Notions of Existence in Frege


  • Dolf Rami Ruhr-Universität Bochum



In this paper, I aim to present the main components of my non-standard interpretation of Frege’s views on existence to the English-speaking public (Rami 2017a, 2018, 2019a,b). First, I will outline the standard interpretation and show how to a great but not full extent the standard interpretation can be justified on the basis of Frege’s writings. Second, I show that the main error of the standard interpretation consists in the assimilation of the contents of the ordinary language expressions “exist” (“existiert”) and “there is” (“es gibt”) according to Frege. Third, I evaluate possible sources for this unfounded assimilation. After that, I outline my alternative interpretation that distinguishes in opposition to other non-standard interpretations between a substantive and a deflationary part of Frege’s complete conception of existence in analogy to Frege’s analysis of truth and negation. Fifthly, I justify my interpretation by the reconstruction of a so far overlooked master argument of Frege against the above-mentioned assimilation. In the last section, I introduce and discuss five objections against my interpretation that came to my attention.


Aristotle, 1984. The Complete Works of Aristotle, Volumes I and II, edited by Jonathan Barnes. Princeton, NJ: Princeton University Press.

Beaney, Michael, 1996. Frege: Making Sense. London: Duckworth.

Bencivenga, Ermanno, 2002. “Free Logic.” In Handbook of Philosophical Logic, Volume 3, edited by Dov M. Gabbay and Franz Guenthner, pp. 373–426. Dordrecht: Springer.

Crane, Tim, 2013. Objects of Thought. Oxford: Oxford University Press.

Currie, Gregory, 1982. Frege: An Introduction to His Philosophy. Brighton: Harvester Press.

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

Frege, Gottlob, 1879. Begriffsschrift. Halle: Nebert.

———, 1880/81. “Booles rechnende Logik und die Begriffsschrift.” In Frege (1969), pp. 9–52.

———, 1882. “Booles logische Formelsprache und meine Begriffsschrift.” In Frege (1969), pp. 53–59.

———, 1884a. Grundlagen der Arithmetik. Breslau: Koebner.

———, 1884b. “Dialog mit Pünjer über Existenz.” In Frege (1969), pp. 60–75.

———, 1891/92. “Über den Begriff der Zahl.” In Frege (1969), pp. 81–127.

———, 1892a. In Frege (2021), pp. 126–37.

———, 1892b. “Über Sinn und Bedeutung.” In Frege (2021), pp. 107–25.

———, 1895. “Kritische Beleuchtung einiger Punkte in E. Schröders Vorlesungen über die Algebra der Logik.” In ?, pp. 92–112.

———, 1893. Grundgesetze der Arithmetik. I. Band. Jena: Hermann Pohle.

———, 1897. “Logik.” In Frege (1969), pp. 137–63.

———, 1903. “Über die Grundlagen der Geometrie II.” Jahresbericht der Deutschen Mathematiker-Vereinigung 12: 368–75.

———, 1906a. “Einleitung in die Logik.” In Frege (1969), pp. 201–12.

———, 1906b. “Kurze Übersicht meiner logischen Einsichten.” In Frege (1969), pp. 213–18.

———, 1910/11. “Vorlesungen über Begriffsschrift.” History and Philosophy of Logic 17: 1–48.

———, 1914. “Logik in der Mathematik.” In Frege (1969), pp. 219–70.

———, 1915. “Meine grundlegenden logischen Einsichten.” In Frege (1969), pp. 271–72.

———, 1918. “Der Gedanke.” In Frege (2021), pp. 218–32.

———, 1919. “Verneinung.” In Frege (2021), pp. 198–217.

———, 1953. The Foundations of Arithmetic. A Logico-mathematical Enquiry into the Concept of Number, Second edition, edited by J. L. Austin. Oxford: Blackwell.

———, 1969. Nachgelassene Schriften, edited by Hans Hermes, Friedrich Kambartel and Friedrich Kaulbach. Hamburg: Meiner.

———, 1976. Wissenschaftlicher Briefwechsel, edited by Gottfried Gabriel, Hans Hermes, Friedrich Kambartel and Albert Veraart. Hamburg: Meiner.

———, 1979. Posthumous Writings, translated by Peter Long and Roger White, edited by Hans Hermes, Friedrich Kambartel and Friedrich Kaulbach. Chicago: University of Chicago Press.

———, 2007. The Foundations of Arithmetic, edited by Dale Jacquette. London: Longman.

———, 2021. Ausgewählte Schriften zur Philosophie der Logik und der Sprache, edited by Dolf Rami. Göttingen: Vandenhoeck & Ruprecht.

Gabriel, Gottfried and Sven Schlotter, 2017. Frege und die kontinentalen Ursprünge der analytischen Philosophie. Munich: mentis.

Green, Karen, 2015. “Frege on Existence and Non-existence.” Theoria 81: 293–310.

Grice, H. P., 1975. “Logic and Conversation.” In The Logic of Grammar, edited by Donald Davidson and Gilbert Harman, pp. 64–75. Encino, CA: Dickenson.

Haefliger, Gregor, 1994. Über Existenz: Die Ontologie Roman Ingardens. Dordrecht: Kluwer.

Haaparanta, Leila, 1985. Frege’s Doctrine of Being. Helsinki: Acta Philosophica Fennica, Vol. 39.

———, 1986a. “On Frege’s Concept of Being.” In Frege Synthesized, edited by Leila Haaparanta and Jaakko Hintikka, pp. 155–74.

———, 1986b. “Frege on Existence.” In Knuuttila and Hintikka (1985), pp. 269–89.

