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THE LOGICAL SYSTEM OF FREGE’S GRUNDGESETZE: A RATIONAL RECONSTRUCTION
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Frege. Second-Order Logic. Grundgesetze der Arithmetik. Begriffsschrift. Frege’s notion of a Function

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CADET, Méven; PANZA, Marco. THE LOGICAL SYSTEM OF FREGE’S GRUNDGESETZE: A RATIONAL RECONSTRUCTION. Manuscrito: Revista Internacional de Filosofia, Campinas, SP, v. 38, n. 1, p. 5–94, 2015. Disponível em: https://periodicos.sbu.unicamp.br/ojs/index.php/manuscrito/article/view/8641949. Acesso em: 17 jul. 2024.

Resumo

This paper aims at clarifying the nature of Frege’s system of logic, as presented in the first volume of the Grundgesetze. We undertake a rational reconstruction of this system, by distinguishing its propositional and predicate fragments. This allows us to emphasise the differences and similarities between this system and a modern system of classical second-order logic.
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Referências

BLANCHETTE, P. Frege’s Conception of Logic. Oxford U. P., Oxford, New York, etc., 2012.

BRADLEY, R. E. and SANDIFER, C. E. Cauchy’s Cours d’analyse. An Annotated Translation. Springer, Dordrecht, Heidelberg, London, New York, 2009.

BURGESS, J. P. Hintikka and Sandu versus Frege in re arbitrary functions. Philosophia Mathematica, 3rd ser. 1:50–65, 1993.

——. Frege on arbitrary functions. In W. Demopoulos, editor, Frege’s Philosophy of Mathematics , pages 89–107. Harvard U. P., Cambridge (Mass.), London, 1995. This is a revised version of [3].

——. Fixing Frege. Princeton Univ. Press, Princeton and Oxford, 2005.

CAUCHY, A. L. Cours d’analyse de l’École royale polytechnique [...], 1re partie. Analyse algébrique. Debure frères, Paris, 1821.

DEMOPOULOS, W. Frege and the rigorization of analysis. Journal of Philosophical Logic, 23:225–245, 1994.

——.. , editor. Frege’s Philosophy of Mathematics. Harvard U. P., Cambridge (Mass.), London, 1995.

——.. On logicist conceptions of functions and classes. In D. DeVidi, M. Hallett, and P. Clark , editors, Logic, Mathematics, Philosophy: Vintage Enthusiasms. Essays in Honour of J. L. Bell, pages 3–18. Springer-Verlag, Dordrecht, Heidelberg, London, New York, 2011.

——. and BELL, J. L. Frege’s theory of concepts and objects and the interpretation of second-order logic. Philosophia Mathematica, Ser. 3 1:139–156, 1993.

DUMMETT, M. Frege: Philosophy of Language. Duckworth, London, 19731 , 19812 .

——. Frege. Philosophy of Mathematics. Duckworth, London, 1991.

FERRARO, G. and PANZA, M. Lagrange’s theory of analytical functions and his ideal of purity of method. Archive for History of Exact Sciences, 66:95–197, 2012.

FREGE, G. Begriffsschrift, eine der Arithmetischen nachgebildete Formelsprache des reinen Denkens. Nebert, Halle, 1879.

——. Die Grundlagen der Arithmetik. W. Köbner, Breslau, 1884.

——. Function und Begriff. Vortrag, gehalten in der Sitzung vom 9. Januar 1891 der Jenaischen Gesellschaft für Medicin und Naturwissenschaft. H. Pohle, Jena, 1891.

——. Über Begriff und Gegenstand. Vierteljahresschrift für wissenschaftliche Philosophie, 16:192–205, 1892.

——. Grundgesetze der Arithmetik. H. Pohle, Jena, 1893-1903. 2 volumes.

