Explanation, Extrapolation, and Existence

Mark Colyvan (2010) raises two problems for ‘easy road’ nominalism about mathematical objects. The first is that a theory’s mathematical commitments may run too deep to permit the extraction of nominalistic content. Taking the math out is, or could be, like taking the hobbits out of Lord of the Rings. I agree with the ‘could be’, but not (or not yet) the ‘is’. A notion of logical subtraction is developed that supports the possibility, questioned by Colyvan, of bracketing a theory’s mathematical aspects to obtain, as remainder, what it says ‘mathematics aside’. The other problem concerns explanation. Several grades of mathematical involvement in physical explanation are distinguished, by analogy with Quine’s three grades of modal involvement. The first two grades plausibly obtain, but they do not require mathematical objects. The third grade is likelier to require mathematical objects. But it is not clear from Colyvan’s example that the third grade really obtains

Definitions, consistent and inconsistent

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43411/1/11098_2004_Article_BF00989672.pd

Can Modal Skepticism Defeat Humean Skepticism?

My topic is moderate modal skepticism in the spirit of Peter van Inwagen. Here understood, this is a conservative version of modal empiricism that severely limits the extent to which an ordinary agent can reasonably believe “exotic” possibility claims. I offer a novel argument in support of this brand of skepticism: modal skepticism grounds an attractive (and novel) reply to Humean skepticism. Thus, I propose that modal skepticism be accepted on the basis of its theoretical utility as a tool for dissolving philosophical paradox

Bunge’s Mathematical Structuralism Is Not a Fiction

In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involved in mathematical knowledge, in particular its dependence on mental/brain states and material objects

Are Counterpossibles Epistemic?

It has been suggested that intuitions supporting the nonvacuity of counterpossibles can be explained by distinguishing an epistemic and a metaphysical reading of counterfactuals. Such an explanation must answer why we tend to neglect the distinction of the two readings. By way of an answer, I offer a generalized pattern for explaining nonvacuity intuitions by a stand-and-fall relationship to certain indicative conditionals. Then, I present reasons for doubting the proposal: nonvacuists can use the epistemic reading to turn the table against vacuists, telling apart significant from spurious intuitions. Moreover, our intuitions tend to survive even if we clear-headedly intend a metaphysical reading

Descriptions, truth value intuitions, and questions

International audienceSince the famous debate between Russell (Mind 14: 479–493, 1905, Mind 66: 385–389, 1957) and Strawson (Mind 59: 320–344, 1950; Introduction to logical theory, 1952; Theoria, 30: 96–118, 1964) linguistic intuitions about truth values have been considered notoriously unreliable as a guide to the semantics of definite descriptions. As a result, most existing semantic analyses of definites leave a large number of intuitions unexplained. In this paper, I explore the nature of the relationship between truth value intuitions and non-referring definites. Inspired by comments in Strawson (Introduction to logical theory, 1964), I argue that given certain systematic considerations, one can provide a structured explanation of conflicting intuitions. I show that the intuitions of falsity, which proponents of a Russellian analysis often appeal to, result from evaluating sentences in relation to specific questions in context. This is shown by developing a method for predicting when sentences containing non-referring definites elicit intuitions of falsity. My proposed analysis draws importantly on Roberts (in: Yoon & Kathol (eds.) OSU working papers in Linguistics: vol. 49: Papers in Semantics 1998; in: Horn & Ward (eds.) Handbook of pragmatics, 2004) and recent research in the semantics and pragmatics of focus

Real Potential

There\u27s a student in my philosophy class who has real potential. I might express this thought in any of the following ways: She is potentially a philosopher ; She is a potential philosopher ; She has the potential to be a philosopher. The first way uses a cognate of potential as an adverb to modify is. The second ways uses potential as an adjective to modify philosopher. However, the third way uses potential as a noun to refer to something that the student has. What kind of thing is this potential? One worry about even asking this question is that this nominalization of the adjective potential suggests a metaphysical picture that is an artifact of language. This is even more strongly suggested by the less ambiguous nominalization potentiality. Once we have the term potentiality, we have a new kind of entity to countenance, and questions about its nature arise. One might argue, just because we use the word potentiality, we should not think that it refers to a thing that someone can have. There is something disingenuous about such an argument. It proceeds as if the adverbial and adjectival uses of potential are unproblematic, and questions only arise with the nominalization. But it is not obvious what it means to potentially be something, or what it means to be a potential something. To say that someone is potentially a philosopher is to talk about a way of being that falls short of actuality. And a potential philosopher is not a kind of philosopher at all. So what is it? Each of the three above formulations is a modal claim. If there is anything philosophical puzzling about a potentiality claim, it is not going to go away by translating it into an equivalent modal claim. In this chapter I defend the existence of potentialities against anti-realist arguments, and make a proposal as to their nature. The proposal, in short, is that potentialities are properties, specifically dispositions, though more needs to be said about properties and dispositions. I will do this in Part I. In Part II, I will address two lines of argument against potentialities: that they are reducible, and that they are causally inert