book description

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.

Reviews

'The book provides interesting philosophical, mainly historical, views on the dynamics of conceptual changes which fall under the considered domain of concept expansion.'

Source: Zentralblatt für Mathematik und ihre Grenzgebiete Mathematics Abstracts

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Contents

Contents
References
References
References
Ahlfors, L. V. (1979), Complex Analysis. McGraw-Hill, Singapore
Benacerraf, P. (1983), “What Numbers Could Not Be.” In Philosophy of Mathematics, ed. P. Benacerraf and H. Putnam. Cambridge University Press, Cambridge
Benacerraf, P. (1996), “What Mathematical Truth Could Not Be – I.” In The Philosophy of Mathematics Today, ed. M. Schirn. Clarendon Press, Oxford. Mathematics Today, ed. M. Schirn Press, Oxford
Boolos, G. (1986), “Saving Frege from Contradiction.” Proceedings of the Aristotelian Society, 87, pp. 137–51
Buzaglo, M. (forthcoming), Solomon Maimon's Metaphysics: A Reconstruction. Pittsburgh University Press, Pittsburgh
Crowe, M. (1992), “Ten ‘Laws’ Concerning Patterns of Change in the History of Mathematics.” Reprinted in Revolutions in Mathematics, ed. Donald Gillies. Clarendon Press, Oxford
Diamond, C. (1995), The Realistic Spirit. MIT Press, Cambridge MA
Dummett, M. (1973), Frege: Philosophy of Language. Duckworth, London
Dummett, M. (1978), “The Justification of Deduction.” Reprinted in Truth and Other Enigmas. Duckworth, London, pp. 290–318
Fine, K. (1985), Reasoning with Arbitrary Objects. Basil Blackwell, Oxford
van Frassen, B. C. (1966), “Singular Terms, Truth-Value Gaps, and Free Logic.” Journal of Philosophy, 63
van Frassen, B. C. (1978), “Rejoinder: On a Kantian Conception of Language.” In Paradox of the Liar, ed. R. L. Martin. Ridgeview Publishing Company, California, pp. 59–66
Frege, G. (1977a), Grundgesetze der Arithmetik, trans. P. E. B. Jourdain and J. Stachelroth. In Translations from the Philosophical Writings of G. Frege, ed. P. Geach and M. Black, Basil Blackwell, Oxford
Frege, G. (1977b), “Negation.” In Translations from the Philosophical Writings of G. Frege, ed. P. Geach and M. Black. Basil Blackwell, Oxford
Frege, G. (1979), Posthumous Writings, ed. H. Hermes, F. Kambartel, and F. Kaulbach. University of Chicago Press, Chicago
Frege, G. (1980), Foundations of Arithmetic. Northwestern University Press, Chicago
Frege, G. (1984), Collected Papers on Mathematics, Logic and Philosophy, ed. B. McGuinness. Basil Blackwell, Oxford
Gibson, J. J. (1950), The Perception of the Visual World. Houghton Mifflin, Boston
Güdel, K. (1983a), “What is Cantor's Continuum Problem?” In Philosophy of Mathematics, ed. P. Benacerraf and H. Putnam. Cambridge University Press, Cambridge, pp. 447–69
Güdel, K. (1983b), “Russell's Mathematical Logic.” In Philosophy of Mathematics, ed. P. Benacerraf and H. Putnam. Cambridge University Press, Cambridge, pp. 470–86
Gupta, H. (1968), “On the Rule of Existential Specification in Systems of Natural Deduction.” Mind, 77, pp. 96–103
Hankel, H. (1867), Theorie der complexen Zahlen Systeme. Klein
Hilbert, D. (1983), “On the Infinite.” In Philosophy of Mathematics, ed. P. Benacerraf and H. Putnam. Cambridge University Press, Cambridge, pp. 183–206
Hintikka, J. (1965), “Are Logical Truths Analytic?” Philosophical Review, 74, pp. 178–203
Hintikka, J. (1967), “Kant on the Mathematical Method.” The Monist, 51, pp. 352–75
Hintikka J. (1969), “On Kant's Notion of Intuition (Anschauung).” In The First Critique, ed. Terence Penelhum and J. J. MacIntosh. Wadsworth, Belmont
Hintikka, J. (1972), “Kantian Intuitions.” Inquiry, 15, pp. 341–5
