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This seems a strange set of onward links as MT is not a common phrase in everyday language comparable to non-sequitur and is more appropriately linked with philosophical, linguistic or mathematics in my view. Thoughts on change? MKT92
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)
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)
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)
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
(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 and 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
I deleted the following from the page:
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)
"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)
All watch-dogs that detect an intruder bark [can you prove this is true always and everywhere? No.] This watch-dog did not bark Therefore, no intruder was detected by this watch-dog [false because the first premise is not true]
The second syllogism is certainly valid - it meets all of the criteria for being a valid syllogism (it doesn't commit any logical fallacies and follows the form correctly) but the first premise cannot be proven. Therefore the only consequence of this argument cannot be true. A negative is not proven here unless the first premise is true. —Preceding unsigned comment added by 121.73.151.5 ( talk) 05:25, 6 March 2011 (UTC)
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)
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)
The following expression is not quite right:
The turnstiles are unnecessary.
It should be like this:
The usage of turnstile does not apply in this form of expression. If we need to use a turnstile, we can use it in the following way:
Which is read like this: given and , there is a way to prove .
However, the above-mentioned incorrect expression reads like this: "given this and this as theorems in a system (system L for example), there would be a way to show that this is also a theorem of the system", which is a wrong and irrelevant reading. We do not have such expression in propositional logic.
Therefore, I am going to correct the expression.
Eric 23:52, 30 November 2007 (UTC)
I think it is really all up to definition. Since is not defined in this article and no explicit link to its definition is given, it really can't be taken to formally. As I have experienced, is usually used to denote the provability of a formula in some calculus, whereas is used to denote truth. is often abbreviated by or even . 95.208.111.88 ( talk) 18:15, 15 December 2014 (UTC)
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)
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)
The example is obviously wrong and should be removed. The Kaufmann experiments (1902 - 1906) showed the velocity dependence of electron mass (see http://en.wikipedia.org/wiki/Walter_Kaufmann_(physicist)). Tommo 2008-11-16 1:21
"In logic, modus tollendo tollens[1] (Latin for "the way that denies by denying")[2] is the formal name for indirect proof or proof by contraposition (contrapositive inference), often abbreviated to MT or modus tollens"
Is this true? Can someone include a full quotation from a logic textbook which argues this?
My understanding is that the contrapositive of is . For instance if your premises are and you may prove that follows by proof by contraposition: from and you get by modus ponens. Now if you have modus tollens as a rule of inference, then follows in one step by application of that rule.
-- Andyf ( talk) 12:31, 5 August 2008 (UTC)
Line | Data | Action |
---|---|---|
1 | P -> Q | A |
2 | P | A |
3 | Q | 1,2 MT |
4 | ~Q | A |
5 | ~P | 1,4 RAA (2) |
6 | ~Q -> ~P | 1 ->I (4) |
C | P -> Q |- ~Q -> ~P | Q.E.D. |
-- Philosopher Let us reason together. 06:26, 31 October 2008 (UTC)
It would be nice to add a sentence discussing the relationship with the contrapositive. Right now all the article says is that modus tollens is often confused with the contrapositive. The above distinction [essentially, (P => Q) => (~Q => ~P) being contraposition, and ((P => Q), ~Q) => ~P being modus tollens) would be a nice time saver for those familiar with the contrapositive. 08:26, 3 June 2011 (UTC) — Preceding unsigned comment added by 24.220.188.43 ( talk)
Proof by contraposition should be the first proof listed, since it directly corresponds to the method of removal, which is contrary to the method of positioning. The problem seems to be that the message of the methods have been lost in antiquity, which in the practice of logic, really seems to be trivial and unimportant. In fact, this whole discussion section begins by using a faulty definition of modus tollens. This faulty definition is negligible when either teaching or making use of the method, yet it seems to be necessary to use a more accurate definition in order to discuss why proof by contraposition should be seen as the primary straightforward proof that follows directly from the title of the method. It seems that the terms affirmation and denial have slipped in as translations that speak more to truth value than the original concept, and is very likely more valuable when teaching the methods. However, the terms do not carry the original message intended by the latin. A brief glance at the wikitionary describes both MP/MT in terms of affirmation and denial. Even so, when a reader uses the same dictionary to review the terms ponens and tollens, this reader is not presented with definitions of affirmation and denial, but definitions of placing and removing, corresponding more closely with these methods of evaluating propositions. This has already been noticed [1]. The shape of this article demonstrates that the method described is a ceremonial method that still works even if the meaning of the title has been lost in time. — Preceding unsigned comment added by 2600:100D:B12F:2B28:C218:85FF:FE74:69E4 ( talk) 21:02, 26 September 2016 (UTC)
I removed this from the intro:
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)
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)
This is a valid query, if using Modus Tollens it seems obvious that it has to be very clear that the rule only applies if P is the only possible reason for ¬Q to be true. There must in reality be an infinite number of reasons why a dog might not bark at an intruder. This example is a poor one. Brennan1 ( talk) 18:07, 19 December 2012 (UTC)
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)
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)
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)
I deleted the Harry Truman example from the "Explanation" section. Here's what I deleted:
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)
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This seems a strange set of onward links as MT is not a common phrase in everyday language comparable to non-sequitur and is more appropriately linked with philosophical, linguistic or mathematics in my view. Thoughts on change? MKT92
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)
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)
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)
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
(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 and 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
I deleted the following from the page:
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)
"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)
All watch-dogs that detect an intruder bark [can you prove this is true always and everywhere? No.] This watch-dog did not bark Therefore, no intruder was detected by this watch-dog [false because the first premise is not true]
The second syllogism is certainly valid - it meets all of the criteria for being a valid syllogism (it doesn't commit any logical fallacies and follows the form correctly) but the first premise cannot be proven. Therefore the only consequence of this argument cannot be true. A negative is not proven here unless the first premise is true. —Preceding unsigned comment added by 121.73.151.5 ( talk) 05:25, 6 March 2011 (UTC)
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)
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)
The following expression is not quite right:
The turnstiles are unnecessary.
