In the last decades two different and apparently unrelated lines of research have increasingly connected mathematics and evolutionism. Indeed, on the one hand different attempts to formalize darwinism have been made, while, on the other hand, different attempts to naturalize logic and mathematics have been put forward. Those researches may appear either to be completely distinct or at least in some way convergent. They may in fact both be seen as supporting a naturalistic stance. Evolutionism is indeed crucial for a (...) naturalistic perspective, and formalizing it seems to be a way to strengthen its scientificity. The paper shows that, on the contrary, those directions of research may be seen as conflicting, since the conception of knowledge on which they rest may be undermined by the consequences of accepting an evolutionary perspective. (shrink)

Scientific Realism (SR) has three crucial aspects: 1) the centrality of the concept of truth, 2) the idea that success is a reliable indicator of truth, and 3) the idea that the Inference to the Best Explanation is a reliable inference rule. It will be outlined how some realists try to overcome the difficulties which arise in justifying such crucial aspects relying on an adaptationist view of evolutionism, and why such attempts are inadequate. Finally, we will briefly sketch some of (...) the main difficulties the realist has to face in defending those crucial aspects, and how such difficulties are deeply related: they derive from the inability of SR to satisfyingly avoid the sceptical challenge of the criterion of truth. Indeed, SR seems not to be able to fill the so-called ‘epistemic gap’ (Sankey 2008). In fact, the epistemic gap cannot be filled in no way other than obtaining a criterion of truth, but such a criterion cannot be obtained if the epistemic gap obtains. (shrink)

This chapter tries to answer the following question: How should we conceive of the method of mathematics, if we take a naturalist stance? The problem arises since mathematical knowledge is regarded as the paradigm of certain knowledge, because mathematics is based on the axiomatic method. Moreover, natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some authors tried to naturalize (...) mathematics by relying on evolutionism. But several difficulties arise when we try to do this. This chapter suggests that, in order to naturalize mathematics, it is better to take the method of mathematics to be the analytic method, rather than the axiomatic method, and thus conceive of mathematical knowledge as plausible knowledge. (shrink)

Nominalism in formal ontology is still the thesis that the only acceptable domain of quantification is the first-order domain of particulars. Nominalists may assert that second-order well-formed formulas can be fully and completely interpreted within the first-order domain, thereby avoiding any ontological commitment to second-order entities, by means of an appropriate semantics called “substitutional”. In this paper I argue that the success of this strategy depends on the ability of Nominalists to maintain that identity, and equivalence relations more in general, (...) is first-order and invariant. Firstly, I explain why Nominalists are formally bound to this first-order concept of identity. Secondly, I show that the resources needed to justify identity, a certain conception of identity invariance, are out of the Nominalist’s reach. (shrink)

According to Bernard Williams, philosophy is a humanistic discipline essentially different from the sciences. While the sciences describe the world as it is in itself, independent of perspective, philosophy tries to make sense of ourselves and of our activities. Only the humanistic disciplines, in particular philosophy, can do this, the sciences have nothing to say about it. In this note I point out some limitations of Williams’ view and outline an alternative view.

The view that the subject matter of epistemology is the concept of knowledge is faced with the problem that all attempts so far to define that concept are subject to counterexamples. As an alternative, this article argues that the subject matter of epistemology is knowledge itself rather than the concept of knowledge. Moreover, knowledge is not merely a state of mind but rather a certain kind of response to the environment that is essential for survival. In this perspective, the article (...) outlines an answer to four basic questions about knowledge: What is the role of knowledge in human life? What is the relation between knowledge and reality? How is knowledge acquired? Is there any a priori knowledge? (shrink)

In a very influential paper Rota stresses the relevance of mathematical beauty to mathematical research, and claims that a piece of mathematics is beautiful when it is enlightening. He stops short, however, of explaining what he means by ‘enlightening’. This paper proposes an alternative approach, according to which a mathematical demonstration or theorem is beautiful when it provides understanding. Mathematical beauty thus considered can have a role in mathematical discovery because it can guide the mathematician in selecting which hypothesis to (...) consider and which to disregard. Thus aesthetic factors can have an epistemic role qua aesthetic factors in mathematical research. (shrink)