A paradox is a seemingly sound piece of reasoning, based on apparently true assumptions, but which leads to a contradiction,[1] such as in the barber paradoxPuzzle derived from Bertrand Russell's paradox, one of the most famous paradoxes in the foundation of set theory.. Following on from the work of the mathematician and philosopher F. R. Ramsey, and the mathematician G. Peano, philosphers have routinely distinguished between logical and semantic paradoxes.[2]
Logical contradictions involve mathematical or logical terms such as class or number, and demonstrate that our logic or mathematics is problematic. But semantic contradictions also involve notions such as thought, language, and symbolism, which according to Ramsey are empirical, informal terms. Hence semantic paradoxes are rooted in faulty ideas about thought or language.[3]
The significance of semantic paradoxes is that they expose fundamental flaws in our understanding of semantic concepts such as truth, as evidenced by the liar paradox.[3]
