Dummett on the Time-Continuum

Ulrich Meyer
2005 Philosophy  
In a recent paper, Michael Dummett has argued that the classical model of time as a continuum of instants has to be rejected: 'it allows as possibilities what reason rules out, and leaves it to the contingent laws of physics to rule out what a good model of physical reality would not even be able to describe.' 1 My aim here is to argue otherwise. 2 Some philosophers might reject the classical model because it is what Dummett calls super-realist: it postulates states of affairs that are in
more » ... s that are in principle beyond our ken, such as whether a given instant has a rational or irrational coordinate. There is little doubt that Dummett himself finds super-realism unpalatable, but that is not how he argues in this paper. As he makes clear elsewhere, he also shares the intuitionists' misgivings about the continuum itself, but that is again an issue that he wants to put aside. He wants to show, 'on grounds acceptable to the classical mathematician, that the classical continuum is an inadequate model of physical time.' 3 The contention is that the classical model of time fails on its own terms, and that it has consequences that even its advocates would have to recognize as untenable. Dummett presents three alleged problem cases for the classical model. Since they raise different issues, I will discuss them separately. But they all have one important feature in common: they present examples of physical quantities that change their magnitude discontinuously. Such discontinuous changes might well be ruled out by the laws of nature, but Dummett argues that they have to be Philosophy 80 2005 135
doi:10.1017/s0031819105000082 fatcat:tiyerhkj5zcxpme6z25uqfxnce