On Certainty and the Philosophy of Mathematics

Chenbei Xiao (University of Vienna)

Abstract: 

Daniele Moyal-Sharrock attributes to Wittgenstein what I will call a 'radically non-epistemic view of mathematics and certainties'. According to this view, Wittgenstein holds that mathematical sentences as well as certainties:

1. are true at most in an entirely empty sense and thus are not propositions;
2. they cannot be justified;
3. they are prior to empirical knowledge;
4. they are ineffable, i.e. they cannot be uttered in a meaningful way;
5. their primary function is semantic: they define the meaning of terms.

(Other authors, e.g. Marie McGinn, have defended somewhat similar interpretations -- though McGinn's acceptance of (4) is less clear.) I shall criticise the radically non-epistemic view of mathematics and certainties and develop an alternative interpretation of the relevant texts by Wittgenstein point by point: mathematical sentences as well as certainties are true and are propositions; some of them can be justified; in some important senses they are not prior to empirical knowledge; they are not ineffable; and their function is not only semantic but also epistemic. It seems appropriate to call this alternative the 'epistemic view of mathematics and certainties'.

About the speaker:

Martin Kusch is Professor of Philosophy of Science and Epistemology at the University of Vienna. Prior to taking up this appointment in 2009, he was Professor of Philosophy and Sociology of Science at the Department of History and Philosophy of Science at Cambridge University. His books include Knowledge by Agreement (2002) and A Sceptical Guide to Meaning and Rules(2006). He is currently writing a book on Wittgenstein's views on knowledge, relativism and scepticism.

Followed by a wine reception.

The event is free, but registration is required. Please email [email protected] 

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