|
Józef Maria Bocheński
Józef Maria Bocheński or Innocentius Bochenski (Czuszów, Congress Poland, Russian Empire, 30 August 1902 – 8 February 1995, Fribourg, Switzerland) was a Polish Dominican, logician and philosopher. Biography Born on 30 August 1902 in Czuszów, then part of the Russian Empire, to a family with patriotic and pro-independence traditions. His predecessors had fought in the Napoleonic wars and various national uprisings. His father, Adolf Józef Bocheński (1870–1936), who greatly developed the family estate, was a landowning activist, volunteer in the 1920 war and a doctor of agricultural sciences; his interest in economic history influenced Józef’s own reflections on economic doctrine and his personal aversion to Marxism. Józef’s mother, Maria Małgorzata née Dunin-Borkowska (1882–1931), was interested in theology, the author of the biographies of St John of the Cross and St Teresa of Jesus and the founder of a parish in Ponikwa. In charge of raising the children, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Converse Conditional
In logic and mathematics, the converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the 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 ''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 statement is "If I am mortal, then I am ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Czuszów
Czuszów is a village in the administrative district of Gmina Pałecznica, within Proszowice County, Lesser Poland Voivodeship, in southern Poland. It lies approximately south-east of Pałecznica, north-east of Proszowice, and north-east of the regional capital Kraków Kraków (), or Cracow, is the second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city dates back to the seventh century. Kraków was the official capital of Poland until 1596 .... References Villages in Proszowice County {{Proszowice-geo-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dominican Order
The Order of Preachers ( la, Ordo Praedicatorum) abbreviated OP, also known as the Dominicans, is a Catholic mendicant order of Pontifical Right for men founded in Toulouse, France, by the Spanish priest, saint and mystic Dominic of Caleruega. It was approved by Pope Honorius III via the papal bull ''Religiosam vitam'' on 22 December 1216. Members of the order, who are referred to as ''Dominicans'', generally carry the letters ''OP'' after their names, standing for ''Ordinis Praedicatorum'', meaning ''of the Order of Preachers''. Membership in the order includes friars, nuns, active sisters, and lay or secular Dominicans (formerly known as tertiaries). More recently there has been a growing number of associates of the religious sisters who are unrelated to the tertiaries. Founded to preach the Gospel and to oppose heresy, the teaching activity of the order and its scholastic organisation placed the Preachers in the forefront of the intellectual life of the Middle Ag ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Converse Nonimplication
In logic, converse nonimplication is a logical connective which is the negation of converse implication (equivalently, the negation of the converse of implication). Definition Converse nonimplication is notated P \nleftarrow Q, or P \not \subset Q, and is logically equivalent to \neg (P \leftarrow Q) Truth table The truth table of P \nleftarrow Q . Notation Converse nonimplication is notated p \nleftarrow q, which is the left arrow from converse implication ( \leftarrow), negated with a stroke (). Alternatives include * p \not\subset q, which combines converse implication's \subset, negated with a stroke (). * p \tilde q, which combines converse implication's left arrow (\leftarrow) with negation's tilde (\sim). * M''pq'', in Bocheński notation Properties falsehood-preserving: The interpretation under which all variables are assigned a truth value of 'false' produces a truth value of 'false' as a result of converse nonimplication Natural language Grammatical Exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Disjunction
In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive formula R \lor S , assuming that R abbreviates "it is raining" and S abbreviates "it is snowing". In classical logic, disjunction is given a truth functional semantics according to which a formula \phi \lor \psi is true unless both \phi and \psi are false. Because this semantics allows a disjunctive formula to be true when both of its disjuncts are true, it is an ''inclusive'' interpretation of disjunction, in contrast with exclusive disjunction. Classical proof theoretical treatments are often given in terms of rules such as disjunction introduction and disjunction elimination. Disjunction has also been given numerous non-classical treatments, motivated by problems including Aristotle's sea battle argument, Heisenberg's uncertainty principle, as well ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False (logic)
In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective. In a truth-functional system of propositional logic, it is one of two postulated truth values, along with its negation, truth. Usual notations of the false are 0 (especially in Boolean logic and computer science), O (in prefix notation, O''pq''), and the up tack symbol \bot. Another approach is used for several formal theories (e.g., intuitionistic propositional calculus), where a propositional constant (i.e. a nullary connective), \bot, is introduced, the truth value of which being always false in the sense above. It can be treated as an absurd proposition, and is often called absurdity. In classical logic and Boolean logic In Boolean logic, each variable denotes a truth value which can be either true (1), or false (0). In a classical propositional calculus, each proposition will be assigned a truth value of either true or false. Some systems of classical l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contradiction
In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect." In modern formal logic and type theory, the term is mainly used instead for a ''single'' proposition, often denoted by the falsum symbol \bot; a proposition is a contradiction if false can be derived from it, using the rules of the logic. It is a proposition that is unconditionally false (i.e., a self-contradictory proposition). This can be generalized to a collection of propositions, which is then said to "contain" a contradiction. History By creation of a paradox, Plato's '' Euthydemus'' dialogue demonstrates the need for the notion of ''contradiction''. In the ensuing ... [...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] |
Tautology (logic)
In mathematical logic, a tautology (from el, ταυτολογία) is a formula or assertion that is true in every possible interpretation. An example is "x=y or x≠y". Similarly, "either the ball is green, or the ball is not green" is always true, regardless of the colour of the ball. The philosopher Ludwig Wittgenstein first applied the term to redundancies of propositional logic in 1921, borrowing from rhetoric, where a tautology is a repetitive statement. In logic, a formula is satisfiable if it is true under at least one interpretation, and thus a tautology is a formula whose negation is unsatisfiable. In other words, it cannot be false. It cannot be untrue. Unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. A formula that is neither a tautology nor a contradiction is said to be Contingency (philosophy), logically contingent. Such a formula can be made either true or false based on the values assigned to its propositi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polish Notation
Polish notation (PN), also known as normal Polish notation (NPN), Łukasiewicz notation, Warsaw notation, Polish prefix notation or simply prefix notation, is a mathematical notation in which operators ''precede'' their operands, in contrast to the more common infix notation, in which operators are placed ''between'' operands, as well as reverse Polish notation (RPN), in which operators ''follow'' their operands. It does not need any parentheses as long as each operator has a fixed number of operands. The description "Polish" refers to the nationality of logician Jan Łukasiewicz, who invented Polish notation in 1924. The term ''Polish notation'' is sometimes taken (as the opposite of ''infix notation'') to also include reverse Polish notation. When Polish notation is used as a syntax for mathematical expressions by programming language interpreters, it is readily parsed into abstract syntax trees and can, in fact, define a one-to-one representation for the same. Because of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
