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Sum Of Logic
The ''Summa Logicae'' ("Sum of Logic") is a textbook on logic by William of Ockham. It was written around 1323. Systematically, it resembles other works of medieval logic, organised under the basic headings of the Aristotelian Predicables, Categories, terms, propositions, and syllogisms. These headings, though often given in a different order, represent the basic arrangement of scholastic works on logic. This work is important in that it contains the main account of Ockham's nominalism, a position related to the problem of universals. Book I. On Terms Book II. On Propositions Book III. On Syllogisms Part I. On Syllogisms Part II. On Demonstration * These 41 chapters are a systematic exposition of Aristotle's Posterior Analytics. Part III. On Consequences * The first 37 chapters of Part II are a systematic exposition of Aristotle's Topics. In Part III, Ockham deals with the definition and division of consequences, and provides a treatment of Aristotle's Top ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. Informal logic examines arguments expressed in natural language whereas formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a specific logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments, which consist of a set of premises that leads to a conclusion. An example is the argument from the premises "it's Sunday" and "if it's Sunday then I don't have to work" leading to the conclusion "I don't have to wor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Antecedent (logic)
An antecedent is the first half of a hypothetical proposition, whenever the if-clause precedes the then-clause. In some contexts the antecedent is called the ''protasis''. Examples: * If P, then Q. This is a nonlogical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q. In the implication "\phi implies \psi", \phi is called the antecedent and \psi is called the consequent.Sets, Functions and Logic - An Introduction to Abstract Mathematics, Keith Devlin, Chapman & Hall/CRC Mathematics, 3rd ed., 2004 Antecedent and consequent are connected via logical connective to form a proposition. * If X is a man, then X is mortal. "X is a man" is the antecedent for this proposition while "X is mortal" is the consequent of the proposition. * If men have walked on the Moon, then I am the king of France. Here, "men have walked on the Moon" is the antecedent and "I am the king of France" is the consequent. Let y=x+1. * If x=1 then y=2,. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fallacy Of Accent
The fallacy of accent (also known as ''accentus'', from its Latin denomination, and misleading accent) is a verbal fallacy that reasons from two different vocal readings of the same written words. In English, the fallacy typically relies on prosodic stress, the emphasis given to a word within a phrase, or a phrase within a sentence. The fallacy has also been extended to grammatical ambiguity caused by missing punctuation. History Among the thirteen types of fallacies in his book ''Sophistical Refutations'', Aristotle lists a fallacy he calls (''prosody''), later translated in Latin as '' accentus''. He gives as an example: The fallacy turns here on the varying pronunciation of ''ου'', meaning "where" in the first and third occurrences, and "not" in the second. These would later be distinguished in writing with diacritics, but they were not in Aristotle's time. Aristotle noted that fallacies of this form were rare in contemporary Greek. They are rarer still in languages like E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fallacy Of Division
The fallacy of division is an informal fallacy that occurs when one reasons that something that is true for a whole must also be true of all or some of its parts. An example: # The second grade in Jefferson Elementary eats a lot of ice cream # Carlos is a second-grader in Jefferson Elementary # Therefore, Carlos eats a lot of ice cream The converse of this fallacy is called fallacy of composition, which arises when one fallaciously attributes a property of some part of a thing to the thing as a whole. If a system as a whole has some property that none of its constituents has (or perhaps, it has it but not as a ''result'' of some constituents having that property), this is sometimes called an '' emergent'' property of the system. The term ''mereological fallacy'' refers to approximately the same incorrect inference that properties of a whole are also properties of its parts. History Both the fallacy of division and the fallacy of composition were addressed by Aristotle in '' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Fallacy Of Composition
The fallacy of composition is an informal fallacy that arises when one inference, infers that something is true of the whole from the fact that it is true of some part of the whole. A trivial example might be: "This tire is made of rubber; therefore, the vehicle of which it is a part is also made of rubber." That is fallacious, because vehicles are made with a variety of parts, most of which are not made of rubber. The fallacy of composition can apply even when a fact is true of every proper part of a greater entity, though. A more complicated example might be: "No atoms are Life, alive. Therefore, nothing made of atoms is alive." This is a statement most people would consider incorrect, due to emergence, where the whole possesses properties not present in any of the parts. The fallacy of composition is related to the fallacy of hasty generalization, in which an unwarranted inference is made from a statement about a sample to a statement about the population from which the sample i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Amphibology
Syntactic ambiguity, also known as structural ambiguity, amphiboly, or amphibology, is characterized by the potential for a sentence to yield multiple interpretations due to its ambiguous syntax. This form of ambiguity is not derived from the varied meanings of individual words but rather from the relationships among words and clauses within a sentence, concealing interpretations beneath the word order. Consequently, a sentence presents as syntactically ambiguous when it permits reasonable derivation of several possible grammatical structures by an observer. In jurisprudence, the interpretation of syntactically ambiguous phrases in statutory texts or contracts may be done by courts. Occasionally, claims based on highly improbable interpretations of such ambiguities are dismissed as being frivolous litigation and without merit. The term ''parse forest'' refers to the collection of all possible syntactic structures, known as '' parse trees'', that can represent the ambiguous sente ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Equivocation
