Self-refuting idea
Encyclopedia
Self-refuting 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 accused by their detractors of being self-refuting, and such accusations are therefore almost always controversial, with defenders claiming that the idea is being misunderstood or that the argument
Argument
In philosophy and logic, an argument is an attempt to persuade someone of something, or give evidence or reasons for accepting a particular conclusion.Argument may also refer to:-Mathematics and computer science:...

 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
Consistency
Consistency can refer to:* Consistency , the psychological need to be consistent with prior acts and statements* "Consistency", an 1887 speech by Mark Twain...

 (circular reasoning
Circular reasoning
Circular reasoning, or in other words, paradoxical thinking, is a type of formal logical fallacy in which the proposition to be proved is assumed implicitly or explicitly in one of the premises. For example:"Only an untrustworthy person would run for office...

) or exception
Exception
Exception may refer to:* An action that is not part of ordinary operations or standards* Exception handling, in programming languages** or a programming interrupt itself of which exception handling is meant to deal with....

 (self contradiction
Contradiction
In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

). 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
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...

 developed his "Theory of Types" to formalize a set of rules that would prevent such statements (more formally Russell's paradox
Russell's paradox
In the foundations of mathematics, Russell's paradox , discovered by Bertrand Russell in 1901, showed that the naive set theory created by Georg Cantor leads to a contradiction...

) 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
Kurt Gödel
Kurt Friedrich Gödel was an Austrian logician, mathematician and philosopher. Later in his life he emigrated to the United States to escape the effects of World War II. One of the most significant logicians of all time, Gödel made an immense impact upon scientific and philosophical thinking in the...

 showed that it must contain independent
Independence (mathematical logic)
In mathematical logic, independence refers to the unprovability of a sentence from other sentences.A sentence σ is independent of a given first-order theory T if T neither proves nor refutes σ; that is, it is impossible to prove σ from T, and it is also impossible to prove from T that...

 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
Complete theory
In mathematical logic, a theory is complete if it is a maximal consistent set of sentences, i.e., if it is consistent, and none of its proper extensions is consistent...

 and consistent
Consistency proof
In logic, a consistent theory is one that does not contain a contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if and only if it has a model, i.e. there exists an interpretation under which all...

.

Indirectly self-denying statements or "fallacy of the stolen concept"

Objectivists
Objectivism (Ayn Rand)
Objectivism is a philosophy created by the Russian-American philosopher and novelist Ayn Rand . Objectivism holds that reality exists independent of consciousness, that human beings have direct contact with reality through sense perception, that one can attain objective knowledge from perception...

 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
Pierre-Joseph Proudhon
Pierre-Joseph Proudhon was a French politician, mutualist philosopher and socialist. He was a member of the French Parliament, and he was the first person to call himself an "anarchist". He is considered among the most influential theorists and organisers of anarchism...

's assertion, "All property is theft"
Property is theft!
Property is theft! is a slogan coined by French anarchist Pierre-Joseph Proudhon in his 1840 book What is Property? Or, an Inquiry into the Principle of Right and of Government....

.
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 slogan is not an instance of the stolen concept fallacy under Proudhon's intended meaning. 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.
http://www.marxists.org/reference/subject/economics/proudhon/property/ch01.htm 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
Usufruct
Usufruct is the legal right to use and derive profit or benefit from property that either belongs to another person or which is under common ownership, as long as the property is not damaged or destroyed...

 rights idea. In What is Property?
What Is Property?
What Is Property?: or, An Inquiry into the Principle of Right and of Government is an influential work of nonfiction on the concept of property and its relation to anarchist philosophy by the French anarchist and mutualist Pierre-Joseph Proudhon, first published in 1840.In the book, Proudhon most...

 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. Para-consistent logic has been criticized as an attempt to evade contradiction as it consists of sub-contrary variates and not contradicting statements as it is often claimed.

Brain in a Vat

Brain in a vat
Brain in a vat
In philosophy, the brain in a vat is an element used in a variety of thought experiments intended to draw out certain features of our ideas of knowledge, reality, truth, mind, and meaning...

 is a thought experiment
Thought experiment
A thought experiment or Gedankenexperiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences...

