# Mathematics and Forms of Life

## DOI:

https://doi.org/10.15845/nwr.v4i0.3357## Keywords:

Mathematics, form of life, Wittgenstein Ludwig## 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’.

## 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.

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