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Buridan Formula
In quantified modal logic, the Buridan formula and the converse Buridan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas are named in honor of the medieval philosopher Jean Buridan by analogy with the Barcan formula and the converse Barcan formula introduced as axioms by Ruth Barcan Marcus. The Buridan formula The Buridan formula is: :\Diamond \forall x Fx \rightarrow \forall x\Diamond Fx. In English, the schema reads: If possibly everything is F, then everything is possibly F. It is equivalent in a classical modal logic In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators \Diamond A \leftrightarrow \lnot\Box\lnot A that is also closed under the rule \frac. Alternatively, one can gi ... (but not necessarily in other form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modal Logic
Modal logic is a collection of formal systems developed to represent statements about necessity and possibility. It plays a major role in philosophy of language, epistemology, metaphysics, and natural language semantics. Modal logics extend other systems by adding unary operators \Diamond and \Box, representing possibility and necessity respectively. For instance the modal formula \Diamond P can be read as "possibly P" while \Box P can be read as "necessarily P". Modal logics can be used to represent different phenomena depending on what kind of necessity and possibility is under consideration. When \Box is used to represent epistemic necessity, \Box P states that P is epistemically necessary, or in other words that it is known. When \Box is used to represent deontic necessity, \Box P states that P is a moral or legal obligation. In the standard relational semantics for modal logic, formulas are assigned truth values relative to a ''possible world''. A formula's truth value at ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Buridan
Jean Buridan (; Latin: ''Johannes Buridanus''; – ) was an influential 14th-century French people, French Philosophy, philosopher. Buridan was a teacher in the Faculty (division)#Faculty of Art, faculty of arts at the University of Paris for his entire career who focused in particular on logic and the works of Aristotle. Buridan sowed the seeds of the Copernican Revolution in Europe. He developed the concept of Theory of impetus, impetus, the first step toward the modern concept of inertia and an important development in the History of science in the Middle Ages, history of medieval science. His name is most familiar through the thought experiment known as Buridan's ass, but the thought experiment does not appear in his extant writings. Life Education and career Buridan was born sometime before 1301, perhaps at or near the town of Béthune in Picardy, France,Zupko 2015, §1 or perhaps elsewhere in the diocese of Arras. He received his education in Paris, first at the Collège d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Barcan Formula
In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas were introduced as axioms by Ruth Barcan Marcus, in the first extensions of modal propositional logic to include quantification.Journal of Symbolic Logic (1946),11 and (1947), 12 under Ruth C. Barcan Related formulas include the Buridan formula. The Barcan formula The Barcan formula is: :\forall x \Box Fx \rightarrow \Box \forall x Fx. In English, the schema reads: If every x is necessarily F, then it is necessary that every x is F. It is equivalent to :\Diamond\exists xFx\to\exists x\Diamond Fx. The Barcan formula has generated some controversy because—in terms of possible world semantics—it implies that all objects which exist in any possible world (accessible to the actual wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Converse Barcan Formula
In quantified modal logic, the Barcan formula and the converse Barcan formula (more accurately, schemata rather than formulas) (i) syntactically state principles of interchange between quantifiers and modalities; (ii) semantically state a relation between domains of possible worlds. The formulas were introduced as axioms by Ruth Barcan Marcus, in the first extensions of modal propositional logic to include quantification.Journal of Symbolic Logic (1946),11 and (1947), 12 under Ruth C. Barcan Related formulas include the Buridan formula. The Barcan formula The Barcan formula is: :\forall x \Box Fx \rightarrow \Box \forall x Fx. In English, the schema reads: If every x is necessarily F, then it is necessary that every x is F. It is equivalent to :\Diamond\exists xFx\to\exists x\Diamond Fx. The Barcan formula has generated some controversy because—in terms of possible world semantics—it implies that all objects which exist in any possible world (accessible to the actual wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ruth Barcan Marcus
Ruth Barcan Marcus (; born Ruth Charlotte Barcan; 2 August 1921 – 19 February 2012) was an American academic philosopher and logician best known for her work in modal and philosophical logic. She developed the first formal systems of quantified modal logic and in so doing introduced the schema or principle known as the Barcan formula. (She would also introduce the now standard "box" operator for necessity in the process.) Marcus, who originally published as Ruth C. Barcan, was, as Don Garrett notes "one of the twentieth century's most important and influential philosopher-logicians". Timothy Williamson, in a 2008 celebration of Marcus' long career, states that many of her "main ideas are not just original, and clever, and beautiful, and fascinating, and influential, and way ahead of their time, but actually – I believe – ''true''". Academic career and service Ruth Barcan (as she was known before marrying the physicist Jules Alexander Marcus in 1942 Gendler, T. S."Ruth B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
