|
Dialetheism
Dialetheism (; from Greek 'twice' and 'truth') is the view that there are statements that are both true and false. More precisely, it is the belief that there can be a true statement whose negation is also true. Such statements are called "true contradictions", ''dialetheia'', or nondualisms. Dialetheism is not a system of formal logic; instead, it is a thesis about truth that influences the construction of a formal logic, often based on pre-existing systems. Introducing dialetheism has various consequences, depending on the theory into which it is introduced. A common mistake resulting from this is to reject dialetheism on the basis that, in traditional systems of logic (e.g., classical logic and intuitionistic logic), every statement becomes a theorem if a contradiction is true, trivialising such systems when dialetheism is included as an axiom.Ben Burgis, Visiting Professor of Philosophy at the University of Ulsan in South Korea, iBlog&~Blog Other logical systems, however ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paraconsistent Logic
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 contradiction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trivialism
Trivialism is the logical theory that all statements (also known as propositions) are true and, consequently, that all contradictions of the form "p and not p" (e.g. the ball is red and not red) are true. In accordance with this, a trivialist is a person who believes everything is true. In classical logic, trivialism is in direct violation of Aristotle's law of noncontradiction. In philosophy, trivialism is considered by some to be the complete opposite of skepticism. Paraconsistent logics may use "the law of non-triviality" to abstain from trivialism in logical practices that involve true contradictions. Theoretical arguments and anecdotes have been offered for trivialism to contrast it with theories such as modal realism, dialetheism and paraconsistent logics. Overview Etymology ''Trivialism'', as a term, is derived from the Latin word ''trivialis,'' meaning commonplace, in turn derived from the ''trivium'', the three introductory educational topics (grammar, logic, and rhet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Liar Paradox
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie", the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. Assume that "this sentence is false" is true, then we can trust its content, which states the opposite and thus causes a contradition. Similarly, we get a contradiction when we assume the opposite. History The Epimenides paradox (c. 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graham Priest
Graham Priest (born 1948) is a philosopher and logician who is distinguished professor of philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne, where he was Boyce Gibson Professor of Philosophy and also at the University of St Andrews. Life Priest was educated at St John's College, Cambridge and the London School of Economics. His thesis advisor was John Lane Bell. He also holds a DLitt from the University of Melbourne. Priest was elected a corresponding fellow of the Australian Academy of the Humanities in 1995. In addition to his work in philosophy and logic, Priest practised karate-do. He is 3rd dan, International Karate-do Shobukai; 4th dan, shitō-ryū, and an Australian National kumite referee and kata judge. Presently, he practices tai chi. Philosophical work Priest is known for his defence of dialetheism, his in-depth analyses of the logical paradoxes (holding the thesis that there is a uniform treatment for many ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Richard Sylvan
Richard Sylvan (13 December 1935 – 16 June 1996) was a New Zealand–born philosopher, logician, and environmentalist. Biography Sylvan was born Francis Richard Routley in Levin, New Zealand, and his early work is cited with this surname. He studied at Victoria University College of the University of New Zealand (now Victoria University of Wellington), and then Princeton University, before taking positions successively at several Australian institutions, including the University of Sydney. From 1971 until his death in Bali, Indonesia, he was a fellow at the Research School of Social Sciences (RSSS) at the Australian National University in Canberra. Sylvan was married to the philosopher/environmentalist Val Routley (later, Val Plumwood), with whom he worked closely for twenty years before their separation in 1982. After his divorce from Plumwood, he married Louise Sylvan (née Mirlin) in 1983 and adopted the last name ''Sylvan'' (an English word meaning "of the forest") to r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jc Beall
Jc Beall is an American philosopher working in philosophy of logic and philosophical logic, who since 2020, holds the O’Neill Family Chair of Philosophy at the University of Notre Dame. He was previously the Board of Trustees Distinguished Professor of Philosophy at the University of Connecticut. Education and career Beall earned a BA in philosophy from Grove City College. Beall earned his Ph.D. in philosophy from the University of Massachusetts, Amherst, and joined the faculty at the University of Connecticut as an assistant professor in 2000. He has also held part-time or visiting appointments at Yonsei University, University of Tasmania, University of Aberdeen, St Andrews University and University of Otago. Philosophical work Beall is best known in philosophy for contributions to philosophical logic (particularly non-classical logic) and to the philosophy of logic. Beall, together with Greg Restall (an Australian logician and philosopher), is a pioneer of a widely discus ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contradiction
