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Inclusive Logic
A free logic is a logic with fewer existential clause, existential presuppositions than classical logic. Free logics may allow for Term (first-order logic), terms that do not denote any object. Free logics may also allow structure (mathematical logic), models that have an empty domain. A free logic with the latter property is an inclusive logic. Explanation In classical logic there are theorems that clearly presuppose that there is something in the domain of discourse. Consider the following classically valid theorems. :1. \forall xA \Rightarrow \exists xA :2. \forall x \forall rA(x) \Rightarrow \forall rA(r) :3. \forall rA(r) \Rightarrow \exists xA(x) A valid scheme in the theory of First-order logic#Equality and its axioms, equality which exhibits the same feature is :4. \forall x(Fx \rightarrow Gx) \land \exists xFx \rightarrow \exists x(Fx \land Gx) Informally, if F is '=y', G is 'is Pegasus', and we substitute 'Pegasus' for y, then (4) appears to allow us to infer f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premises in a topic-neutral way. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Formal logic contrasts with informal logic, which is associated with informal fallacies, critical thinking, and argumentation theory. While there is no general agreement on how formal and informal logic are to be distinguished, one prominent approach associates their difference with whether the studied arguments are expressed in formal or informal languages. Logic plays a central role in multiple fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises together with a conclusion. Premises and conclusions are usually un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Axiom
An axiom, postulate, or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Ancient Greek word (), meaning 'that which is thought worthy or fit' or 'that which commends itself as evident'. The term has subtle differences in definition when used in the context of different fields of study. As defined in classic philosophy, an axiom is a statement that is so evident or well-established, that it is accepted without controversy or question. As used in modern logic, an axiom is a premise or starting point for reasoning. As used in mathematics, the term ''axiom'' is used in two related but distinguishable senses: "logical axioms" and "non-logical axioms". Logical axioms are usually statements that are taken to be true within the system of logic they define and are often shown in symbolic form (e.g., (''A'' and ''B'') implies ''A''), while non-logical axioms (e.g., ) are actually ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Of Opposition
In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate ''On Interpretation'' and its distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram. This was done several centuries later by Apuleius and Boethius. Summary In traditional logic, a proposition (Latin: ''propositio'') is a spoken assertion (''oratio enunciativa''), not the meaning of an assertion, as in modern philosophy of language and logic. A '' categorical proposition'' is a simple proposition containing two terms, subject () and predicate (), in which the predicate is either asserted or denied of the subject. Every categorical proposition can be reduced to one of four logical forms, named , , , and based on the Latin ' (I affirm), for the affirmative propositions and , and ' (I deny), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wesley C
Wesley may refer to: People and fictional characters * Wesley (name), a given name and a surname Places United States * Wesley, Arkansas, an unincorporated community * Wesley, Georgia, an unincorporated community * Wesley Township, Will County, Illinois * Wesley, Iowa, a city in Kossuth County * Wesley Township, Kossuth County, Iowa * Wesley, Maine, a town * Wesley Township, Washington County, Ohio * Wesley, Oklahoma, an unincorporated community * Wesley, Indiana, an unincorporated town * Wesley, West Virginia, an unincorporated community Elsewhere * Wesley, a hamlet in the township of Stone Mills, Ontario, Canada * Wesley, Dominica, a village * Wesley, New Zealand, a suburb of Auckland * Wesley, Eastern Cape, South Africa, a town Schools * Wesley College (other) * Wesley Institute, Sydney, Australia * Wesley Seminary, Marion, Indiana * Wesley Biblical Seminary, Jackson, Mississippi * Wesley Theological Seminary, Washington, DC * Wesley University of Science and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theory Of Descriptions
The theory of descriptions is the philosopher Bertrand Russell's most significant contribution to the philosophy of language. It is also known as Russell's theory of descriptions (commonly abbreviated as RTD). In short, Russell argued that the syntactic form of descriptions (phrases that took the form of "The aardvark" and "An aardvark") is misleading, as it does not correlate their logical and/or semantic architecture. While descriptions may seem fairly uncontroversial phrases, Russell argued that providing a satisfactory analysis of the linguistic and logical properties of a description is vital to clarity in important philosophical debates, particularly in semantic arguments, epistemology and metaphysical elements. Since the first development of the theory in Russell's 1905 paper " On Denoting", RTD has been hugely influential and well-received within the philosophy of language. However, it has not been without its critics. In particular, the philosophers P. F. Strawson and K ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, artificial intelligence, cognitive science, computer science and various areas of analytic philosophy, especially philosophy of mathematics, philosophy of language, epistemology, and metaphysics.Stanford Encyclopedia of Philosophy"Bertrand Russell" 1 May 2003. He was one of the early 20th century's most prominent logicians, and a founder of analytic philosophy, along with his predecessor Gottlob Frege, his friend and colleague G. E. Moore and his student and protégé Ludwig Wittgenstein. Russell with Moore led the British "revolt against idealism". Together with his former teacher A. N. Whitehead, Russell wrote ''Principia Mathematica'', a milestone in the development of classical logic, and a major attempt to reduce the whole ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Willard Van Orman Quine
