Once upon a time, logical conventionalism was the most popular philosophical theory of logic. It was heavily favored by empiricists, logical positivists, and naturalists. According to logical conventionalism, linguistic conventions explain logical truth, validity, and modality. And conventions themselves are merely syntactic rules of language use, including inference rules. Logical conventionalism promised to eliminate mystery from the philosophy of logic by showing that both the metaphysics and epistemology of logic fit into a scientific picture of reality. For naturalists of all (...) stripes, this was paradise. Alas, paradise was lost. By the end of the twentieth century, logical conventionalism had been almost universally abandoned. But more recently, it has been revitalized. This chapter provides an overview of logical conventionalism and its history, clears away misunderstandings, and briefly responds to both the canonical objections to conventionalism (from Quine, Dummett, Boghossian, and many others) as well as new objections (from Field and Golan). From paradise lost, to paradise regained: logical conventionalism is back. (shrink)

One common attitude toward abstract objects is a kind of platonism: a view on which those objects are mind-independent and causally inert. But there's an epistemological problem here: given any naturalistically respectable understanding of how our minds work, we can't be in any sort of contact with mind-independent, causally inert objects. So platonists, in order to avoid skepticism, tend to endorse epistemological theories on which knowledge is easy, in the sense that it requires no such contact—appeals to Boghossian’s notion of (...) epistemic analyticity are particularly common here, as are appeals to some broadly pragmatic account of the good standing of basic beliefs. I argue, though, that these appeals are hopeless: an argument adapted from the Benacerraf–Field challenge shows that, even if some such theory can deliver the verdict that our beliefs about abstract objects have some prima facie good standing, this good standing will inevitably be defeated. (shrink)

According to what Hume termed an ‘establish’d maxim’, nothing absolutely impossible is imaginable. It has recently been claimed against this that given the ubiquity of stipulative imagination, where one imagines a proposition simply by adding it as a stipulation about the imagined situation, it seems that we can imagine any impossibility whatsoever, even plain contradictions: all we need to do is add them as stipulations. The aim of this article is both to defend Hume’s maxim against this objection and – (...) hopefully interestingly – to do so while granting the assumption that adding something as a stipulation is a valid way of imagining something. To this end, appeal is made to a particular development of a second Humeanism, according to which necessary truths are analytic in the sense that their truth follows from their meaning. Their analyticity, it is then argued, secures that they are true in all imagined situations. Therefore, even if it is right that a valid way of imagining something is to add it as a stipulation, attempting to stipulate that, say, some imaginary bachelor is also married is bound to fail: you can’t stipulate it to be the case because it really isn’t the case. (shrink)

The positivists’ notion of truth in virtue of meaning presupposes that the truth of certain sentences can be explained merely by reference to semantic rules. The currently most popular objection to the notion denies the possibility of such semantic explanations, on the grounds that semantic rules can only explain what a sentence says, but not whether what a sentence says is true. Though recent critics of the objection have insisted that semantic rules do explain the truth of certain sentences, the (...) very notion of a semantic explanation is often left unclear. This paper proposes to define the notion of semantic explanation as a valid argument that derives the truth of a sentence from accepted semantic rules. The account offered will then be used to respond to some of the most pressing objections to the idea of truth in virtue of meaning. (shrink)

[Use code AUFLY30 for 30% off on the OUP website.] One central aim of science is to provide explanations of natural phenomena. What role(s) does mathematics play in achieving this aim? How does mathematics contribute to the explanatory power of science? Rules to Infinity defends the thesis, common though perhaps inchoate among many members of the Vienna Circle, that mathematics contributes to the explanatory power of science by expressing conceptual rules, rules which allow the transformation of empirical descriptions. Mathematics should (...) not be thought of as describing, in any substantive sense, an abstract realm of eternal mathematical objects, as traditional platonists have thought. In Rules to Infinity, this view, which I call mathematical normativism, is updated with contemporary philosophical tools, and it is argued that normativism is compatible with mainstream semantic theory. This allows the normativist to accept that there are mathematical truths, while resisting the platonistic idea that there exist abstract mathematical objects that explain such truths. Furthermore, Rules to Infinity defends a particular account of the distinction between scientific explanations that are in some sense distinctively mathematical – those that explain natural phenomena in some uniquely mathematical way – and those that are only standardly mathematical, and it lays out desiderata for any account of this distinction. Normativism is compared with other prominent views in the philosophy of mathematics such as neo-Fregeanism, fictionalism, conventionalism, and structuralism. Rules to Infinity serves as an entry point into debates at the forefront of philosophy of science and mathematics, and it defends novel positions in these debates. (shrink)