Talk:Contraposition

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

Should the article say it uses an Euler diagram instead of a Venn diagram?

The article says it utilizes a Venn diagram to illustrate contraposition, but isn't in actuality an Euler diagram? 80.221.242.122 (talk) 20:47, 3 March 2013 (UTC)

You are correct, a Venn diagram shows all possible related sets, empty or not. widdma (talk) 08:43, 24 September 2013 (UTC)

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)

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

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)

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)

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

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)

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

contraposition

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

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

header

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)

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)

As nonsense, the header cannot be technically accurate! Look again, it starts by saying that contraposition (normally, in bold) is a logical relationship between two conditional statements. Then, it gives the "bat is a mammal" statement and its contrapositive. Since now, it concentrates exclusively on the properties of original statement and its contrapositive, leaving any contraposition behind. That is, no contraposition anymore, nor how it is related to the original statement and its contrapositive (or, which relationship is implied by the def? -- This is not clear at all). Instead, it says that The contrapositive of a conditional statement is true if the original statement is true. This undermines any sense completely. Which the conditional statement are you talking about? Telling about the contrapositive of conditional makes me to think that there is a conditional besides the original and its contrapositive. [Self-chensorship] such technicality. --Javalenok (talk) 11:37, 15 December 2012 (UTC)

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)

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.

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)

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)

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)

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)

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

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)

"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)

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)

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)

Yes, the articles on contraposition and transposition should be merged. 31.52.252.253 (talk) 23:12, 1 September 2018 (UTC)

Many, possibly all, uses of "contradiction" in this article are improper.

I explained why in the history. Blindman shady 01:22, 5 February 2012 (UTC)

I think there may be a confusion between normal English usage and some technical terms here.

As I see it, if B is the negation of A, then A and B contradict each other: if one is true, the other must be false & vice-versa.

I've edited the last definition in the boxed table to comply with this. If you don't like what I've put, please improve it (and not just reverse it), because I feel the original was not only unsound but confusing, at least to me. Dendropithecus (talk) 22:56, 1 April 2012 (UTC)

I think that your edit is more clear, and I changed some more to match. My guess is that this article was written by someone who was thinking about the square of opposition or something like that. But the word "contradiction" did not make sense in the modern sense when it was used here. — Carl (CBM · talk) 23:08, 1 April 2012 (UTC)

That all looks good to me. I've just removed a redundant instance of "contradiction" that you may have missed. Dendropithecus (talk) 00:16, 2 April 2012 (UTC)

Intuitive explanation

The example is a bit ironic given that there's ~3000M dark-haired girls in the whole world but only ~200M girls total in the US. I.e. it would take 15x longer using the contrapositive. 101.161.153.133 (talk) 23:36, 30 October 2014 (UTC)

Dayum

Man, was I disappointed when I found out this page was not about the posing in the Contra game series... 84.112.78.162 (talk) 21:51, 5 December 2012 (UTC)

Five-way merger discussion

There are five Wikipedia articles that seem to be about the same thing. Can these be combined down to fewer, or just one? Or if there are important distinctions that cannot be handled in one merged article, the distinctions need to be explained! Not every term needs an article...could some of these just be soft links to wiktionary entries? The five are:

• Contraposition
• Modus tollens
• Proof by contrapositive
• Contraposition (traditional logic)
• Transposition (logic)

Do these differ, or not? Must they all have separate articles? I hope not. --doncram 23:22, 4 May 2015 (UTC)

• I would support such a merger for the reasons you created. But none should soft redirect; direct them all to the same WP article. Red Slash 00:15, 6 May 2015 (UTC)

