Topics Truth

Question If elegance or simplicity is an indicator of truth in math or science, is this principle inductive? For instance: when a theorist claims simplicity in support of his theory, is he saying in effect "Well, in the past I've found that simpler theories tend to be correct; so simplicity should be taken to favor my theory in this case." Or is there supposed to be something else, something intrinsic to simplicity, perhaps, which makes it significant?

Accepted:
January 4, 2011

Comments

t does not seem to me that appeals to this principle are based on induction--although there may well be cases in which the appeal is so based, and, consequently, I think that case studies of the extent to which this principle is applied, and when it is applied, on what basis, would be very interesting and most illuminating. It seems to me to that appeals to this sort of principle rest on one of a variety of methodological--or one might even say, metaphysical, presuppositions, of which I give a couple of examples: (i) a principle of epistemic parsimony or conservatism, that one should not multiply theoretical entities unnecessarily (sometimes called 'Ockham's razor') and that, consequently, one should prefer simpler to more complicated explanations when all else is equal; (ii) perhaps in conjunction with (i)--although they need not be conjoined--an assumption that the phenomenon in question ought to be simple, because the phenomenon is an instantiation, say, of a divine plan (cf. Einstein, "God does not play dice"), or because nature is simple (an assumption that strikes me as unwarranted), and so a hypothesis meant to apply to nature ought also to be simple as well.