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Non Sequitur (logic)
In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur (; Latin for " tdoes not follow") is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic.Harry J. Gensler, ''The A to Z of Logic'' (2010) p. 74. Rowman & Littlefield, It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic. While a logical argument is a non sequitur if, and only if, it is invalid, the term "non sequitur" typically refers to those types of invalid arguments which do not constitute formal fallacies covered by particular terms (e.g., affirming the consequent). In other words, in practice, "''non s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophical Logic
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic. An important issue for philosophical logic is the question of how to classify the great variety of non-classical logical systems, many of which are of rather recent origin. One form of classification often found in the literature is to distinguish between extended logics and deviant logics. Logic itself can be defined as the s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some sources claim the term was coined by Pythagoras ( BCE), although this theory is disputed by some. Philosophical methods include questioning, critical discussion, rational argument, and systematic presentation. in . Historically, ''philosophy'' encompassed all bodies of knowledge and a practitioner was known as a ''philosopher''."The English word "philosophy" is first attested to , meaning "knowledge, body of knowledge." "natural philosophy," which began as a discipline in ancient India and Ancient Greece, encompasses astronomy, medicine, and physics. For example, Newton's 1687 ''Mathematical Principles of Natural Philosophy'' later became classified as a book of physics. In the 19th century, the growth of modern research universiti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Begging The Question
In classical rhetoric and logic, begging the question or assuming the conclusion (Latin: ') is an informal fallacy that occurs when an argument's premises assume the truth of the conclusion, instead of supporting it. For example: * "Green is the best color because it is the greenest of all colors" This statement claims that the color green is the best because it is the greenest – which it presupposes is the best. It is a type of circular reasoning: an argument that requires that the desired conclusion be true. This often occurs in an indirect way such that the fallacy's presence is hidden, or at least not easily apparent.Herrick (2000) 248. History The original phrase used by Aristotle from which ''begging the question'' descends is: τὸ ἐξ ἀρχῆς (or sometimes ἐν ἀρχῇ) αἰτεῖν, "asking for the initial thing". Aristotle's intended meaning is closely tied to the type of dialectical argument he discusses in his '' Topics'', book VIII: a formalized ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affirmative Conclusion From A Negative Premise
Affirmative conclusion from a negative premise (illicit negative) is a formal fallacy that is committed when a categorical syllogism has a positive conclusion and one or two negative premises. For example: :''No fish are dogs, and no dogs can fly, therefore all fish can fly.'' The only thing that can be properly inferred from these premises is that some things that are not fish cannot fly, provided that dogs exist. Or: :''We don't read that trash. People who read that trash don't appreciate real literature. Therefore, we appreciate real literature.'' This could be illustrated mathematically as :If A \cap B = \emptyset and B \cap C = \emptyset then A\subset C. It is a fallacy because any valid forms of categorical syllogism that assert a negative premise must have a negative conclusion. See also * Negative conclusion from affirmative premises, in which a syllogism is invalid because the conclusion is negative yet the premises are affirmative * Fallacy of exclusive premises A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illicit Minor
Illicit minor is a formal fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion. This fallacy has the following argument form: :All A are B. :All A are C. :Therefore, all C are B. ''Example:'' : All cats are felines. : All cats are mammals. : Therefore, all mammals are felines. The minor term here is mammal, which is not distributed in the minor premise "All cats are mammals", because this premise is only defining a property of possibly some mammals (i.e., that they're cats.) However, in the conclusion "All mammals are felines", mammal ''is'' distributed (it is talking about all mammals being felines). It is shown to be false by any mammal that is not a feline; for example, a dog. ''Example:'' : Pie is good. : Pie is unhealthy. : Thus, all good things are unhealthy. See also * Illicit major * Syllogistic fallacy A syllogism ( grc-gre, συλλογισμός, ''syl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Illicit Major
