Talk:Denying the antecedent

is a double page with Non sequitur (logic), i suggest it should redirect to that page.
 * Old, but I'll bite. This is a specific type of non sequitur, but this page (and related pages on logical fallacies) go into more depth than non sequitur (logic) should. —Cuiviénen 20:10, 11 February 2007 (UTC)

in the definition given here, if P is a necessary condition for Q, is it still a fallacy? Somaticvibe 21:39, 19 February 2007 (UTC)


 * no. --YbborT 22:11, 19 February 2007 (UTC)


 * "if P is a necessary condition for Q, is it still a fallacy". No, because then If P, then Q becomes If, and only if, P, then Q, which also implies If Q, then P. Then, by the modus tollens, not P, therefore not Q. &mdash; Isilanes 10:58, 22 February 2007 (UTC)

This is a horrible article!
Really should win an award for leftist crap (which is saying a lot on Wikipedia)! — Preceding unsigned comment added by 96.249.195.72 (talk) 20:21, 8 June 2014 (UTC) I've heard a lot of things called politically biased before, but never a simple rule of logic! Ultan42 (talk) 23:10, 12 August 2014 (UTC)

Turing Quote
It looks to me as if this quote was intended to mean "if and only if," and thus is not a relevant example to this section. &mdash; Twey 02:56, 21 October 2007 (UTC)


 * Read the essay. Turing explicitly intends the argument to be invalid: he erects it only to knock it down.  271828182 03:13, 21 October 2007 (UTC)


 * Yes, but quoting the article out of context leads to confusion here, because I think most people would agree with Turing's fake argument because it rests upon the common notion people hold that "people are machines if and only if they follow a set of rules to live by", as Twey pointed out. Obviously Turing does not agree with that proposition, but that is not obvious reading the wiki article.  —Preceding unsigned comment added by 144.80.57.194 (talk) 05:58, 15 February 2008 (UTC)


 * Misreading a conditional as a biconditional, however common it may be, is simply an error. Indeed, it is a major reason why denying the antecedent is a widespread fallacy.  That the error is not obvious is the point, as the text introducing the example explicitly observes. 271828182 (talk) 03:42, 16 February 2008 (UTC)


 * Turing begins the essay by defining machines, as discrete machines; machines for Turing are by definition ones which only follow sets of rules. If you had an 'object' which did not follow rules, I don't think Turing would count it as a 'machine'. There is an implied premise which makes the argument valid. That being that machines are things which follow rules. March 4 2008.


 * Yes. Turing discusses just such an additional premise, and goes on to argue against it, in the passage cited.  271828182 (talk) 17:26, 4 March 2008 (UTC)


 * Just a viewpoint from a random reader browsing through - I read the quote from Turing, and came here to the talk page to see if it was controversial, because given certain prior beliefs about people, machines, and rules, the quote from Turing stands as a valid argument. The sentence after the example that's supposed to point out why Turings argument is wrong: "However, men could still be machines that do not follow a definite set of rules." is very shaky in the context of Turings use of the word machine, in that a machine in this context is something that *must* follow a definite set of rules. The terms used, by definition, bring extra conditions to the argument. Please consider removing this example, and replace it with one without the same baggage as it only adds confusion to an article seeking to clearly explain the fallacy.


 * The problem exists in this comment section too. User "271828182" claimed denying the antecedent is a widespread fallacy precisely because of 'misreading,' or perhaps he really meant 'misusing' a conditional as a biconditional. If he didn't mean it that way, he should have: the problem doesn't come from misreading them, because face it, when people use a conditional in DA they very often mean a biconditional. The problem then is in people not clarifying that when they do use DA.


 * In fact, the correct form of denying the antecedent is widespread, because most of the time when people use it they DO mean 'if and only if,' and in public speech, that's how things work: we are not required to logically outline EXACTLY what we mean every time we say it, often things are implied, even in the most rigid social camps. Replacing "if and only if" with "if" alone is a completely understandable, forgivable and permissible linguistic choice. And it doesn't cause problems in day to day speech. In fact, it's rather coy and snotty and actually ignorant of us to accuse people of using a fallacy when we know what they really meant. 16:57, 25 April 2012 (UTC)

There is so much wrong in the above comment ... it actually contains a fallacy of denial of the antecedent within it. This article is about the fallacy of denial of the antecedent of a conditional ... that people often non-fallaciously deny the antecedent of a biconditional -- that is, that they employ modus tollens -- is irrelevant. What is relevant is that people also often commit the fallacy described in the article. To note this fact is not coy, snotty, or ignorant (a heavy case of pot/kettle/black there), nor is it an accusation of using a fallacy against people not using a fallacy -- what a ridiculous failure of logic; it's like saying that those who point out that "literally" is often misused are accusing people who use it correctly of using it incorrectly. Or like saying that some brunettes dye their hair blond is an accusation against natural blonds.

