With respect to the confirmation of mathematical propositions, proof possesses an epistemological authority unmatched by other means of confirmation. This paper is an investigation into why this is the case. I make use of an analysis drawn from an early reliability perspective on knowledge to help make sense of mathematical proofs singular epistemological status.

I critically examine confirmational holism as it pertains to the indispensability arguments for mathematical Platonism. I employ a distinction between pure and applied mathematics that grows out of the often overlooked symbiotic relationship between mathematics and science. I argue that this distinction undercuts the notion that mathematical theories fall under the holistic scope of the confirmation of our scientific theories.Keywords: Confirmational holism; Indispensability argument; Mathematics; Application; Science.

Much of the current thought concerning mathematical ontology and epistemology follows Quine and Putnam in looking to the indispensable application of mathematics in science. A standard assumption of the indispensability approach is some version of confirmational holism, i.e., that only "sufficiently large" sets of beliefs "face the tribunal of experience." In this paper I develop and defend a distinction between a pure mathematical theory and a mathematized scientific theory in which it is applied. This distinction allows for the possibility that (...) pure mathematical theories are systematically insulated from such confirmation in virtue of their being distinct from the "sufficiently large" blocks of scientific theory that are empirically confirmed. (shrink)

Despite being one of the most dependable methods used by applied mathematicians and engineers in handling complex systems, the finite element method commits variational crimes. This paper contextualizes the concept of variational crime within a broader account of mathematical practice by explaining the tradeoff between complexity and accuracy involved in the construction of numerical methods. We articulate two standards of accuracy used to determine whether inexact solutions are good enough and show that, despite violating the justificatory principles of one, the (...) finite element method nevertheless succeeds in obtaining its legitimacy from the other. (shrink)

Call an explanation in which a non-mathematical fact is explained—in part or in whole—by mathematical facts: an extra-mathematical explanation. Such explanations have attracted a great deal of interest recently in arguments over mathematical realism. In this article, a theory of extra-mathematical explanation is developed. The theory is modelled on a deductive-nomological theory of scientific explanation. A basic DN account of extra-mathematical explanation is proposed and then redeveloped in the light of two difficulties that the basic theory faces. The final view (...) appeals to relevance logic and uses resources in information theory to understand the explanatory relationship between mathematical and physical facts. 1Introduction2Anchoring3The Basic Deductive-Mathematical Account4The Genuineness Problem5Irrelevance6Relevance and Information7Objections and Replies 7.1Against relevance logic7.2Too epistemic7.3Informational containment8Conclusion. (shrink)