Illicit major is a formal fallacy committed in a categorical syllogism that is invalid because its major term is undistributed in the major premise but distributed in the conclusion. This fallacy has the following argument form: #''All A are B'' #''No C are A'' #''Therefore, no C are B'' Example: #''All dogs are mammals'' #''No cats are dogs'' #''Therefore, no cats are mammals'' In this argument, the major term is "mammals". This is distributed in the conclusion (the last statement) because we are making a claim about a property of ''all'' mammals: that they are not cats. However, it is not distributed in the major premise (the first statement) where we are only talking about a property of ''some'' mammals: Only some mammals are dogs. The error is in assuming that the converse of the first statement (that all mammals are dogs) is also true. However, an argument in the following form differs from the above, and is valid (Camestres): #''All A are B'' #''No B are C'' #''Therefore, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacy Of The Undistributed Middle
The fallacy of the undistributed middle () is a formal fallacy that is committed when the middle term in a categorical syllogism is not distributed in either the minor premise or the major premise. It is thus a syllogistic fallacy. Classical formulation In classical syllogisms, all statements consist of two terms and are in the form of "A" (all), "E" (none), "I" (some), or "O" (some not). The first term is distributed in A statements; the second is distributed in O statements; both are distributed in "E" statements, and none are distributed in I statements. The fallacy of the undistributed middle occurs when the term that links the two premises is never distributed. In this example, distribution is marked in boldface: # All Z is B # All Y is B # Therefore, all Y is Z B is the common term between the two premises (the middle term) but is never distributed, so this syllogism is invalid. B would be distributed by introducing a premise which states either All B is Z, or Some B is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacy Of Four Terms
The fallacy of four terms ( la, quaternio terminorum) is the formal fallacy that occurs when a syllogism has four (or more) terms rather than the requisite three, rendering it invalid. Definition Categorical syllogisms always have three terms: :Major premise: All fish have fins. :Minor premise: All goldfish are fish. :Conclusion: All goldfish have fins. Here, the three terms are: "goldfish", "fish", and "fins". Using four terms invalidates the syllogism: :Major premise: All fish have fins. :Minor premise: All goldfish are fish. :Conclusion: All humans have fins. The premises do not connect "humans" with "fins", so the reasoning is invalid. Notice that there are four terms: "fish", "fins", "goldfish" and "humans". Two premises are not enough to connect four different terms, since in order to establish connection, there must be one term common to both premises. In everyday reasoning, the fallacy of four terms occurs most frequently by equivocation: using the same word or phra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of philosophy within the Lyceum and the wider Aristotelian tradition. His writings cover many subjects including physics, biology, zoology, metaphysics, logic, ethics, aesthetics, poetry, theatre, music, rhetoric, psychology, linguistics, economics, politics, meteorology, geology, and government. Aristotle provided a complex synthesis of the various philosophies existing prior to him. It was above all from his teachings that the West inherited its intellectual lexicon, as well as problems and methods of inquiry. As a result, his philosophy has exerted a unique influence on almost every form of knowledge in the West and it continues to be a subject of contemporary philosophical discussion. Little is known about his life. Aristotle was born in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prior Analytics
The ''Prior Analytics'' ( grc-gre, Ἀναλυτικὰ Πρότερα; la, Analytica Priora) is a work by Aristotle on reasoning, known as his syllogistic, composed around 350 BCE. Being one of the six extant Aristotelian writings on logic and scientific method, it is part of what later Peripatetics called the ''Organon''. Modern work on Aristotle's logic builds on the tradition started in 1951 with the establishment by Jan Łukasiewicz of a revolutionary paradigm. His approach was replaced in the early 1970s in a series of papers by John Corcoran and Timothy Smiley—which inform modern translations of ''Prior Analytics'' by Robin Smith in 1989 and Gisela Striker in 2009. The term ''analytics'' comes from the Greek words ''analytos'' (ἀναλυτός, 'solvable') and ''analyo'' (ἀναλύω, 'to solve', literally 'to loose'). However, in Aristotle's corpus, there are distinguishable differences in the meaning of ἀναλύω and its cognates. There is also the possi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Soundness
In logic or, more precisely, deductive reasoning, an argument is sound if it is both valid in form and its premises are true. Soundness also has a related meaning in mathematical logic, wherein logical systems are sound if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system. Definition In deductive reasoning, a sound argument is an argument that is valid and all of its premises are true (and as a consequence its conclusion is true as well). An argument is valid if, assuming its premises are true, the conclusion ''must'' be true. An example of a sound argument is the following well-known syllogism: : ''(premises)'' : All men are mortal. : Socrates is a man. : ''(conclusion)'' : Therefore, Socrates is mortal. Because of the logical necessity of the conclusion, this argument is valid; and because the argument is valid and its premises are true, the argument is sound. However, an argument can be valid without ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
