Indispensability arguments are used as a way of working out what there is: our best science tells us what things there are. Some philosophers think that indispensability arguments can be used to show that we should be committed to the existence of mathematical objects (numbers, functions, sets). Do indispensability arguments also deliver conclusions about the modal properties of these mathematical entities? Colyvan (in Leng, Paseau, Potter (eds) Mathematical knowledge, OUP, Oxford, 109-122, 2007) and Hartry Field (Realism, mathematics and modality, Blackwell, (...) Oxford, 1989) each suggest that a consequence of the empirical methodology of indispensability arguments is that the resulting mathematical objects can only be said to exist (or not exist) contingently. Kristie Miller has argued that this line of thought doesn’t work (Miller in Erkenntnis, 77 (3), 335-359, 2012). Miller argues that indispensability arguments are in direct tension with contingentism about mathematical objects, and that they cannot tell us about the modal status of mathematical objects. I argue that Miller’s argument is crucially imprecise, and that the best way of making it clearer no longer shows that the indispensability strategy collapses or is unstable if it delivers contingentist conclusions about what there is. (shrink)

Evidential holism begins with something like the claim that “it is only jointly as a theory that scientific statements imply their observable consequences.” This is the holistic claim that Elliott Sober tells us is an “unexceptional observation”. But variations on this “unexceptional” claim feature as a premise in a series of controversial arguments for radical conclusions, such as that there is no analytic or synthetic distinction that the meaning of a sentence cannot be understood without understanding the whole language of (...) which it is a part and that all knowledge is empirical knowledge. This paper is a survey of what evidential holism is, how plausible it is, and what consequences it has. Section 1 will distinguish a range of different holistic claims, Sections 2 and 3 explore how well motivated they are and how they relate to one another, and Section 4 returns to the arguments listed above and uses the distinctions from the previous sections to identify holism's role in each case. (shrink)