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Denying The Antecedent
Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form: :If ''P'', then ''Q''. :Therefore, if not ''P'', then 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. In this example, a valid conclusion would be: ~P or Q. The name ''denying the antecedent'' derives from the premise "not ''P''", which denies the "if" clause of the conditional premise. One way to demonstrate the invalidity of this argument form is with an example that has true premises but an obviously false conclusion. For example: :If you are a ski instructor, then you have a job. :You are not a ski ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Fallacy
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] |
If And Only If
In logic and related fields such as mathematics and philosophy, "if and only if" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of either one of the connected statements requires the truth of the other (i.e. either both statements are true, or both are false), though it is controversial whether the connective thus defined is properly rendered by the English "if and only if"—with its pre-existing meaning. For example, ''P if and only if Q'' means that ''P'' is true whenever ''Q'' is true, and the only case in which ''P'' is true is if ''Q'' is also true, whereas in the case of ''P if Q'', there could be other scenarios where ''P'' is true and ''Q'' is ... [...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 ). 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 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 must be either simultaneously true, or simultaneously false. In ordinary English (a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Tollens
In propositional logic, ''modus tollens'' () (MT), also known as ''modus tollendo tollens'' (Latin for "method of removing by taking away") and denying the consequent, is a deductive argument form and a rule of inference. ''Modus tollens'' 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 of a ''modus tollens'' argument resembles a syllog ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Modus Ponens
In propositional logic, ''modus ponens'' (; MP), also known as ''modus ponendo ponens'' (Latin for "method of putting by placing") or 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 closely related to another valid form of argument, ''modus tollens''. Both have apparently similar but invalid forms such as affirming the consequent, denying the antecedent, and evidence of absence. Constructive dilemma is the disjunctive version of ''modus ponens''. Hypothetical syllogism is closely related to ''modus ponens'' and sometimes thought of as "double ''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 d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Affirming The Consequent
Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement (e.g., "If the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("The room is dark, so the lamp is broken"), even though that statement may not be true. This arises when a consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room"). Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes. The opposite statement, denying the consequent, ''is'' a valid form of argument (modus tollens). Formal description Affirming the consequent is the action of taking a true statement P \to Q and invalidly concluding its converse Q \ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
President Of The United States
The president of the United States (POTUS) is the head of state and head of government of the United States of America. The president directs the executive branch of the federal government and is the commander-in-chief of the United States Armed Forces. The power of the presidency has grown substantially since the first president, George Washington, took office in 1789. While presidential power has ebbed and flowed over time, the presidency has played an increasingly strong role in American political life since the beginning of the 20th century, with a notable expansion during the presidency of Franklin D. Roosevelt. In contemporary times, the president is also looked upon as one of the world's most powerful political figures as the leader of the only remaining global superpower. As the leader of the nation with the largest economy by nominal GDP, the president possesses significant domestic and international hard and soft power. Article II of the Constitution establ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Equality
Logical equality is a logical operator that corresponds to equality in Boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value ''true'' if both functional arguments have the same logical value, and '' false'' if they are different. It is customary practice in various applications, if not always technically precise, to indicate the operation of logical equality on the logical operands ''x'' and ''y'' by any of the following forms: :\begin x &\leftrightarrow y & x &\Leftrightarrow y & \mathrm Exy \\ x &\mathrm y & x &= y \end Some logicians, however, draw a firm distinction between a ''functional form'', like those in the left column, which they interpret as an application of a function to a pair of arguments — and thus a mere indication that the value of the compound expression depends on the values of the component expressions — and an ''equational form'', like those in the right column, which they interpret as an as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logical Biconditional
In logic and mathematics, the logical biconditional, sometimes known as the material biconditional, is the logical connective (\leftrightarrow) used to conjoin two statements and to form the statement " if and only if ", where is known as the '' antecedent'', and the ''consequent''. This is often abbreviated as " iff ". Other ways of denoting this operator may be seen occasionally, as a double-headed arrow (↔ or ⇔ may be represented in Unicode in various ways), a prefixed E "E''pq''" (in Łukasiewicz notation or Bocheński notation), an equality sign (=), an equivalence sign (≡), or ''EQV''. It is logically equivalent to both (P \rightarrow Q) \land (Q \rightarrow P) and (P \land Q) \lor (\neg P \land \neg Q) , and the XNOR (exclusive nor) boolean operator, which means "both or neither". Semantically, the only case where a logical biconditional is different from a material conditional is the case where the hypothesis is false but the conclusion is true. In this case ... [...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] |
Inverse (logic)
In logic, an inverse is a type of conditional sentence which is an immediate inference made from another conditional sentence. More specifically, given a conditional sentence of the form P \rightarrow Q , the inverse refers to the sentence \neg P \rightarrow \neg Q . Since an inverse is the contrapositive of the converse, inverse and converse are logically equivalent to each other. For example, substituting propositions in natural language for logical variables, the inverse of the following conditional proposition :"If it's raining, then Sam will meet Jack at the movies." would be :"If it's not raining, then Sam will not meet Jack at the movies." The inverse of the inverse, that is, the inverse of \neg P \rightarrow \neg Q , is \neg \neg P \rightarrow \neg \neg Q , and since the double negation of any statement is equivalent to the original statement in classical logic, the inverse of the inverse is logically equivalent to the original conditional P \rightarrow Q . Thus it is p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computing Machinery And Intelligence
"Computing Machinery and Intelligence" is a seminal paper written by Alan Turing on the topic of artificial intelligence. The paper, published in 1950 in ''Mind'', was the first to introduce his concept of what is now known as the Turing test to the general public. Turing's paper considers the question "Can machines think?" Turing says that since the words "think" and "machine" cannot be clearly defined we should "replace the question by another, which is closely related to it and is expressed in relatively unambiguous words." To do this, he must first find a simple and unambiguous idea to replace the word "think", second he must explain exactly which "machines" he is considering, and finally, armed with these tools, he formulates a new question, related to the first, that he believes he can answer in the affirmative. Turing's test Rather than trying to determine if a machine is thinking, Turing suggests we should ask if the machine can win a game, called the " Imitation Game" ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
