Talk:Modus tollens

message: 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)
thread_title:  Paradox deleted 

message: "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.
The example of a watch-dog is also bad.  It is actually not a valid syllogism.  Here is what Wikipedia has right now:
If the watch-dog detects an intruder, the dog will bark.
"The dog did nothing in the night-time."
Therefore, no intruder was detected by the watch-dog.
A valid syllogism does not presume something - the first premise is not provable but merely probable.  To correct this (which makes it valid but not necessarily true) one would have to say:
You are mistaken. In formal logic validity has nothing to do with whether or not the premises are true.  — Preceding unsigned comment added by 69.169.162.217 (talk) 18:27, 10 November 2011 (UTC)
thread_title:  Bad Example 

message: I removed a paragraph which was left in after an earlier edit. It was generally confusing and remaining version is esentially correct so I didn't feel the need to add anything else.
The removed paragraph included the folling argument
"Because though B exists if A exists, A might also exist without the existence of B at all."
Which is actually wrong, specifically it contradicts modus tollens. If the original editor sees this I encourage him or her to think it through again before reverting the article. 
Note to last poster (Bad Example):
There's something to be said about illustrating MT with true premises but it's hardly a requirement. The quoted argument is MT, though I agree that we could argue one of the premises (P->Q) is not true. Sorry, if I'm just stating the obvious here.
86.101.162.160 18:43, 28 May 2007 (UTC)
thread_title:  Edit 

message: Someone had changed it at some point. However, this form really is "modus ponendo tollens." Modus tollendo tollens is the way of denying by denying: ~B, ~A → B  ==> A
Gregbard 10:17, 8 August 2007 (UTC)
thread_title:  Latin 

message: The following expression is not quite right:
\frac{\vdash P\to Q ~~~ \vdash\neg Q}{\vdash \neg P}
The turnstiles are unnecessary.
:They are very necessary if one want to prove things which require assumptions.  But yes, really you'd want to write
:\frac{\Gamma \vdash P\to Q ~~~ \Gamma \vdash\neg Q}{\Gamma \vdash \neg P}
:--Andyf (talk) 12:19, 5 August 2008 (UTC)
thread_title:  Not quite right 

message: I have a sense that I should be able to follow this article, but it is very difficult.
Will someone please provide in this talk page, another example (or 2) of Modus tollens, and also the same examples in the form Modus ponens?
Thank you, Wanderer57 (talk) 02:56, 30 January 2008 (UTC)
thread_title:  Help 

message: This relativity example seems quite strange to me. First of all, was this effect never contradicted? (I believe there must be newer experiments showing clearly a variation on the mass of an electron) Second, we are talking about logic. So it seems to me wrong to mention that Einstein would have refuted this argument based on a certain intuitive "plausibility" of alternative theories... -- NIC1138 (talk) 16:43, 4 June 2008 (UTC)
replies: text: Two years ago it was suggested that this example should be deleted.  I don't see any argument that it should stay, and it does seem to be misleading, so I am deleting it. Geoffrey.landis (talk) 15:51, 4 December 2010 (UTC)
thread_title:  Relativity 

message: I removed this from the intro:
:Buddha was prone to this logical fallacy, and often used it in his discourses.
Unless I've completely misunderstood this article, Modens Tollens isn't a fallacy; I've no idea what the sentence is referring to; and if it's not about modens tollens then it probably shouldn't be in this article. -- Phil Barker 08:44, 29 August 2008 (UTC)
replies: text: Correct, it isn't a fallacy - the user may have been confusing it with "assuming the consequent" or "denying the antecedent".  Unfortunately when you have four similarly-named arguments and two of them are fallacies, some confusion is inevitable.  --Philosopher Let us reason together. 01:07, 4 November 2008 (UTC)
thread_title:  Buddha 

message: * If the watch-dog detects an intruder, the dog will bark.
* The dog did not bark.
* Therefore, no intruder was detected by the watch-dog.
What if the intruder distracted the dog by feeding it a nice juicy steak? --88.108.204.84 (talk) 13:28, 3 June 2011 (UTC)
thread_title:  Watchdog example 