 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
Dream argument
The dream argument is the postulation that the act of dreaming provides preliminary evidence that the senses we trust to distinguish reality from illusion should not be fully trusted, and therefore any state that is dependent on our senses should at the very least be carefully examined and...

.
Philosopher Hilary Putnam
Hilary Putnam
Hilary Whitehall Putnam is an American philosopher, mathematician and computer scientist, who has been a central figure in analytic philosophy since the 1960s, especially in philosophy of mind, philosophy of language, philosophy of mathematics, and philosophy of science...

 argues that some versions of the thought experiment would be inconsistent due to semantic externalism
Semantic externalism
In the philosophy of language, semantic externalism is the view that the meaning of a term is determined, in whole or in part, by factors external to the speaker. According to an externalist position, one can claim without contradiction that two speakers could be in exactly the same brain state at...

. For a brain in a vat that had only ever experienced the simulated world, the denial "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. For the same reason, it can only falsely assert "I'm a brain in vat".

Determinism

It can be argued that to assert determinism
Determinism
Determinism is the general philosophical thesis that states that for everything that happens there are conditions such that, given them, nothing else could happen. There are many versions of this thesis. Each of them rests upon various alleged connections, and interdependencies of things and...

 as a rational claim in a debate is doubly self-defeating.
  1. To count as rational, a belief must be freely chosen, which according to the determinist is impossible
  2. Any kind of debate seems to be posited on the idea that the parties involved are trying to change each others minds.


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, such programs are themselves not rational because they simply follow a certain deterministic pre-programmed path and nothing more. If the program itself is false, then the outcome will also be false, yet the algorithm will never understand it is false hence any deterministic entity is proven to be incapable of rationality. Similarly, if the program is correct, then the outcome should be correct as well via a pre-determined step-by-step process. A computer algorithm can be programmed to give out correct answers as well as incorrect. One cannot call the computer itself rational or irrational, because it didn't do any "thinking", it simply did what its pre-determined code told it to do. Therefore, whatever answer its code says is correct, the computer algorithm's final outcome will also say that is correct. One could make a computer algorithm give you any answer that one wishes, all that matters is the code entered. Therefore, a computer algorithm obtained the correct answer simply because it already had the correct path given to it by its programmer. Furthermore, one has to take into consideration that it is a human being who is doing the programming in the first place. Therefore, assuming the human to have free will, it is the human's own free will that programmed the deterministic algorithm in a certain way so as to allow behavior that seems 'rational' even though it is not. This proves that any attempt to avoid the self-refuting conclusions of determinism is impossible.

Ethical Egoism

It has been argued that extreme ethical egoism
Ethical egoism
Ethical egoism is the normative ethical position that moral agents ought to do what is in their own self-interest. It differs from psychological egoism, which claims that people can only act in their self-interest. Ethical egoism also differs from rational egoism, which holds merely that it is...

 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
Mary Midgley
Mary Midgley, née Scrutton , is an English moral philosopher. She was a Senior Lecturer in Philosophy at Newcastle University and is known for her work on science, ethics and animal rights. She wrote her first book, Beast And Man: The Roots of Human Nature , when she was in her fifties...

 claims 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.

Several other philosophers argue that Eliminative materialism
Eliminative materialism
Eliminative materialism is a materialist position in the philosophy of mind. Its primary claim is that people's common-sense understanding of the mind is false and that certain classes of mental states that most people believe in do not exist...

 is self-refuting.

However, other forms of materialism
Materialism
In philosophy, the theory of materialism holds that the only thing that exists is matter; that all things are composed of material and all phenomena are the result of material interactions. In other words, matter is the only substance...

 may escape this kind of argument because, rather than eliminating the mental
Mind
The concept of mind is understood in many different ways by many different traditions, ranging from panpsychism and animism to traditional and organized religious views, as well as secular and materialist philosophies. Most agree that minds are constituted by conscious experience and intelligent...

