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Something (concept)
Something and anything are concepts of existence in ontology, contrasting with the concept of nothing. Both are used to describe the understanding that what exists is not nothing without needing to address the existence of everything. The philosopher, David Lewis, has pointed out that these are ''necessarily'' vague terms, asserting that "ontological assertions of common sense are correct if the quantifiers—such words as "something" and "anything"—are restricted roughly to ordinary or familiar things." The idea that "something" is the opposite of "nothing" has existed at least since it was proposed by the Neoplatonist philosopher Porphyry in the 3rd century. One of the most basic questions of both science and philosophy is: why is there something rather than nothing at all? A question that follows from this is whether it is ever actually possible for there to be nothing at all, or whether there must always be something. Grammatically, "''something'' and ''anything'' are co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Concept
Concepts are defined as abstract ideas. They are understood to be the fundamental building blocks of the concept behind principles, thoughts and beliefs. They play an important role in all aspects of cognition. As such, concepts are studied by several disciplines, such as linguistics, psychology, and philosophy, and these disciplines are interested in the logical and psychological structure of concepts, and how they are put together to form thoughts and sentences. The study of concepts has served as an important flagship of an emerging interdisciplinary approach called cognitive science. In contemporary philosophy, there are at least three prevailing ways to understand what a concept is: * Concepts as mental representations, where concepts are entities that exist in the mind (mental objects) * Concepts as abilities, where concepts are abilities peculiar to cognitive agents (mental states) * Concepts as Fregean senses, where concepts are abstract objects, as opposed to mental ob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Propositional Function
In propositional calculus, a propositional function or a predicate is a sentence expressed in a way that would assume the value of true or false, except that within the sentence there is a variable (''x'') that is not defined or specified (thus being a free variable), which leaves the statement undetermined. The sentence may contain several such variables (e.g. ''n'' variables, in which case the function takes ''n'' arguments). Overview As a mathematical function, ''A''(''x'') or ''A''(''x'', ''x'', ..., ''x''), the propositional function is abstracted from predicates or propositional forms. As an example, consider the predicate scheme, "x is hot". The substitution of any entity for ''x'' will produce a specific proposition that can be described as either true or false, even though "''x'' is hot" on its own has no value as either a true or false statement. However, when a value is assigned to ''x'' , such as lava, the function then has the value ''true''; while one assigns to ''x ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existentialist Concepts
Existentialism ( ) is a form of philosophical inquiry that explores the problem of human existence and centers on human thinking, feeling, and acting. Existentialist thinkers frequently explore issues related to the meaning, purpose, and value of human existence, and the role of personal agency in transforming one's life. In the view of an existentialist, the individual's starting point is phenomenological, grounded in the immediate direct experience of life. Key concepts include "existential angst", a sense of dread, disorientation, confusion, or anxiety in the face of an apparently meaningless or absurd world, and also authenticity, courage, and human-heartedness. Existentialism is associated with several 19th- and 20th-century European philosophers who shared an emphasis on the human subject, despite often profound differences in thought. Among the earliest figures associated with existentialism are philosophers Søren Kierkegaard and Friedrich Nietzsche and novelist Fyo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Much Ado About Nothing
''Much Ado About Nothing'' is a comedy by William Shakespeare thought to have been written in 1598 and 1599.See textual notes to ''Much Ado About Nothing'' in ''The Norton Shakespeare'' ( W. W. Norton & Company, 1997 ) p. 1387 The play was included in the ''First Folio'', published in 1623. The play is set in Messina and revolves around two romantic pairings that emerge when a group of soldiers arrive in the town. The first, between Claudio and Hero, is nearly altered by the accusations of the villain, Don John. The second romance, between Claudio's friend Benedick and Hero's cousin Beatrice, takes centre stage as the play goes on, with both characters' wit and banter providing much of the humour. Through "noting" (sounding like "nothing", and meaning gossip, rumour, overhearing), Benedick and Beatrice are tricked into confessing their love for each other, and Claudio is tricked into believing that Hero is not a maiden (virgin). The title's play on words references t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate Variable
In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation (between terms), but which has not been specifically assigned any particular relation (or meaning). Common symbols for denoting predicate variables include capital roman letters such as P, Q and R, or lower case roman letters, e.g., x. In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond to propositional variables which can stand for well-formed formulas of the same logic, and such variables can be quantified by means of (at least) second-order quantifiers. Notation Predicate variables should be distinguished from predicate constants, which could be represented either with a different (exclusive) set of predicate letters, or by their own symbols which really do have their own specific meaning in their domain of discourse: e.g. =, \ \in , \ \le,\ <, \ \sub,... . If letters are ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Valuation (logic)
