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Self-refuting ideas or self-defeating ideas are ideas or statements whose falsehood is a logical consequence of the act or situation of holding them to be true. Many ideas are called self-refuting by their detractors, and such accusations are therefore almost always controversial, with defenders stating that the idea is being misunderstood or that the argument is invalid. For these reasons, none of the ideas below are unambiguously or incontrovertibly self-refuting. These ideas are often used as axioms, which are definitions taken to be true (tautological assumptions), and cannot be used to test themselves, for doing so would lead to only two consequences: consistency (circular reasoning) or exception (self contradiction). It is important to know that the conclusion of an argument that is self-refuting is not necessarily false, since it could be supported by another, more valid, argument.
Directly self-denying statements 
The Epimenides paradox is a statement of the form "this statement is false". Such statements troubled philosophers, especially when there was a serious attempt to formalize the foundations of logic. Bertrand Russell developed his "Theory of Types" to formalize a set of rules that would prevent such statements (more formally Russell's paradox) being made in symbolic logic. This work has led to the modern formulation of axiomatic set theory. While Russell's formalization didn't contain such paradoxes, Kurt Gödel showed that it must contain independent statements. Any logical system that is rich enough to contain elementary arithmetic contains at least one proposition whose interpretation is "this proposition is unprovable" (from within the logical system concerned), and hence no such system can be both complete and consistent.
Indirectly self-denying statements or "fallacy of the stolen concept" 
Objectivists define the fallacy of the stolen concept: the act of using a concept while ignoring, contradicting or denying the validity of the concepts on which it logically and genetically depends. An example of the stolen concept fallacy is anarchist Pierre-Joseph Proudhon's statement, "All property is theft".
- While discussing the hierarchical nature of knowledge, Nathaniel Branden states, "Theft" is a concept that logically and genetically depends on the antecedent concept of "rightfully owned property"—and refers to the act of taking that property without the owner's consent. If no property is rightfully owned, that is, if nothing is property, there can be no such concept as "theft." Thus, the statement "All property is theft" has an internal contradiction: to use the concept "theft" while denying the validity of the concept of "property," is to use "theft" as a concept to which one has no logical right—that is, as a stolen concept.
Others have said the statement is fallacious only on a superficial reading of Proudhon, devoid of context. Proudhon used the term "property" with reference to claimed ownership in land, factories, etc. He believed such claims were illegitimate, and thus a form of theft from the commons. Proudhon explicitly states that the phrase "property is theft" is analogous to the phrase "slavery is murder". According to Proudhon, the slave, though biologically alive, is clearly in a sense "murdered". The "theft" in his terminology does not refer to ownership any more than the "murder" refers directly to physiological death, but rather both are meant as terms to represent a denial of specific rights.  Others point out that the difference between the two examples is that "slavery is murder," unlike "property is theft," does not make a statement that denies the validity of one of the concepts it utilizes. We should note as well that Proudhon does not actually say all property is theft-he is referring to a very specific kind of property rights. Proudhon favored another kind, which he called possession, based on occupancy and use, a sort of usufruct rights idea. In What is Property? he therefore says with the apparent contradiction "property is theft" to denote one sort he feels is this, "property is liberty", referring to the kind he favored, and "property is impossible" to make it clear any sort of property rights cannot be absolute. Separate concepts are therefore laid out, in a way that can be confusing, especially if one does not know them.
In logic 
Self-refutation plays an important role in some inconsistency tolerant logics (e.g. paraconsistent logics and Direct Logic) that lack proof by contradiction. For example, the negation of a proposition can be proved by showing that the proposition infers its own negation. Likewise, it can be inferred that a proposition cannot be proved by (1) showing that a proof would infer the negation of the proposition or by (2) showing a proof would infer that the negation of the proposition can be proved.
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Brain in a vat 
Brain in a vat is a thought experiment in philosophy which is premised upon the skeptical hypothesis that one could actually be a brain in a vat receiving electrical input identical to that which would be coming from the nervous system. Similar premises are found in Descartes's evil demon and dream argument. Philosopher Hilary Putnam argues that some versions of the thought experiment would be inconsistent due to semantic externalism. For a brain in a vat that had only ever experienced the simulated world, the statement "I'm not a brain in a vat" is true. The only possible brains and vats it could be referring to are simulated, and it's true that it's not a simulated brain in a simulated vat. By the same argument, saying "I'm a brain in vat" would be false.
- To count as rational, a belief must be freely chosen, which according to the determinist is impossible
- Any kind of debate seems to be posited on the idea that the parties involved are trying to change each other's minds.
The argument does not succeed against the compatibilistic view, since in the latter there is no conflict between determinism and free will. Moreover, the argument fails if one denies either of the above or its implicit implications. That is, one could avoid the argument by maintaining that free will is not required for rationality or for trying to change one's mind. The latter is a sensible position insofar as one could be determined to try to persuade someone of something, and the listener could be determined to accept it. There is no internal contradiction in that view.
