Mathematics and Metaphilosophy

The Element discusses the problem of mathematical knowledge and its philosophical ramifications, arguing that the justificatory challenge arises from disagreement over axioms and the reliability challenge arises from the possibility of different beliefs. It concludes with a complementary pluralism about modality, logic, and normative theory, highlighting its surprising implications.

Format: Paperback / softback
Length: 75 pages
Publication date: 30 June 2022
Publisher: Cambridge University Press

The Element delves into the intricate problem of mathematical knowledge and its far-reaching philosophical implications. It argues that the central challenge arises when disagreements over fundamental axioms culminate in disagreements over intuitions. This justificatory challenge becomes particularly pressing when it comes to explaining the justification of our mathematical beliefs, which can be challenged or defeasible. Furthermore, the Element raises the reliability challenge, emphasizing the possibility that we could have held different beliefs without any significant difference in our cognitive landscape.

The Element demonstrates that mathematical facts are not readily accessible through empirical means, contrary to the position of Quine. It further argues that they cannot be disregarded or dismissed, as suggested by Field. However, the Element posits an intriguing possibility: that mathematical facts may be so abundant that our knowledge of them remains essentially unmysterious. This suggests that our understanding of mathematics may not require a deep and intricate explanation, but rather a vast accumulation of empirical observations and logical inferences.

In conclusion, The Element offers a comprehensive exploration of the nature of mathematical knowledge and its philosophical ramifications. It challenges traditional views and presents a pluralistic perspective on modality, logic, and normative theory. This pluralism engenders a sense of perspectivalism and indeterminacy, while also vindicating Carnap's pragmatism, transposed to the realm of realism. The Element's insights and arguments provide valuable contributions to the ongoing discourse on the foundations of mathematics and its philosophical implications.

Weight: 103g
ISBN-13: 9781108995405