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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 No B is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Fallacy
In logic and philosophical logic, philosophy, a formal fallacy is a pattern of reasoning rendered validity (logic), invalid by a flaw in its logical structure. propositional calculus, Propositional logic, for example, is concerned with the meanings of sentences and the relationships between them. It focuses on the role of logical operators, called propositional connectives, in determining whether a sentence is true. An error in the sequence will result in a deductive argument that is invalid. The argument itself could have true premises, but still have a false logical consequence, conclusion. Thus, a formal fallacy is a fallacy in which 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 fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Co-premise
A co-premise is a premise in reasoning and informal logic which is not the main supporting reason for a contention or a lemma, but is logically necessary to ensure the validity of an argument. One premise by itself, or a group of co-premises can form a reason. Logical structure Every significant term or phrase appearing in a premise of a simple argument, should also appear in the contention/conclusion or in a co-premise. But this by itself does not guarantee a valid argument, see the fallacy of the undistributed middle for an example of this. Sometimes a co-premise will not be explicitly stated. This type of argument is known as an 'enthymematic' argument, and the co-premise may be referred to as a 'hidden' or an 'unstated' co-premise and will often be subject to an inference objection. In this argument map An argument map or argument diagram is a visual representation of the structure of an argument. An argument map typically includes all the key components of the argu ... [...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] |
The Purloined Letter
"The Purloined Letter" is a short story by American author Edgar Allan Poe. It is the third of his three detective stories featuring the fictional C. Auguste Dupin, the other two being "The Murders in the Rue Morgue" and " The Mystery of Marie Rogêt". These stories are considered to be important early forerunners of the modern detective story. It first appeared in the literary annual ''The Gift for 1845'' (1844) and soon was reprinted in numerous journals and newspapers. Plot summary The unnamed narrator is with the famous Parisian amateur detective C. Auguste Dupin when they are joined by G—, prefect of the Paris police. G— brings to Dupin's attention the theft from the queen's royal boudoir of a letter addressed to her. The thief is the unscrupulous Minister D—, who switched the letter for one of no importance during a visit with the queen and who has since been using its contents to blackmail her. Dupin agrees with two conclusions formed by G—: that the letter has no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Edgar Allan Poe
Edgar Allan Poe (; January 19, 1809 – October 7, 1849) was an American writer, poet, editor, and literary critic who is best known for his poetry and short stories, particularly his tales involving mystery and the macabre. He is widely regarded as one of the central figures of Romanticism and Gothic fiction in the United States and of early American literature. Poe was one of the country's first successful practitioners of the short story, and is generally considered to be the inventor of the detective fiction genre. In addition, he is credited with contributing significantly to the emergence of science fiction. He is the first well-known American writer to earn a living exclusively through writing, which resulted in a financially difficult life and career.. Poe was born in Boston. He was the second child of actors David Poe Jr., David and Eliza Poe, Elizabeth "Eliza" Poe. His father abandoned the family in 1810, and when Eliza died the following year, Poe was taken in by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Premise
A premise or premiss is a proposition—a true or false declarative statement—used in an argument to prove the truth of another proposition called the conclusion. Arguments consist of a set of premises and a conclusion. An argument is meaningful for its conclusion only when all of its premises are true. If one or more premises are false, the argument says nothing about whether the conclusion is true or false. For instance, a false premise on its own does not justify rejecting an argument's conclusion; to assume otherwise is a logical fallacy called denying the antecedent. One way to prove that a proposition is false is to formulate a sound argument with a conclusion that negates that proposition. An argument is sound and its conclusion logically follows (it is true) if and only if the argument is valid ''and'' its premises are true. An argument is valid if and only if it is the case that whenever the premises are all true, the conclusion must also be true. If there exis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Grandpa Backpack Undistributed Middle
Grandparents, individually known as grandmother and grandfather, or Grandma and Grandpa, are the parents of a person's father or mother – paternal or maternal. Every sexually reproducing living organism who is not a genetic chimera has a maximum of four genetic grandparents, eight genetic great-grandparents, sixteen genetic great-great-grandparents, thirty-two genetic great-great-great-grandparents, sixty-four genetic great-great-great-great-grandparents, etc. In the history of modern humanity, around 30,000 years ago, the number of modern humans who lived to be a grandparent increased. It is not known for certain what spurred this increase in longevity, but it is generally believed that a key consequence of three generations being alive together was the preservation of information which could otherwise have been lost; an example of this important information might have been where to find water in times of drought. In cases where parents are unwilling or unable to provide ade ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First-order Logic
First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables. Rather than propositions such as "all humans are mortal", in first-order logic one can have expressions in the form "for all ''x'', if ''x'' is a human, then ''x'' is mortal", where "for all ''x"'' is a quantifier, ''x'' is a variable, and "... ''is a human''" and "... ''is mortal''" are predicates. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic. A theory about a topic, such as set theory, a theory for groups,A. Tarski, ''Undecidable Theories'' (1953), p. 77. Studies in Logic and the Foundation of Mathematics, North-Holland or a formal theory o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Denying The Antecedent
Denying the antecedent (also known as inverse error or fallacy of the inverse) is a formal fallacy of inferring the inverse from an original statement. Phrased another way, denying the antecedent occurs in the context of an indicative conditional statement and assumes that the negation of the antecedent implies the negation of the consequent. It is a type of mixed hypothetical syllogism that takes on the following form: :If ''P'', then ''Q''. :Not ''P''. :Therefore, not ''Q''. which may also be phrased as :P \rightarrow Q (P implies Q) :\therefore \neg P \rightarrow \neg Q (therefore, not-P implies not-Q) Arguments of this form are invalid. Informally, this means that arguments of this form do not give good reason to establish their conclusions, even if their premises are true. The name ''denying the antecedent'' derives from the premise "not ''P''", which denies the "if" clause (antecedent) of the conditional premise. The only situation where one may deny the an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Middle Term
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 concerne ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affirming The Consequent
In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the antecedent is true. It takes on the following form: :: If ''P'', then ''Q''. :: ''Q''. :: Therefore, ''P''. which may also be phrased as : P \rightarrow Q (P implies Q) : \therefore Q \rightarrow P (therefore, Q implies P) For example, it may be true that a broken lamp would cause a room to become dark. It is not true, however, that a dark room implies the presence of a broken lamp. There may be no lamp (or any light source). The lamp may also be off. In other words, the consequent (a dark room) can have other antecedents (no lamp, off-lamp), and so can still be true even if the stated antecedent is not. Converse errors are comm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
