|
Denying the antecedent (also known as vacuous implication) is a type of logical fallacy. In dialectic, the term logical fallacy properly refers to a formal fallacy: a flaw in the structure of a deductive argument which renders the argument invalid. ...
Suppose in an argument one were to deny the "if" part of a conditional (the antecedent) first, and conclude with the denial of "then" part (the consequent). In logic, an argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. ...
The term conditional is used in linguistics and logic to refer to related concepts about sentences of the form If X, then Y (ie. ...
- If P, then Q.
- P is false.
- Therefore, Q is false.
This argument form has the name denying the antecedent, because in arguing this way one does indeed deny the antecedent in the second premise. This is a non sequitur (irrelevant conclusion). If we argue this way, we make a mistake. One can see this with an example: In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables. ...
Non sequitur is Latin for it does not follow. ...
- If I'm asleep, my eyes are closed.
- I'm not asleep.
- Therefore, my eyes are not closed.
Clearly, the fact that my eyes are closed when I sleep does not exclude the possibility that I might close my eyes while being fully awake. Instead, the correct logical deduction from the initial statement would be the contrapositive "If my eyes are not closed, then I am not asleep". In predicate logic, the contrapositive (or transposition) of the statement p implies q is not-q implies not-p. ...
When embedded in a more complicated argument, this invalid inference may be convincing because of confusion between the meanings of if and if and only if. Denying the antecedent is valid if the first premise asserts "if and only if" rather than "if", such that I not only always close my eyes when I'm asleep, but I also only close my eyes when I'm asleep (not when I'm awake). ...
In propositional calculus, or logical calculus in mathematics, the logical conditional is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ...
↔ ⇔ ≡ logical symbols representing iff. ...
This article discusses validity in logic, for the term in the social sciences see validity (psychometric). ...
See also
Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. ...
In Logic, Modus ponens (Latin: mode that affirms) is a valid, simple argument form (often abbreviated to MP): If P, then Q. P. Therefore, Q. or in logical operator notation: P → Q P ⊢ Q where ⊢ represents the logical assertion. ...
Modus tollens (Latin: mode that denies) is the formal name for indirect proof or proof by contrapositive, often abbreviated to MT. It can also be referred to as denying the consequent. ...
External links - safalra.com: Denying The Antecedent
|
Feeds |
Contact