Paradoxes: how to learn loving them, and stop worrying

Abstract

Paradoxes have represented an area of research where the interplay between mathematical methods of investigation and conceptual analysis proved to be particularly fruitful. As is well known, the discovery of paradoxes at the end of the nineteenth century occasioned the debate on the foundations of mathematics, which in turn was pivotal for the development of contemporary logic. However, rather than remaining a phenomenon confined in this area, paradoxes also arose in other contexts and became a matter of dispute which was also important for domains such as philosophy of logic and language, epistemology, decision theory, computer science. The book by Roy T. Cook under review aims at illustrating the richness of the debate on paradoxes, as well as suggesting a unifying view of them. This is done by taking into account a representative number and variety of paradoxical arguments which the author explains and discusses in detail. Cook’s initial remarks are intended as a guide for the inexperienced hitchhiker in the galaxy of paradoxes, to whom he explains what is a paradox (9), what is an antinomy (14) and what is the relationship between the two (14–15). As a consequence of these definitions, Cook also makes clear what is a solution to a paradox and groups solutions into types according to whether they are directed toward rejecting one of the premises needed for the paradox to go through, whether they reject the reasoning of it instead, whether they suggest acceptance of the conclusion, whether they aim at rejecting the concept the paradox is about (20). Cook’s analysis is exercised on Zeno’s famous arguments against motion in the very same chapter (22–26) and exploited further in the subsequent ones. For the development of logic, there are two kinds of paradoxes that proved to be crucial. The first of them includes the Liar and the so-called semantic paradoxes which involve the notion of truth. To paradoxes of this sort is devoted Chapter 2 of