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Formality of logic and Frege’s Begriffsschrift

Published online by Cambridge University Press:  01 January 2020

Daniele Mezzadri
Daniele Mezzadri*
Affiliation:
Department of Philosophy, College of Humanities and Social Sciences, United Arab Emirates University, Al Ain, UAE
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Abstract

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’.

Keywords

FregeBegriffsschriftlogicformalityuniversalism
Type
Articles
Information
Canadian Journal of Philosophy , Volume 49 , Issue 2 , March 2019 , pp. 182 - 207
Copyright
Copyright © Canadian Journal of Philosophy 2018

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References

Blanchette, P., 2014. “Frege on Formality and the 1906 Independence Test.” In Formalism and Beyond: On the Nature of Mathematical Discourse, edited by Link, G., 97–118. Boston: De Gruyter.Google Scholar
Conant, J., 1991. “The Search for Logically Alien Thought: Descartes, Kant, Frege, and the Tractatus.” Philosophical Topics, 20 (1): 115–180. doi:10.5840/philtopics19922015.CrossRefGoogle Scholar
Currie, G., 1982. Frege. An Introduction to His Philosophy. Sussex: Harvester Press.Google Scholar
Dummett, M., 1981. The Interpretation of Frege’s Philosophy. London: Duckworth.Google Scholar
Dutilh Novaes, C., 2011. “The Different Ways in Which Logic Is (Said to Be) Formal.” History and Philosophy of Logic, 32 (4): 303–332. doi:10.1080/01445340.2011.555505.CrossRefGoogle Scholar
Frege, G., 1879. “Conceptual-Notation. A Formula Language of Pure Thought Modelled upon the Formula Language of Arithmetic.” In Conceptual Notation and Related Articles, Translated and edited by Bynum, Terrel W., 101–203. Oxford: Clarendon Press.Google Scholar
Frege, G., 1882. “On the Scientific Justification of a Conceptual Notation.” In Conceptual Notation and Related Articles, Translated and edited by Bynum, Terrel W., 83–89. Oxford: Clarendon Press.Google Scholar
Frege, G., 1882–3. “On the Aim of the ‘Conceptual Notation’.” In Conceptual Notation and Related Articles, Translated and edited by Bynum, Terrel W., 90–100. Oxford: Clarendon Press.Google Scholar
Frege, G., 1884. The Foundations of Arithmetic. Translated by Austin, John L.. Oxford: Blackwell. 1968.Google Scholar
Frege, G., 1885. “On Formal Theories of Arithmetic.” In Collected Papers on Mathematics, Logic, and Philosophy, edited by McGuinness, B., Translated by Black, Max et al., 112–121. Oxford: Blackwell.Google Scholar
Frege, G., 1893–1903. Basic Laws of Arithmetic. Derived Using Concept-Script. Translated and edited by Ebert, Philip, Rossberg, Marcus and Wright, Crispin. Oxford: Oxford University Press. 2013.Google Scholar
Frege, G., 1906. “On the Foundations of Geometry: Second Series.” In Collected Papers on Mathematics, Logic, and Philosophy, edited by McGuinness, B., Translated by Black, Max et al, 293–340. Oxford: Blackwell.Google Scholar
Frege, G., 1918–9. “Logical Investigations: I Thoughts.” In Collected Papers on Mathematics, Logic, and Philosophy, edited by McGuinness, B., Translated by Black, Max et al., 351–372. Oxford: Blackwell.Google Scholar
Frege, G., 1972. Conceptual Notation and Related Articles. Translated and edited by Bynum, Terrel W.. Oxford: Clarendon Press. Translated by Long, Peter and White, Roger, edited by Hermes, H., Kambartel, F., Kaulbach, F. Google Scholar
Frege, G., 1979a. “Boole’s Logical Calculus and the Concept-Script.” In Posthumous Writings, edited by Hermes, H., Kambartel, F., and Kaulbach, F., Translated by Long, Peter and White, Roger, 9–46. Oxford: Blackwell.Google Scholar
Frege, G., 1979b. “Boole’s Logical Formula-Language and My Concept-Script.” In Posthumous Writings, edited by Hermes, H., Kambartel, F., and Kaulbach, F., Translated by Long, Peter and White, Roger, 47–52. Oxford: Blackwell.Google Scholar
Frege, G., 1979c. “Logic.” In Posthumous Writings, edited by Hermes, H., Kambartel, F., and Kaulbach, F., Translated by Long, Peter and White, Roger, 1–8. Oxford: Blackwell.Google Scholar
Frege, G., 1979d. “Logic.” In Posthumous Writings, edited by Hermes, H., Kambartel, F., and Kaulbach, F., Translated by Long, Peter and White, Roger, 126–151. Oxford: Blackwell.Google Scholar
Frege, G., 1980. Philosophical and Mathematical Correspondence. Translated by Kaal, Hans, edited by Gabriel, Gottfried et al.. Blackwell: Oxford.Translated by Black, Max et al, edited by McGuinness, Brian Google Scholar
