Talk:Contraposition (traditional logic)

• I would like to open a discussion about this page and the page on Contrapositive. My training is in philosophical logic and I am not a mathematician, so... The page on "contraposition" states what I know as an "obvert contrapositive", and not a contrapositive at all, in the strict sense. The tautology it states, when considering it as an obvert contrapostive, is missing two steps. Contraposition as an immediate inference is actually only one step in the method of deriving the tautology stated. The obvert contrapositive is immediated inferred from the contrapositive. So, the contrapositive as stated is wrong in name, and the proof is lacking in steps. This page on "contraposition" seems to follow the example of the page on contrapositive. My example is in Aristotelian Logic.

Original Proposition	Obversion	Contrapositive	Obverted Contrapositive
(A) All S is P	(E) No S is non-P	(E) No non-P is S	(A) All non-P is non-S
(E) No S is P	(A) All S is non-P	(I) Some non-P is S	(O) Some non-P is not non-S
(I) Some S is P	(O) Some S is not non-P	None	None
(O) Some S is not P	(I) Some S is non-P	(I) Some non-P is S	(O) Some non-P is not non-S

Hoping for feedback. Amerindianarts 09:27, 7 September 2005 (UTC)

Discussion on merging contrapositive and contraposition

I disagree with merging the articles.

In terms of philosophic logic the current article on the contrapositive is confused. The contrapositive is the product of a method of inference termed "contraposition" and is limited to traditional logic, or categorical propositions. In symbolic logic the contrapositive is eliminated in the process of transposition. The current article on the contrapositive confuses these two types of inference and their respective applications within traditional logic and symbolic logic. Meaning, the first part of the article on the contrapositive can be eliminated. It is handled by the article on Transposition. The second part of the article on the contrapositive can be merged with the article on contraposition. I might add that this applies to logic in philosophy. If the mathematicians have some notion of the contrapositive in symbolism other than transposition, I am not aware of it.Amerindianarts 18:09, 24 November 2005 (UTC)

Many standard introductions to logic call transposition "contraposition". To leave it entirely out here would be a mistake. KSchutte 22:04, 7 December 2005 (UTC)

The article on transposition covers its relation to contraposition. Texts covering the rule of transposition usually don't refer to contraposition, which is a method for categorical propositions, and not material implication. The articles on contrapositive and contraposition have already been merged. Amerindianarts 22:56, 7 December 2005 (UTC)

Also, contraposition is a type of inference, and transposition is a rule of inference. Their respective articles imply this. A categorical proposition can have more than one contrapositive with differences in the distribution of its terms. For this reason Venn diagrams are useful for measuring their validity, and not truth tables, which are more appropriate for the rules, e.g. transposition. Amerindianarts 23:21, 7 December 2005 (UTC)

Contraposition vs transposition

I think the reason for the recent edit "Added clarification on exactly what contraposition is" is erroneous. Irving Copi as well as other logicians drop the usage of the term "contraposition" when referring to inferences using other than categorical propositions, preferring to cite the rule of transposition for material implication and preserving "contraposition" for the process of inference in traditional logic. I Also cite the Encyclopedia of Philosophy, Susan Stebbing, and just about every other Logic book I have seen.

Read the rest of the article if you haven't already. The rule of transposition is referred to. I will wait (shortly) for a response and source before considering a revert.Amerindianarts 22:08, 31 March 2006 (UTC)

If "contraposition" is a term of mathematics, then perhaps the current article should either be renamed "contraposition (logic)" or sections on "traditional logic" and "mathematical" added, or perhaps even a new article "contraposition (mathematics)" authored. The problem is that the statement "Starting with a proposition α→β we use the classical logic proof rule contraposition to deduce the contrapositive" is not proper to the current context (philosophical logic) of the article, and in fact an error. The reasons are:

• (1) "classical logic proof rule contraposition to deduce the contrapositive" is erroneous. The classic proof was given by Aristotle in Prior Analytics and done in a syllogistic reasoning process. It is NOT a rule in the classic proof, it is a natural reasoning PROCESS.
• (2) The classic proof by Aristotle is limited to categorical propositions with existence given through the use of the copula. As such, there is nothing "conditional" to the process.
• (3) In regard to (2), in material implication or a conditional statement the antecedent is assumed to be true, and the following proof is a conditional, assuming the rule of existential import. "Conditional" means exactly that, and is unlike a categorical proposition using the copula to imply existence.
• (4) In regard to (2) and (3), the problem of existence and the square of opposition in traditional logic was brought to light by George Boole. The doctrine of existential import and conditional proof eventually intended to rectify this, but the point is that it was accomplished as the RULE of transposition, and the PROCESS of contraposition was been restricted to the classic proof of Aristotle's logic, because they are DIFFERENT. Thus, I reverted. Amerindianarts 06:12, 1 April 2006 (UTC)