In logic, equivocation ("calling two different things by the same name") is an informal fallacy resulting from the use of a particular word or expression in multiple senses within an argument. It is a type of ambiguity that stems from a phrase having two or more distinct meanings, not from the grammar or structure of the sentence. Fallacy of four terms Equivocation in a syllogism (a chain of reasoning) produces a fallacy of four terms (). Below is an example: : Since only man umanis rational. : And no woman is a man ale : Therefore, no woman is rational. The first instance of "man" implies the entire human species, while the second implies just those who are male. Motte-and-bailey fallacy Equivocation can also be used to conflate two positions which share similarities, one modest and easy to defend and one much more controversial. The arguer advances the controversial position, but when challenged, they insist that they are only advancing the more modest position. See ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Sophistical Refutations
''Sophistical Refutations'' (; ) is a text in Aristotle's ''Organon'' in which he identified thirteen fallacies.Sometimes listed as twelve. According to Aristotle, this is the first work to treat the subject of deductive reasoning in ancient Greece (''Soph. Ref.'', 34, 183b34 ff.). Overview ''On Sophistical Refutations'' consists of 34 chapters. The book naturally falls in two parts: chapters concerned with tactics for the Questioner (3–8 and 12–15) and chapters concerned with tactics for the Answerer (16–32). Besides, there is an introduction (1–2), an interlude (9–11), and a conclusion (33–34). Fallacies identified The fallacies Aristotle identifies in Chapter 4 (formal fallacies) and 5 (informal fallacies) of this book are the following: :Fallacies in the language or formal fallacies (''in dictionem''): # Equivocation # Amphiboly # Composition # Division # Accent # Figure of speech A figure of speech or rhetorical figure is a word or phrase that intentiona ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Liar Paradox
In philosophy and logic, the classical liar paradox or liar's paradox or antinomy of the liar is the statement of a liar that they are lying: for instance, declaring that "I am lying". If the liar is indeed lying, then the liar is telling the truth, which means the liar just lied. In "this sentence is a lie", the paradox is strengthened in order to make it amenable to more rigorous logical analysis. It is still generally called the "liar paradox" although abstraction is made precisely from the liar making the statement. Trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. Assume that "this sentence is false" is true, then we can trust its content, which states the opposite and thus causes a contradition. Similarly, we get a contradiction when we assume the opposite. History The Epimenides paradox (c. 600 BC) has been suggested as an example of the liar paradox, but they are not logically equivalent. The semi-mythica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Theory Of Obligationes
''Obligationes'' or disputations ''de obligationibus'' were a medieval disputation format common in the 13th and 14th centuries. Despite the name, they had nothing to do with ethics or morals but rather dealt with logical formalisms; the name comes from the fact that the participants were "obliged" to follow the rules. Typically, there were two disputants, one ''Opponens'' and one ''Respondens''. At the start of a debate, both the disputants would agree on a ‘''positum''’, usually a false statement. The task of ''Respondens'' was to answer rationally to the questions from the ''Opponens'', assuming the truth of the ''positum'' and without contradicting himself. On the opposite, the task of the ''Opponens'' was to try to force the ''Respondens'' into contradictions. Several styles of ''Obligationes'' were distinguished in the medieval literature with the most widely studied being called "''positio''" (positing). "Obligational" disputations resemble recent theories of counterfac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Albert Of Saxony (philosopher)
Albert of Saxony (Latin: ''Albertus de Saxonia''; c. 1320 – 8 July 1390) was a German philosopher and mathematician known for his contributions to logic and physics. He was bishop of Halberstadt from 1366 until his death. Life Albert was born at Rickensdorf near Helmstedt, the son of a farmer in a small village. Due to his talent, he was sent to study at the Charles University in Prague, University of Prague and the University of Paris. At Paris, he became a Master of Arts (a professor), and held this post from 1351 until 1362. He also studied theology at the College of Sorbonne, although without receiving a degree. In 1353, he was Rector (academia), rector of the University of Paris. After 1362, Albert went to the court of Pope Urban V in Avignon as an envoy of Rudolf IV, Duke of Austria to negotiate the founding of the University of Vienna. The negotiations were successful, and Albert became the first rector in 1365. In 1366, Albert was elected bishop of Halberstadt (counted ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
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Jean Buridan
Jean Buridan (; ; Latin: ''Johannes Buridanus''; – ) was an influential 14thcentury French scholastic philosopher. Buridan taught in the faculty of arts at the University of Paris for his entire career and focused in particular on logic and on the works of Aristotle. Buridan sowed the seeds of the Copernican Revolution in Europe. He developed the concept of impetus, the first step toward the modern concept of inertia and an important development in the 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 du Cardinal Lemoine and then at the University of Paris, receiving his Master of Arts degree and formal l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |