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Philosophy Of Logic
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterization, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argument
An argument is a statement or group of statements called premises intended to determine the degree of truth or acceptability of another statement called conclusion. Arguments can be studied from three main perspectives: the logical, the dialectical and the rhetorical perspective. In logic, an argument is usually expressed not in natural language but in a symbolic formal language, and it can be defined as any group of propositions of which one is claimed to follow from the others through deductively valid inferences that preserve truth from the premises to the conclusion. This logical perspective on argument is relevant for scientific fields such as mathematics and computer science. Logic is the study of the forms of reasoning in arguments and the development of standards and criteria to evaluate arguments. Deductive arguments can be valid, and the valid ones can be sound: in a valid argument, premisses necessitate the conclusion, even if one or more of the premises is false ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting points of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ontology
In metaphysics, ontology is the philosophical study of being, as well as related concepts such as existence, becoming, and reality. Ontology addresses questions like how entities are grouped into categories and which of these entities exist on the most fundamental level. Ontologists often try to determine what the categories or highest kinds are and how they form a system of categories that encompasses classification of all entities. Commonly proposed categories include substances, properties, relations, states of affairs and events. These categories are characterized by fundamental ontological concepts, including particularity and universality, abstractness and concreteness, or possibility and necessity. Of special interest is the concept of ontological dependence, which determines whether the entities of a category exist on the most fundamental level. Disagreements within ontology are often about whether entities belonging to a certain category exist and, if so, how they ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy Of Science
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultimate purpose of science. This discipline overlaps with metaphysics, ontology, and epistemology, for example, when it explores the relationship between science and truth. Philosophy of science focuses on metaphysical, epistemic and semantic aspects of science. Ethical issues such as bioethics and scientific misconduct are often considered ethics or science studies rather than the philosophy of science. There is no consensus among philosophers about many of the central problems concerned with the philosophy of science, including whether science can reveal the truth about unobservable things and whether scientific reasoning can be justified at all. In addition to these general questions about science as a whole, philosophers of science consi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Quantifier
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some". It is usually denoted by the logical operator symbol ∃, which, when used together with a predicate variable, is called an existential quantifier ("" or "" or "). Existential quantification is distinct from universal quantification ("for all"), which asserts that the property or relation holds for ''all'' members of the domain. Some sources use the term existentialization to refer to existential quantification. Basics Consider a formula that states that some natural number multiplied by itself is 25. : 0·0 = 25, or 1·1 = 25, or 2·2 = 25, or 3·3 = 25, ... This would seem to be a logical disjunction because of the repeated use of "or". However, the ellipses make this impossible to integrate and to interpret it as a disjunction in formal logic. Instead, the statement could be rephrased more formally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Singular Term
A singular term is a paradigmatic referring device in a language. Singular terms are of philosophical importance for philosophers of language, because they ''refer'' to things in the world, and the ability of words to refer calls for scrutiny. Overview Singular terms are defined as expressions that purport to denote or designate particular individual people, places, or other objects. They contrast with ''general terms'' (such as "car" or "chair") which can apply to more than one thing. There are various kinds of singular terms: proper names (e.g. "Matthew"), definite descriptions (e.g. "the second fisherman in the boat"), singular personal pronouns (e.g. "she"), demonstrative pronouns (e.g. "this"), etc. Historically, various definitions for "singular term" have been offered: # A term that tells us which individual is being talked about. (John Stuart Mill, Arthur Prior, P. F. Strawson) # A term that is grammatically singular, i.e. a proper name (''proprium nomen''), a demonstrati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relation To Other Disciplines
Relation or relations may refer to: General uses *International relations, the study of interconnection of politics, economics, and law on a global level *Interpersonal relationship, association or acquaintance between two or more people *Public relations, managing the spread of information to the public *Sexual relations, or human sexual activity *Social relation, in social science, any social interaction between two or more individuals Logic and philosophy *Relation (philosophy), links between properties of an object *Relational theory, framework to understand reality or a physical system Mathematics A finitary or ''n''-ary relation is a set of ''n''-tuples. Specific types of relations include: *Relation (mathematics) *Binary relation (or correspondence, dyadic relation, or 2-place relation) *Equivalence relation *Homogeneous relation *Reflexive relation *Serial relation *Ternary relation (or triadic, 3-adic, 3-ary, 3-dimensional, or 3-place relation) Relation may also ref ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaphysics Of Logic
Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of consciousness and the relationship between mind and matter, between substance and attribute, and between potentiality and actuality. The word "metaphysics" comes from two Greek words that, together, literally mean "after or behind or among he study ofthe natural". It has been suggested that the term might have been coined by a first century CE editor who assembled various small selections of Aristotle's works into the treatise we now know by the name ''Metaphysics'' (μετὰ τὰ φυσικά, ''meta ta physika'', 'after the ''Physics'' ', another of Aristotle's works). Metaphysics studies questions related to what it is for something to exist and what types of existence there are. Metaphysics seeks to answer, in an abstract and ful ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Truth
Truth is the property of being in accord with fact or reality.Merriam-Webster's Online Dictionarytruth 2005 In everyday language, truth is typically ascribed to things that aim to represent reality or otherwise correspond to it, such as beliefs, propositions, and declarative sentences. Truth is usually held to be the opposite of falsehood. The concept of truth is discussed and debated in various contexts, including philosophy, art, theology, and science. Most human activities depend upon the concept, where its nature as a concept is assumed rather than being a subject of discussion; these include most of the sciences, law, journalism, and everyday life. Some philosophers view the concept of truth as basic, and unable to be explained in any terms that are more easily understood than the concept of truth itself. Most commonly, truth is viewed as the correspondence of language or thought to a mind-independent world. This is called the correspondence theory of truth. Various theo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fundamental Concepts
Fundamental may refer to: * Foundation of reality * Fundamental frequency, as in music or phonetics, often referred to as simply a "fundamental" * Fundamentalism, the belief in, and usually the strict adherence to, the simple or "fundamental" ideas based on faith in a system of thought * ''The Fundamentals'', a set of books important to Christian fundamentalism * Any of a number of fundamental theorems identified in mathematics, such as: ** Fundamental theorem of algebra, awe theorem regarding the factorization of polynomials ** Fundamental theorem of arithmetic, a theorem regarding prime factorization * Fundamental analysis, the process of reviewing and analyzing a company's financial statements to make better economic decisions Music * Fun-Da-Mental, a rap group * ''Fundamental'' (Bonnie Raitt album), 1998 * ''Fundamental'' (Pet Shop Boys album) * ''Fundamental'' (Puya album), 1999 * ''Fundamental'' (Mental As Anything album) * ''The Fundamentals'' (album) Other uses * " ... [...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] |
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