——. Was ist eine funktion? In S. Meyer, editor, Festschrift Ludwig Boltzmann gewidmet zum sechzigsten Geburtstage, 20. Februar 1904, pages 656–666. J. A. Barth, Leipzig, 1904.

——. The Foundations of Arithmetic. Blackwell, Oxford, 1953. Translated by J. L. Austin.

——. Translations from the Philosophical Writings of Gottlob Frege. Basil Blackwell, Oxford, 1960. Ed. by P. Geach, and M. Black.

——. Basic Laws of Arithmetic. Oxford University Press, Oxford, 2013. Edited by P. Ebert, M. Rosberg and C. Wright. Translated with an Introduction by P. Ebert and M. Rosberg. With a Foreword by C. Wright and an Afterword by R.T. Cook.

GOLDFARB, W. Frege’s conception of logic. In M. Potter and T. Ricketts, editors, The Cambridge Companion to Frege, pages 63–85. Cambridge U. P., Cambridge U. P., 2010.

HECK R. The development of arithmetic in Frege’s Grundgesetze der Arithmetic. Journal of Symbolic Logic, 58:579–601, 1993.

——. Reading Frege’s Grundgesetze. Clarendon Press, Oxford, 2012.

——. and STANLEY, J. Reply to Hintikka and Sandu: Frege and second-order logic. The Journal of Philosophy, 90:416–424, 1993.

HINTIKKA, J. and SANDU, G. The skeleton in Frege’s cupboard: The standard versus nonstandard distinction. The Journal of Philosophy, 89:290–315, 1992.

LAGRANGE, J.-L. Théorie des fonctions analytiques [...]. Courcier, Paris, 1813. Re-edited in [29], vol. IX.

——. Œuvres de Lagrange. Gauthier-Villars, Paris, 1867-1892. 14 vols.; edited by M. J.-A. Serret [et G. Darboux]. [30] ——. Théorie des fonctions analytiques [...]. Impr. de la République, Paris, Prairial an V: May-June 1797.

LANDINI, G. Frege’s Notations: What They Are and How They Mean. Palgrave MacMilan, Basingstoke (Hampshire, UK), 2012.

MENDELOSON, E. Introduction to Mathematical Logic. Chapman and Hall, London, etc., 1997. Fourth edition.

PANZA, M. From Lagrange to Frege: Functions and expressions. In H. Benis Sinaceur, M. Panza and G. Sandu, Functions and Genrality of Logic: Reflections on Dedekind’s and Frege’s Logicisms, forthcoming for Springer.

POTTER, M. Reason’s Nearest Kin. Philosophies of Arithmetic from Kant to Carnap. Oxford U. P., Oxford, New York, etc., 2000.

——. and RICKETTS, T. , editors. The Cambridge Companion to Frege. Cambridge U. P., Cambridge, New York, etc, 2010.

SANDU, G. Ramsey and the notion of arbitrary function. In M. J. Frpolli, editor, F. P. Ramsey. Critical Reassessment, pages 237–256. Continuum, London, New York, 2005.

SCHIRN, M. Frege’s approach to the foundations of analysis (1874–1903). History and Philosophy of Logic, 34(3):266–292, 2013.

SIMONS, P. Frege’s theory of real numbers. History and Philosophy of Logic, 8:25–44, 1987. Also in [8], pp. 358-383.

SNYDER, E. and SHAPIRO, S. Frege on the real numbers. In M. Rossberg and P. Ebert, editors, The Oxford Handbook of Frege’s Grundgesetze. Oxford Univ. Press, Forthcoming.

WEINER, J. Frege in Perspective. Cornell University Press, Ithaca (N.Y), 1990.

——. Understanding Frege’s project. In M. Potter and T. Ricketts, editors, The Cambridge Companion to Frege, pages 32–62. Cambridge U. P., Cambridge, New York, etc., 2010.

WRIGHT, C. Frege’s Conception of Numbers as Objects. Aberdeen Univ. Press, Aberdeen, 1983.

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