, they seek to identify it with, or reduce it to, the material. For instance, identity theorists such as J. J. C. Smart
J. J. C. Smart
John Jamieson Carswell "Jack" Smart AC is an Australian philosopher and academic who is currently Emeritus Professor of Philosophy at Monash University, Australia...

, Ullin Place
Ullin Place
Ullin Place was a British philosopher and psychologist. Along with J. J. C. Smart, he developed the identity theory of mind. Place was born in Yorkshire and studied under Gilbert Ryle at Oxford University. There, he became acquainted with philosophy of mind in the logical behaviorist tradition,...

 and E. G. Boring claim that ideas exist materially as patterns of neural structure and activity.. The claims made by Smart and other however, have been criticized and found to be incoherent on the account of materialism as any philosophy of mind that reduces the mental to the material is still problematic as it denies the efficacy of the mind and its contents. As J.P. Moreland explains, such attempts are problematic as they amount to mere semantic tricks.

Epimenides paradox

The first notable self-refuting idea is the Epimenides paradox
Epimenides paradox
The Epimenides paradox is a problem in logic. It is named after the Cretan philosopher Epimenides of Knossos , There is no single statement of the problem; a typical variation is given in the book Gödel, Escher, Bach, by Douglas Hofstadter:...

, a statement attributed to Epimenides, a Cretan philosopher, that "All Cretans are liars". Interpreted (for the present purpose) as meaning "no Cretan ever speaks the truth" this cannot be true if uttered by a Cretan.
For the purpose of creating a self-refuting statement, this paradox might be better stated as "I am lying." This is because the first statement does not, if false, necessarily mean that the speaker is telling the truth (the third option being "some Cretans do not speak the truth"). The second statement has no third alternative—the speaker's statement is either true or false.

Evolutionary Naturalism

Alvin Plantinga
Alvin Plantinga
Alvin Carl Plantinga is an American analytic philosopher and the emeritus John A. O'Brien Professor of Philosophy at the University of Notre Dame. He is known for his work in philosophy of religion, epistemology, metaphysics, and Christian apologetics...

 argues in his Evolutionary argument against naturalism
Evolutionary argument against naturalism
The evolutionary argument against naturalism is a philosophical argument regarding a perceived tension between biological evolutionary theory and philosophical naturalism — the belief that there are no supernatural entities or processes...

 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 utlizes cognitive faculties, such as evolutionary theory would be undermined. In this particular case, since it's the confluence of evolutionary theory and naturalism that cause the self-contradiction, one would be forced to abandon naturalism in order to salvage evolutionary theory from falling into obscurity.
This argument has been supported

Foundationalism

The philosopher Anthony Kenny
Anthony Kenny
Sir Anthony John Patrick Kenny FBA is an English philosopher whose interests lie in the philosophy of mind, ancient and scholastic philosophy, the philosophy of Wittgenstein and the philosophy of religion...

 argues that the idea, "common to theists like Aquinas and Descartes and to an atheist like Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...

" that "Rational belief [is] either self-evident or based directly or indirectly on what is evident" (which he termed "foundationalism" following Plantinga
Alvin Plantinga
Alvin Carl Plantinga is an American analytic philosopher and the emeritus John A. O'Brien Professor of Philosophy at the University of Notre Dame. He is known for his work in philosophy of religion, epistemology, metaphysics, and Christian apologetics...

) 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 belief
Basic belief
Under the epistemological view called foundationalism, basic beliefs are the axioms of a belief system.Foundationalism holds that all beliefs must be justified in order to be believed...

s (reformed foundationalism).

Relativism

It is often asserted that relativism
Relativism
Relativism is the concept that points of view have no absolute truth or validity, having only relative, subjective value according to differences in perception and consideration....

 about truth
Truth
Truth has a variety of meanings, such as the state of being in accord with fact or reality. It can also mean having fidelity to an original or to a standard or ideal. In a common usage, it also means constancy or sincerity in action or character...

 must be applied to itself. The cruder form of the argument concludes that since the relativist is asserting relativism as 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
Norm (philosophy)
Norms are concepts of practical import, oriented to effecting an action, rather than conceptual abstractions that describe, explain, and express. Normative sentences imply “ought-to” types of statements and assertions, in distinction to sentences that provide “is” types of statements and assertions...

 force over someone who has different basic beliefs.

