Should Mathematicians Play Dice?

Don Berry

Abstract


 It is an established part of mathematical practice that mathematicians demand

deductive proof before accepting a new result as a theorem. However, a wide

variety of probabilistic methods of justification are also available. Though such

procedures may endorse a false conclusion even if carried out perfectly, their

robust structure may mean they are actually more reliable in practice once implementation

errors are taken into account. Can mathematicians be rational

in continuing to reject these probabilistic methods as a means of establishing a

mathematical claim? In this paper, I give reasons in favour of their doing so.

Rather than appealing directly to individual epistemological considerations, the

discussion offers a normative constraint on what constitutes a good mathematical

argument. This I call ‘Univocality’, the requirement that the underlying

concepts all have clear defining conditions.


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