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Self-refuting Idea
A self-refuting idea or self-defeating idea is an idea or statement 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). Variations Directly self-denying statements Directly self-denying statements are characterised by being necessarily (or inherently) false. The Epimenides paradox is a statement of the form "this statement is false". Such statements troubled philosophers, es ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Consequence
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statement (logic), statements that hold true when one statement logically ''follows from'' one or more statements. A Validity (logic), valid logical argument is one in which the Consequent, conclusion is entailed by the premises, because the conclusion is the consequence of the premises. The philosophical analysis of logical consequence involves the questions: In what sense does a conclusion follow from its premises? and What does it mean for a conclusion to be a consequence of premises?Beall, JC and Restall, Greg, Logical Consequence' The Stanford Encyclopedia of Philosophy (Fall 2009 Edition), Edward N. Zalta (ed.). All of philosophical logic is meant to provide accounts of the nature of logical consequence and the nature of logical truth. Logical consequence is logical truth, necessary and Formalism (philosophy of mathematics), formal, by wa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Consistency Proof
In deductive logic, a consistent theory (mathematical logic), theory is one that does not lead to a logical contradiction. A theory T is consistent if there is no Formula (mathematical logic), formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences of T. Let A be a set of Closed-form expression, closed sentences (informally "axioms") and \langle A\rangle the set of closed sentences provable from A under some (specified, possibly implicitly) formal deductive system. The set of axioms A is consistent when there is no formula \varphi such that \varphi \in \langle A \rangle and \lnot \varphi \in \langle A \rangle. A ''trivial'' theory (i.e., one which proves every sentence in the language of the theory) is clearly inconsistent. Conversely, in an principle of explosion, explosive formal system (e.g., classical or intuitionistic propositional or first-order logics) every inconsistent theory is trivial. Consistency of a theory is a sy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 rigorously tested to determine whether it is in fact reality. Synopsis While dreaming, one does not normally realize one is dreaming. On more rare occasions, the dream may be contained inside another dream with the very act of realizing that one is dreaming, itself, being only a dream that one is not aware of having. This has led philosophers to wonder whether it is possible for one ever to be certain, at any given point in time, that one is not in fact dreaming, or whether indeed it could be possible for one to remain in a perpetual dream state and never experience the reality of wakefulness at all. In Western philosophy this philosophical puzzle was referred to by Plato ( ''Theaetetus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evil Demon
The evil demon, also known as ''Deus deceptor'', malicious demon, and evil genius, is an epistemological concept that features prominently in Cartesian philosophy. In the first of his 1641 ''Meditations on First Philosophy'', Descartes imagines that a malevolent God or an evil demon, of "utmost power and cunning has employed all his energies in order to deceive me." This malevolent God or evil demon is imagined to present a complete illusion of an external world, so that Descartes can say, "I shall think that the sky, the air, the earth, colours, shapes, sounds and all external things are merely the delusions of dreams which he has devised to ensnare my judgement. I shall consider myself as not having hands or eyes, or flesh, or blood or senses, but as falsely believing that I have all these things." Some Cartesian scholars opine that the malevolent God or evil demon is also omnipotent, and thus capable of altering mathematics and the fundamentals of logic, though omnipoten ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skeptical Hypothesis
Philosophical skepticism ( UK spelling: scepticism; from Greek σκέψις ''skepsis'', "inquiry") is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even rejects very plausible knowledge claims that belong to basic common sense. Philosophical skeptics are often classified into two general categories: Those who deny all possibility of knowledge, and those who advocate for the suspension of judgment due to the inadequacy of evidence. This distinction is modeled after the differences between the Academic skeptics and the Pyrrhonian skeptics in ancient Greek philosophy. Pyrrhonian skepticism is a practice of suspending judgement, and skepticism in this sense is understood as a way of life that helps the practitioner achieve inner peace. Some types of philosophical skepticism reject all forms of knowledge while others limit this rejection to certain fields, for example, knowledge about moral doctrin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thought Experiment