message: After some thought, I've removed this bit:
Modus tollens became well known when it was used by Karl Popper in his proposed response to the problem of induction, falsificationism. However, here the use of modus tollens is much more controversial, as "truth" or "falsity" are inappropriate concepts to apply to theories (which are generally approximations to reality) and experimental findings (whose interpretation is often contingent on other theories).
It needs a citation in at least two places.  The publicity claim and the appropriateness claim.  And it's not terribly well written.  But I'm not sure it's really relevant enough, even if the claim proves to be correct.  If it were right in some way and relevant, it would still need to be rewritten.  As it stands, it looks like a claim about the nature of truth, which is odd to have in an article about a rule of inference.  I suspect that the first disjunct is wrongheaded.  The second disjunct seems more plausible and related to Popper in appropriate ways, but still seems odd.  Oh yeah, and it's in the wrong place.
Since it seems irrelevant and probably false or disputed, I'm not bothering to try to figure out what it's saying to rewrite it.  For now, it comes out.
Notapipe (talk) 04:22, 5 June 2012 (UTC)
thread_title:  Popper 

message: These abominations, as well as entire article (to a lesser extent), suggest that modus tollens depends on proof by contradiction, which is wrong. I propose to wipe it out like a similar abomination was wiped out of modus ponens, and add a text explaining that modus tollens has nothing to do with excluded middle and so, instead. Objections? Incnis Mrsi (talk) 11:53, 13 April 2013 (UTC)
replies: text: Claiming that something is a formal proof isn't claiming that it "depends on" whatever premises and proof system used. Modus tollens can be a basic inferential rule in your proof system, but in a system where it isn't, it can be proven as a theorem with some other rules (or axioms). The link you point to in the other page raises reasons for deletion different than those you offer here: that the proof system in that article is not specified. Fine, I have nothing to say to that kind of objection. But it's not the case that proving something implies that it depends on the steps you take or the assumptions made in the proof.2601:B:C580:2D9:CAF7:33FF:FE77:D800 (talk) 02:00, 26 April 2015 (UTC)
thread_title:  “Formal Proof” (so named) 

message: In the "Explanation" section I changed "This is a valid argument since it is not possible for the premises to be true and the conclusion false" to "This is a valid argument since it is not possible for the conclusion to be false if the premises are true", since under the former formulation the following is a valid argument: "2+2=5, therefore the cow jumped over the moon".Bobblond (talk) 04:52, 21 July 2013 (UTC)
thread_title:  edit 

message: I  deleted the Harry Truman example from the "Explanation" section. Here's what I deleted: 
::Another example:
:::"An honest public servant can't become rich in politics." - Harry Truman, 1954, is logically equivalent to "You can't get rich in politics unless you're a crook." I.e., ((H =>^R) & R) =>^H, and (H =>^R) = (R =>^H), where R stands for "rich in (from) politics".
I deleted it because the Truman quotation does not contain an inference. It's simply a restatment of a conditional premise. Truman is saying something like, "If a person is an honest public servant, then that person cannot become rich in politics." However, he is not obviously denying the consequent, and therefore he's not stating--or apparently even implying--a full modus tollens argument. To do that, he would have to say something like "An honest public servant can't become rich in politics, and Smith has gotten damn rich in politics." (Note that the conclusion in this revised argument, that Smith is dishonest, remains unstated.)
For all I know, the historical record may actually include more information. The context may have been pregnant with unstated premises, or Truman may have simply said more than is quoted here. As it stands, however, the example appears to confuse the statement of a conditional premise with the statement of a modus tollens. It is a common misconception that a conditional statement by itself constitutes an inference, and this example may promote that misconception.
I recommend it be replaced with a better example.  — Preceding unsigned comment added by 75.170.165.11 (talk) 13:42, 4 August 2017 (UTC)
thread_title:  Deletion of Harry Truman Example