As for the Turing example, it is quite appropriate here, as Turing presented it as one of several fallacious arguments against the notion that machines can think, and it obviously is not a biconditional and it would be most silly to take it as one -- it clearly isn't meant to assert that man would be no better than a machine only if he conducted his life by a definite set of rules. As for how a man who doesn't conduct his life by a definite set of rules can still be a machine -- adaptive machines can implement a fixed set of rules internally (an algorithm) while having quite irregular behavior that is largely governed by their environment. (A la nurture vs. nature ... it's not one or the other, it's both.) The definite set of rules that meat machines follow is not to be found by studying their whole-body conduct, but rather by examining their internal components -- cells, which follow incredibly complex but definite rules. -- 96.247.231.243 (talk) 05:24, 1 January 2014 (UTC)

The Turing quote is confusing because Turing claims it is an example of a different fallacy. I have no idea why he classified it that way, but it makes the example's use here less well-chosen than it might be. (That is, I don't think the usage is technically wrong, but I think it invites misunderstandings needlessly, given what Turning himself claims about it.) — Preceding unsigned comment added by 62.255.73.246 (talk) 02:53, 15 June 2017 (UTC)

To His Coy Mistress

 * Is this link appropriate (in the "see also" section)? The editor who included it says that the poem is a good example of denying the antecedent... I don't really see it so clear. Opinions? &mdash; Isilanes 20:37, 4 March 2007 (UTC)


 * "Had we but world enough and time, this coyness, lady, were no crime" = "If we had time, then it'd be okay to be coy." (If A, then B)
 * "But at my back I always hear time's winged chariot drawing near" = "We don't have time." (Not A)
 * "Now let us sport while we may" = "Coyness is a crime, or, Let's Get It On" (Not B)

271828182 00:25, 5 March 2007 (UTC)


 * Correction: "If and only if we had time." (Iff A then B) You really don't think he meant it this way? This is a truly pure logician's way of looking at it, but it ignores social reality. Marvell clearly meant that ONLY if we have time is it okay to be coy, but we do not have time, so we must have sex. As silly as the premise is, if it WERE true, the argument would be sound. Which means that as it is, the argument is valid. It's no use to get squeamish around implication, since it's used so often in reality. Chicopac (talk) —Preceding undated comment added 16:44, 25 April 2012 (UTC).
 * No, you are obviously wrong, this obviously was not meant as a biconditional, else a) there would be no reason for the syllogism and b) the premise would assert that there is no reason to be coy other than having no time, which is obviously false. This is a true blue DA fallacy and the people saying it isn't are simply thinking fallaciously, of the DA sort. -- 96.247.231.243 (talk) 05:54, 1 January 2014 (UTC)

Very good! On other hand, the argument does seem valid. edward (buckner) 15:55, 5 March 2007 (UTC)


 * Really? Walk up to a woman on the street and tell her that the only reason she could possibly have for not sleeping with you on the spot is if there were time to do it later, and report how things "seem" to you when she gives her response. -- 96.247.231.243 (talk) 05:54, 1 January 2014 (UTC)

I think it is valid, but as an instance of the principle of sufficient reason. If it were the case that A, then that would be a reason for B. But it is not the case that A.  Thus (assuming a supressed premiss to the effect that there is no other reason for being B), the principle of sufficient reason implies not-B. But hang on. There has to be a sufficient reason for not B, doesn't there? Let me think about that. edward (buckner) 15:58, 5 March 2007 (UTC)


 * This is severe logical failure. DA is a fallacy exactly because it requires this "supressed [sic] premiss" in order to go through. In this case, that premise -- that there is no reason not to have sex other than lack of time is obviously false. -- 96.247.231.243 (talk) 05:54, 1 January 2014 (UTC)

Or another interpretation could be:

If we wait, there is time (to wait) But there is no time Therefore we don't wait


 * I must admit there is a temptation to rescue the poem by reading the first line as a biconditional. But to stick to what Marvell wrote, we must conclude that not only is the poet's motive impure, but so too is his logic. 271828182 01:03, 6 March 2007 (UTC)


