# Paradoxes of set and property

DOI
10.4324/9780415249126-Y024-1
DOI: 10.4324/9780415249126-Y024-1
Version: v1,  Published online: 1998
Retrieved September 21, 2020, from https://www.rep.routledge.com/articles/thematic/paradoxes-of-set-and-property/v-1

Etymologically, a paradox is something ‘against’ (‘para’) ‘[common] opinion’ (‘dox’). Nowadays it means a claim that seems absurd but has an argument to sustain it. A paradox appears ‘paradoxical’ when one is uncertain which premise to abandon.

The paradoxes about sets involve the principle of comprehension, which states that, for any concept, there is a class of all those objects for which the concept is true. (We use the terms ‘class’ and ‘set’ interchangeably, thus allowing each author discussed below to keep his own terminology.) Historically, the paradoxes about sets are related to the traditional antinomies of the infinite (as expressed, for example, by Galileo), to Zeno’s paradoxes and to Kant’s antinomies (see §4 below).