Skepticism

Philosophical skeptics claim "nothing can be known". Can that claim itself be known, or is it self-refuting? One very old response to this problem is Academic skepticism
Academic skepticism
Academic skepticism refers to the skeptical period of ancient Platonism dating from around 266 BC, when Arcesilaus became head of the Platonic Academy, until around 90 BC, when Antiochus of Ascalon rejected skepticism. Like their fellow Pyrrhonists, they maintained that knowledge of things is...

: an exception is made for the skeptic's own claim. This leads to further debate about consistency and special pleading
Special pleading
Special pleading is a form of spurious argumentation where a position in a dispute introduces favorable details or excludes unfavorable details by alleging a need to apply additional considerations without proper criticism of these considerations themselves. Essentially, this involves someone...

. 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.

Scientism

The statement "no statements are true unless they can be proven scientifically", is claimed to be self-refuting insofar as it cannot be proven scientifically; the same goes for essentially similar views like "no statements are true unless they can be shown empirically to be true". (This kind of issue was a serious problem for logical positivism
Logical positivism
Logical positivism is a philosophy that combines empiricism—the idea that observational evidence is indispensable for knowledge—with a version of rationalism incorporating mathematical and logico-linguistic constructs and deductions of epistemology.It may be considered as a type of analytic...

.)

Solipsism

On the face of it, a statement of solipsism
Solipsism
Solipsism is the philosophical idea that only one's own mind is sure to exist. The term comes from Latin solus and ipse . Solipsism as an epistemological position holds that knowledge of anything outside one's own mind is unsure. The external world and other minds cannot be known, and might not...

 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
Entertainment
Entertainment consists of any activity which provides a diversion or permits people to amuse themselves in their leisure time. Entertainment is generally passive, such as watching opera or a movie. Active forms of amusement, such as sports, are more often considered to be recreation...

.

The solipsist can adopt the rather surreal
Surrealism
Surrealism is a cultural movement that began in the early 1920s, and is best known for the visual artworks and writings of the group members....

 maneuver of claiming that their 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" are both claimed to be self-refuting on the basis that they can neither be empirically verified nor falsified.

Wittgenstein's Tractatus

The Tractatus Logico-Philosophicus
Tractatus Logico-Philosophicus
The Tractatus Logico-Philosophicus is the only book-length philosophical work published by the Austrian philosopher Ludwig Wittgenstein in his lifetime. It was an ambitious project: to identify the relationship between language and reality and to define the limits of science...

 is an unusual example of a self-refuting argument, in that Ludwig Wittgenstein
Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein was an Austrian philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language. He was professor in philosophy at the University of Cambridge from 1939 until 1947...

 explicitly admits to the issue at the end of the work:


"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
Søren Kierkegaard
Søren Aabye Kierkegaard was a Danish Christian philosopher, theologian and religious author. He was a critic of idealist intellectuals and philosophers of his time, such as Georg Wilhelm Friedrich Hegel, Friedrich Wilhelm Joseph Schelling and Karl Wilhelm Friedrich Schlegel...

 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

  • Contradiction
    Contradiction
    In classical logic, a contradiction consists of a logical incompatibility between two or more propositions. It occurs when the propositions, taken together, yield two conclusions which form the logical, usually opposite inversions of each other...

  • Paradox
    Paradox
    Similar to Circular reasoning, A paradox is a seemingly true statement or group of statements that lead to a contradiction or a situation which seems to defy logic or intuition...

  • Performative contradiction
    Performative contradiction
    A performative contradiction arises when the propositional content of a statement contradicts the presuppositions of asserting it. An example of a performative contradiction is the statement "this statement can't be asserted" because the very act of asserting it presupposes it can be...

  • Self-defeating prophecy
    Self-defeating prophecy
    A self-defeating prophecy is the complementary opposite of a self-fulfilling prophecy: a prediction that prevents what it predicts from happening. This is also known as the "prophet's dilemma"....

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