 * You have failed severely here by leaving out what it is that there is no time for -- not "waiting", but having sex. The poem obviously does not contain a biconditional -- there are plenty of reasons not to have sex other than having time to do it later. -- 96.247.231.243 (talk) 05:54, 1 January 2014 (UTC)


 * Forgive my English literature ignorance, but... is this poem so notable and well know that deserves mention? Is this the best known and most clear example of DA in English literature? A Wikipedia reader following the link will have her doubts on the DA subject decreased, or increased, by reading this poem? Regarding the explanation of the DA in the poem above, I have my doubts. I understand the following: "Had we but world enough and time, this coyness, lady, were no crime", not as "If we had time, then it'd be okay to be coy.", but rather, "Only if we had time would coyness be OK", or, in other words, the "if" is an "if and only if", so the reasoning of the poet is correct by the modus tollens. The poet means that the only reason for being coy would be to have plenty of time in their hands (which is not the case), not that it would be one of many reasons. &mdash; Isilanes 08:31, 6 March 2007 (UTC)
 * Only if we had time would coyness be OK -- but that's obviously BS; there are many reasons to be coy other than having time to do the deed later. What you are arguing is that this DA is a not a fallacy because, if the conditional were a biconditional, it wouldn't be one. Sorry, but that puts the cart before the horse, altering the stated premise simply to avoid this being a fallacy -- but it is one; a bit of nefarious rhetoric. -- 96.247.231.243 (talk) 05:54, 1 January 2014 (UTC)


 * I don't know if best known as DA, but, trust me, this is a very well poem. I found it quite amusing and a good example.  edward (buckner) 12:56, 6 March 2007 (UTC)
 * On the reading of it, yes, that's possible. But the reading of 'but' in 'if we had but an X' usually implies sufficient condition, not necessary.  Thus a fallacy.  edward (buckner) 12:59, 6 March 2007 (UTC)


 * Well, it is a very famous poem. Is it the clearest example of DA?  No, but non-textbook examples of logical fallacies are seldom obvious.  ("Had we but" is not equivalent to iff: do a Google search on an equivalent phrase such as "had I but" to see many examples of usage where the iff reading makes no sense.)  Will a Wikipedia reader grasp that the poem is an example of DA?  Maybe, maybe not.  Will they read some great poetry and see how fallacious inferences can go generally unnoticed?  I would hope so. 271828182 17:36, 6 March 2007 (UTC)


 * "Had I but a little slice of bread, I would not be dying of hunger!" "Ah. So a piece of ham wouldn't have helped."


 * Great! I just wanted to rest assured that its addition would be positive, as it seems it is. &mdash; Isilanes 18:08, 6 March 2007 (UTC)

Well, didn't see this, weird and amusing, but shouldn't this be cross-linked in the actual article on the poem? Obscurans 01:41, 11 July 2007 (UTC)

The discussion here about the poem's guilt or innocence over containing the fallacy is well and fine, but as it stands currently, linking to the poem detracts more than it adds to this article. Neither page makes reference to the other over the presumed error. Currently, the poem's page notes, "The logical form of the poem runs: if... but... therefore...", which is not even cited. While the See Also section is not total serious business like the rest of the content is, I still find the link's inclusion egregious, distracting at best:


 * 1) if you were not already aware of the poem's offending part(s), you will have to discover it yourself, either by your own analysis or through researching other analyses.
 * 2) this article is already somewhat inaccessible, in my opinion, to the reading level of the layman, so giving him or her this as further reading, without any encyclopedic information to explain, is confusing and unnecessary.
 * 3) this is not a particularly noteworthy example of denying the antecedent.
 * 4) without including some explanation of applicability or noteworthiness, the link is superfluous and serves no encyclopedic function. While it may be interesting for a Wikia page on a more specific subject, like a Fallacy Wikia or a 17th Century Poetry Wikia, it's likely of interest and use to very few.

Thus, I am going to remove it, but offer a suggestion for compromise: it would better serve the article if we included in the main text an offending excerpt from the poem along with an explanation of its invalidity, alongside the other examples. This would be I think the easiest way to justify linking to the poem, although even then it's a tenuous justification. Zach99998 (talk) 07:12, 14 October 2011 (UTC)


 * Probably a better solution is just to delete the see-also William M. Connolley (talk) 07:40, 14 October 2011 (UTC)


 * I was the original editor who classified "To His Coy Mistress" as a correct form of denying the antecedent, but I did so within that poem's entry. I don't know if this had any influence on including it here. For one, I agree that as it is the "see also" link on this page is more confusing than not. But my biggest issue is that the most common usage of DA is barely mentioned here, and I think incorporating the Marvell poem in the article to explain DA with 'if and only if' might be a good way, as another editor suggested.