English Language
English is a West Germanic language of the Indo-European language family, with its earliest forms spoken by the inhabitants of early medieval England. It is named after the Angles, one of the ancient Germanic peoples that migrated to the island of Great Britain. Existing on a dialect continuum with Scots, and then closest related to the Low Saxon and Frisian languages, English is genealogically West Germanic. However, its vocabulary is also distinctively influenced by dialects of France (about 29% of Modern English words) and Latin (also about 29%), plus some grammar and a small amount of core vocabulary influenced by Old Norse (a North Germanic language). Speakers of English are called Anglophones. The earliest forms of English, collectively known as Old English, evolved from a group of West Germanic (Ingvaeonic) dialects brought to Great Britain by Anglo-Saxon settlers in the 5th century and further mutated by Norse-speaking Viking settlers starting in the 8th and 9th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classical Modal Logic
In modal logic, a classical modal logic L is any modal logic containing (as axiom or theorem) the duality of the modal operators \Diamond A \leftrightarrow \lnot\Box\lnot A that is also closed under the rule \frac. Alternatively, one can give a dual definition of L by which L is classical if and only if it contains (as axiom or theorem) \Box A \leftrightarrow \lnot\Diamond\lnot A and is closed under the rule \frac. The weakest classical system is sometimes referred to as E and is non-normal. Both algebraic and neighborhood semantics characterize familiar classical modal systems that are weaker than the weakest normal modal logic K. Every regular modal logic is classical, and every normal modal logic In logic, a normal modal logic is a set ''L'' of modal formulas such that ''L'' contains: * All propositional tautologies; * All instances of the Kripke schema: \Box(A\to B)\to(\Box A\to\Box B) and it is closed under: * Detachment rule (''modus po ... is regular and hence ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nominalism
In metaphysics, nominalism is the view that universals and abstract objects do not actually exist other than being merely names or labels. There are at least two main versions of nominalism. One version denies the existence of universalsthings that can be instantiated or exemplified by many particular things (e.g., strength, humanity). The other version specifically denies the existence of abstract objectsobjects that do not exist in space and time. Most nominalists have held that only physical particulars in space and time are real, and that universals exist only ''post res'', that is, subsequent to particular things. However, some versions of nominalism hold that some particulars are abstract entities (e.g., numbers), while others are concrete entities – entities that do exist in space and time (e.g., pillars, snakes, bananas). Nominalism is primarily a position on the problem of universals. It is opposed to realist philosophies, such as Platonic realism, which assert that ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Realism
Philosophical realism is usually not treated as a position of its own but as a stance towards other subject matters. Realism about a certain kind of thing (like numbers or morality) is the thesis that this kind of thing has ''mind-independent existence'', i.e. that it is not just a mere appearance in the eye of the beholder. This includes a number of positions within epistemology and metaphysics which express that a given thing instead exists independently of knowledge, thought, or understanding. This can apply to items such as the physical world, the past and future, other minds, and the self, though may also apply less directly to things such as universals, mathematical truths, moral truths, and thought itself. However, realism may also include various positions which instead reject metaphysical treatments of reality entirely. Realism can also be a view about the properties of reality in general, holding that reality exists independent of the mind, as opposed to non-realist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Of Spain
__NOTOC__ Peter of Hispania ( la, Petrus Hispanus; Portuguese and es, Pedro Hispano; century) was the author of the ', later known as the ', an important medieval university textbook on Aristotelian logic. As the Latin ''Hispania'' was considered to include the entire Iberian Peninsula, he is traditionally and usually identified with the medieval Portuguese scholar and ecclesiastic Peter Juliani, who was elected Pope John XXI in 1276. The identification is sometimes disputed, usually by Spanish authors, who claim the author of the ' was a Castilian Blackfriar. He is also sometimes identified as Petrus Ferrandi Hispanus ( 1254 1259). Life The author of the ' is assumed to have studied under John Pagus. Philosophical works There are a large volume of manuscripts and printed editions of the ', indicative of its great success throughout European universities well into the seventeenth century. The most recent edition is Peter of Hispania (Petrus Hispanus Portugalensis), ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
