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In propositional logic, modus tollens (/ ˈ m oʊ d ə s ˈ t ɒ l ɛ n z /) (MT), also known as modus tollendo tollens (Latin for "mode that by denying denies") [2] and denying the consequent, [3] 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 ...
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 ...
Affirming the consequent – the antecedent in an indicative conditional is claimed to be true because the consequent is true; if A, then B; B, therefore A. [10] Denying the antecedent – the consequent in an indicative conditional is claimed to be false because the antecedent is false; if A, then B; not A, therefore not B. [10]
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. [4] The first to explicitly describe the argument form modus ponens was Theophrastus. [5]
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 antecedent would be if the antecedent and consequent represent the same proposition, in which case the argument is trivially valid (and it would beg the question ...
In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is the consequent. The second premise "affirms" the antecedent. The conclusion, that the consequent must be true, is deductively valid. A mixed hypothetical syllogism has four possible forms, two of which are valid, while the other two are invalid.
Two invalid argument forms are affirming the consequent and denying the antecedent. Affirming the consequent All dogs are animals. Coco is an animal. Therefore, Coco is a dog. Denying the antecedent All cats are animals. Missy is not a cat. Therefore, Missy is not an animal.
In classical logic, disjunctive syllogism [1] [2] (historically known as modus tollendo ponens (MTP), [3] Latin for "mode that affirms by denying") [4] is a valid argument form which is a syllogism having a disjunctive statement for one of its premises. [5] [6] An example in English: I will choose soup or I will choose salad. I will not choose ...