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Classical Logic
Classical logic (or standard logic) or Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy. Characteristics Each logical system in this class shares characteristic properties: Gabbay, Dov, (1994). 'Classical vs non-classical logic'. In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, (Eds), ''Handbook of Logic in Artificial Intelligence and Logic Programming'', volume 2, chapter 2.6. Oxford University Press. # Law of excluded middle and double negation elimination # Law of noncontradiction, and the principle of explosion # Monotonicity of entailment and idempotency of entailment # Commutativity of conjunction # De Morgan duality: every logical operator is dual to another While not entailed by the preceding conditions, contemporary discussions of classical logic normally only include propositional and first-order logics. Shapiro, Stewart (2000). Classical Logic. In St ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deductive Logic
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that it is impossible for the premises to be true and the conclusion to be false. For example, the inference from the premises "all men are mortal" and "Socrates is a man" to the conclusion "Socrates is mortal" is deductively valid. An argument is ''sound'' if it is valid ''and'' all its premises are true. One approach defines deduction in terms of the intentions of the author: they have to intend for the premises to offer deductive support to the conclusion. With the help of this modification, it is possible to distinguish valid from invalid deductive reasoning: it is invalid if the author's belief about the deductive support is false, but even invalid deductive reasoning is a form of deductive reasoning. Deductive logic studies under what conditions an argument is valid. According to the semantic approach, an argument is valid if th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Antiquity
Classical antiquity, also known as the classical era, classical period, classical age, or simply antiquity, is the period of cultural History of Europe, European history between the 8th century BC and the 5th century AD comprising the interwoven civilizations of ancient Greece and ancient Rome, Rome known together as the Greco-Roman world, centered on the Mediterranean Basin. It is the period during which ancient Greece and Rome flourished and had major influence throughout much of Europe, North Africa, and West Asia. Classical antiquity was succeeded by the period now known as late antiquity. Conventionally, it is often considered to begin with the earliest recorded Homeric Greek, Epic Greek poetry of Homer (8th–7th centuries BC) and end with the fall of the Western Roman Empire in 476 AD. Such a wide span of history and territory covers many disparate cultures and periods. ''Classical antiquity'' may also refer to an idealized vision among later people of what was, in Ed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Begriffsschrift Titel
''Begriffsschrift'' (German for, roughly, "concept-writing") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book. ''Begriffsschrift'' is usually translated as ''concept writing'' or ''concept notation''; the full title of the book identifies it as "a formula language, modeled on that of arithmetic, for pure thought." Frege's motivation for developing his formal approach to logic resembled Gottfried Wilhelm Leibniz, Leibniz's motivation for his ''calculus ratiocinator'' (despite that, in the foreword Frege clearly denies that he achieved this aim, and also that his main aim would be constructing an ideal language like Leibniz's, which Frege declares to be a quite hard and idealistic—though not impossible—task). Frege went on to employ his logical calculus in his research on the foundations of mathematics, carried out over the next quarter-century. This is the first work in Analytical Philosophy, a field that later British and Anglo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Venn
John Venn, Fellow of the Royal Society, FRS, Fellow of the Society of Antiquaries of London, FSA (4 August 1834 – 4 April 1923) was an English mathematician, logician and philosopher noted for introducing Venn diagrams, which are used in logic, set theory, probability, statistics, and computer science. In 1866, Venn published ''The Logic of Chance'', a groundbreaking book which espoused the frequency theory of probability, arguing that probability should be determined by how often something is forecast to occur as opposed to "educated" assumptions. Venn then further developed George Boole's theories in the 1881 work ''Symbolic Logic'', where he highlighted what would become known as Venn diagrams. Early life John Venn was born on 4 August 1834 in Kingston upon Hull, Yorkshire, to Martha Sykes and Rev. Henry Venn (Church Missionary Society), Henry Venn, who was the rector of the parish of Drypool. His mother died when he was three years old. Venn was descended from a long ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
William Stanley Jevons