It should be like this:
The usage of turnstile does not apply in this form of expression. If we need to use a turnstile, we can use it in the following way:
Which is read like this: given and , there is a way to prove .
However, the above-mentioned incorrect expression reads like this: "given this and this as theorems in a system (system L for example), there would be a way to show that this is also a theorem of the system", which is a wrong and irrelevant reading. We do not have such expression in propositional logic.
Therefore, I am going to correct the expression.
Eric 23:52, 30 November 2007 (UTC)
I think it is really all up to definition. Since is not defined in this article and no explicit link to its definition is given, it really can't be taken to formally. As I have experienced, is usually used to denote the provability of a formula in some calculus, whereas is used to denote truth. is often abbreviated by or even . 95.208.111.88 ( talk) 18:15, 15 December 2014 (UTC)
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)
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)
The example is obviously wrong and should be removed. The Kaufmann experiments (1902 - 1906) showed the velocity dependence of electron mass (see http://en.wikipedia.org/wiki/Walter_Kaufmann_(physicist)). Tommo 2008-11-16 1:21
"In logic, modus tollendo tollens[1] (Latin for "the way that denies by denying")[2] is the formal name for indirect proof or proof by contraposition (contrapositive inference), often abbreviated to MT or modus tollens"
Is this true? Can someone include a full quotation from a logic textbook which argues this?
My understanding is that the contrapositive of is . For instance if your premises are and you may prove that follows by proof by contraposition: from and you get by modus ponens. Now if you have modus tollens as a rule of inference, then follows in one step by application of that rule.
-- Andyf ( talk) 12:31, 5 August 2008 (UTC)
Line | Data | Action |
---|---|---|
1 | P -> Q | A |
2 | P | A |
3 | Q | 1,2 MT |
4 | ~Q | A |
5 | ~P | 1,4 RAA (2) |
6 | ~Q -> ~P | 1 ->I (4) |
C | P -> Q |- ~Q -> ~P | Q.E.D. |
-- Philosopher Let us reason together. 06:26, 31 October 2008 (UTC)
It would be nice to add a sentence discussing the relationship with the contrapositive. Right now all the article says is that modus tollens is often confused with the contrapositive. The above distinction [essentially, (P => Q) => (~Q => ~P) being contraposition, and ((P => Q), ~Q) => ~P being modus tollens) would be a nice time saver for those familiar with the contrapositive. 08:26, 3 June 2011 (UTC) — Preceding unsigned comment added by 24.220.188.43 ( talk)
Proof by contraposition should be the first proof listed, since it directly corresponds to the method of removal, which is contrary to the method of positioning. The problem seems to be that the message of the methods have been lost in antiquity, which in the practice of logic, really seems to be trivial and unimportant. In fact, this whole discussion section begins by using a faulty definition of modus tollens. This faulty definition is negligible when either teaching or making use of the method, yet it seems to be necessary to use a more accurate definition in order to discuss why proof by contraposition should be seen as the primary straightforward proof that follows directly from the title of the method. It seems that the terms affirmation and denial have slipped in as translations that speak more to truth value than the original concept, and is very likely more valuable when teaching the methods. However, the terms do not carry the original message intended by the latin. A brief glance at the wikitionary describes both MP/MT in terms of affirmation and denial. Even so, when a reader uses the same dictionary to review the terms ponens and tollens, this reader is not presented with definitions of affirmation and denial, but definitions of placing and removing, corresponding more closely with these methods of evaluating propositions. This has already been noticed [1]. The shape of this article demonstrates that the method described is a ceremonial method that still works even if the meaning of the title has been lost in time. — Preceding unsigned comment added by 2600:100D:B12F:2B28:C218:85FF:FE74:69E4 ( talk) 21:02, 26 September 2016 (UTC)
I removed this from the intro:
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)
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)
This is a valid query, if using Modus Tollens it seems obvious that it has to be very clear that the rule only applies if P is the only possible reason for ¬Q to be true. There must in reality be an infinite number of reasons why a dog might not bark at an intruder. This example is a poor one. Brennan1 ( talk) 18:07, 19 December 2012 (UTC)
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)
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)
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)
I deleted the Harry Truman example from the "Explanation" section. Here's what I deleted:
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)