 * Denying the antecedent in its valid form is, in fact, far and away the most commonly used form of denying the antecedent in everyday speech, as in Marvell's poem. Technically, those who say we can't know for sure that his poem was the 'if and only if' form of DA are correct, but technicality has no place in public speech. It would be ignorant to ignore the implications of virtually everyone when they make a DA claim, which is, I would argue, at least as often 'if and only if' as it is not. For some examples: "If the surgery goes well, my dad will survive." "If the chemotherapy works, I will survive." "If I'm hungry after class tonight, I will eat." These are just a few examples where the person implicitly means to include 'if and only if,' and where denying the antecedent would in fact also deny the consequent. I think this article would be served by including this obvious fact in the article.


 * As it is, it's actually more confusing to readers of the article: they will leave the article thinking that, invariably, denying the antecedent is wrong, accusing people they hear of being logically invalid even while that person innocently meant to, but did not, include 'if and only if.' Chicopac (talk) —Preceding undated comment added 16:31, 25 April 2012 (UTC).


 * The premise is most certainly not a biconditional; if it were, then a) there would be no need for this bit of of nefarious rhetoric and b) it would be blatantly false -- it clearly isn't true that the only valid reason for being "coy" is that there is time to not be "coy" later. It's amazing that anyone who lives in the real world of male-female relationships could think that this argument ("we're out of time and having more time would be the only valid reason not to screw right now") is valid.


 * "If the surgery goes well, my dad will survive." -- this and your other examples are not biconditionals -- your dad can survive even if the surgery doesn't go well (if someone says that and you ask "what if it doesn't go well", they're likely to say "then we'll hope for a miracle" or "then he may end up a vegetable", not "then he's sure to die"), you can survive even if the chemo doesn't work (you could be successfully treated by other, stronger chemo, or radiation, or have spontaneous remission), you might eat even if you aren't hungry (intelligent people leave open such possibilities as a friend coming by with homemade cookies) -- it's ironic that you insist that most cases of DA aren't fallacies, that people know how to reason validly, and then present three DA fallacies as examples of non-fallacious reasoning. -- 96.247.231.243 (talk) 05:54, 1 January 2014 (UTC)

well...
If I have a boyfriend, I will go to the dance tomorrow.

I don't have a boyfriend.

But I can still go to the dance tomorrow. —Preceding unsigned comment added by 68.101.123.219 (talk) 19:37, 17 February 2008 (UTC)


 * Actually this might be a more relevant and understandable example for the article. 118.90.72.183 (talk) 15:00, 7 June 2008 (UTC)


 * Actually, in DA, it should actually be:

"If I have a boyfriend, I will go to the dance tomorrow.

I don't have a boyfriend.

So I can't go to the dance tomorrow."

64.231.120.29 (talk) 02:19, 14 June 2008 (UTC)


 * But again, let's get realistic. When a teenage girl says "If I have a boyfriend, I will go to the dance tomorrow," they are implying that they will not go if they don't have such a boyfriend. This is the valid form of denying the antecedent, which I argue should get more play time in this article. Chicopac (talk) 16:47, 25 April 2012 (UTC)
 * No, they are implying no such thing. This article is about logical fallacies, its not a portal to Cyc. -- 96.247.231.243 (talk) —Preceding undated comment added 06:18, 1 January 2014 (UTC)

Don't understand the proof that subject form of argument is sometimes valid
The following sentence implies that denying the antecedent is sometimes a valid argument.


 * "Arguments of this form are invalid (except in the rare cases where such an argument also instantiates some other, valid, form). "

It goes on to demonstrate that if an argument of the form "denying the antecedent" is arbitrarily altered by adding some other condition, then the modified argument may be valid, thus proving that there is an exception to the rule that denying the antecedent is fallacious.

The new, randomly introduced argument, is somewhat similar to the original argument, but according to the definition of the form given above, it is not an example of this form. Therefore, I don't understand how this proves that the first argument, denying the antecedent, was "valid in this case".

