How should physical entities be characterized? Physicalists, who have most to do with the notion, usually characterize the physical by reference to two components: 1. The physical entities are the entities treated by fundamental physics with the proviso that 2. Physical entities are not fundamentally mental (that is, do not individually possess or bestow mentality) Here I explore the extent to which the appeals to fundamental physics and to the NFM (“no fundamental mentality”) constraint are appropriate for characterizing the physical, (...) especially for purposes of formulating physicalism. Ultimately, I motivate and defend a version of an account incorporating both components: The physics-based NFM account: An entity existing at a world w is physical iff (i) it is treated, approximately accurately, by current or future (in the limit of inquiry, ideal) versions of fundamental physics at w, and (ii) it is not fundamentally mental (that is, does not individually either possess or bestow mentality). (shrink)

In the Grundlagen , Frege offers eight main arguments, together with a series of more minor supporting arguments, against Mill’s view that numbers are “properties of external things”. This paper reviews all eight of these arguments, arguing that none are conclusive.

It has been argued that the attempt to meet indispensability arguments for realism in mathematics, by appeal to counterfactual statements, presupposes a view of mathematical modality according to which even though mathematical entities do not exist, they might have existed. But I have sought to defend this controversial view of mathematical modality from various objections derived from the fact that the existence or nonexistence of mathematical objects makes no difference to the arrangement of concrete objects. This defense of the controversial (...) view of mathematical modality obviously falls far short of a full endorsement of the counterfactual approach, but I hope my remarks may serve to help keep such an approach a live option. (shrink)

An attempt was made to show how we can plausibly commit to mathematical realism. For the purpose of illustration, a defence of natural realism for arithmetic was developed that draws upon the American pragmatist’s, Hillary Putnam’s, early and later writings. Natural realism is the idea that truth is recognition-transcendent and knowable. It was suggested that the natural realist should embrace, globally, what N. Tennant has identified as M-realism (Tennant 1997, 160). M-realism is the idea that one rejects bivalence and assents (...) to the recognition-transcendent requirement. It was argued that over-all—for all domains—the natural realist should be a M-realist, with the aim of clarifying the realist debate for arithmetic. (shrink)