Talk:Contraposition

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Previous talk page notes may be found at Talk:Contraposition (traditional logic).

Contradiction

I'm not fluent in english, so I don't dare to start messing up the page. But I'm pretty sure there's something wrong with the example about contradiction. I slightly agree that these shouldn't even be on this page in the first place. But the story about red objects having color is totally messed up.

If contradiction is the correct english term for turning $A\Rightarrow B$ into $A\Rightarrow \neg B$ then the contradiction og the red-color thing would be something like: A red object does not have a color.

The claim about truth of contradictions under truth is also wrong. I'd suggest to remove all these altogether, since the page is not about logic in general. —Preceding unsigned comment added by 94.18.143.116 (talk) 19:00, 29 April 2011 (UTC)[reply]

Thanks for your efforts, though! :) —Preceding unsigned comment added by 94.18.143.116 (talk) 18:56, 29 April 2011 (UTC)[reply]

I believe he's right about contradictions under the section "Truth". Consider the statement "Politicians are dishonest." As defined here, a contradiction would be "Bob is an honest politician." If Bob really is honest, then it disproves the original statement. But let's say that we learn that Bob tells lies sometimes. The original statement does not stand proven; there might still be an honest politician somewhere (named Abe ,maybe?) A contradiction being false does not prove the statement it contradicts. Perhaps it's just the wording.

He's also right about the article's title, "Contraposition", it's not "Inverses, Converses, Contrapositives and Stuff Like That". There should be such an article; if this is that article the title's wrong.

Applications

The example given is rather confusing and may give the casual reader the impression that proving by the contrapositive is the same as proving by contradiction. Donald Hosek 03:22, 4 July 2007 (UTC)[reply]

The example with houses and buildings is not very obvious to me, since I think not every reader sees the same set/subset relation on them. I know people who claim that buildings and houses are mutually exclusive. Anton

It is claimed that the following is the case: "The contrapositive is 'If an object is not a building, then it is not a house'..." However, There are quite clearly people who live in boxes, which are not buildings but certainly are houses (unless the definition of house is such that House(x) is biconditional with Building(x) rather than simply conditional). I would suggest finding a simpler relationship that is provably true in all cases on virtue of the definition of it's parts, AND remains a conditional statement. For example, "If an object does not have color, then it is not red," would be an excellent and undisprovable example. edit: i was in class, and have edited this and signed it with my home laptop.--24.107.9.33 17:27, 12 November 2007 (UTC)[reply]

Because it was not disputed, I have edited it to reflect the clearer original statement "All Red things are Colored." --24.107.9.33 (talk) 04:23, 30 November 2007 (UTC) aka MilquetoastCJW[reply]

A conditional statement doesn't always makes sense, if it doesn't then it would be false but still a converse statement. 72.18.39.72 (talk) 22:01, 17 December 2007 (UTC)[reply]

that's quite a completely different discussion on the nature of meaning and connotation versus rationality and truth-value. For the purposes of an example, Red v. Color will do much better than a conditional which is false to begin with. --97.91.175.154 (talk) 23:49, 9 April 2008 (UTC) aka MilquetoastCJW[reply]

contraposition

give me money —Preceding unsigned comment added by 71.249.100.12 (talk) 00:27, 20 November 2007 (UTC)[reply]

No. Now go cry.--97.91.175.154 (talk) 23:51, 9 April 2008 (UTC)[reply]

Is it possible to write a more confusing header for an article? I know enough logic to know that it is technically accurate, but this is not wikipedia quality! (This comment is most likely time sensitive) 68.144.80.168 (talk) 14:06, 23 June 2008 (UTC)[reply]

I wrote that header, to replace one that was, actually, technically inaccurate. I think it is much more important for the header to be strictly correct that being a "gist" of the idea which isn't actually fully right. I don't think the technical language is a bad thing - it gets the strict definition out of the way, and then gives an example for anyone who didn't get it with just that alone. I will also revise it now to see if I can make it easier. --Aquillyne-- (talk) 11:06, 25 June 2008 (UTC)[reply]

this page is about CONTRAPOSITION

not contradiction, converse or inverse! contraposition! why are we talking about the others at all!? --Aquillyne-- (talk) 19:40, 21 October 2008 (UTC)[reply]

I'm really not sure. It was here when I arrived, so i tried to make it better. Do you think we should take the others out of the article entirely? They seem to be (albeit mildly) helpful as a contrast for better understanding and clarity. Then again, I'm up for rethinking the concept of the page with you.--134.124.73.201 (talk) 20:50, 11 March 2009 (UTC), aka MilquetoastCJW.[reply]

Why not say "Contraposition is distinct from ... " and the link to the pages for the related concepts.

