Strictures on an Exhibition

Frege on his Primitive Laws


  • Alexander Robert Yates University of St Andrews/University of Stirling



In Grundgesetze der Arithmetik, Frege tried to show that arithmetic is logical by giving gap-free proofs from what he took to be purely logical basic laws. But how do we come to judge these laws as true, and to recognize them as logical? The answer must involve giving an account of the apparent arguments Frege provides for his axioms. Following Sanford Shieh, I take these apparent arguments to instead be exhibitions: the exercise of a logical capacity in order to bring us into a state of judgement. I provide an account of what sort of inferential capacities are at play in such exhibitions, and explain how they lead us to judge that Frege’s primitive laws are general and undeniable. I will also situate my account with respect to other rival interpretations, particularly the elucidatory interpretations of Joan Weiner and Thomas Ricketts.

Author Biography

Alexander Robert Yates, University of St Andrews/University of Stirling

University of St Andrews/University of Stirling. PhD completed.


Antonelli, Aldo and Robert May, 2000. “Frege’s New Science.” Notre Dame Journal of Formal Logic 31: 242–70.

Baker, Gordon and Peter Hacker, 1984. Frege: Logical Excavations. Oxford: Blackwell.

Bell, David, 1981. “The Place of the Grundlagen in Frege’s Development.” Philosophical Quarterly 31(124): 209–24.

Blanchette, Patricia A., 2012. Frege’s Conception of Logic. Oxford: Oxford University Press.

Burge, Tyler, 1998. “Frege on Knowing the Foundation.” In Burge (2005), pp. 317–55.

———, 2005. Truth, Thought, Reason: Essays on Frege. Oxford: Oxford University Press.

Chomsky, Noam, 1965. Aspects of the Theory of Syntax. Cambridge, MA: MIT Press.

Dummett, Michael, 1973. Frege: Philosophy of Language. London: Duckworth.

———, 1981. The Interpretation of Frege’s Philosophy. London: Duckworth.

———, 1991a. Frege and other Philosophers. Oxford: Clarendon Press.

———, 1991b. Frege: Philosophy of Mathematics. Cambridge, MA: Harvard University Press.

Ebert, Philip A. and Marcus Rossberg, eds., 2019. Essays on Frege’s Basic Laws of Arithmetic. Oxford: Oxford University Press.

Frege, Gottlob, 1879 [1967]. “Begriffsschrift.”: 3–82.

———, 1879 [1997]. “Begriffsschrift Selections.” In Frege (1997), pp. 47–78.

———, 1879-91 [1979]. “Logic.” In Frege (1979), pp. 1–8.

———, 1880-81 [1979]. “Boole’s Logical Calculus and the Concept-Script.” In Frege (1979), pp. 9–46.

———, 1884 [1953]. The Foundations of Arithmetic, Second revised edition. Oxford: Blackwell.

———, 1885 [1984]. “On Formal Theories of Arithmetic.” In Frege (1984), pp. 112–21.

———, 1891 [1984]. “Function and Concept.” In Frege (1984), pp. 137–56.

———, 1892 [1984]. “On Sense and Meaning.” In Frege (1984), pp. 157–77.

———, 1893 [2013]. “Basic Laws of Arithmetic, volume I.”. In Frege (2013).

———, 1897 [1984]. “On Mr. Peano’s Conceptual Notation and My Own.” In Frege (1984), pp. 234–48.

———, 1897 [1984]. “Logic: Extract.” In Frege (1997), pp. 227–50.

———, 1899 [1980]. “Letter to Hilbert, 27 December 1899.” In Frege (1980), pp. 34–38.

———, 1899-1906 [1979]. “On Euclidean Geometry.” In Frege (1979), pp. 167–69.

———, 1903 [2013]. “Basic Laws of Arithmetic volume II.”. In Frege (2013).

———, 1903 [1984]. “On the Foundations of Geometry: First Series.” In Frege (1984), pp. 273–84.

———, 1906 [1979]. “17 Key Sentences on Logic.” In Frege (1979), pp. 174–75.

———, 1906 [1984]. “On the Foundations of Geometry: Second Series.” In Frege (1984), pp. 293–340.

———, 1914 [1979]. “Logic in Mathematics.” In Frege (1979), pp. 203–50.

———, 1918 [1984]. “Logical Investigations I: Thoughts.” In Frege (1984), pp. 351–72.

———, 1919 [1979]. “Notes for Ludwig Darmstadter.” In Frege (1979).

———, 1979. Posthumous Writings, edited by Hans Hermes, Friedrich Kambartel and Friedrich Kaulbach. Chicago: University of Chicago Press.

