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Syncategorema
In logic and linguistics, an expression is syncategorematic if it lacks a denotation but can nonetheless affect the denotation of a larger expression which contains it. Syncategorematic expressions are contrasted with categorematic expressions, which have their own denotations. For example, consider the following rules for interpreting the plus sign. The first rule is syncategorematic since it gives an interpretation for expressions containing the plus sign but does not give an interpretation for the plus sign itself. On the other hand, the second rule does give an interpretation for the plus sign itself, so it is categorematic. # ''Syncategorematic'': For any numeral symbols "n" and "m", the expression "n + m" denotes the sum of the numbers denoted by "n" and "m". # ''Categorematic'': The plus sign "+" denotes the operation of addition. Syncategorematicity was a topic of research in medieval philosophy since syncategorematic expressions cannot stand for any of Aristotle's cat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Of Sherwood
William of Sherwood or William Sherwood (Latin: ''Guillielmus de Shireswode''; ), with numerous variant spellings, was a medieval English scholastic philosopher, logician, and teacher. Little is known of his life, but he is thought to have studied in Paris, was a master at Oxford in 1252, treasurer of Lincoln from 1254/1258 onwards, and a rector of Aylesbury. He was the author of two books which were an important influence on the development of scholastic logic: ''Introductiones in Logicam'' (Introduction to Logic), and '' Syncategoremata''. These are the first known works to deal in a systematic way with what is now called supposition theory, known in William's time as the ''logica moderna''. Life William was probably born in Nottinghamshire, between 1200 and 1210. In common with many educated English men of that time, he may have studied at Oxford University or the University of Paris, or both. There are examples in his logical work which suggest he was a master at Paris. (For ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Pagus
John Pagus (; fl. first half of the 13th century) was a scholastic philosopher at the University of Paris, generally considered the first logician writing at the Arts faculty at Paris. Life He is thought to have been a Master of Arts in the 1220s and to have taught Peter of Spain. At that time he was writing on syncategorematic terms.Parts published in H. A. G. Braakhuis, ''De 13de Eeuwse Tractaten over Syncategorematische Termen''. Vol. I, Ph. Diss., Leiden University, 1979. Works *''Appellationes'' *Commentary on the ''Sentences ''The Four Books of Sentences'' (''Libri Quattuor Sententiarum'') is a book of theology written by Peter Lombard in the 12th century. It is a systematic compilation of theology, written around 1150; it derives its name from the ''sententiae'' o ...'' *''Rationes super Predicamenta Aristotelis'' *''Syncategoremata'' Notes References * Hein Hansen (ed.) ''John Pagus on Aristotle's Categories. A Study and Edition of the Rationes super Praedicamenta'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Terminism
Terminism is the Christian doctrine that there is a time limit for repentance from sin, after which God no longer wills the conversion and salvation of that person. This limit is asserted to be known to God alone, making conversion urgent. Among pietists such as Quakers, the doctrine permitted the co-existence, over the span of a human life, of human free will and God's sovereignty. Terminism in salvation Terminism in salvation is also mentioned in Max Weber's famous sociological work ''The Protestant Ethic and the Spirit of Capitalism''. " erminismassumes that grace is offered to all men, but for everyone either once at a definite moment in his life or at some moment for the last time" (Part II, Ch. 4, Section B). Weber offers in the same paragraph that terminism is "generally (though unjustly) attributed to Pietism by its opponents". Philosophical terminism Terminism is defined by rhetorician Walter J. Ong, who links it to nominalism, as "a concomitant of the highly qu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Semantics
Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ..., linguistics and computer science. History In English, the study of meaning in language has been known by many names that involve the Ancient Greek word (''sema'', "sign, mark, token"). In 1690, a Greek rendering of the term ''semiotics'', the interpretation of signs and symbols, finds an early allusion in John Locke's ''An Essay Concerning Human Understanding'': The third Branch may be called [''simeiotikí'', "semiotics"], or the Doctrine of Signs, the most usual whereof being words, it is aptly enough ter ... [...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] |
Supposition Theory
