|
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 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), for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square Of Opposition, Set Diagrams
In geometry, a square is a regular polygon, regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal sides. As with all rectangles, a square's angles are right angles (90 degree (angle), degrees, or Pi, /2 radians), making adjacent sides perpendicular. The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called square (algebra), squaring. Equal squares can tile the plane edge-to-edge in the square tiling. Square tilings are ubiquitous in tiled floors and walls, graph paper, image pixels, and game boards. Square shapes are also often seen in building floor plans, origami paper, food servings, in graphic design and heraldry, and in instant photos and fine art. The formula for the area of a square forms the basis of the calculation of area and motivates the search for methods for s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modern Philosophy
Modern philosophy is philosophy developed in the modern era and associated with modernity. It is not a specific doctrine or school (and thus should not be confused with ''Modernism''), although there are certain assumptions common to much of it, which helps to distinguish it from earlier philosophy. The 17th and early 20th centuries roughly mark the beginning and the end of modern philosophy. How much of the Renaissance should be included is a matter for dispute; likewise, modernity may or may not have ended in the twentieth century and been replaced by postmodernity. How one decides these questions will determine the scope of one's use of the term "modern philosophy." Modern Western philosophy How much of Renaissance intellectual history is part of modern philosophy is disputed: The Early Renaissance is often considered less modern and more medieval compared to the later High Renaissance. Later, by the 17th and 18th centuries, the major figures in philosophy of mind, epis ... [...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] |
William Of Ockham
William of Ockham or Occam ( ; ; 9/10 April 1347) was an English Franciscan friar, scholastic philosopher, apologist, and theologian, who was born in Ockham, a small village in Surrey. He is considered to be one of the major figures of medieval thought and was at the centre of the major intellectual and political controversies of the 14th century. He is commonly known for Occam's razor, the methodological principle that bears his name, and also produced significant works on logic, physics and theology. William is remembered in the Church of England with a commemoration corresponding to the commonly ascribed date of his death on 10 April. Life William of Ockham was born in Ockham, Surrey, around 1287. He received his elementary education in the London House of the Greyfriars. It is believed that he then studied theology at the University of OxfordSpade, Paul Vincent (ed.). ''The Cambridge Companion to Ockham''. Cambridge University Press, 1999, p. 20.He has long been claim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Syllogism
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 concern ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terence Parsons
Terence Dwight Parsons (1939–2022) was an American philosopher, specializing in philosophy of language and metaphysics. He was emeritus professor of philosophy at UCLA. Life and career Parsons was born in Endicott, New York and graduated from the University of Rochester with a BA in physics. He received his PhD from Stanford University in 1966. He was a full-time faculty member at the University of Illinois at Chicago from 1965 to 1972, at the University of Massachusetts at Amherst from 1972 to 1979, at the University of California at Irvine from 1979 to 2000, and at the University of California at Los Angeles from 2000 to 2012. In 2007, he was elected to the American Academy of Arts and Sciences. Philosophical work Parsons worked on the semantics of natural language to develop theories of truth and meaning for natural language similar to those devised for artificial languages by philosophical logicians. Heavily influenced by Alexius Meinong, he wrote ''Nonexistent Objects'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Abelard
Peter Abelard (12 February 1079 – 21 April 1142) was a medieval French scholastic philosopher, leading logician, theologian, teacher, musician, composer, and poet. This source has a detailed description of his philosophical work. In philosophy he is celebrated for his logical solution to the problem of universals via nominalism and conceptualism and his pioneering of intent in ethics. Often referred to as the " Descartes of the twelfth century", he is considered a forerunner of Rousseau, Kant, and Spinoza. He is sometimes credited as a chief forerunner of modern empiricism. In Catholic theology, he is best known for his development of the concept of limbo, and his introduction of the moral influence theory of atonement. He is considered (alongside Augustine) to be the most significant forerunner of the modern self-reflective autobiographer. He paved the way and set the tone for later epistolary novels and celebrity tell-alls with his publicly distributed letter, ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraposition (traditional Logic)
In logic and mathematics, contraposition, or ''transposition'', refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as . The contrapositive of a statement has its antecedent and consequent negated and swapped. Conditional statement P \rightarrow Q. In formulas: the contrapositive of P \rightarrow Q is \neg Q \rightarrow \neg P . If ''P'', Then ''Q''. — If not ''Q'', Then not ''P''. "If ''it is raining,'' then ''I wear my coat''." — "If ''I don't wear my coat,'' then ''it isn't raining''." The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true. Contraposition ( \neg Q \rightarrow \neg P ) can be compared with three other operations: ; Inversion (the inverse), \neg P \rightarrow \neg Q:"If ''it is not raining,'' then ''I don't wear my coat''." Unlike the contrapositive, the inverse's truth value is not at all dependent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Obversion
In traditional logic, obversion is a "type of immediate inference in which from a given proposition another proposition is inferred whose subject is the same as the original subject, whose predicate is the contradictory of the original predicate, and whose quality is affirmative if the original proposition's quality was negative and vice versa".Quoted definition is from: Brody, Bobuch A. "Glossary of Logical Terms". ''Encyclopedia of Philosophy''. Vol. 5–6, p. 70. Macmillan, 1973. Also, Stebbing, L. Susan. ''A Modern Introduction to Logic''. Seventh edition, pp. 65–66. Harper, 1961, and Irving Copi's ''Introduction to Logic'', p. 141, Macmillan, 1953. All sources give virtually identical explanations. Copi (1953) and Stebbing (1931) both limit the application to categorical propositions, and in ''Symbolic Logic'', 1979, Copi limits the use of the process, remarking on its "absorption" into the Rules of Replacement in quantification and the axioms of class algebra. The quality ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Converse (logic)
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the Material conditional, implication ''P'' → ''Q'', the converse is ''Q'' → ''P''. For the categorical proposition ''All S are P'', the converse is ''All P are S''. Either way, the truth of the converse is generally independent from that of the original statement.Robert Audi, ed. (1999), ''The Cambridge Dictionary of Philosophy'', 2nd ed., Cambridge University Press: "converse". Implicational converse Let ''S'' be a statement of the form ''P implies Q'' (''P'' → ''Q''). Then the ''converse'' of ''S'' is the statement ''Q implies P'' (''Q'' → ''P''). In general, the truth of ''S'' says nothing about the truth of its converse, unless the Antecedent (logic), antecedent ''P'' and the consequent ''Q'' are logically equivalent. For example, consider the true statement "If I am a human, then I am mortal." The converse of that stateme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contraposition
In logic and mathematics, contraposition, or ''transposition'', refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as . The contrapositive of a statement has its antecedent and consequent negated and swapped. Conditional statement P \rightarrow Q. In formulas: the contrapositive of P \rightarrow Q is \neg Q \rightarrow \neg P . If ''P'', Then ''Q''. — If not ''Q'', Then not ''P''. "If ''it is raining,'' then ''I wear my coat''." — "If ''I don't wear my coat,'' then ''it isn't raining''." The law of contraposition says that a conditional statement is true if, and only if, its contrapositive is true. Contraposition ( \neg Q \rightarrow \neg P ) can be compared with three other operations: ; Inversion (the inverse), \neg P \rightarrow \neg Q:"If ''it is not raining,'' then ''I don't wear my coat''." Unlike the contrapositive, the inverse's truth value is not at all dependen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
