Is Frege’s Impasse concerning Predicative Functions Shared by Aristotle and Wittgenstein?

Virginia M. Giouli

doi:10.13135/2704-8195/9220

Virginia M. Giouli University of Reading https://orcid.org/0000-0002-1923-4769

DOI: https://doi.org/10.13135/2704-8195/9220

Keywords: Realism/Non-realism argument, Square of oppositions, Wittgenstein, Aristotle's Anti-realism

Abstract

The idea of rejecting a certain form of transcendental realism fits perfectly with Wittgenstein’s and Aristotle’s anti-realistic account of the world, and may serve in a humanly accessible form of realism to implement the resolution of Frege’s epistemological impasses. Frege has taught us that it is possible to discover reality solely through the use of reason. Aristotle and Wittgenstein, on the other hand, have warned us that any such attempt at discovery is fraught with difficulty; it is the task of thinkers to painfully (even frustratingly) seek to uncover the order and laws underlying what really exists in the world. Frege’s rationality is finally seen to be decreasing, as it takes refuge in meanings of concepts and results in his almost total silence as regards their predicative functions. Able, if reluctant, to understand the way out of the impasse in that there can be no other criteria than the ordinary ones for what is habitually done, the way suggested by Aristotle’s use of the “square of oppositions”, Frege paves the way for a philosophical understanding of Aristotle’s and Wittgenstein’s rejection of a robust form of realism in favour of a less demanding form of it.

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Author Biography

Virginia M. Giouli, University of Reading

Dr Virginia M. Giouli, born in Athens, Greece, studied Ancient Greek Literature and Philosophy at the National and Kapodistrian University of Athens. Having gained her Ph.D. in Philosophy at the University of Reading, U.K., she is a member of many international Societies for Philosophy and a collaborator of International Philosophical Journals. Giouli, referred to as the “researcher of the logically impossible”, is a member of the Onassis Scholars’ Association. She has taught Philosophy in the National and Kapodistrian University of Athens. As an internationally respected figure in the field of philosophy, she has been invited to nominate candidates for the Kyoto Prize in Arts and Philosophy, presented by the Inamori Foundation, Kyoto, Japan. Her angle on the logically impossible has been elaborated in many languages, in a long series of publications, monographs and papers presented at International Congresses. Her Work follows Plato’s idea of τιθήνη (nurturer or mother of becoming), thus in turn recreating the historical flux of ideas. Her interests include the transhuman, transgender studies, post-apocalyptic notions, Marxism, and the digital mind. These link up with Aristotle’s “craftsmanship” model which is mirrored in her own philosophical account of the world.

References

Ackrill, John Lloyd. 1972-1973. “Aristotle’s Definitions of ‘Psyche’”. Proceedings of the Aristotelian Society 73: 119-133.

Aristotle. 1984a. De Interpretatione. Prior Analytics. Posterior Analytics. Physics in The Complete Works of Aristotle, Barnes Jonathan, edited by. Princeton: Princeton University Press.

Aristotle. 1984b. Politics in The Complete Works of Aristotle, Barnes Jonathan, edited by. Princeton: Princeton University Press.

Ayer, Alfred Jules. 1972. Bertrand Russell. Chicago and London: The University of Chicago Press.

Ayer, Alfred Jules. 1973. The Central Questions of Philosophy. Harmondsworth: Penguin.

Ayer, Alfred Jules. 1975. “Self-evidence” in Phenomenology and Philosophical Understanding, Pivčević Edo, edited by, 79-92. Cambridge: Cambridge University Press.

Ayer, Alfred Jules. 1982. Philosophy in the Twentieth Century. London: Unwin Hyman Ltd.

Burke, T. E. 1983. The philosophy of Popper. Manchester: Manchester University Press.

Burke, T. E. 1988. “Science as Conjecture and Refutation.” in An Encyclopaedia of Philosophy, Parkinson G.H.R., Burke T.E., Cottingham J.G., Proudfoot M.A., Tiles J.E., edited by, 205-224. London and New York: Routledge.

Burke, T. E. 1995. Questions of Belief. Hants: Avebury.