William Stanley Jevons (; 1 September 1835 – 13 August 1882) was an English economist and logician. Irving Fisher described Jevons's book ''A General Mathematical Theory of Political Economy'' (1862) as the start of the mathematical method in economics. It made the case that economics, as a science concerned with Real versus nominal value (economics), quantities, is necessarily mathematical. In so doing, it expounded upon the "final" (marginal) utility theory of value. Jevons' work, along with similar discoveries made by Carl Menger in Vienna (1871) and by Léon Walras in Switzerland (1874), marked the opening of a new period in the history of economic thought. Jevons's contribution to the Marginal utility#Marginal Revolution, marginal revolution in economics in the late 19th century established his reputation as a leading political economist and logician of the time. Jevons broke off his studies of the natural sciences in London in 1854 to work as an metallurgical assay, ass ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denoted by 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as Logical conjunction, conjunction (''and'') denoted as , disjunction (''or'') denoted as , and negation (''not'') denoted as . Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his ''An Investigation of the Laws of Thought'' (1854). According to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Boole
George Boole ( ; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland. He worked in the fields of differential equations and algebraic logic, and is best known as the author of ''The Laws of Thought'' (1854), which contains Boolean algebra. Boolean logic, essential to computer programming, is credited with helping to lay the foundations for the Information Age. Boole was the son of a shoemaker. He received a primary school education and learned Latin and modern languages through various means. At 16, he began teaching to support his family. He established his own school at 19 and later ran a boarding school in Lincoln. Boole was an active member of local societies and collaborated with fellow mathematicians. In 1849, he was appointed the first professor of mathematics at Queen's College, Cork (now University C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Existential Import
A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defined by Aristotle in his 350 BC book '' Prior Analytics''), a deductive syllogism arises when two true premises (propositions or statements) validly imply a conclusion, or the main point that the argument aims to get across. For example, knowing that all men are mortal (major premise), and that Socrates is a man (minor premise), we may validly conclude that Socrates is mortal. Syllogistic arguments are usually represented in a three-line form: All men are mortal. Socrates is a man. Therefore, Socrates is mortal.In antiquity, two rival syllogistic theories existed: Aristotelian syllogism and Stoic syllogism. From the Middle Ages onwards, ''categorical syllogism'' and ''syllogism'' were usually used interchangeably. This article is concerne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bernard Bolzano
Bernard Bolzano (, ; ; ; born Bernardus Placidus Johann Nepomuk Bolzano; 5 October 1781 – 18 December 1848) was a Bohemian mathematician, logician, philosopher, theologian and Catholic priest of Italian extraction, also known for his liberal views. Bolzano wrote in German, his native language. For the most part, his work came to prominence posthumously. Family Bolzano was the son of two pious Catholics. His father, Bernard Pompeius Bolzano, was an Italian who had moved to Prague, where he married Maria Cecilia Maurer who came from Prague's German-speaking family Maurer. Only two of their twelve children lived to adulthood. Career When he was ten years old, Bolzano entered the Gymnasium of the Piarists in Prague, which he attended from 1791 to 1796. Bolzano entered the University of Prague in 1796 and studied mathematics, philosophy and physics. Starting in 1800, he also began studying theology, becoming a Catholic priest in 1804. He was appointed to the new chair of p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculus Ratiocinator
The ''calculus ratiocinator'' is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned ''characteristica universalis'', a universal conceptual language. Two views There are two contrasting points of view on what Leibniz meant by ''calculus ratiocinator''. The first is associated with computer software, the second is associated with computer hardware. Analytic view The received point of view in analytic philosophy and formal logic, is that the ''calculus ratiocinator'' anticipates mathematical logic—an "algebra of logic". The analytic point of view understands that the ''calculus ratiocinator'' is a formal inference engine or computer program, which can be designed so as to grant primacy to calculations. That logic began with Frege's 1879 ''Begriffsschrift'' and C.S. Peirce's writings on logic in the 1880s. Frege intended his "concept script" to be a ''calcul ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leibniz
Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to many other branches of mathematics, such as binary arithmetic and statistics. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labor. He is a prominent figure in both the history of philosophy and the history of mathematics. He wrote works on philosophy, theology, ethics, politics, law, history, philology, games, music, and other studies. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science. Leibniz contributed to the field of libr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