Also, what is going on with the 'contradiction' entry anyway? Where did 'shades of red' suddenly come from? - The contradiction is that there exists at least one OBJECT which is red, but which does not have colour. But anyway, best to remove this and link to the contradiction page in any event. Jaymax (talk) 23:31, 14 March 2009 (UTC)[reply]

The comparisons to the others serve to illustrate the differences between similar (and often confusing) topics in logic. Pages that simply say "not to be confused with _____", might save space, but also not inform the reader about how the topics are different without having the reader look up the other topics. The comparisons to contradiction, converse aren't too excessive, certainly aren't enough to confuse the reader, and give the reader some insight as to what is different and why. Jheiv (talk) 02:25, 15 March 2009 (UTC)[reply]

Same as Transposition?

I can't see the difference between transposition (logic) and contrapositive (logic). Should we merge? --Michael C. Price ^talk 09:00, 29 March 2009 (UTC)[reply]

oh my, someone was just trolling like a jerk here. sorry Micheal Price. Contraposition is for whole categories, making no presuppositions about middle-terms. "All Bachelors are unmarried," is contraposed by "No Bachelor is Married." From the first proposition, the second proposition is immediately inferred; the subject of the second is the contradictory of the first predicate (that is, "no bachelors are unmarried" would be a contradiction). This, again, is an immediate inference, and used primarily for categorical logic.

Transposition on the other hand is the name given to the rule of inference which governs the immediate inferences of Contraposition, but also the more mechanical inferences of Modus Tollens and Modus Ponens. It is generally used instead of contraposition in dealing with hypotheticals and material implications [(A -> B) , ergo (-B -> -A)]; in this case, similar to contraposition, the antecedent of the second is the contradictory of the consequent of the first (-B -> B).

It's not really that clear a differnece, don't feel horrible; but it should be noted that there is a distinct difference between the categorical inferences of Contraposition and the implicative inferences of Transposition.

cheers.--134.124.73.201 (talk) 17:07, 28 April 2009 (UTC)[reply]

I hope someone makes that clear in the article. --Michael C. Price ^talk 21:13, 29 April 2009 (UTC)[reply]

The reason you are confused Michael Price is because this article is awful and really unnecessary. The categorical position is handled by the article on Contraposition (traditional logic) and the implicative nature is handled by the article Transposition (logic). This article is defined by mathematicians and they do not recognize or understand the difference between implicative and categorical statements.Amerindianarts (talk) 09:39, 2 May 2009 (UTC)[reply]

"This article is defined by mathematicians and they do not recognize or understand the difference between implicative and categorical statements." HAHAHAHAHAHA! Making an obviously false categorical statement that implies you're an ignorant douche; now that's an example for the Irony page. --134.124.73.201 (talk) 20:57, 8 May 2009 (UTC)[reply]

The content of the above comment by 134.124.73.201 (talk) is sufficient to show who the ignorant person really is. People like this who bad-mouth and name call but don't have the balls to register really don't have any business here, and they definitely lack credibility. Amerindianarts (talk) 08:36, 11 May 2009 (UTC)[reply]

I just checked the contributions of this user 134.124.73.201 (talk). Absolutely nothing substantive. Just stupid, off the wall comments with no content, bad grammar, and lack of logical thought. As a matter of fact, this is probably an alias used by another user when they wish to cuss, name call, trash talk, and make stupid comments that they wouldn't make under their real ID. I guess the good in this is that it shows that they may have an inkling of conscience by using a false ID to mask their insolence, but a definite lack of consciousness or conscientiousness. Amerindianarts (talk) 08:50, 11 May 2009 (UTC)[reply]

Many, possibly all, uses of "contradiction" is improper.

I explained why in the history. Blind man shady 01:22, 5 February 2012 (UTC)[reply]