- A fallacy in which one or more of the concepts (or premises) on which an argument depends are (usually implicitly) denied by the argument itself, thus meaning the arguer is taking two or more opposed positions at the same time. Named by Ayn Rand (and discussed in more detail here), but arguably discovered earlier. Popular in anti-science literature where scientific processes will be used in an attempt to discredit their own underlying assumptions.
"The latest research in zero-point field quantum physics shows that it is possible to make a perpetual motion machine, and that the first law of thermodynamics does not apply in the quantum domain."
- Zero-point field theories include conservation of mass / energy as an assumption. They would disprove themselves if they actually made this conclusion.
"Quantum Physics has proven that reality does not exist objectively" (the less advanced version of the above argument).
- The notion of "proof" assumes the objective existence of something to prove in the first place. Additionally, if nothing existed objectively, there would be no reliable methods of proof, including Quantum Physics.
Many statements or ideas have been alleged to be self-refuting. Of course, not everyone agrees in each case that they are self-refuting.