Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from an original statement. It is a type of mixed hypothetical syllogism in the form:[1]
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 (antecedent) 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:
That argument is intentionally bad, but arguments of the same form can sometimes seem superficially convincing, as in the following example offered by Alan Turing in the article "Computing Machinery and Intelligence":
If each man had a definite set of rules of conduct by which he regulated his life he would be no better than a machine. But there are no such rules, so men cannot be machines.[2]
However, men could still be machines that do not follow a definite set of rules. Thus, this argument (as Turing intends) is invalid.
It is possible that an argument that denies the antecedent could be valid if the argument instantiates some other valid form. For example, if the claims P and Q express the same proposition, then the argument would be trivially valid, as it would beg the question. In everyday discourse, however, such cases are rare, typically only occurring when the "if-then" premise is actually an "if and only if" claim (i.e., a biconditional/equality). The following argument is not valid, but would be if the first premise was "If I can veto Congress, then I am the US President." This claim is now modus tollens, and thus valid.
[This is a case of the fallacy denying the antecedent as written because it matches the formal symbolic schema at beginning. The form is taken without regard to the content of the language.]
^ abcMatthew C. Harris. "Denying the antecedent". Khan academy.
^Turing, Alan (October 1950), "Computing Machinery and Intelligence", Mind, LIX (236): 433–460, doi:10.1093/mind/LIX.236.433, ISSN 0026-4423
External linksedit
FallacyFiles.org: Denying the Antecedent
safalra.com: Denying The Antecedent
January 01, 1970
denying, antecedent, this, article, needs, additional, citations, verification, please, help, improve, this, article, adding, citations, reliable, sources, unsourced, material, challenged, removed, find, sources, news, newspapers, books, scholar, jstor, decemb. This article needs additional citations for verification Please help improve this article by adding citations to reliable sources Unsourced material may be challenged and removed Find sources Denying the antecedent news newspapers books scholar JSTOR December 2016 Learn how and when to remove this message Denying the antecedent sometimes also called inverse error or fallacy of the inverse is a formal fallacy of inferring the inverse from an original statement It is a type of mixed hypothetical syllogism in the form 1 If P then Q Not P Therefore not Q which may also be phrased as P Q displaystyle P rightarrow Q P implies Q P Q displaystyle therefore neg P rightarrow neg Q therefore not P implies not Q 1 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 antecedent 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 instructor Therefore you have no job 1 That argument is intentionally bad but arguments of the same form can sometimes seem superficially convincing as in the following example offered by Alan Turing in the article Computing Machinery and Intelligence If each man had a definite set of rules of conduct by which he regulated his life he would be no better than a machine But there are no such rules so men cannot be machines 2 However men could still be machines that do not follow a definite set of rules Thus this argument as Turing intends is invalid It is possible that an argument that denies the antecedent could be valid if the argument instantiates some other valid form For example if the claims P and Q express the same proposition then the argument would be trivially valid as it would beg the question In everyday discourse however such cases are rare typically only occurring when the if then premise is actually an if and only if claim i e a biconditional equality The following argument is not valid but would be if the first premise was If I can veto Congress then I am the US President This claim is now modus tollens and thus valid If I am President of the United States then I can veto Congress I am not President Therefore I cannot veto Congress This is a case of the fallacy denying the antecedent as written because it matches the formal symbolic schema at beginning The form is taken without regard to the content of the language See also editAffirming the consequent Modus ponens Modus tollens Necessity and sufficiency Plausible reasoningReferences edit a b c Matthew C Harris Denying the antecedent Khan academy Turing Alan October 1950 Computing Machinery and Intelligence Mind LIX 236 433 460 doi 10 1093 mind LIX 236 433 ISSN 0026 4423External links editFallacyFiles org Denying the Antecedent safalra com Denying The Antecedent Retrieved from https en wikipedia org w index php title Denying the antecedent amp oldid 1213405016, wikipedia, wiki, book, books, library,