Supposition theory was a branch of medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of reference, plurality, tense, and modality, within an Aristotelian context. Philosophers such as John Buridan, William of Ockham, William of Sherwood, Walter Burley, Albert of Saxony, and Peter of Spain were its principal developers. By the 14th century it seems to have drifted into at least two fairly distinct theories, the theory of "supposition proper", which included an " ampliation" and is much like a theory of reference, and the theory of "modes of supposition" whose intended function is not clear. Supposition proper Supposition was a semantic relation between a term and what that term was being used to talk about. So, for example, in the suggestion ''Drink another cup'', the term ''cup'' is suppositing for the wine contained in the cup. The logical ''suppositum'' of a term was the object the term referred to. (In grammar, ''suppositum'' was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective \lor can be used to join the two atomic formulas P and Q, rendering the complex formula P \lor Q . Common connectives include negation, disjunction, conjunction, and implication. In standard systems of classical logic, these connectives are interpreted as truth functions, though they receive a variety of alternative interpretations in nonclassical logics. Their classical interpretations are similar to the meanings of natural language expressions such as English "not", "or", "and", and "if", but not identical. Discrepancies between natural language connectives and those of classical logic have motivated nonclassical approaches to natural language meaning as well as approaches which pair a classical compositional semantics wi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Quantifier
In formal semantics, a generalized quantifier (GQ) is an expression that denotes a set of sets. This is the standard semantics assigned to quantified noun phrases. For example, the generalized quantifier ''every boy'' denotes the set of sets of which every boy is a member: \ This treatment of quantifiers has been essential in achieving a compositional semantics for sentences containing quantifiers. Type theory A version of type theory is often used to make the semantics of different kinds of expressions explicit. The standard construction defines the set of types recursively as follows: #''e'' and ''t'' are types. #If ''a'' and ''b'' are both types, then so is \langle a,b\rangle #Nothing is a type, except what can be constructed on the basis of lines 1 and 2 above. Given this definition, we have the simple types ''e'' and ''t'', but also a countable infinity of complex types, some of which include: \langle e,t\rangle;\qquad \langle t,t\rangle;\qquad \langle\langle e,t\rangle, t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Compositionality
In semantics, mathematical logic and related disciplines, the principle of compositionality is the principle that the meaning of a complex expression is determined by the meanings of its constituent expressions and the rules used to combine them. This principle is also called Frege's principle, because Gottlob Frege is widely credited for the first modern formulation of it. The principle was never explicitly stated by Frege, and it was arguably already assumed by George Boole decades before Frege's work. The principle of compositionality is highly debated in linguistics, and among its most challenging problems there are the issues of contextuality, the non-compositionality of idiomatic expressions, and the non-compositionality of quotations. History Discussion of compositionality started to appear at the beginning of the 19th century, during which it was debated whether what was most fundamental in language was compositionality or contextuality, and compositionality was usuall ... [...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''). 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 evaluate to false, and strings with content (like "abc"), other numbers, and objects evaluate to true. Sometimes these classes of expressions are called "truthy" and "falsy" / "false". Classical logic In classical logic, with its intended semantics, the truth values are ''true'' (denoted by ''1'' or the verum ⊤), and '' untrue'' or '' false'' (denoted by ''0'' or the falsum ⊥); that is, classical logic is a two-valued logic. This set of two values is also called the Boolean domain. Corresponding semantics of log ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type System
In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer program, such as variables, expressions, functions, or modules. A type system dictates the operations that can be performed on a term. For variables, the type system determines the allowed values of that term. Type systems formalize and enforce the otherwise implicit categories the programmer uses for algebraic data types, data structures, or other components (e.g. "string", "array of float", "function returning boolean"). Type systems are often specified as part of programming languages and built into interpreters and compilers, although the type system of a language can be extended by optional tools that perform added checks using the language's original type syntax and grammar. The main purpose of a type system in a programming language ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lambda Calculus
Lambda calculus (also written as ''λ''-calculus) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. It is a universal model of computation that can be used to simulate any Turing machine. It was introduced by the mathematician Alonzo Church in the 1930s as part of his research into the foundations of mathematics. Lambda calculus consists of constructing § lambda terms and performing § reduction operations on them. In the simplest form of lambda calculus, terms are built using only the following rules: * x – variable, a character or string representing a parameter or mathematical/logical value. * (\lambda x.M) – abstraction, function definition (M is a lambda term). The variable x becomes bound in the expression. * (M\ N) – application, applying a function M to an argument N. M and N are lambda terms. The reduction operations include: * (\lambda x.M \rightarrow(\l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
