Logical paradoxes

Internet Encyclopedia of Philosophy (2001)
A paradox is generally a puzzling conclusion we seem to be driven towards by our reasoning, but which is highly counterintuitive, nevertheless. There are, amongst these, a large variety of paradoxes of a logical nature which have teased even professional logicians, in some cases for several millennia. But what are now sometimes isolated as 'the logical paradoxes' are a much less heterogeneous collection: they are a group of antinomies centered on the notion of self-reference, some of which were known in Classical times, but most of which became particularly prominent in the early decades of last century. Quine distinguished amongst paradoxes such antinomies. He did so by first isolating the 'veridical' and 'falsidical' paradoxes, which, although puzzling riddles, turned out to be plainly true, or plainly false, after some inspection. In addition, however, there were paradoxes which 'produce a self-contradiction by accepted ways of reasoning', and which, Quine thought, established 'that some tacit and trusted pattern of reasoning must be made explicit, and henceforward be avoided or revised' (Quine 1966, p7). We will first look, more broadly, and historically, at several of the main conundrums of a logical nature which have proved difficult, some since antiquity, before concentrating later on the more recent troubles with paradoxes of self-reference. They will all be called 'logical paradoxes'.
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