———, 1980. Philosophical and Mathematical Correspondence, edited by Gottfried Gabriel, Hans Hermes, Friedrich Kambartel, Christian Thiel and Albert Veraart. Chicago: University of Chicago Press.

———, 1984. Collected Papers on Mathematics, Logic, and Philosophy, edited by Brian McGuinness. Oxford: Blackwell.

———, 1997. The Frege Reader, edited by Michael Beaney. Oxford: Blackwell.

———, 2013. Basic Laws of Arithmetic, translated by Philip Ebert and Marcus Rossberg. Oxford: Oxford University Press.

Gabbay, Dov M. and John Woods, eds., 2004. Handbook of the History of Logic. Oxford: Elsevier.

Glanzberg, Michael, ed., 2018. The Oxford Handbook of Truth. Oxford: Oxford University Press.

Haaparanta, Leila, 1985. “Frege’s Doctrine of Being.” Acta Philosophica Fennica 39: 1–182.

Heck, Richard Kimberly, 2012. Reading Frege’s Grundgesetze. Oxford: Oxford University Press.

Heck, Richard Kimberly and Robert May, 2018. “Truth in Frege.” In Glanzberg (2018), pp. 193–215.

Kemp, Gary, 1995. “Truth in Frege’s ‘Law of Truth’.” Synthese 105(1): 31–51.

Klement, Kevin, 2002. Frege and the Logic of Sense and Reference. New York: Routeledge.

Kremer, Michael, 2000. “Judgment and Truth in Frege.” Journal of the History of Philosophy 38(4): 549–81.

Levine, James, 2002. “Analysis and Decomposition in Frege and Russell.” The Philosophical Quarterly 52(207): 195–216.

Linnebo, Øystein, 2003. “Frege’s Conception of Logic: From Kant to Grundgesetze.” Manuscrito 26(2): 235–52.

MacFarlane, John, 2002. “Frege, Kant, and the Logic in Logicism.” The Philosophical Review 111(1): 25–65.

Mezzadri, Daniele, 2015. “Frege on the Normativity and Constitutivity of Logic for Thought, I.” Philosophy Compass 10(9): 583–91.

———, 2018. “Logic, Judgment, and Inference: What Frege Should Have Said about Illogical Thought.” Journal of the History of Philosophy 7(4): 727–46.

Milne, Peter, 2010. “Frege’s Folly: Bearerless Names and Basic Law V.” In Potter and Ricketts (2010).

Pedriali, Walter, 2019. “When Logic Gives Out: Frege on Basic Logical Laws.” In Ebert and Rossberg (2019), pp. 57–89.

Pelletier, Francis, 2001. “Did Frege Believe Frege’s Principle?.” Journal of Logic, Language, and Information 10: 81–114.

Potter, Michael and Thomas Ricketts, eds., 2010. The Cambridge Companion to Frege. Cambridge: Cambridge University Press.

Proops, Ian, 2007. “Russell and the Universalist Conception of Logic.” Noûs 41(1): 1–32.

Ricketts, Thomas, 1996. “Logic and Truth in Frege.” Proceedings of the Aristotelian Society: Supplementary Volume 70: 121–40.

Ricketts, Thomas, 1997. “Truth-Values and Courses-of-Value in Frege’s Grundgesetze.” In Early Analytic Philosophy, edited by William Tait. Chicago: Open Court.

Shieh, Sanford, 2019. Necessity Lost: Modality and Logic in Early Analytic Philosophy. Oxford: Oxford University Press.

Sluga, Hans, 1977. “Frege’s Alleged Realism.” Inquiry 20: 227–42.

Sluga, Hans D., 1980. Gottlob Frege. New York: Routledge.

Stanley, Jason, 1996. “Truth and Metatheory in Frege.” Pacific Philosophical Quarterly 77(1): 45–71.

Steinberger, Florian, 2017. “Frege and Carnap on the Normativity of Logic.” Synthese 194: 143–62.

Stroud, Barry, 1979. “Inference, Belief, and Understanding.” Mind 88(305): 179–96.

Sullivan, Peter, 2004. “Frege’s Logic.” In Gabbay and Woods (2004), pp. 659–750.

———, 2010. “Dummett’s Frege.” In Potter and Ricketts (2010), pp. 86–117.

Taschek, William, 2008. “Truth, Assertion, and the Horizontal: Frege on ‘The Essence of Logic’.” Mind 117(466): 375–401.

van Heijenoort, Jean, ed., 1967. From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1932. Cambridge, MA: Harvard University Press.

Weiner, Joan, 1990. Frege in Perspective. Ithaca, NY: Cornell University Press.

———, 2005. “Semantic Descent.” Mind 114(454): 321–54.

———, 2010. “Understanding Frege’s Project.” In Potter and Ricketts (2010), pp. 32–62.