Quantifier variance faces a number of difficulties. In this paper we first formulate the view as holding that the meanings of the quantifiers may vary, and that languages using different quantifiers may be charitably translated into each other. We then object to the view on the basis of four claims: (i) quantifiers cannot vary their meaning extensionally by changing the domain of quantification; (ii) quantifiers cannot vary their meaning intensionally without collapsing into logical pluralism; (iii) quantifier variance is not an (...) ontological doctrine; (iv) quantifier variance is not compatible with charitable translation and as such is internally inconsistent. In light of these troubles, we recommend the dissolution of quantifier variance and suggest that the view be laid to rest. (shrink)

As part of the development of an epistemology for mathematics, some Platonists have defended the view that we have (i) intuition that certain mathematical principles hold, and (ii) intuition of the properties of some mathematical objects. In this paper, I discuss some difficulties that this view faces to accommodate some salient features of mathematical practice. I then offer an alternative, agnostic nominalist proposal in which, despite the role played by mathematical intuition, these difficulties do not emerge.

This paper examines two alleged limitations in the use of formal languages: on the one hand, the trade-offs between expressive and inferential power, and on the other, the phenomenon of system imprisonment. After reconceptualizing the issue, we consider the role played by modality in the understanding of certain aspects of mathematical structures and argue for its centrality.

In this paper, we examine two conceptions of the application of logic and assess their comparative merits. The first is a platonist monist conception that characterizes the logical consequence relation as an abstract relation among propositions. We argue that this proposal, which insists on logic’s topic neutrality, accommodates very well the objectivity of logic. From this perspective, there are no constraints on particular topics. As a result, we have the universality that allows us to go through a wide scope of (...) contexts where logic is applied. In contrast, a non-platonist pluralist conception is examined, and it characterizes the variety of logical consequence relations as concrete, context-dependent in particular cases, and topic-dependent. As will become clear, this conception is particularly well suited to make room for the applications of logic. We conclude that, in order to solve the ontological debate about logic, we need to go beyond its applications. (shrink)