Why fallibilism is wrong for maths

Paul Ernest contrasts absolutism in mathematics with fallibilism and tries to convince us that the latter is acceptable (THES, September 6). Towards the end he denies any expectation of converting his "opponents" to fallibilism in mathematics. Of course not, because it sounds all wrong.

Mathematics is the subject to which people cleave when they are looking for as secure truths as we can hope to find. To emphasise human frailty in such a context is a classic example of "inappropriate conjunction" - like introducing jokes into prayer, or serving ice cream with bacon. Of course everything we do has a residual fallibility, but what is the point of emphasising this banal fact, which can only have the effect of eroding the subject's ultimate appeal?

To say baldly that mathematics is "invented" and to call it a "game" is to simplify to the point where the most important qualifications disppear. Yes, in a sense Newton and Liebnitz did invent the calculus: they tried to put together a gadget which would enable them to predict trajectories. They succeeded in "constructing" such a gadget: but they could not guarantee its success. It worked because the world was like that. We now know that mathematical structures can be used to predict many effects in physics with extraordinary accuracy. This fact alone says that physical reality and mathematics must be closely related in some way. But there is also a lack of complete identity, because we can envisage sequences of events which, it can be seen, could never be described mathematically. This shows that physical reality as a whole cannot be described mathematically. (See my series of articles in Cogito 1992-94.) We are beginning to make progress at last, teasing out some of the paradoxes about truth and existence which have dogged mathematics for more than 90 years.

But the way forward is not via Punch-and-Judy type debates of the fallibilism vs absolutist kind.

CHRIS ORMELL Senior fellow, University of East Anglia