1. Grelling-Nelson Paradox:
This paradox requires one to understand the definitions of two words. Autological and heterological. Autological words are those words that describe themselves, for example multisyllabic is an autological word, because it is itself multisyllabic. Heterological means the opposite of autological, that is heterological words are words which do not describe themselves. For example, monosyllabic is heterological, because it is not itself monosyllabic. The paradox arises when one is asked: is heterological, heterological? This creates a paradox because heterological is heterological if and only if (iff) it is not. That is if heterological is autological, then it is heterological; and if it is heterological, then it is autological. This leads to a logical contradiction.
2. Russell’s Antinomy:
This was discovered by philosopher Bertrand Russell and goes as follows: If R is the set of all sets which are not members of themselves, then R is a member of itself and it is not a member of itself at the same time. This is a clear logical contradiction. In set theory notation this paradox is let then iff .
3. The Liar’s Paradox:
This paradox is created when one states “I am lying.” If he is lying, then he is telling the truth, and vice versa. Another version of this is Epimenides paradox. There are ways of analyzing these paradoxes using so-called metalanguages, allowing truth and falsity to be assessed independently.
4. Olber’s Paradox:
Astronomer Heinrich Olber, his paradox is summed up in the phrase: “why is the night sky dark?” He reasoned that since the night sky was full of bright stars it should be bright, and, yet it isn’t. Why not?
Sources: Weisstein, E. (2016). Paradoxes, Wolfram Mathworld. Retrieved from mathworld.wolfram.com/topics/paradoxes.html.