Burke, T. E. 2000. The Philosophy of Whitehead. London: Greenwich Exchange.

Caston, Victor. 1993. “Aristotle and Supervenience.” Southern Journal of Philosophy 31: 107-135.

Charles, David. 1984. Aristotle’s Philosophy of Action. London: Duckworth.

Charles, David. 1988. “Aristotle on Hypothetical Necessity and Irreducibility” in Pacific Philosophical Quarterly 69: 1-53.

Charles, David. 1997. “Method and Argument in the Study of Aristotle, A Critical Notice of The Cambridge Companion to Aristotle” in Oxford Studies in Ancient Philosophy 15: 231-257.

Charles, David. 2000. Aristotle on Meaning and Essence. Oxford: Clarendon Press.

Charles, David. 2003. “Wittgenstein’s Builders and Aristotle’s Craftsmen” in Perspectives on Greek Philosophy. Sharples R.W., edited by, 103-126. Hampshire: Ashgate.

Charles, David. 2009. “Aristotle’s Psychological Theory” in Proceedings of the Boston Area Colloquium in Ancient Philosophy vol. 24, Cleary John, Gurtler Gary, edited by, 1-29. Leiden: Brill.

Charles, David. 2010. Definition in Greek Philosophy. Oxford: Oxford University Press.

Charles, David. 2010. “The Paradox in the Meno and Aristotle’s Attempts to Resolve It” in Definition in Greek Philosophy, Charles David, edited by, 115-150. Oxford: Oxford University Press. Cobb-Stevens, Richard. 1990. Husserl and Analytic Philosophy. Dordrecht, Boston, London: Kluwer Academic Publishers.

Cottingham, John. 1984. Rationalism. Wintle Justin, edited by. London: Paladin Books, Granada Publishing Ltd.

Crivelli, Paolo. 1996. “Notes on Aristotle’s Conception of Truth.” in Οδοί Διζήσιος: Le vie della Ricerca. Studi di onore di Francesco Adorno, Funghi M. S., edited by, 147-159. Firenze.

Dummett, Michael. 1955. “The Context Principle Centre of Frege’s Philosophy” in Logik und Mathematik, Ingolf Max, Werner Stelzner, edited by, 3-19. Berlin: de Gruyter.

Dummett, Michael. 1981a. The Interpretation of Frege’s Philosophy. London: Duckworth.

Dummett, Michael. 1981b. Frege. Philosophy of Language. Cambridge, MA: Harvard University Press.

Frege, Gottlob. 1879. Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle: Verlag von Louis Nebert.

Frege, Gottlob. 1891. Function und Begriff. Jena.

Frege, Gottlob. 1892. “Über Sinn und Bedeutung”. Zeitschrift für Philosophie und Philosophische Kritik 100: 25-50.

Frege, Gottlob. 1893. Grundgesetze der Arithmetik. Jena: Hermann Pohle.

Frege, Gottlob. 1903. “Über die Grundlagen der Geometrie”. Jahresbericht der Deutschen Mathematiker-Vereinigung: 319-324 and 368-375.

Frege, Gottlob. 1953. The Foundations of Arithmetik [Die Grundlagen der Arithmetik]. Engl. tr. J. L. Austin. Oxford: Blackwell.

Frege, Gottlob. 1969a. “Logik” in Nachgelassene Schriften, Hermes H., Kambartel F., Kaulbach F., edited by, 137-163. Hamburg: Felix Meiner.

Frege, Gottlob. 1969b. “Booles rechnende Logik und die Begriffsschrift” in Nachgelassene Schriften, Hermes H., Kambartel F., Kaulbach F., edited by, 9-53.

Frege, Gottlob. 2013. Basic Laws of Arithmetic [Grundgesetze der Arithmetik]. Engl. tr. P.A. Ebert, M. Rossberg. Oxford: Oxford University Press.

Giouli, Virginia. 2012a. The Taming of Power: A Christian Critique of Theories of Historical Development. Athens: Publications of The Hellenic Society for Philosophical Studies.

Giouli, Virginia. 2012b. How is Social Science Possible? An Aristotelian Critique of Normativism in Sociological Methodology. Athens: Livanis.

