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Antecedent and consequent are connected via logical connective to form a proposition. If is a man, then is mortal. " is a man" is the antecedent for this proposition while "is mortal" is the consequent of the proposition. If men have walked on the Moon, then I am the king of France.
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) under the logic of modus tollens. A related fallacy is affirming the consequent.
In propositional logic, modus ponens (/ ˈ m oʊ d ə s ˈ p oʊ n ɛ n z /; MP), also known as modus ponendo ponens (from Latin 'mode that by affirming affirms'), [1] implication elimination, or affirming the antecedent, [2] is a deductive argument form and rule of inference. [3] It can be summarized as "P implies Q. P is true. Therefore, Q ...
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]
A mixed hypothetical syllogism has two premises: one conditional statement and one statement that either affirms or denies the antecedent or consequent of that conditional statement. For example, If P, then Q. P. ∴ Q. In this example, the first premise is a conditional statement in which "P" is the antecedent and "Q" is 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 ...
The logical relationship that holds between propositions when the truth of one (the antecedent) guarantees the truth of another (the consequent). logical monism The philosophical position that there is only one correct logic or logical system that accurately captures the principles of valid reasoning.
In mathematics and logic, a vacuous truth is a conditional or universal statement (a universal statement that can be converted to a conditional statement) that is true because the antecedent cannot be satisfied. [1] It is sometimes said that a statement is vacuously true because it does not really say anything. [2]