Goldfarb, W., 2001. “Frege’s Conception of Logic.” In Future Pasts. The Analytic Tradition in Twentieth-Century Philosophy, edited by Floyd, J. and Shieh, S., 25–41. Oxford: Oxford University Press.CrossRefGoogle Scholar
Goldfarb, W. D., 1979. “Logic in the Twenties: The Nature of the Quantifier.” The Journal of Symbolic Logic, 44 (3): 351–368. doi:10.2307/2273128.CrossRefGoogle Scholar
Heck, R., 2010. “Frege and Semantics.” In The Cambridge Companion to Frege, edited by Potter, M. and Ricketts, T., 342–378. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Heck, R. G., and May, R.. 2011. “The Composition of Thoughts.” Noûs, 45 (1): 126–166. doi:10.1111/j.1468-0068.2010.00769.x.CrossRefGoogle Scholar
Kanterian, E., 2012. Frege. A Guide for the Perplexed. London: Continuum.Google Scholar
Kemp, G., 1996. “Frege’s Sharpness Requirement.” The Philosophical Quarterly, 46 (183): 168–184. doi:10.2307/2956385.CrossRefGoogle Scholar
Kemp, G., 1998. “Propositions and Reasoning in Russell and Frege.” Pacific Philosophical Quarterly, 79 (3): 218–235. doi:10.1111/1468-0114.00059.CrossRefGoogle Scholar
Klement, K., 2002. Frege and the Logic of Sense and Reference. Abingdon: Routledge.Google Scholar
Klement, K., 2010. “Gottlob Frege.” In The Routledge Companion to Nineteenth Century Philosophy, edited by Moyar, D., 858–886. Abingdon: Routledge.Google Scholar
Korte, T., 2010. “Frege’s Begriffsschrift as a Lingua Characteristica.” Synthese, 174 (2): 283–294. doi:10.1007/s11229-008-9422-7.CrossRefGoogle Scholar
Linnebo, Ø., 2003. “Frege’s Conception of Logic: From Kant to Grundgesetze.” Manuscrito, 26 (2): 235–252.Google Scholar
Macbeth, D., 2005. Frege’s Logic. Cambridge, MA: Harvard University Press.CrossRefGoogle Scholar
MacFarlane, J., 2000. “What Does it Mean to Say that Logic is Formal?” PhD diss., University of Pittsburgh.Google Scholar
MacFarlane, J., 2002. “Frege, Kant, and the Logic in Logicism.” The Philosophical Review, 111 (1): 25–65. doi:10.1215/00318108-111-1-25.CrossRefGoogle Scholar
Mezzadri, D., 2015. “Frege on the Normativity and Constitutivity of Logic for Thought I.” Philosophy Compass, 10 (9): 583–591. doi:10.1111/phc3.12248.CrossRefGoogle Scholar
Peregrin, J., 2000. “‘Fregean’ Logic and ‘Russellian’ Logic’.” Australasian Journal of Philosophy, 78 (4): 557–574. doi:10.1080/00048400012349801.CrossRefGoogle Scholar
Proops, I., 2007. “Russell and the Universalist Conception of Logic.” Noûs, 41 (1): 1–32. doi:10.1111/j.1468-0068.2007.00635.x.CrossRefGoogle Scholar
Ricketts, T., 1986. “Objectivity and Objecthood: Frege’s Metaphysics of Judgement.” In Frege Synthesized, edited by Haaparanta, L. and Hintikka, J., 65–95. Dordrecht: Reidel.CrossRefGoogle Scholar
Ricketts, T., 1996a. “Logic and Truth in Frege.” Proceedings of the Aristotelian Society, Supp. Vol.70 (1): 121–140. doi:10.1093/aristoteliansupp/70.1.121.CrossRefGoogle Scholar
Ricketts, T., 1996b. “Pictures, Logic, and the Limits of Sense in Wittgenstein’s Tractatus.” In The Cambridge Companion to Wittgenstein, edited by Sluga, H. and Stern, D., 59–99. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Russell, B., 1919. Introduction to Mathematical Philosophy. London: Allen & Unwin.Google Scholar
Simons, P., 1996. “The Horizontal.” In Frege: Importance and Legacy, edited by Schirn, M., 280–300. Berlin: De Gruyter.Google Scholar
Sluga, H., 1980. Gottlob Frege. Abingdon: Routledge.Google Scholar
Sullivan, P. M., 2004. “Frege’s Logic.” In Handbook of the History of Logic, edited by Gabbay, D. M. and Woods, J., 659–750. Vol. 3. Amsterdam: Elsevier BV.Google Scholar
Sullivan, P. M., Forthcoming. “Varieties of Alien Thought.” In The Logical Alien, edited by Miguens, S. and Travis, C.. Cambridge, MA: Harvard University Press.Google Scholar
Tappenden, J., 2005. “Metatheory and Mathematical Practice in Frege.” In Gottlob Frege. Critical Assessments of Leading Philosophers, edited by Beaney, M. and Reck, E., 190–228. Vol. II. Abingdon: Routledge.Google Scholar
Taschek, W. W., 2008. “Truth, Assertion, and The Horizontal. Frege on The 'Essence Of Logic'.” Mind, 117 (466): 375-401. doi: 10.1093/mind/fzn039.CrossRefGoogle Scholar
Textor, M., 2011. Frege on Sense and Reference. Abingdon: Routledge.CrossRefGoogle Scholar
Van Heijenoort, J., 1967. “Logic as Calculus and Logic as Language.” Synthese, 17 (1): 324–330. doi:10.1007/BF00485036.CrossRefGoogle Scholar