Giouli, Virginia. 2020a. “Ryoji Ikeda’s Art-work exemplifies Aristotle’s Account of the World as a Mathematical Proposition”. Logoi.ph VI, n. 16: 121-131.

Giouli, Virginia. 2020b. “The Body-Mind Problem in Aristotle’s Philosophy of Time.” Episteme 11: 87- 101.

Giouli, Virginia. 2020c. “The Individual, Powers and the Idea of Punishment in Aristotle”. Società e diritti 5 n. 10: 183-196.

Giouli, Virginia. 2021. “The True Objects of Knowledge in Plato and Wittgenstein”. Episteme 12: 43-59.

Giouli, Virginia. 2022a. The Imaginary in Vizyenos’ Philosophy; Ancient and Modern Components. Athens: Govostis.

Giouli, Virginia. 2022b. “Aristotle’s Non-realistic Account of the World”. Chôra 20: 267-290.

Giouli, Virginia. 2022c. “Is Aristotle’s Psychology Wittgenstein’s? Sociological Methodology and Schizophrenic Mind; Scientific Methodology and Computational Mind”. Episteme 13: 37-78.

Giouli, Virginia. 2023. “Aristotle’s Material Reductionist Account of History of Philosophy”. S&F 29: 151-167.

Hacker, Peter. 1996. Wittgenstein’s Place in Twentieth-Century Analytic Philosophy. London: Blackwell.

Hacker, Peter. 2003. “Wittgenstein, Carnap and the New American Wittgensteinians”. Philosophical Quarterly 53: 1-23.

Hintikka, Jaakko. 1975. The Intentions of Intentionality and Other New Models for Modalities. Dordrecth/Boston: Reidel.

Hintikka, Merrill B., and Jaakko Hintikka. 1989. Investigating Wittgenstein. Oxford: Blackwell.

Leszl, Walter. 1981. “Mathematics, Axiomatization, and the Hypotheses” in Aristotle on Science: The Posterior Analytics: Proceedings of the Eighth Symposium Aristotelicum, Berti E., edited by, 271-328. Padova: Editrice Antenore.

Linnebo, Øystein. 2018. Thin Objects: An Abstractionist Account. Oxford: Oxford University Press.

Moutsopoulos, Evanghelos. 1975. Ideas. Athens: Hermes.

Parsons, Terence. 2021. “The Traditional Square of Opposition” in The Stanford Encyclopedia of Philosophy, Zalta Edward N., edited by. Fall 2021. https://plato.stanford.edu/archives/ fall2021/entries/square/

Pivčević, Edo. 1975. “Concepts, Phenomenology and Philosophical Understanding” in Phenomenology and Philosophical Understanding, Pivčević Edo, edited by, 271-286. Cambridge: Cambridge University Press.

Rothschild, Daniel. 2012. “Expressing Credences”. Proceedings of the Aristotelian Society CXII, n. 1: 99-114.

Whitehead, Alfred North. 1926. Science and the Modern World. Cambridge: At the University Press.

Wittgenstein, Ludwig. 1953. Philosophical Investigations. Anscombe G. E. M., Rhees R., edited by. Eng. tr. G. E. M. Anscombe. Oxford: Basil Blackwell.

Wittgenstein, Ludwig. 1961. Tractatus Logico-Philosophicus. Engl. tr. D. F. Pears, B. F. McGuinness. London: Routledge and Kegan Paul.

Wittgenstein, Ludwig. 1966. Lectures and Conversations. Barrett Cyril, edited by. Oxford: Basil Blackwell.

Wittgenstein, Ludwig. 1979. Notebooks 1914-1916. von Wright G.H., Anscombe G.E.M., edited by. Engl. tr. G.E.M. Anscombe. Oxford: Blackwell.

Wittgenstein, Ludwig. 1982. “MS 107” in von Wright, Georg Henrik, Wittgenstein. Oxford: Blackwell.

Zacharopoulou, Katerina. 2021. “Poetics of Digital Art; Charles Sandison, The Garden of Light” in The Era of the Images, https://sandison.fi.