One can also consider a deterministic computer algorithm which is able to make a correct conclusion, such as a mathematical calculation or fingerprint identification. However, on some notions of "rationality", such programs are themselves not rational because they simply follow a certain deterministic pre-programmed path and nothing more. This does not apply if one takes on a position with regards to rationality analogous to compatibilism, namely, one could simply view rationality as the property of correctly executing the laws of logic, in which case there simply is no contradiction with determinism. The contradiction would arise if one defines "rationality" in a manner that is incompatiblist. Some argue that machines cannot "think", and if rationality is defined so that it requires human-like thought, this might pose a problem. But the view that machines cannot "think" in principle is rejected by most philosophers who accept a Computational theory of mind.
Ethical egoism 
It has been argued that extreme ethical egoism is self-defeating. Faced with a situation of limited resources, egoists would consume as much of the resource as they could, making the overall situation worse for everybody. Egoists rejoin that if the situation becomes worse for everybody, that would include the egoist, so it is not in fact in their rational self-interest to take things to such extremes.
Eliminative materialism 
The philosopher Mary Midgley states that the idea that "nothing exists except matter" is also self-refuting because if it were true neither it, nor any other idea, would exist, and similarly that an argument to that effect would be self-refuting because it would deny its own existence.
However, other forms of materialism may escape this kind of argument because, rather than eliminating the mental, they seek to identify it with, or reduce it to, the material. For instance, identity theorists such as J. J. C. Smart, Ullin Place and E. G. Boring state that ideas exist materially as patterns of neural structure and activity. Christian apologist J.P. Moreland states that such arguments are based on semantics.
Epimenides paradox 
The first notable self-refuting idea is the Epimenides paradox, a statement attributed to Epimenides, a Cretan philosopher, that "All Cretans are liars". If interpreted as meaning "no Cretan ever speaks the truth," this cannot be true if uttered by a Cretan.
A more common example is the self-refuting statement "I am lying" (because the first statement allows the possibility "some Cretans do not speak the truth," the speaker being one of them). The second statement has no third alternative—the speaker's statement is either true or false.
Evolutionary naturalism 
Alvin Plantinga argues in his evolutionary argument against naturalism that the combination of naturalism and Evolution is "in a certain interesting way self-defeating" because if it were true there would be insufficient grounds to believe that human cognitive faculties are reliable. Consequently, if human cognitive abilities are unreliable, then any human construct, which by implication utilizes cognitive faculties, such as evolutionary theory, would be undermined. In this particular case, it is the confluence of evolutionary theory and naturalism that, according to the argument, undermine the reason for believing themselves to be true. Since Plantinga originally formulated the argument, a few theistic philosophers and Christian apologists have agreed. There has also been a considerable backlash of papers arguing that the argument is flawed in a number of ways, one of the more recent ones published in 2011 by Feng Ye (see also the references in the Evolutionary argument against naturalism article).
The philosopher Anthony Kenny argues that the idea, "common to theists like Aquinas and Descartes and to an atheist like Russell" that "Rational belief [is] either self-evident or based directly or indirectly on what is evident" (which he termed "foundationalism" following Plantinga) is self-refuting on the basis that this idea is itself neither self-evident nor based directly or indirectly on what is evident and that the same applies to other formulations of such foundationalism. However, the self-evident impossibility of infinite regress can be offered as a justification for foundationalism. Following the identification of problems with "naive foundationalism", the term is now often used to focus on incorrigible beliefs (modern foundationalism), or basic beliefs (reformed foundationalism).
It is often stated that relativism about truth must be applied to itself. The cruder form of the argument concludes that since the relativist is calling relativism an absolute truth, it leads to a contradiction. Relativists often rejoin that in fact relativism is only relatively true, leading to a subtler problem: the absolutist, the relativist's opponent, is perfectly entitled, by the relativist's own standards, to reject relativism. That is, the relativist's arguments can have no normative force over someone who has different basic beliefs.
Philosophical skeptics state that "nothing can be known." Can that statement itself be known, or is it self-refuting? One very old response to this problem is Academic skepticism: an exception is made for the skeptic's own statement. This leads to further debate about consistency and special pleading. Another response is to accept that "nothing can be known" cannot itself be known, so that it is not known whether anything is knowable or not. This is Pyrrhonic skepticism. However, the issue can be pressed further. To state that "nothing can be known" is itself unknowable, is to state that we know for a fact that "nothing can be known" is unknowable. This admits at least one form of knowledge, and the metaphysical proposition "I can discern truth". It is therefore self-refuting; only justified through an infinite regress of not knowing knowledge claims and not knowing that you can know them ad infinitum.
On the face of it, a statement of solipsism is — at least performatively — self-defeating, because a statement assumes another person to whom the statement is made. (That is to say, an unexpressed private belief in solipsism is not self-refuting). This, of course, assumes the solipsist would not communicate with a hallucination, even if just for self-amusement.
One response is that the solipsist's interlocutor is in fact a figment of their imagination, but since their interlocutor knows they are not, they are not going to be convinced.
