Is it always wrong to deny the antecedent?

Question

Denying the antecedent: "if p then q,not p, therefore not q"

OK that's clearly invalid, but I was recently in an argument with someone who asserted some p in support of some q, and I pointed out that p was false. He accused me of denying the antecedent, although not in those words. My point was that, since one of his premisses (p) was false, his argument was unsound (rather than invalid).

Is that correct? And how often is challenging the soundness of an argument confused with denying the antecedent?

score 2 · Answer 1 · answered Aug 22 '14 at 02:33

If your point truly was about the soundness of his argument, as others have aptly answered, you are correct.

It's worth noting, in addition, that limited to the details you've provided, your interlocutor could not legitimately accuse you of committing a "denying the antecedent" fallacy, because you did not deliver an argument, but a proposition.

You merely "pointed out that p was false," which is a proposition - it has a truth value.

A challenge of interpreting informal debate (and all forms of informal argumentation) is inferring formal arguments (or, for that matter, whether arguments are even being implied).

We are to assume that your interlocutor's implicit argument was (if p, then q; p therefore q) and that your response was (if p, then q; not p; therefore (if p, then q; p therefore q) is unsound). However, your interlocutor may have inferred your argument to be (if p, then q; not p, therefore not q) in which case he would of course have been correct is his accusation.

score 1 · Answer 2 · edited Apr 13 '17 at 12:42

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You are correct about your assertion of unsoundness. for a brief(ish) rundown of what constitutes a sound and valid argument see my answer to the question here:

How are rules of inference established as valid?

edited Apr 13 '17 at 12:42

Community

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answered Aug 15 '14 at 13:59

JonS

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score 1 · Answer 3 · answered Aug 15 '14 at 19:32

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And how often is challenging the soundness of an argument confused with denying the antecedent?

It probably goes hand in hand with not paying any attention to opposing arguments: so it probably depends who you're talking to.

Yes they used the term wrong, but good luck in convincing them, I imagine most people who use the internet have no conception of soundness or validity.

answered Aug 15 '14 at 19:32

I imagine most people who use the internet have no conception of soundness or validity. Lol. – quis est ille Aug 15 '14 at 21:17

score 0 · Answer 4 · answered Aug 16 '14 at 10:09

The argument would by definition be not sound if it contains a false premise.

But that would not make the argument invalid since validity refers to having a form where if all premises are true, then the conclusion must be true whereas soundness refers to having validity and all true premises.

Consider for instance the following:

(1) If an animal is squirrel, then it is cute
(2) a flying squirrel is a squirrel
(3) A flying squirrel is not a squirrel
Therefore, a flying squirrel is cute.

The argument as stated is not sound because the premises are not all true. It is, however, as written valid -- because it is impossible to get all premises true and a false conclusion (because it is impossible for (2) and (3) to be simultaneously true as opposites).

Two points of caution:

But that being said, if the premise is unnecessary to the argument, then it could be excised and produce a valid or sound argument (or an invalid or unsound argument).

Ergo, if we excise (3), then the argument would be sound. A principle of charitable reading would tell us to ignore the extraneous premise.

Second, be careful of claiming that (C) A -> B is false when A is false. (Confusing the falseness of a claim for the falseness of a premise.

Finally, I would probably avoid the word "wrong" as it's potentially confusing especially because we have words like "sound" and "valid" to use instead.

Is it always wrong to deny the antecedent?

4 Answers4