Mathematics and Forms of Life

Main Article Content

Severin Schroeder

Abstract

According to Wittgenstein, mathematics is embedded in, and partly constituting, a form of life. Hence, to imagine different, alternative forms of elementary mathematics, we should have to imagine different practices, different forms of life in which they could play a role. If we tried to imagine a radically different arithmetic we should think either of a strange world (in which objects unaccountably vanish or appear) or of people acting and responding in very peculiar ways. If such was their practice, a calculus expressing the norms of representation they applied could not be called false. Rather, our criticism could only be to dismiss such a practice as foolish and to dismiss their norms as too different from ours to be called ‘mathematics’.

Section
Special Issue
Author Biography

Severin Schroeder, University of Reading

Severin Schroeder is Associate Professor in Philosophy at the University of Reading. He has written three monographs on Wittgenstein: Wittgenstein: The Way Out of the Fly Bottle (2006), Wittgenstein Lesen (2009), and Das Privatsprachen-Argument (1998). He is the editor of Wittgenstein and Contemporary Philosophy of Mind (Palgrave 2001) and Philosophy of Literature (Wiley-Blackwell 2010). He is currently working on a book on Wittgenstein’s philosophy of mathematics (Routledge).​

References

Rhees, R., 1970. “On Continuity: Wittgenstein’s Ideas, 1938”. In his Discussions of Wittgenstein. London: Routledge, pp. 104-57.

Schroeder, S., 2014. “Mathematical Propositions as Rules of Grammar”. In Grazer Philosophische Studien 89, pp. 23-38.

Wittgenstein, L., 1961. Tractatus Logico-Philosophicus. Translated by D. F. Pears and B. F. McGuinness. London: Routledge & Kegan Paul. [TLP]

Wittgenstein, L.1976. Wittgenstein’s Lectures on the Foundations of Mathematics: Cambridge, 1939. Edited by Cora Diamond. Hassocks, Sussex: Harvester Press. [LFM]

Wittgenstein, L., 1978. Remarks on the Foundations of Mathematics. Third Edition. Edited by G. H. von Wright, Rush Rhees and G. E. M. Anscombe. Translated by G. E. M. Anscombe. Oxford: Blackwell. [RFM]

Wittgenstein, L., 1982. Last Writings on the Philosophy of Psychology. Vol. 1. Edited by G.H. von Wright & H. Nyman. Translated by C.G. Luckhardt & M.A.E. Aue. Oxford: Blackwell. [LW I]

Wittgenstein, L., 2009. Philosophical Investigations. Fourth Edition. Edited by P. M. S. Hacker and Joachim Schulte. Translated by G. E. M. Anscombe, P. M. S. Hacker and Joachim Schulte. Oxford: Wiley-Blackwell. [PI]

Wittgenstein, L., 2009. “Philosophy of Psychology — A Fragment” [formerly called “PI Part II”], in: PI. [PPF]

Wright, C., 1980. Wittgenstein on the Foundations of Mathematics. Cambridge, Mass.:Harvard University Press.