Pluralist mathematical realism, the view that there exists more than one mathematical universe, has become an influential position in the philosophy of mathematics. I argue that, if mathematical pluralism is true (and we have good reason to believe that it is), then mathematical realism cannot (easily) be justified by arguments from the indispensability of mathematics to science. This is because any justificatory chain of inferences from mathematical applications in science to the total body of mathematical theorems can cover at most (...) one mathematical universe. Indispensability arguments may thus lose their central role in the debate about mathematical ontology. (shrink)

I argue that recent attempts to deflect Access Problems for realism about a priori domains such as mathematics, logic, morality, and modality using arguments from evolution result in two kinds of explanatory overkill: the Access Problem is eliminated for contentious domains, and realist belief becomes viciously immune to arguments from dispensability, and to non-rebutting counter-arguments more generally.

The existence of fundamental moral disagreements is a central problem for moral realism and has often been contrasted with an alleged absence of disagreement in mathematics. However, mathematicians do in fact disagree on fundamental questions, for example on which set-theoretic axioms are true, and some philosophers have argued that this increases the plausibility of moral vis-à-vis mathematical realism. I argue that the analogy between mathematical and moral disagreement is not as straightforward as those arguments present it. In particular, I argue (...) that pluralist accounts of mathematics render fundamental mathematical disagreements compatible with mathematical realism in a way in which moral disagreements and moral realism are not. 11. (shrink)

Maimonides famously holds that, while it is perfectly possible to know (and say) that God exists, it is impossible to know (and say) what God is like because any positive attri- bution contradicts God’s essential oneness. Consequently, pure equivocity obtains between descriptions of the divine and descriptions of any other being. But this raises a puzzle: Knowledge of God seems vacuous if we lack all comprehension of God’s nature - so how can we have any comprehension of the divine without (...) being able to say what it is that we know? In this essay, I defend the substantiality of the concept of knowledge of God on Maimonides’ apophatic picture. Drawing on the concept of non-propositional knowledge, I argue that knowledge and comprehension can come apart, which lends support to Maimonides’ thesis that knowledge of God, though substantial and objective, cannot be expressed. (shrink)

Drawing an analogy between modal structuralism about mathematics and theism, I o er a structuralist account that implicitly de nes theism in terms of three basic relations: logical and metaphysical priority, and epis- temic superiority. On this view, statements like `God is omniscient' have a hypothetical and a categorical component. The hypothetical component provides a translation pattern according to which statements in theistic language are converted into statements of second-order modal logic. The categorical component asserts the logical possibility of the (...) theism struc- ture on the basis of uncontroversial facts about the physical world. This structuralist reading of theism preserves objective truth-values for theistic statements while remaining neutral on the question of ontology. Thus, it o ers a way of understanding theism to which a naturalist cannot object, and it accommodates the fact that religious belief, for many theists, is an essentially relational matter. (shrink)

This essay provides an overview of the ways in which contemporary philosophers have tried to make sense of ineffability as encountered in aesthetic contexts. Section 1 sets up the problem of aesthetic ineffability by putting it into historical perspective. Section 2 specifies the kinds of questions that may be raised with regard to aesthetic ineffability, as well as the kinds of answer each one of those questions would require. Section 3 investigates arguments that seek to locate aesthetic ineffability within the (...) object of aesthetic experiences, i.e. within aesthetic content. Section 4 discusses arguments that seek to locate aesthetic ineffability within the subject of aesthetic experience. (shrink)