What is the Task of Frege’s Criteria of Referentiality?
DOI:
https://doi.org/10.15173/jhap.v14i5.6028Abstract
It is generally assumed that Frege’s solution to the problem of referential indeterminacy in the first volume of Grundgesetze is based on a contextualist conception of reference that is spelt out by his criteria of referentiality. The present paper argues that this assumption is hardly consistent with Frege’s remarks on the task of the criteria in the second volume. They leave no doubt that the criteria are not to be understood as explanations of the concept of reference, but as explanations of the requirement that in the exact sciences all concepts must have sharp boundaries. The crux of the problem of referential indeterminacy is that, to sharply delimit the boundaries of a vague or ambiguous concept, we have almost only concepts at our disposal that also lack sharp boundaries. To solve it, we need a non-inductive method for the complete determination of concepts. It is provided by Frege’s criteria of referentiality. They define a kind of “holistic” method for the complete determination of concepts according to which vague and ambiguous concepts must be completely determined in a reciprocal manner.
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References
Bentzen, Bruno. 2019. “Frege on Referentiality and Julius Caesar in Grundgesetze Section 10.” Notre Dame Journal of Formal Logic 60: 617–37.
Blanchette, Patricia. 2012. Frege’s Conception of Logic. Oxford: Oxford University Press.
———. 2015. “Reply to Cook, Rossberg and Wehmeier.” Journal for the History of Analytic Philosophy 3: 1–13.
Dummett, Michael. 1981. The Interpretation of Frege’s Philosophy. Cambridge: Harvard University Press.
———. 1991a. Frege and Other Philosophers. Oxford: Clarendon Press.
———. 1991b. Frege: Philosophy of Mathematics. London: Duckworth.
Ebert, Philip A., and Marcus Rossberg. 2019. Essays on Frege’s Basic Laws of Arithmetic. Oxford: Oxford University Press.
Ebert, Philip, and Marcus Rossberg. 2019. “Mathematical Creation on Frege’s Grundgesetze.” In Essays on Frege’s Basic Laws of Arithmetic, edited by Philip Ebert and Marcus Rossberg, 325–42. Oxford: Oxford University Press.
Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Louis Nebert.
———. 1884. Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl. Breslau: Koebner.
———. 1892. “Über Sinn und Bedeutung.” Zeitschrift für Philosophie und philosophische Kritik 100: 25–50.
———. 1893. Grundgesetze der Arithmetik (Jena) I.
———. 1903. Grundgesetze der Arithmetik (Jena) II.
———. 1960. The Foundations of Arithmetic: A Logico-Mathematical Enquiry into the Concept of Number. Translated by J. L. Austin. New York: Harper Brothers.
———. 1969. “Ausführungen über Sinn und Bedeutung.” In Posthumous writing. In: Gottlob Frege, Nachgelassene Schriften und Wissenschaftlicher Briefwechsel, edited by H. Hermes, F. Kambartel, and F. Kaulbach, vol. 1, 1:128–36. Hamburg: Meiner.
———. 1976. “Frege and Russell.” In Gottlob Frege, Nachgelassene Schriften und Wissenschaftlicher Briefwechsel, edited by G. Gabriel, H. Hermes, F. Kambartel, C. Thiel, and A. Veraart, vol. 2, 2:212–13. Hamburg: Meiner.
———. 1997a. “Comments on Sinn and Bedeutung.” In The Frege Reader, 172–80.
———. 1997b. “Letter to Russell.” In The Frege Reader, 253–54.
———. 1997c. The Frege Reader. Edited by M. Beaney. Oxford: Blackwell.
———. 2013a. “Basic Laws of Arithmetic, Vol. I.” In Basic Laws of Arithmetic, edited by P. A. Ebert and M. Rossberg, I, 1–253. Oxford: Oxford University Press.
———. 2013b. “Basic Laws of Arithmetic, Vol. II.” In Basic Laws of Arithmetic, edited by P. A. Ebert and M. Rossberg, II, 1–266. Oxford: Oxford University Press.
Greimann, Dirk. 2025. “Frege’s Caesar Problem in Grundlagen and His Demand for the Completeness of Definitions.” History and Philosophy of Logic, 1–14.
Heck, Richard G. 1997. “The Julius Caesar Objection.” In Language, Thought, and Logic: Essays in Honour of Michael Dummett, edited by Richard G. Heck, 273–308. Oxford: Oxford University Press.
———. 2011. Frege’s Theorem. Oxford: Oxford University Press.
———. 2012. Reading Frege’s Grundgesetze. Oxford: Oxford University Press.
Jeshion, Robin. 2001. “Frege’s Notions of Self-Evidence.” Mind 110: 937–76.
———. 2004. “Frege: Evidence for Self-Evidence.” Mind 113: 131–38.
Kemp, Gary. 1996. “Frege’s Sharpness Requirement.” The Philosophical Quarterly 46: 168–84.
———. 2005. “Caesar from Frege’s Perspective.” Dialectica 59: 179–99.
Landini, Gregory. 2012. Frege’s Notations. What They Are and What They Mean. New York: Palgrave Macmillan.
Linnebo, Øystein. 2004. “Frege’s Proof of Referentiality.” Notre Dame Journal of Formal Logic 45: 73–98.
———. 2019. The Context Principle in Frege’s Grundgesetze.
Quine, Willard Van Orman. 1963. Set Theory and Its Logic. Cambridge: Harvard University Press.
———. 1968. “Epistemology Naturalized.” In Ontological Relativity and Other Essays, 69–90. New York: Columbia University Press.
Schirn, Matthias. 2003. “Fregean Abstraction, Referential Indeterminacy and the Logical Foundations of Arithmetic.” Erkenntnis 59: 203–32.
———. 2018. “The Semantics of Value-Range Names and Frege’s Proof of Referentiality.” The Review of Symbolic Logic 11: 224–78.
Sluga, Hans. 1980. Frege. London: Routledge and Kegan Paul.
Wehmeier, Kai. 2015. “Critical Remarks on Frege’s Conception of Logic by Patricia Blanchette.” Journal for the History of Analytical Philosophy 3: 1–9.
Weiner, Joan. 2007. “What’s in a Numeral? Frege’s Answer.” Mind 116: 677–716.
———. 2019. “Why Does Frege Care Whether Julius Caesar Is a Number? Section 10 of Grundgesetze and the Context Principle.” In Essays on Frege’s Basic Laws of Arithmetic, edited by P. A. Ebert and M. Rossberg, 115–41. Oxford: Oxford University Press.
———. 2021. Taking Frege at His Word. Oxford: Oxford University Press.
Wright, Crispin. 2019. “How Did the Serpent of Inconsistency Enter Frege’s Paradise?” In Essays on Frege’s Basic Laws of Arithmetic, 411–36.
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