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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] |
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] |
True Contradiction
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] |
Trivium
The trivium is the lower division of the seven liberal arts and comprises grammar, logic, and rhetoric. The trivium is implicit in ("On the Marriage of Philology and Mercury") by Martianus Capella, but the term was not used until the Carolingian Renaissance, when it was coined in imitation of the earlier quadrivium. Grammar, logic, and rhetoric were essential to a classical education, as explained in Plato's dialogues. The three subjects together were denoted by the word ''trivium'' during the Middle Ages, but the tradition of first learning those three subjects was established in Education in ancient Greece, ancient Greece, by rhetoricians such as Isocrates. Contemporary iterations have taken various forms, including those found in certain British and American universities (some being part of the Classical education movement) and at the independent Oundle School in the United Kingdom. Etymology Etymologically, the Latin word means "the place where three roads meet" ( + ); h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absurdity
Absurdity is the state or condition of being unreasonable, meaningless, or so unsound as to be irrational. "Absurd" is the adjective used to describe absurdity, e.g., "Tyler and the boys laughed at the absurd situation." It derives from the Latin ''absurdum'' meaning "out of tune". The Latin ''surdus'' means "deaf", implying stupidity. Absurdity is contrasted with being realistic or reasonable In general usage, absurdity may be synonymous with nonsense, meaninglessness, fancifulness, foolishness, bizarreness, wildness. In specialized usage, absurdity is related to extremes in bad reasoning or pointlessness in reasoning; ridiculousness is related to extremes of incongruous juxtaposition, laughter, and ridicule; and nonsense is related to a lack of meaningfulness. Absurdism is a concept in philosophy related to the notion of absurdity. Philosophy Ancient Greece The Classical Greek philosopher Plato often used "absurdity" to describe very poor reasoning, or the conclusion fro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Principle Of Explosion
In classical logic, intuitionistic logic, and similar logical systems, the principle of explosion is the law according to which any statement can be proven from a contradiction. That is, from a contradiction, any proposition (including its negation) can be inferred; this is known as deductive explosion. The proof of this principle was first given by 12th-century French philosopher William of Soissons. Due to the principle of explosion, the existence of a contradiction ( inconsistency) in a formal axiomatic system is disastrous; since any statement can be proven, it trivializes the concepts of truth and falsity. Around the turn of the 20th century, the discovery of contradictions such as Russell's paradox at the foundations of mathematics thus threatened the entire structure of mathematics. Mathematicians such as Gottlob Frege, Ernst Zermelo, Abraham Fraenkel, and Thoralf Skolem put much effort into revising set theory to eliminate these contradictions, resulting in the mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Actualism
In analytic philosophy, actualism is the view that everything there ''is'' (i.e., everything that has ''being'', in the broadest sense) is actual. Another phrasing of the thesis is that the domain of unrestricted quantification ranges over all and only actual existents. The denial of actualism is possibilism, the thesis that there are some entities that are ''merely possible'': these entities have being but are not actual and, hence, enjoy a "less robust" sort of being than do actually existing things. An important, but significantly different notion of possibilism known as '' modal realism'' was developed by the philosopher David Lewis. On Lewis's account, the actual world is identified with the physical universe of which we are all a part. Other possible worlds exist in exactly the same sense as the actual world; they are simply spatio-temporally unrelated to our world, and to each other. Hence, for Lewis, "merely possible" entities—entities that exist in other possible wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Possible World
A possible world is a complete and consistent way the world is or could have been. Possible worlds are widely used as a formal device in logic, philosophy, and linguistics in order to provide a semantics for intensional and modal logic. Their metaphysical status has been a subject of controversy in philosophy, with modal realists such as David Lewis arguing that they are literally existing alternate realities, and others such as Robert Stalnaker arguing that they are not. Logic Possible worlds are one of the foundational concepts in modal and intensional logics. Formulas in these logics are used to represent statements about what ''might'' be true, what ''should'' be true, what one ''believes'' to be true and so forth. To give these statements a formal interpretation, logicians use structures containing possible worlds. For instance, in the relational semantics for classical propositional modal logic, the formula \Diamond P (read as "possibly P") is actually true if and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth Predicate
In formal theories of truth, a truth predicate is a fundamental concept based on the sentences of a formal language as interpreted logically. That is, it formalizes the concept that is normally expressed by saying that a sentence, statement or idea "is true." Languages which allow a truth predicate Based on "Chomsky Definition", a language is assumed to be a countable set of sentences, each of finite length, and constructed out of a countable set of symbols. A theory of syntax is assumed to introduce symbols, and rules to construct well-formed sentences. A language is called fully interpreted if meanings are attached to its sentences so that they all are either true or false. A fully interpreted language ''L'' which does not have a truth predicate can be extended to a fully interpreted language ''Ľ'' that contains a truth predicate ''T'', i.e., the sentence ''A'' ↔ ''T''(⌈''A''⌉) is true for every sentence ''A'' of ''Ľ'', where ''T''(⌈''A''⌉) stands for "the sentence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Universal Quantification
In mathematical logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any", "for all", "for every", or "given an arbitrary element". It expresses that a predicate can be satisfied by every member of a domain of discourse. In other words, it is the predication of a property or relation to every member of the domain. It asserts that a predicate within the scope of a universal quantifier is true of every value of a predicate variable. It is usually denoted by the turned A (∀) logical operator symbol, which, when used together with a predicate variable, is called a universal quantifier ("", "", or sometimes by "" alone). Universal quantification is distinct from ''existential'' quantification ("there exists"), which only asserts that the property or relation holds for at least one member of the domain. Quantification in general is covered in the article on quantification (logic). The universal quantifier is en ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The University Of Melbourne
The University of Melbourne (colloquially known as Melbourne University) is a public research university located in Melbourne, Australia. Founded in 1853, it is Australia's second oldest university and the oldest in the state of Victoria. Its main campus is located in Parkville, an inner suburb north of Melbourne's central business district, with several other campuses located across the state of Victoria. Incorporated in the 19th century by the colony of Victoria, the University of Melbourne is one of Australia's six sandstone universities and a member of the Group of Eight, Universitas 21, Washington University's McDonnell International Scholars Academy, and the Association of Pacific Rim Universities. Since 1872, many independent residential colleges have become affiliated with the university, providing accommodation for students and faculty, and academic, sporting and cultural programs. There are nine colleges and five university-owned halls of residence located on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
