Talk:Modus tollens

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Contents 1 Misc. 2 Making sense of 217.*? 3 Paradox deleted 4 Bad Example

[edit] Misc.

The sentence:

"That might be a legitimate criticism of the argument, but notice that it does not mean the argument is invalid. "

Doesn't make any sense.

If we cannot assume that there is a connection between the ownership of an axe and guilt in this crime, than we can't make any judgements at all, can we ?

It all loses any meaning.

If there is no connection between the ownership of an axe and guilt in this crime, then who cares if Lizzy owns an axe or not ? It is irrelevant. We cannot make any conclusions.

Do you agree ?

I suggest we drop this.--217.228.220.2 19:05, 4 Jun 2004 (UTC)

The sentence was dropped. I think it makes sense.

We should also drop the rest:

"This may mean that the argument is false, but notice that it does not mean the argument is invalid. An argument can be valid even though it has a false premise; one has to distinguish between validity and soundness."

This sentence is absurd. Obviously the argument is invalid. Who cares if Lizzy owns an axe or not ? It is irrelevant. We cannot make any conclusions.

If the premise is false, the whole argument is not only invalid, it loses any meaning.

It has the same meaning than saying: If roses are red, then Lizzy is the murder.

Lizzy may be the murder or not, we don't know that. But it certainly doesn't have anything to do with the fact that roses are red or not.

I suggest we drop the ending. --217.228.212.196 12:06, 5 Jun 2004 (UTC)

Does every article on logic have to carefully explain the distinction between falsehood and validity? This simple point keeps recurring. The example is of a valid argument that contains a false premise, and therefore a false conclusion. The problem appears to be with 217.228.220.2?s understanding of these terms rather than with the argument. Banno 00:13, Jun 6, 2004 (UTC)

I agree with Banno. Read this article and take the quiz to make sure you understand the difference between validity and soundness. Wikiwikifast 04:10, 10 Sep 2004 (UTC)

Or perhaps you are confused? Denying "If Lizzy was the murderer, then she owns an axe" is something completely different from denying the sentence "All dogs have eight legs" in the example given in the article Validity

One thing is denying a fact.

Like in these examples:

Fact: "all dogs have eight legs"

Denial: "not all dogs have eight legs".

Or

Fact:"Lizzy was the murderer"

Denial:"Lizzy was not the murderer"

In the example in this article you do something completely different

You are not denying a fact or assertion. You are denying a if fact A then Fact B connection.

Which is something completely different to which the validity notion does not apply. --217.228.213.50 09:30, 14 Jul 2004 (UTC)

Astonishing. Banno 10:48, Jul 14, 2004 (UTC)

So for you, denying a premisse or denying an "if-then" statement is the same thing ? Do you really believe that denying a "if-then" statement still allows any "validity" or any meaning at all whatsoever ? Now that is astonishing. --217.80.234.166 19:51, 21 Jul 2004 (UTC)

I assume that by 'premisse' you mean 'Premise'? If so, then certainly, provided the conditional is a premise of the argument. Please have the curtesy to restrict your edits to topics of which you have some knowledge. Banno 22:43, Aug 7, 2004 (UTC)

So denying a "premise" is the same that denying an if-then statement ? And you think you know about the topic ? You are only a wiseacre. I don't mind too much if you are an idiot. There are plenty of them. But the priggish remarks have made me puke. I'll leave you to your "domain", wise-guy. --217.228.218.239 19:50, 27 Aug 2004 (UTC)

That would be for the better. Banno 22:08, Aug 27, 2004 (UTC)

Yes, don't discuss it, leave it to the "expert". "Logic" is becoming a sort of religion.

Look: Modus Tollens says

(p>q) & ~q > ~p

Now, (p>q) is one premise of the argument, ~q is the other. Substitute ( r>s) for q,

(p>( r>s)) & ~(r>s) > ~p

and you have denied the premise (r>s).

That is, in this case, denying the premise is denying (r>s). Denying the 'if-then' results in a valid argument that ~p.

It doesn't take an expert to see that, just someone who is willing to spend some time learning. Banno

[edit] Making sense of 217.*?

(A)  If P, then Q.
(B)  Q is false.
(C)  Therefore, P is false, OR (A) is unsound, or (B) is unsound.

Essentially, for me to agree (C), I must agree (A,B). However we find in much popular rhetoric that this is not always the case. Just as 217.* mentioned, there are assumptions in the two arguments which are not necessarily agreed upon by all parties:

(A) If there is fire there, then there is oxygen there.
(B) There is no oxygen there.
(C) Therefore, there is no fire there.

"But", Socrates argues, "I consider the Sun to be firy." (which would invalidate the first premise).

Therefore it does seem relavant to talk about the distinction between soundness snd validity in the articles for MT and MP. (I have added a relevant para. into MP) (20040302)

---

I'm pretty sure the conditional Rules: MP, MT, and Disjunctive Syllogism are the same-- meaning there's a more basic rule that governs them. Maybe I'm wrong 'though.

MP: premise P → Q premise P therefore Q = premise ¬P v Q premise ¬¬P therefore ? by Implication and Double Negation = premise (¬)¬¬P v Q premise(¬)¬P therefore (¬)Q by Disjunctive Syllogism which reads: premise P v Q premise ¬P therefore Q

Now here's MT: premise P → Q premise ¬Q therefore ¬P = premise ¬Q → ¬P premise ¬Q therefore ? by Transposition = premise ¬¬Q v ¬P premise ¬Q therefore ? by Implication = Path One: premise (¬)¬Q v ¬P premise (¬)Q therefore ? = premise (¬)Q → ¬P premise (¬)Q therefore (¬)¬P

or Path Two after Implication: premise Q v ¬P [by Double Negation of Q] premise ¬Q therefore ¬P by Disjunctive Syllogism

[edit] Paradox deleted

I deleted the following from the page:

If a modus tollens argument has only true premises, then it is sound.

The argument is not sound.

Therefore, it is not a modus tollens argument which has only true premises.

Of course, this particular argument would, if applied to itself, create a paradox.

I dunno, as paradoxes go, this one didn't seem particularly clever. "This argument is not sound" essentially says "This statement is false."

More importantly, it seemed more confusing than enlightening in context.

--Jorend 15:25, 6 February 2007 (UTC)

[edit] Bad Example

"If Xavier is the murderer, then he must own a glove that fits. Xavier does not own a glove that fits. Therefore, Xavier was not the murderer."

This is a poor example of modus tollens. It is a specious argument, since Xavier doesn't necessarily have to own a glove that fits to be the murderer; he could have borrowed one and returned it, stolen one only to throw it in the garbage, or may own one that nobody knows about. One relying on empirical data would be more valid.