# Rigour in Proof

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## Abstract

Rigour in proof is of utmost importance for the pluralist, since he has no solid ontology to ground his theory, and his conception of ‘truth’ is also relative (to a theory). In the first section we look at the pluralist’s motivation for rigour. In the second section, we develop a characterisation of rigorous proof. There are several characterisations varying over the account of meaning we attach to mathematical claims and axioms. In the third section, we evaluate the characterisation with reference to our motivation. Lastly, we draw some general conclusions for the pluralist. With the analysis we discover that rigour is a regulative ideal, sensitive to philosophical inclinations.

## Keywords

Formal System Rigorous Proof Regulatory Ideal Large Cardinal Logical Pluralism
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© Springer Science+Business Media Dordrecht 2014