A thought experiment is an imaginary scenario that is meant to elucidate or test an argument or theory. It is often an experiment that would be hard, impossible, or unethical to actually perform. It can also be an abstract hypothetical that is meant to test our intuitions about morality or other fundamental philosophical questions. History The ancient Greek , "was the most ancient pattern of mathematical proof", and existed before Euclidean geometry, Euclidean mathematics, where the emphasis was on the conceptual, rather than on the experimental part of a thought experiment. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the equivalent German term . Ørsted was also the first to use the equivalent term in 1820. By 1883, Ernst Mach used in a different sense, to denote exclusively the conduct of a experiment that would be subsequently performed as a by his students. Physical and mental experimentation could then be contrasted: Mach asked hi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brain In A Vat
In philosophy, the brain in a vat (BIV) is a scenario used in a variety of thought experiments intended to draw out certain features of human conceptions of knowledge, reality, truth, mind, consciousness, and Meaning (philosophy of language), meaning. Gilbert Harman conceived the scenario, which Hilary Putnam turned into a modernized version of René Descartes's evil demon thought experiment. Following many science fiction stories, the scenario involves a mad scientist who might remove a person's brain from the body, suspend it in a vat of life-sustaining liquid, and brain–computer interface, connect its neurons by wires to a supercomputer that would provide it with action potential, electrical impulses identical to those a brain normally receives. According to such stories, the computer would then be simulated reality, simulating reality (including appropriate responses to the brain's own output) and the "disembodied" brain would continue to have perfectly normal conscious exp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof By Contradiction
In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved. In this general sense, proof by contradiction is also known as indirect proof, proof by assuming the opposite, and ''reductio ad impossibile''. A mathematical proof employing proof by contradiction usually proceeds as follows: #The proposition to be proved is ''P''. #We assume ''P'' to be false, i.e., we assume ''¬P''. #It is then shown that ''¬P'' implies falsehood. This is typically accomplished by deriving two mutually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraconsistent Logics
Paraconsistent logic is a type of non-classical logic that allows for the coexistence of contradictory statements without leading to a logical explosion where anything can be proven true. Specifically, paraconsistent logic is the subfield of logic that is concerned with studying and developing "inconsistency-tolerant" systems of logic, purposefully excluding the principle of explosion. Inconsistency-tolerant logics have been discussed since at least 1910 (and arguably much earlier, for example in the writings of Aristotle); however, the term ''paraconsistent'' ("beside the consistent") was first coined in 1976, by the Peruvian philosopher Francisco Miró Quesada Cantuarias. The study of paraconsistent logic has been dubbed paraconsistency, which encompasses the school of dialetheism. Definition In classical logic (as well as intuitionistic logic and most other logics), contradictions entail everything. This feature, known as the principle of explosion or ''ex contradictione se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Property Is Theft!
Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of the property, an owner of property may have the right to consume, alter, share, rent, sell, exchange, transfer, give away, or destroy it, or to exclude others from doing these things, as well as to perhaps abandon it; whereas regardless of the nature of the property, the owner thereof has the right to properly use it under the granted property rights. In economics and political economy, there are three broad forms of property: private property, public property, and collective property (or ''cooperative propert''y). Property may be jointly owned by more than one party equally or unequally, or according to simple or complex agreements; to distinguish ownership and easement from rent, there is an expectation that each party's will with regard to the property be clearly defined and unconditional.. The parties may expe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pierre-Joseph Proudhon
Pierre-Joseph Proudhon (, ; ; 1809 – 19 January 1865) was a French anarchist, socialist, philosopher, and economist who founded mutualist philosophy and is considered by many to be the "father of anarchism". He was the first person to call himself an ''anarchist'', using that term, and is widely regarded as one of anarchism's most influential theorists. Proudhon became a member of the French Parliament after the Revolution of 1848, whereafter he referred to himself as a '' federalist''. Proudhon described the liberty he pursued as the synthesis of community and individualism. Some consider his mutualism to be part of individualist anarchism while others regard it to be part of social anarchism.The Anarchist FAQ Collective; McKay, Ian, ed. (2008/2012). ''An Anarchist Faq''. I/II. Oakland/Edinburgh: AK Press. . . Proudhon, who was born in Besançon, was a printer who taught himself Latin in order to better print books in the language. His best-known assertion is that " p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