I suggest removing the phrase
 * "(except in the rare cases where such an argument also instantiates some other, valid, form)"

Mark.camp (talk) 12:46, 6 January 2009 (UTC)

Seeing no objection, I removed the text which implied that denying the antecedent is sometimes valide. Mark.camp (talk) 23:30, 11 January 2009 (UTC)


 * It didn't say that the form is sometimes valid, it said that some arguments of the form are valid. For example: "[1] If (R or S), then R. [2] ~(R or S). Therefore, [3] ~R."  That is certainly valid (the conclusion follows from De Morgan's laws and conjunction elimination) even though it denies the antecedent in form. -- Atethnekos (Discussion, Contributions) 15:13, 9 May 2012 (UTC)

I came here for a similar reason. I felt the example was poorly explicated on the page but is more understandable directly above this comment. Still, I suggest an easier example of the "conditional validity" of denying the antecedent, such as a categorical encompassing. To demonstrate by form of (if P then Q; not P; therefore not Q): if it is a bug, then it is an insect; it isn't a bug; therefore, it isn't an insect. Since by definition (loosely) insects are categorically subordinate to bugs it is necessarily true that it isn't a insect if it isn't an bug. There is an inherent implication of "if Q then P" by definition in the predicates. Now, you might note that the first premise is not true but this would be a question of soundness,which concerns the truthiness of the premises, not validity, which concerns the form and implication of the meaning of those premises and there might be situational context that makes such a statement true (eg. you might be pulling objects from a box that I filled and I happened to selected many objects but only insect bugs). This might also touch on the topic above concerning some inherited definitional biconditionalism. Scraggle Grackle (talk) 00:29, 11 March 2013 (UTC)
 * I think the one issue with your example is that it is unclear about the status of your premisses. You say that "Q->P" is an implicit premise. Well, that's fine, but an implicit premise is still a premise, and when you include that premise, you no longer have an argument of the denying the antecedent form, I believe. -- Atethnekos (Discussion, Contributions) 02:49, 11 March 2013 (UTC)
 * if it is a bug, then it is an insect -- this premise is false. Deriving a true conclusion from a false premise is trivial, and you have done so here while employing a DA fallacy. Your argument is of the form false -> Q. ~false (i.e., true). Therefore Q. But clearly true -> Q is not a valid argument regardless of whether Q is true (it happens to be, here). There is an inherent implication of "if Q then P" by definition in the predicates -- there is no such "implicit implication" at all. There is a misstated, false, premise, P -> Q, in place of a correct, true, premise, Q -> P. You can't argue that an argument is valid because the valid argument is "inherent" in the meanings of the terms, you have to take the argument as stated. -- 96.247.231.243 (talk) 06:23, 1 January 2014 (UTC)

@96.247.231.243, your particular argument is invalid. I made note that the premise you mentioned is false. Triviality is a moot point here. The point being made is that a contextual syllogistic form of DA is valid; that is circumstantially. Your point about false premise is irrelevant since it does nothing to dissuade of the validity. As I mentioned in the previous post, soundness of a premise has nothing to do with validity. An argument of the particular form that I mentioned in the post is conditionally valid: If P then Q; Not P; therefore not Q. You cannot alter the premises and then reassess the validity as you did here: "clearly true -> Q is not a valid argument regardless of whether Q is true (it happens to be, here)". The form is not If P then Q, P, therefore Q. That isn't the assertion being made. The assertion is that under particular conditions inferences being made by DA are valid. I gave examples and you are criticizing a form that is not being asserted. Please don't target arguments that I am not making. That is strawmanning the argument since that is not the assertion being made. As for this: "there is no such "implicit implication" at all. There is a misstated, false, premise, P -> Q, in place of a correct, true, premise, Q -> P. You can't argue that an argument is valid because the valid argument is "inherent" in the meanings of the terms, you have to take the argument as stated." There is definitely an implication as such, that if it is not an insect then it isn't a bug. There is no requirement to explicate that so you might have to take your advice and take the argument as stated. Since all insects are bugs one can properly deduce that if a thing is not a bug then it is not an insect. This only works because of the contextual tokens taken in the types here. In other words this particular form when not altered to be a different form as you have done is filled with some particular references it becomes valid to use. I even mention conceivable situations in which the first premise is in fact true! Please read. Imagine you have a box with things in it. I filled the box with many things. I only put bugs that are insects inside. Under these conditions the first premise would be true in the reasoning and the DA would be valid and sound should you pull a bug!!!!Scraggle Grackle (talk) 22:54, 19 May 2014 (UTC)