In traditional logic, a contradiction involves a proposition conflicting either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." In modern formal logic and type theory, the term is mainly used instead for a ''single'' proposition, often denoted by the falsum symbol \bot; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History By creation of a paradox, Plato's '' Euthydemus'' dialogue demonstrates the need for the notion of ''contradiction''. In the ensuing ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values ('' true'' or '' false''). Truth values are used in computing as well as various types of logic. Computing In some programming languages, any expression can be evaluated in a context that expects a Boolean data type. Typically (though this varies by programming language) expressions like the number zero, the empty string, empty lists, and null are treated as false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called falsy and truthy. For example, in Lisp, nil, the empty list, is treated as false, and all other values are treated as true. In C, the number 0 or 0.0 is false, and all other values are treated as true. In JavaScript, the empty string (""), null, undefined, NaN, +0, −0 and false are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Paradox
A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true or apparently true premises, leads to a seemingly self-contradictory or a logically unacceptable conclusion. A paradox usually involves contradictory-yet-interrelated elements that exist simultaneously and persist over time. They result in "persistent contradiction between interdependent elements" leading to a lasting "unity of opposites". In logic, many paradoxes exist that are known to be invalid arguments, yet are nevertheless valuable in promoting critical thinking, while other paradoxes have revealed errors in definitions that were assumed to be rigorous, and have caused axioms of mathematics and logic to be re-examined. One example is Russell's paradox, which questions whether a "list of all lists that do not contain themselves" would include itself and showed that attempts to found set theory on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Review Of Symbolic Logic
The Association for Symbolic Logic (ASL) is an international organization of specialists in mathematical logic and philosophical logic. The ASL was founded in 1936, and its first president was Curt John Ducasse. The current president of the ASL is Phokion Kolaitis. Publications The ASL publishes books and academic journals. Its three official journals are: * ''Journal of Symbolic Logic'' – publishes research in all areas of mathematical logic. Founded in 1936, . * ''Bulletin of Symbolic Logic'' – publishes primarily expository articles and reviews. Founded in 1995, . * ''Review of Symbolic Logic'' – publishes research relating to logic, philosophy, science, and their interactions. Founded in 2008, . In addition, the ASL has a sponsored journal: * ''Journal of Logic and Analysis'' publishes research on the interactions between mathematical logic and pure and applied analysis. Founded in 2009 as an open-access successor to the Springer journal ''Logic and Analysis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Many-valued Logic
Many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's Term logic, logical calculus, there were only two possible values (i.e., "true" and "false") for any proposition. Classical two-valued logic may be extended to ''n''-valued logic for ''n'' greater than 2. Those most popular in the literature are Three-valued logic, three-valued (e.g., Jan Łukasiewicz, Łukasiewicz's and Stephen Cole Kleene, Kleene's, which accept the values "true", "false", and "unknown"), four-valued logic, four-valued, nine-valued logic, nine-valued, the finite-valued logic, finite-valued (finitely-many valued) with more than three values, and the infinite-valued logic, infinite-valued (infinitely-many-valued), such as fuzzy logic and probabilistic logic, probability logic. History It is ''wrong'' that the first known classical logician who did not fully accept the law of excluded middle was Aristotle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fuzzy Logic
Fuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. By contrast, in Boolean algebra, Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term ''fuzzy logic'' was introduced with the 1965 proposal of fuzzy set theory by mathematician Lotfi A. Zadeh, Lotfi Zadeh. Fuzzy logic had, however, been studied since the 1920s, as Łukasiewicz logic, infinite-valued logic—notably by Jan Łukasiewicz, Łukasiewicz and Alfred Tarski, Tarski. Fuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). These models have the capability of recognising, representing, manipulating, in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