Willard Van Orman Quine (; known to his friends as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century". From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. Quine was a teacher of logic and set theory. Quine was famous for his position that first order logic is the only kind worthy of the name, and developed his own system of mathematics and set theory, known as New Foundations. In philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the Quine–Putnam indispensability argument, an argument for the reality of mathematical entities.Colyvan, Mark"Indispensability Arguments in the Philosophy of Mathematics" The Stanford Encyclopedi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Karel Lambert
Karel Lambert (born 1928) is an American philosopher and logician at the University of California, Irvine and the University of Salzburg. He has written extensively on the subject of free logic, a term which he coined. Lambert's law Lambert's law is the major principle in any free definite description theory that says: For all x, x = the y (A) if and only if (A(x/y) & for all y (if A then y = x)). Free logic itself is an adjustment of a given standard predicate logic such as to relieve it of existential assumptions, and so make it a free logic. Taking Bertrand Russell's predicate logic in his ''Principia Mathematica'' as standard, one replaces universal instantiation, \forall x \,\phi x \rightarrow \phi y, with universal specification (\forall x \,\phi x \land E!y \,\phi y) \rightarrow \phi z. Thus universal statements, like "All men are mortal," or "Everything is a unicorn," do not presuppose that there are men or that there is anything. These would be symbolized, with the appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jaakko Hintikka
Kaarlo Jaakko Juhani Hintikka (12 January 1929 – 12 August 2015) was a Finnish philosopher and logician. Life and career Hintikka was born in Helsingin maalaiskunta (now Vantaa). In 1953, he received his doctorate from the University of Helsinki for a thesis entitled ''Distributive Normal Forms in the Calculus of Predicates''. He was a student of Georg Henrik von Wright. Hintikka was a Junior Fellow at Harvard University (1956-1969), and held several professorial appointments at the University of Helsinki, the Academy of Finland, Stanford University, Florida State University and finally Boston University from 1990 until his death. He was the prolific author or co-author of over 30 books and over 300 scholarly articles, Hintikka contributed to mathematical logic, philosophical logic, the philosophy of mathematics, epistemology, language theory, and the philosophy of science. His works have appeared in over nine languages. Hintikka edited the academic journal ''Synthese'' fr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Generalization
In predicate logic, existential generalization (also known as existential introduction, ∃I) is a valid rule of inference that allows one to move from a specific statement, or one instance, to a quantified generalized statement, or existential proposition. In first-order logic, it is often used as a rule for the existential quantifier (\exists) in formal proofs. Example: "Rover loves to wag his tail. Therefore, something loves to wag its tail." Example: "Alice made herself a cup of tea. Therefore, Alice made someone a cup of tea." Example: "Alice made herself a cup of tea. Therefore, someone made someone a cup of tea." In the Fitch-style calculus: : Q(a) \to\ \exists\, Q(x) , where Q(a) is obtained from Q(x) by replacing all its free occurrences of x (or some of them) by a. Quine According to Willard Van Orman Quine, universal instantiation and existential generalization are two aspects of a single principle, for instead of saying that \forall x \, x=x implies \text=\te ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Clause
An existential clause is a clause that refers to the existence or presence of something, such as "There is a God" and "There are boys in the yard". The use of such clauses can be considered analogous to existential quantification in predicate logic, which is often expressed with the phrase "There exist(s)...". Different languages have different ways of forming and using existential clauses. For details on the English forms, see English grammar: ''There'' as pronoun. Formation Many languages form existential clauses without any particular marker by simply using forms of the normal copula verb (the equivalent of English ''be''), the subject being the noun (phrase) referring to the thing whose existence is asserted. For example, the Finnish sentence , meaning "There are boys in the yard", is literally "On the yard is boys". Some languages have a different verb for that purpose: Swedish has , literally "It is found boys on the yard". On the other hand, some languages do not re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists''"'' is a quantifier, while ''x'' is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic is usually a first-order logic together with a specified domain of discourse (over which the quantified variables range), finitely many functions from that domain to itself, finitely many predicates defined on that domain, and a set of ax ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