———, 2012. “On “Being” and Being: Frege between Carnap and Heidegger.” In Categories of Being: Essays on Metaphysics and Logic, edited by Leila Haaparanta and Heikki J. Koskinen, pp. 319–37. New York: Oxford University Press.

———, 2020. “Frege on “Es gibt”, Being in a Realm, and

(Meta-)Ontology.” In Metametaphysics and the Sciences: Historical and Philosophical Perspectives, edited by Frode Kjosavik and Camilla Serck-Hanssen, pp. 81–98. New York: Routledge.

Hintikka, Jaakko, 1986. “Kant, Existence, Predication and the Ontological Argument.” In Knuuttila and Hintikka (1985), pp. 249–68.

Horn, Laurence R., 1984. “A New Taxonomy for Pragmatic Inference: Q-based and R-based Implicature.” In Meaning, Form and Use in Context, edited by Deborah Schiffrin, pp. 11–42. Washington, DC: Georgetown University Press.

———, 1989. A Natural History of Negation. Chicago: University of Chicago Press.

Kant, Immanuel and Gottlob Benjamin Jäsche, 1800/1920. Immanuel Kants Logik. Ein Handbuch zu Vorlesungen. Leipzig: Meiner.

Kenny, Anthony, 1995. Frege: An Introduction to the Founder of Modern Analytic Philosophy. Oxford: Blackwell.

Knuuttila, Simo and Jaakko Hintikka, eds., 1985. The Logic of Being. Dordrecht: Reidel.

Kripke, Saul A., 2013. Reference & Existence. Oxford: Oxford University Press.

Künne, Wolfgang, 2010. Die Philosophische Logik Gottlob Freges. Frankfurt: Klostermann.

Lehmann, Scott, 2002. “More Free Logic.” In Handbook of Philosophical Logic, Second edition, Volume 5, edited by Dov M. Gabbay and Franz Guenthner, pp. 197–259. Dordrecht: Springer.

Levinson, Stephen C., 1983. Pragmatics. Cambridge: Cambridge University Press.

Lotze, Hermann, 1874/1989. Logik. Erstes Buch. Vom Denken, edited by Gottfried Gabriel. Hamburg: Meiner.

Mendelsohn, Richard, 2005. The Philosophy of Gottlob Frege. Cambridge: Cambridge University Press.

Miller, Barry, 2000. The Fullness of Being. A New Paradigm for Existence. Notre Dame: University of Notre Dame Press.

Moore, G. E., 1936. “Is Existence a Predicate?” Proceedings of the Aristotelian Society, Supplementary Volumes 15: 175–88.

Priest, Graham, 2009. “Not to Be.” In The Routledge Companion to Metaphysics, edited by Robin Le Poidevin, Peter Simons, Andrew McGonigal and Ross Cameron, pp. 234–45. London: Routledge.

Quine, W. V. O., 1948. “On What There is.” Review of Metaphysics 2: 21–36.

———, 1960. Word & Object, New Edition. Cambridge, MA: MIT Press.

Russell, Bertrand and Alfred North Whitehead, 1910. Principia Mathematica, Vol. 1. Cambridge: Cambridge University Press.

Russell, Bertrand, 1918/1985. The Philosophy of Logical Atomism. London: Routledge.

Rami, Dolf, 2014. “Existence as a Property of Individuals.” Erkenntnis 79: 503–23.

———, 2017a. “Existenz.” In Handbuch für Metaphysik, edited by Markus Schrenk. Berlin: Springer.

———, 2017b. “Drei Varianten des Paradoxons der Nicht-Existenz.” Deutsche Zeitschrift für Philosophie 65(4): 657–89.

———, 2018. Existenz und Anzahl. Eine kritische Untersuchung zu Freges Konzeption der Existenz. Paderborn: mentis.

———, 2019a. “Precis zu Existenz und Anzahl.” Zeitschrift für Philosophische Forschung 73(3): 411–17.

———, 2019b. “Repliken.” Zeitschrift für Philosophische Forschung 73(3): 429–34.

———, 2020. “Single-Domain Free Logic and the Problem of Compositionality.” Synthese online first.

Rautenberg, Wolfgang, 2010. A Concise Introduction to Mathematical Logic. New York: Springer.

Rosefeldt, Tobias, 2019. “Alles existiert.” Zeitschrift für Philosophische Forschung 73(3): 423–28.

Schröder, Ernst, 1890. Vorlesungen über die Algebra der Logik. (exakte Logik). erster Band. Leipzig: Teubner.

———, 1891. Vorlesungen über die Algebra der Logik. (exakte Logik). zweiter Band. Leipzig: Teubner.

Sluga, Hans, 1980. Gottlob Frege. London: Routledge.

Stuhlmann-Laeisz, Rainer, 1975. “Freges Auseinandersetzung mit der Auffassung von “Existenz” als einem Prädikat der ersten Stufe und Kants Argumentation gegen den ontologischen Gottesbeweis.” In Frege und die moderne Grundlagenforschung, edited by Christian Thiel, pp. 119–33. Meisenheim: Verlag Anton Hain.

van Inwagen, Peter, 2008. “McGinn on Existence.” Philosophical Quarterly 58(230): 36–58.

Wiggins, David, 1995. “The Kant-Frege-Russell-View of Existence: Toward the Rehabilitation of the Second-Level View.” In Modality, Morality and Belief, edited by Walter Sinnott-Armstrong, Diana Raffman and Nicholas Asher, pp. 93–113. Cambridge: Cambridge University Press.

Williams, C. J. F., 1981. What is Existence? Oxford: Oxford University Press.