Abstract: Proponents of indispensability arguments claim that the pervasiveness of mathematics in our best scientific theories, and its apparent indispensability for the purposes of adequately formulating those theories, afford us with strong empirical grounds for believing in mathematical entities. One response to these arguments, which I refer to as “the no-miracle response,” involves maintaining that since mathematical entities (if they exist) are causally inert, we need not postulate their existence in order to explain the empirical success of our best scientific theories. I argue that this response either fails or turns out to be superfluous.
On Believing in Neutrons but not Numbers (Significantly Revised 10/26/12)
Abstract: Scientific realists who do not want to be mathematical realists face a challenge. It seems that our justification for believing in unobservable entities like quarks and neutrons primarily stems from the fact that their existence is implied by our best, most well-confirmed scientific theories. But our best scientific theories are shot through with mathematics and thereby also imply the existence of mathematical entities. Doesn’t epistemological consistency demand, if one believes in concrete unobservables, that one believe in mathematical entities as well? Elliott Sober has suggested a line of response to this challenge of which scientific realists who are not mathematical realists might want to avail themselves. But (as I argue) it is not obvious that the suggested line of response succeeds. I then show how to extend this line of response so that it does meet the above challenge.
Abstract: Many have claimed that the apparent fine-tuning of the universe is evidence that it is but one of numerous (perhaps infinitely many) universes. This claim has been forcefully challenged by Roger White. White, developing an objection originally put forward by Ian Hacking, compellingly argues that those who claim that the apparent fine-tuning of our universe provides evidence for there being a large number of universes commit what Hacking dubbed “the inverse gambler’s fallacy.” In this paper, I defend White’s thesis from an objection that has been raised by Nick Bostrom.
Abstract: Various commentators have charged Aristotle’s discussion of time in Physics IV 10-14 with being illicitly circular. In this paper, I defend Aristotle’s account from such charges. I do so by arguing that those who make them fail to properly understand Aristotle’s aims. In particular, I argue that Aristotle is attempting to dissolve certain puzzles that arise for him because he holds a presentist view of time. I further argue that once Aristotle’s aims are properly understood, the charge that his account of time is illicitly circular is seen to be misplaced.
Abstract: Theistic activism is the view that there are Platonic entities such as propositions and properties and that all such entities are causally dependent on God’s mental activity for their existence. A common objection to theistic activism, however, is that it inevitably involves committing its adherents to positing illicit explanatory circularity. In this paper, I respond to a powerful development of this objection on the part of Michael Bergmann and Jeffrey Brower.