Paradoxes of set and property

DOI: 10.4324/9780415249126-Y024-1
Version: v1,  Published online: 1998
Retrieved December 05, 2020, from

1. General comments

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).

Citing this article:
Moore, Gregory H.. General comments. Paradoxes of set and property, 1998, doi:10.4324/9780415249126-Y024-1. Routledge Encyclopedia of Philosophy, Taylor and Francis,
Copyright © 1998-2020 Routledge.

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