In logic and model theory, a valuation can be: *In propositional logic, an assignment of truth values to propositional variables, with a corresponding assignment of truth values to all propositional formulas with those variables. *In first-order logic and higher-order logics, a structure, (the interpretation) and the corresponding assignment of a truth value to each sentence in the language for that structure (the valuation proper). The interpretation must be a homomorphism, while valuation is simply a function. Mathematical logic In mathematical logic (especially model theory), a valuation is an assignment of truth values to formal sentences that follows a truth schema. Valuations are also called truth assignments. In propositional logic, there are no quantifiers, and formulas are built from propositional variables using logical connectives. In this context, a valuation begins with an assignment of a truth value to each propositional variable. This assignment can be uniquely ext ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Variables And Bound Variables
In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation (symbol) that specifies places in an expression where substitution may take place and is not a parameter of this or any container expression. Some older books use the terms real variable and apparent variable for free variable and bound variable, respectively. The idea is related to a placeholder (a symbol that will later be replaced by some value), or a wildcard character that stands for an unspecified symbol. In computer programming, the term free variable refers to variables used in a function that are neither local variables nor parameters of that function. The term non-local variable is often a synonym in this context. A bound variable, in contrast, is a variable that has been ''bound'' to a specific value or range of values in the domain of discourse or universe. This may be achieved through the use of logical quantifi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Assertion
In mathematical logic, a judgment (or judgement) or assertion is a statement or enunciation in a metalanguage. For example, typical judgments in first-order logic would be ''that a string is a well-formed formula'', or ''that a proposition is true''. Similarly, a judgment may assert the occurrence of a free variable in an expression of the object language, or the provability of a proposition. In general, a judgment may be any inductively definable assertion in the metatheory. Judgments are used in formalizing deduction systems: a logical axiom expresses a judgment, premises of a rule of inference are formed as a sequence of judgments, and their conclusion is a judgment as well (thus, hypotheses and conclusions of proofs are judgments). A characteristic feature of the variants of Hilbert-style deduction systems is that the ''context'' is not changed in any of their rules of inference, while both natural deduction and sequent calculus contain some context-changing rules. Thus, if w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Relation
In mathematics, a binary relation associates elements of one set, called the ''domain'', with elements of another set, called the ''codomain''. A binary relation over Set (mathematics), sets and is a new set of ordered pairs consisting of elements in and in . It is a generalization of the more widely understood idea of a unary function. It encodes the common concept of relation: an element is ''related'' to an element , if and only if the pair belongs to the set of ordered pairs that defines the ''binary relation''. A binary relation is the most studied special case of an Finitary relation, -ary relation over sets , which is a subset of the Cartesian product X_1 \times \cdots \times X_n. An example of a binary relation is the "divides" relation over the set of prime numbers \mathbb and the set of integers \mathbb, in which each prime is related to each integer that is a Divisibility, multiple of , but not to an integer that is not a multiple of . In this relation, for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Property (philosophy)
In logic and philosophy (especially metaphysics), a property is a characteristic of an Object (philosophy), object; a red object is said to have the property of redness. The property may be considered a form of object in its own right, able to possess other properties. A property, however, differs from individual objects in that it may be instantiation principle, instantiated, and often in more than one object. It differs from the logical/mathematical concept of class (set theory), class by not having any concept of extensionality, and from the philosophical concept of class (philosophy), class in that a property is considered to be distinct from the objects which possess it. Understanding how different individual entities (or particulars) can in some sense have some of the same properties is the basis of the problem of universals. Terms and usage A property is any member of a class of entities that are capable of being attributed to objects. Terms similar to ''property'' include ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Predicate (mathematical Logic)
In logic, a predicate is a symbol which represents a property or a relation. For instance, in the first order formula P(a), the symbol P is a predicate which applies to the individual constant a. Similarly, in the formula R(a,b), R is a predicate which applies to the individual constants a and b. In the semantics of logic, predicates are interpreted as relations. For instance, in a standard semantics for first-order logic, the formula R(a,b) would be true on an interpretation if the entities denoted by a and b stand in the relation denoted by R. Since predicates are non-logical symbols, they can denote different relations depending on the interpretation used to interpret them. While first-order logic only includes predicates which apply to individual constants, other logics may allow predicates which apply to other predicates. Predicates in different systems * In propositional logic, atomic formulas are sometimes regarded as zero-place predicates In a sense, these are nullar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
