Skip to main content Accessibility help
×
  1. Home
  2. Books
  3. The Logic of Concept Expansion
  • Cited by 6
      • Show more authors
      • You may already have access via personal or institutional login
    • Select format
    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      December 2001
      ISBN:
      9780511487460
      9780521807623
      9780521041058
      DOI:
      https://doi.org/10.1017/CBO9780511487460
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.43kg, 196 Pages
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.3kg, 196 Pages
      • Subjects:
      Area Studies, Logic, History, European Studies, Philosophy, Russian and East European History
    You may already have access via personal or institutional login
    • Selected: Digital
    Add to cart View cart Buy from Cambridge.org
    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

    Refine List

    Actions for selected content:

    Select all | Deselect all
    • View selected items
    • Export citations
    • Download PDF (zip)
    • Save to Kindle
    • Save to Dropbox
    • Save to Google Drive

    Save Search

    You can save your searches here and later view and run them again in "My saved searches".

    Please provide a title, maximum of 40 characters.
    Cancel
    ×

    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

    Metrics

    Full text views

    Total number of HTML views: 0
    Total number of PDF views: 0 *
    Loading metrics...

    Book summary page views

    Total views: 0 *
    Loading metrics...

    * Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

    Usage data cannot currently be displayed.

    Accessibility standard: Unknown

    Why this information is here

    This section outlines the accessibility features of this content - including support for screen readers, full keyboard navigation and high-contrast display options. This may not be relevant for you.

    Accessibility Information

    Accessibility compliance for the PDF of this book is currently unknown and may be updated in the future.