This article elaborates the epistemic indispensability argument, which fully embraces the epistemic contribution of mathematics to science, but rejects the contention that such a contribution is a reason for granting reality to mathematicalia. Section 1 introduces the distinction between ontological and epistemic readings of the indispensability argument. Section 2 outlines some of the main flaws of the first premise of the ontological reading. Section 3 advances the epistemic indispensability argument in view of both applied and pure mathematics. And Sect. 4 (...) makes a case for the epistemic approach, which firstly calls into question the appeal to inference to the best explanation in the defense of the indispensability claim; secondly, distinguishes between mathematical and physical posits; and thirdly, argues that even though some may think that inference to the best explanation works in the postulation of physical posits, no similar considerations are available for postulating mathematicalia. (shrink)

In this paper I present two cases, taken from the history of science, in which mathematics and physics successfully interplay. These cases provide, respectively, an example of the successful application of mathematics in astronomy and an example of the successful application of mechanics in mathematics. I claim that an illustration of these cases has a twofold value in the context of the applicability debate. First, it enriches the debate with an historical perspective which is largely omitted in the contemporary discussion. (...) Second, it reveals a component of the applicability problem that has received little attention. This component concerns the successful application of physical principles in mathematical practice. With the help of the two examples, in the final part of the paper I address the following question: are successful applications of mathematics to physics and successful applications of physics to mathematics two sides of the same problem? (shrink)

In ontological debates, realists typically argue for their view via one of two approaches. The _Quinean approach_ employs naturalistic arguments that say our scientific practices give us reason to affirm the existence of a kind of entity. The _Fregean approach_ employs linguistic arguments that say we should affirm the existence of a kind of entity because our discourse contains reference to those entities. These two approaches are often seen as distinct, with _indispensability arguments_ typically associated with the former, but not (...) the latter, approach. This paper argues for a connection between the two approaches on the grounds that the typical arguments of the Fregean approach can be reformulated as indispensability arguments. This connection is significant in at least two ways. First, it implies that indispensability arguments provide a common framework within which to compare the Quinean and Fregean approaches, which allows for a more precise delineation of the two approaches. Second, it implies the possibility of analogical relations that allow proponents and opponents of each approach to draw upon the ideas that have been developed regarding the other. (shrink)

I argue that modal epistemology should pay more attention to questions about the structure and function of modal thought. We can treat these questions from synchronic and diachronic angles. From a synchronic perspective, I consider whether a general argument for the epistemic support of modal though can be made on the basis of modal thoughs’s indispensability for what Enoch and Schechter (2008) call rationally required epistemic projects. After formulating the argument, I defend it from various objections. I also examine the (...) possibility of considering the indispensability of modal thought in terms of its components. Finally, I argue that we also need to approach these issues from a diachronic perspective, and I sketch how to approach this task. (shrink)

This draft preprint presents a nine step argument for “Connectionist Structuralism” (CS), an account of the ontology of abstract objects that is neither purely nominalist nor purely platonist. CS is a common, often implicit assumption in parts of the artificial intelligence literature, but such discussions have not presented formal accounts of the position or engaged with metaphysical issues that potentially undermine it. By making the position legible and presenting an initial case for it, we hope to support a constructive dialogue (...) between AI researchers and philosophers of metaphysics that helps both sides to refine the position. -/- CS proposes that each abstract object we can draw on in human analysis corresponds to a particular subset of an individual person’s brain structure whose functionality is isomorphic to a subset of the nodes and connections in a suitable connectionist network. In other words, abstract objects are physically realised, but in individual brains, rather than only in the referent objects (pure nominalism) or in metaphysical universals (pure platonism). -/- This paper’s minimum claim is that CS can account for all abstract object predicables regarding sensible properties, such as “is red” or “is a square”. Using evidence from cognitive neuroscience, machine learning, and evolutionary biology, as well as a fully traceable toy example, we describe how CS can support our core cognitive uses of such sensible properties and can account for our core phenomenal experiences of them. In the former, CS provides sufficient albeit imperfect inferential safety, whose limitations are argued to strengthen rather than weaken the case for CS as describing human behaviour. In the latter, four target phenomenal features are accounted for – abstract objects as feeling intangible, non-located, transparent, and unchanging - along with accounts for further phenomena such as semantic refinement, the Stroop effect, synaesthesia, semantic clarity, sensory overload, and satiation. -/- Our minimum claim concerns the day-to-day usage and felt experience of abstract objects, but we suggest also an extended claim in which CS can form the basis of a pragmatic sufficient logic. As such, the initial outline of a response is provided for five common objections to positions that seek to ground abstract objects without reference to metaphysically stand-alone universals: referential opacity; identity of indiscernibles; infinite regression; non-physical concepts; and necessary truths. These outlines lay the foundation for (but do not seek to formally demonstrate) an extended CS account that addresses other abstract objects, including issues relating to their use in mathematics and formal logic. -/- The CS account leads to a four-layer hierarchy of similarity for whether your “red” is the same as mine. Considering both semantic and phenomenal similarity, we conclude that our “reds” are likely non-identical but can be made close enough for practical purposes. Finally, we describe how future work could elaborate CS as a metaphysical project and how confidence in it could be tested through empirical research. (shrink)