• I think modus tollens should definitely be kept separate from the other four. This is both for historical and systematic reasons. Historically, the quartet of inference rules modus (ponendo) ponens, modus (tollendo) tollens, modus ponendo tollens and modus tollendo ponens go back, if not by name, to at least the 2nd century CE, possibly going back to Theophrastus, and the corresponding quartet of argument forms was correctly described by the early Stoic Chrysippus. The four argument forms were taught as part of traditional logic courses at least until the mid-20th century, as separate from the rule of contraposition, which was also already known in antiquity. The confusion of modus tollens and a rule of contraposition can be traced back to some scholia in late antiquity and may have originated with Neo-Platonism trying to integrate elements of both Stoic and Peripatetic logic into their logic. In antiquity it was a defining feature of the Greek equivalents to the inference rules of the modi ponens and tollens that they had a categorical sentence or proposition (a literal, if you want) as conclusion. In most of modern (i.e. post-medieval non-contemporary) logic, the modi ponens and tollens were also kept apart from a rule of contraposition (and kept apart from Contraposition (traditional logic). Contraposition (traditional logic) is also quite different from the remaining three, and I think it would be confusing to many to have this in the same article as contraposition. One reason the five articles appear to be similar is that they wrongly conflate different things. The talk of the law of contrapositive in the header of the modus tollens article in particular seems wrong and confusing.--Flosfa (talk) 01:12, 22 October 2015 (UTC)

• Actually, I just went ahead and removed the misleading reference to the law of contrapositive from modus tollens. --Flosfa (talk) 01:25, 22 October 2015 (UTC)

• Oppose most, but merge Transposition (logic) with Proof by contrapositive: Modus tollens is a rule of deductive inference. It has nothing to do with rearranging an existing formula; it lets you go from the negated conclusion to the negated antecedent. Transposition (logic) and Contraposition are slightly different things, the former a rule of inference and the latter a logical equivalence or tautology. Proof by contrapositive does appear to be the same as transposition, however. That leaves us with Contraposition (traditional logic), which (so far as I can tell) is about logical quantifiers, but the article is very unclear to me and probably needs cleanup. --NYKevin 19:28, 28 February 2016 (UTC)

• Oppose all. They are all good topics, but are currently (obviously from the proposal) not anywhere sufficiently explained and distinguished for a layman. This is a general encyclopedia, so we need to fix this. For a start work on the introductions, and provide more material, not less. Andrewa (talk) 13:40, 21 August 2016 (UTC)

Closing, given no consensus over more than 2 years. Klbrain (talk) 10:29, 16 September 2017 (UTC)

Bayes' theorem

Contraposition is obviously an instance of Bayes' theorem. It is illustrated with a simple proof and has a source reference, so please leave the section Correspondence to other mathematical frameworks. It is certainly not a fringe view. — Preceding unsigned comment added by Josang (talk • contribs) 06:15, 9 August 2017 (UTC)

It certainly may be as you say, but the reference is to your own work and as the author you are not in a position to decide on the notability of the concept. This is why we rely almost exclusively on reliable secondary sources, so that editors are not required to make the distinctions that need expertise in the field. --Bill Cherowitzo (talk) 17:09, 9 August 2017 (UTC)

The correspondence to Bayes' theorem is obvious (just check the math), and therefore very relevant for the concept of contraposition. I know that the reference is my own, which might look sus, but I know of no other reference where the correspondence is explicitly described. Since both contraposition and Bayes' theorem are very prominent concepts in logic/mathematics it's important that readers of Wikipedia who want to understand those concepts become aware of the correspondence. --Audun Jøsang —Preceding undated comment added 19:53, 9 August 2017 (UTC)

Proposed merge with Contraposition (traditional logic)

Not clear that this is distinct from the topic at the non-disambiguated title, and Contraposition is not so long that the traditional logic section needs to be spun-off Wug·a·po·des​ 18:04, 18 July 2019 (UTC)

Oppose merge; the articles are sufficiently well-linked, and there are sufficient discipline-specific or historical differences that these are worth discussing separately. Klbrain (talk) 07:33, 8 May 2020 (UTC)

What is the name of the system of notation being used on this page?

The system of symbolic logic notation used on this page, with right angle thingies for negation and rightward pointing arrows for if-then statements, is not the only one. What is it called? Is it the most common notation? If not, what is the most notation? If I wanted to write out a statement of logic on a sign or a T-shirt and have it be recognized by as many geeks as possible, which system of notation should I use? Pciszek (talk) 14:34, 6 June 2020 (UTC)