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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] |
Propositional Calculus
The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called ''first-order'' propositional logic to contrast it with System F, but it should not be confused with first-order logic. It deals with propositions (which can be Truth value, true or false) and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives representing the truth functions of Logical conjunction, conjunction, Logical disjunction, disjunction, Material conditional, implication, Logical biconditional, biconditional, and negation. Some sources include other connectives, as in the table below. Unlike first-order logic, propositional logic does not deal with non-logical objects, predicates about them, or Quantifier (logic), quantifiers. However, all the machinery of pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rhinoceros (play)
''Rhinoceros'' () is a play by playwright Eugène Ionesco, written in 1959. The play was included in Martin Esslin's essay on post-war avant-garde drama " The Theatre of the Absurd", although scholars have also rejected this label as too interpretatively narrow. Over the course of three acts, the inhabitants of a small, provincial French town turn into rhinoceroses; ultimately the only human who does not succumb to this mass metamorphosis is the central character, Bérenger, a flustered everyman figure who is initially criticized in the play for his drinking, tardiness, and slovenly lifestyle and then, later, for his increasing paranoia and obsession with the rhinoceroses. The play is often read as a response and criticism to the sudden upsurge of Fascism and Nazism during the events preceding World War II, and explores the themes of conformity, culture, fascism, responsibility, logic, mass movements, mob mentality, philosophy and morality. Plot Act 1 The play starts in the tow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Necessity And Sufficiency
In logic and mathematics, necessity and sufficiency are terms used to describe a material conditional, conditional or implicational relationship between two Statement (logic), statements. For example, in the Conditional sentence, conditional statement: "If then ", is necessary for , because the Truth value, truth of is guaranteed by the truth of . (Equivalently, it is impossible to have without , or the falsity of ensures the falsity of .) Similarly, is sufficient for , because being true always implies that is true, but not being true does not always imply that is not true. In general, a necessary condition is one (possibly one of several conditions) that must be present in order for another condition to occur, while a sufficient condition is one that produces the said condition. The assertion that a statement is a "necessary ''and'' sufficient" condition of another means that the former statement is true if and only if the latter is true. That is, the two statements mu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "mode that by denying denies") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens'' is a mixed hypothetical syllogism that takes the form of "If ''P'', then ''Q''. Not ''Q''. Therefore, not ''P''." It is an application of the general truth that if a statement is true, then so is its contrapositive. The form shows that inference from ''P implies Q'' to ''the negation of Q implies the negation of P'' is a valid argument. The history of the inference rule ''modus tollens'' goes back to antiquity. The first to explicitly describe the argument form ''modus tollens'' was Theophrastus. ''Modus tollens'' is closely related to ''modus ponens''. There are two similar, but invalid, forms of argument: affirming the consequent and denying the antecedent. See also contraposition and proof by contrapositive. Explanation The form ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Ponens
In propositional logic, (; MP), also known as (), implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "''P'' implies ''Q.'' ''P'' is true. Therefore, ''Q'' must also be true." ''Modus ponens'' is a mixed hypothetical syllogism and is closely related to another valid form of argument, '' modus tollens''. Both have apparently similar but invalid forms: affirming the consequent and denying the antecedent. Constructive dilemma is the disjunctive version of ''modus ponens''. The history of ''modus ponens'' goes back to antiquity. The first to explicitly describe the argument form ''modus ponens'' was Theophrastus. It, along with '' modus tollens'', is one of the standard patterns of inference that can be applied to derive chains of conclusions that lead to the desired goal. Explanation The form of a ''modus ponens'' argument is a mixed hypothetical syllogism, with two premises and a con ... [...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 No B is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacy Of The Single Cause
The fallacy of the single cause, also known as complex cause, causal oversimplification, causal reductionism, root cause fallacy, and reduction fallacy, is an informal fallacy of questionable cause that occurs when it is assumed that there is a single, simple cause of an outcome when in reality it may have been caused by a number of only jointly sufficient causes. Fallacy of the single cause can be logically reduced to: "X caused Y; therefore, X was the only cause of Y" (although A,B,C...etc. also contributed to Y.) Causal oversimplification is a specific kind of false dilemma A false dilemma, also referred to as false dichotomy or false binary, is an informal fallacy based on a premise that erroneously limits what options are available. The source of the fallacy lies not in an invalid form of inference but in a false ... where conjoint possibilities are ignored. In other words, the possible causes are assumed to be "A xor B xor C" when "A and B and C" or "A and B and not C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fallacies Of Illicit Transference
A fallacy of illicit transference is an informal fallacy occurring when an argument assumes there is no difference between a term in the ''distributive'' (referring to every member of a class) and ''collective'' (referring to the class itself as a whole) sense. There are two variations of this fallacy: * Fallacy of composition – assumes what is true of the parts is true of the whole. This fallacy is also known as "arguing from the specific to the general." :''Since Judy is so diligent in the workplace, this entire company must have an amazing work ethic.'' * Fallacy of division – assumes what is true of the whole is true of its parts (or some subset of parts). In statistics, forms of it are usually referred to as the ecological fallacy. :''Because this company is so corrupt, so must every employee within it be corrupt.'' While fallacious, arguments that make these assumptions may be persuasive because of the representativeness heuristic. See also * Affirming the consequent * ... [...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] |
Confusion Of The Inverse
Confusion of the inverse, also called the conditional probability fallacy or the inverse fallacy, is a logical fallacy whereupon a conditional probability is equated with its inverse; that is, given two events ''A'' and ''B'', the probability of ''A'' happening given that ''B'' has happened is assumed to be about the same as the probability of ''B'' given ''A'', when there is actually no evidence for this assumption. More formally, ''P''(''A'', ''B'') is assumed to be approximately equal to ''P''(''B'', ''A''). Examples Example 1 In one study, physicians were asked to give the chances of malignancy with a 1% prior probability of occurring. A test can detect 80% of malignancies and has a 10% false positive rate. What is the probability of malignancy given a positive test result? Approximately 95 out of 100 physicians responded the probability of malignancy would be about 75%, apparently because the physicians believed that the chances of malignancy given a positive test result we ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Appeal To Consequences
Appeal to consequences, also known as ''argumentum ad consequentiam'' (Latin for "argument to the consequence"), is an argument that concludes a hypothesis (typically a belief) to be either true or false based on whether the premise leads to desirable or undesirable consequences. This is based on an appeal to emotion and is a type of informal fallacy, since the desirability of a premise's consequence does not make the premise true. Moreover, in categorizing consequences as either desirable or undesirable, such arguments inherently contain subjective points of view. In logic, appeal to consequences refers only to arguments that assert a conclusion's truth value (''true or false'') without regard to the formal preservation of the truth from the premises; appeal to consequences does not refer to arguments that address a premise's consequential desirability (''good or bad'', or ''right or wrong'') instead of its truth value. Therefore, an argument based on appeal to consequences is v ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abductive Reasoning
Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher and logician Charles Sanders Peirce beginning in the latter half of the 19th century. Abductive reasoning, unlike deductive reasoning, yields a plausible conclusion but does not definitively verify it. Abductive conclusions do not eliminate uncertainty or doubt, which is expressed in terms such as "best available" or "most likely". While inductive reasoning draws general conclusions that apply to many situations, abductive conclusions are confined to the particular observations in question. In the 1990s, as computing power grew, the fields of law, computer science, and artificial intelligence researchFor examples, see "", John R. Josephson, Laboratory for Artificial Intelligence Research, Ohio State University, and ''Abduc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