@Atethnekos, hidden premises or not, the point being is that there are situational versions of DA validity. You don't have to explicate and reformulate the argument in a different syllogistic form and say this is the only reason because that would only demonstrate that if a form of DA hides a valid syllogistic form on occasion then it too transitionally is valid right? It would only prove the point so I'm not sure what the issue is. Either way, I'm only talking about the example above and these arguments against the whole idea are about whether situational DA validity exists at all. My point was about clarifying the example that is already on the page but I'm happy to talk about this anyway if you like. As stated above twice I gave an example where the premise might, in fact be true and make DA valid and sound.Scraggle Grackle (talk) 22:54, 19 May 2014 (UTC)

"If"?
The article is written like "if" is an implication marker. Which is often isn't, f.ex. imagine an american dialogue:
 * Voter: why don't you veto the congress decision?,
 * Congress man: If I be president, I could veto the decision, now I'm not, and therefore I can't.

The logic is perfect in the context, where "if" signals equivalence, not implication. Normal language doesn't include such a term as "if and only if", and it does allow ambiguous meanings that are distinguished by context. Only logicians believe that their usage of "if" is the same as implication. ... said: Rursus ( m bork³ ) 13:34, 8 January 2010 (UTC)
 * The article is written like "if" is an implication marker. Which is often isn't -- What an ironic fallacy of denial of the antecedent. No number of examples of non-fallacies using "if" will establish that "if" is not used fallaciously. Numerous common examples abound such as "The police protect us from criminals. If you're doing nothing wrong, you have nothing to fear from the police." -- 96.247.231.243 (talk) 06:51, 1 January 2014 (UTC)

Other versions
There is an argument technique that manipulates this fallacy:


 * You stole my candy so you should be executed.
 * No one should be executed just because they stole your candy.
 * Ah-ha, you just implied you stole my candy.

O= My argument is correct P= You stole my candy Q= You should be executed
 * If O, and P, then Q
 * Q is false because O is false
 * If whether Q is true or false depends on O, P must be true

If responded differently:


 * You stole my candy so you should be executed.
 * That is totally wrong, I should not be executed, in fact, I did not even steal your candy.
 * Well, if I do find out that you stole my candy, you should be executed.


 * If O, and P, then Q
 * Q is false because P is false
 * If whether Q is true or false depends on P, O must be true

Is this worth mentioning? 173.183.79.81 (talk) 08:56, 30 January 2011 (UTC)


 * Another possibility would be:


 * If O, and P, then Q
 * Q is simple false
 * You need to state a reason


 * Either way, no counter argument would ever work. 173.183.79.81 (talk) 07:13, 8 February 2011 (UTC)

No, none of that is worth mentioning. -- 96.247.231.243 (talk) 06:53, 1 January 2014 (UTC)

God Save the Queen Link
It is unclear why this edit was left in place. It was an nonconstructive addition on or about November 2010, originated from an ip address and was not signed by it's author. As a general user, seeing this page for the first time I found the reference to be unclear. If it has some purpose in the article, that may need clarification. If not, shall the link be removed? -Andreis —Preceding unsigned comment added by 24.156.67.243 (talk) 01:45, 11 March 2011 (UTC)


 * Removed now. —Mrwojo (talk) 04:59, 11 March 2011 (UTC)

These arguments are invalid? No, not all of them.
"Denying the antecedent, sometimes also called inverse error or fallacy of the inverse, is a formal fallacy of inferring the inverse from the original statement. It is committed by reasoning in the form:

If P, then Q. Not P. Therefore, not Q. which may also be phrased as

P \rightarrow Q (P implies Q) \therefore \neg P \rightarrow \neg Q (therefore, not-P implies not-Q) Arguments of this form are invalid".

Not true.

The falsehood of the argument is only true when P and Q are not mutually exhaustive.

Easy eample: Truth and Falsehood.

If P(True) then Q(Not False). Not P(True) Therefore not Q(Not False).

How about a coin toss?

If heads then not tails. Not heads Therefore tails ( i.e. Not not tails ). — Preceding unsigned comment added by 194.75.238.182 (talk) 14:17, 10 September 2015 (UTC)

Your example with the coin is an invalid argument. Just because the premises and the conclusions are both correct it doesn't mean that the argument is a valid logical link between them. In this case you're relying on the fact that coins only have two sides, which you don't mention. A similar argument about a dice uses exactly the same form, and has true premises and a potentially false conclusion: If one then not six. Not one, therefore six. — Preceding unsigned comment added by 31.221.88.186 (talk) 12:01, 14 September 2015 (UTC)