Hofstadter, D. (1995), Fluid Concepts and Creative Analogies. Basic Books, Harper Collins, New York
Kant, I. (1933), Critique of Pure Reason, trans. N. Kemp Smith. London
Kitcher, P. (1989) “Innovation and Understanding in Mathematics.” Journal of Philosophy, October, pp. 563–4
Klein, F. (1939), Elementary Mathematics from an Advanced Standpoint: Arithmetic, Algebra, Analysis. Dover, New York
Kline, M. (1972), Mathematical Thought from Ancient to Modern Times, 3 vols. Oxford University Press, Oxford
Kripke, S. (1975), “Outline to a Theory of Truth.” Journal of Philosophy, 72, pp. 690–716
Kripke, S. (1982), Wittgenstein on Rules and Private Language. Basil Blackwell, Oxford
Lakatos, I. (1976), Proofs and Refutations. Cambridge University Press, Cambridge
Lakatos, I. (1978), Philosophical Papers, ed. J. Worrall and G. Currie, 2 vols. Cambridge University Press, Cambridge
Lemmon, E. J. (1961), “Quantifier Rules and Natural Deduction.” Mind, 70, pp. 235–8
Maimon, S. (1965), Gesammelte Werke, vols. I–VII. Georg Olms Verlagsbuchhandlung, Hildesheim
Maddy, P. (1990), Realism in Mathematics. Oxford University Press, Oxford
Manders, K. (1989), “Domain Extension and the Philosophy of Mathamatics.” Journal of Philosophy, pp. 553–62
Mikenberg, I. (1977), “From Total to Partial Algebras.” In Mathematical Logic, Proceedings of the First Brazilian Conference, ed. A. Arruda, N. C. A. de Costa, and R. Chuaqui, Dekker, pp. 203–23
Parsons, C. (1979–80), “Mathematical Intuition.” Proceedings of the Aristotelian Society, 80, pp. 145–68
Parsons, C. (1995), “Platonism and Mathematical Intuition in Kurt Güdel's Thought.” Bulletin of Symbolic Logic, 1(1), pp. 44–75
Parsons, C. (1998), “Reason and Intuition.” Synthese, 125(3), pp. 239–315
Peacock, G. (1834), “Report on the Recent Progress and Present State of Certain Branches of Analysis.” In Report on the Third Meeting of the British Association for the Advancement of Science, 1833. London, pp. 185–352
Putnam, H. (1975a), “It Ain't Necessarily So.” Reprinted in Philosophical Papers, vol. I, Cambridge University Press, Cambridge, pp. 237–50
Putnam, H. (1975b), “The Logic of Quantum Mechanics.” In Philosophical Papers, vol. I, Cambridge University Press, Cambridge, pp. 174–97
Putnam, H. (1994), “Rethinking Mathematical Necessity.” In Words and Life, Harvard University Press, Cambridge MA, pp. 245–63
Quine, W. V. (1977), The Ways of Paradox and Other Essays. Harvard University Press, Cambridge MA
Robinson, A. (1955), Complete Theories. North-Holland, Amsterdam
Rudin, W. (1966), Real and Complex Analysis. Tata McGraw-Hill, New Delhi
Russell, B. (1919), Introduction to Mathematical Philosophy, George Allen and Unwin, London
Russell, B. (1956), “On Denoting.” In Logic and Knowledge, ed. R. C. Marsh. George Allen and Unwin, London
Steiner, M. (1998), The Applicability of Mathematics as a Philosophical Problem. Harvard University Press, Cambridge MA
Wang, H. (1996), A Logical Journey: From Güdel to Philosophy, MIT Press, Cambridge MA
Wilson, M. (1995), “Frege: The Royal Road from Geometry.” Nous, 26, 1992, pp. 149–80. Reprinted in Frege's Philosophy of Mathematics, ed. W. Demopoulos. Harvard University Press, Cambridge MA, pp. 108–49
Wittgenstein, L. (1953), Philosophical Investigations. Basil Blackwell, Oxford
Wittgenstein, L. (1967), Remarks on the Foundation of Mathematics, trans. G. E. M. Anscombe. Basil Blackwell, Oxford
Wittgenstein, L. (1974), Philosophical Grammar, trans. A. Kenny. Basil Blackwell, Oxford
Wittgenstein, L. (1988), Tractatus Logico-Philosophicus, trans. C. K. Ogden. Routledge and Kegan Paul, London

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