Verification- and falsification-principles 
The statements "statements are meaningless unless they can be empirically verified" and "statements are meaningless unless they can be empirically falsified" have both been called self-refuting on the basis that they can neither be empirically verified nor falsified. Similar arguments have been made for statements such as "no statements are true unless they can be shown empirically to be true," which was a problem for logical positivism.
Wittgenstein's Tractatus 
"My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it)". (6.54)
However, this idea can be solved in the sense that, even if the argument itself is self-refuting, the effects of the argument elicit understandings that go beyond the argument itself. Søren Kierkegaard describes it as such:
"[The reader] can understand that the understanding is a revocation--the understanding with him as the sole reader is indeed the revocation of the book. He can understand that to write a book and to revoke it is not the same as refraining from writing it, that to write a book that does not demand to be important for anyone is still not the same as letting it be unwritten." (Concluding Unscientific Postscript)
See also 
- Russell B, Whitehead A.N., Principia Mathematica
- The Stolen Concept by Nathaniel Branden - originally published in The Objectivist Newsletter in January 1963.
- Rockwell, L. Performative Contradicitons and Subtle Misunderstandings
- Hewitt, C. “Large-scale Organizational Computing requires Unstratified Reflection and Strong Paraconsistency” Coordination, Organizations, Institutions, and Norms in Agent Systems III Jaime Sichman, Pablo Noriega, Julian Padget and Sascha Ossowski (ed.). Springer-Verlag. 2008.
- Brains in a vat, Reason, Truth, and History ch. 1, Hilary Putnam
- "Determinism". "Determinism is self-defeating. A determinist insists that both determinists and non-determinists are determined to believe what they believe. However, determinists believe self-determinists are wrong and ought to change their view. But "ought to change" implies they are free to change, which, within the incompatibilist view, is contrary to determinism."
- "Ethics" Britannica
- see Mary Midgley The Myths we Live by
- Baker, L. (1987). Saving Belief. Princeton: Princeton University Press. ISBN 0-691-07320-1.
- Reppert, V. (1992). "Eliminative Materialism, Cognitive Suicide, and Begging the Question". Metaphilosophy 23 (4): 378–392. doi:10.1111/j.1467-9973.1992.tb00550.x.
- Boghossian, P. (1990). "The Status of Content". Philosophical Review 99 (2): 157–184. doi:10.2307/2185488. And — (1991). "The Status of Content Revisited". Pacific Philosophical Quarterly 71: 264–278.
- Hill, C. "Identity Theory" (PDF).
- Place, U. T. "Identity Theories". In Nanni, Marco. A Field Guide to the Philosophy of Mind. Società italiana per la filosofia analitica. "To the author a perfect correlation is identity. Two events that always occur together at the same time in the same place, without any temporal or spatial differentiation at all, are not two events but the same event. The mind-body correlations as formulated at present, do not admit of spatial correlation, so they reduce to matters of simple correlation in time. The need for identification is no less urgent in this case."
- "Dictionary of the Philosophy of Mind".
- Moreland, J.P., The Recalcitrant Imago Dei: Human Persons and the Failure of Naturalism
- Alvin Plantinga in Naturalism Defeated?, Ed. James Beilby Cornell University Press, 2002
- John Polkinghorne is an example of a scientist-theologian who is supportive of Plantinga's position
- Richard Swimburne is a philosopher that supports and utilizes Plantinga's argument effectively in his book "The Existence of God"
- Kenny, Anthony (1992). What is Faith?. Oxford: OUP. pp. 9–10. ISBN 0-19-283067-8. This particular chapter is based on a 1982 lecture which may explain the shift in the meaning of the term "foundationalism" since then
- Stanford Encyclopedia of Philosophy on foundationalism
- Cognitive Relativism, Internet Encyclopedia of Philosophy
- The problem of self-refutation is quite general. It arises whether truth is relativized to a framework of concepts, of beliefs, of standards, of practices.Stanford Encyclopedia of Philosophy
- "If truth is relative, then non-relativist points of view can legitimately claim to be true relative to some standpoints." Westacott, E. On the Motivations for Relativism
- The Gallilean Library
- Suber, P. Classical Skepticism
- Internet Encyclopedia of Philosophy
- Russell, B. (1948). Human Knowledge: Its Scope and Limits. New York: Simon and Schuster. p. 180. "As against solipsism it is to be said, in the first place, that it is psychologically impossible to believe, and is rejected in fact even by those who mean to accept it. I once received a letter from an eminent logician, Mrs. Christine Ladd Franklin, saying that she was a solipsist, and was surprised that there were no others. Coming from a logician and a solipsist, her surprise surprised me."
- See e.g. the discussion by Alston, William P. (2003). "Religious language and verificationism". In Moser, Paul K.; Copan, Paul. The Rationality of Theism. New York: Routledge. pp. 26–34. ISBN 0-415-26332-8.
- see e.g. Keith Ward, Is Religion Dangerous?