This article needs rewriting

As written, this article is incredibly inaccessible. In fact, after scouring the page I found it very difficult to find contraposition as I know it: (P $\implies$ Q) $\iff$ (not-Q $\implies$ not-P). Everything is so buried in quantifiers and philosophical discourse that almost no college student will be able to digest it.--Rschwieb 21:52, 17 July 2006 (UTC)

If you "find difficult to find contraposition as I know it" perhaps you should review some basic college texts which students in traditional logic and intro to formal logic use. I recommend L. Susan Stebbing and Irving Copi. That may enlighten you. The rule you refer to is in quantification logic known as the rule of transposition, which has its own article. Some logicians, such as Prior, have referred to it as the "law of contraposition", but because of the existential implications in traditional logic is not quite the same as what traditional logicians refer to as contraposition as a "process" of immediate inference. I might also add that the process of inference in the article is the same as Aristotle's reasoning process in Prior Analytics, and reiterated by Stebbing and Copi. In Symbolic Logic Copi makes no reference to contraposition, but rather the rule of transposition (or what A.N. Prior means by the Law of Contraposition), which are essentially rules which incorporate Aristotle's process without the presupposition that any universal proposition must refer to a class with members.Amerindianarts 22:14, 17 July 2006 (UTC)

How about if, before insulting Rschwieb's intelligence, you take a moment to comprehend that he is approaching this article from a mathematical logic perspective instead of a philosophic one. I am nearing completion of a mathematics degree from Northwestern University, and I too was somewhat overwhelmed by the philosophically technical language in this article. It is true that what is considered a contrapositive to many mathematicians is technically a transposition to philosophers. I don't know where it would be appropriate to put a reference to the differences between the mathematical and philosophical concepts of contraposition, but perhaps one of you philosophers could be so kind as to do so. --Thizzlethethird 04:37, 4 October 2006 (UTC)

Read it again (the article). I am aware of Rschwieb's approach, but think it applies elsewhere. Contraposition to a philosopher deals with categorical propositions. It does not apply to hypotheticals or material implication. A.N. Prior uses the term "contraposition" in regard to transposition, but he refers to it as the "law of...". This basically integrates the traditional process as a rule, and takes for granted the natural language reasoning process of Aristotle (as do most of the traditional inferences as they are defined in mathematical logic). At the level of class algebra or symbolic logic (using Copi's term) the term "contraposition" no longer applies in philosophical logic (see the article Transposition (logic)). This article should be limited to Aristotle's term logic (at least that is the intention) and syllogistic reasoning in natural language of the categorical. Perhaps this article should be retitled to distinguish between contraposition in philosophical logic and contraposition in mathematics, as is the different articles on transposition. I completed my graduate work in philosophy quite some years ago. Mathematicians taking logic courses in the philosophy dept. always ignored, or even belittled traditional logic. It is important in the history of logic to understand it by not confusing it with mathematical definitions. If you do confuse it, you lose the understanding of conceptual development in the history of philosophy. An example of this would be the difference of the traditional concept of "conversion", and the term's use in class algebra and mathematical logic. Stating the rule of the later integrates the natural reasoning process but without detailed explanation gives all the appearances of hasty generalization, or the fallacies Affirming the consequent and Denying the antecedent. A mathematician's education seems to begin at a different point in history than does those interested in philosophic logic (excluding Euclid from this generalization). This integration process seems to be centered in its beginning around the time of Boole's existential distinction. Rschwieb's suggestion of a rewrite is rash. I think it more true to history of logic to have a separate article. Even an added section on the mathematic concept would be more acceptable than a "rewrite", because the traditional section stands as it is. The primal beginning in the explanation of natural reasoning. Explanations in the current article are actually quite verbatim to the sources cited, and is info old enough to be public domain. Amerindianarts 06:53, 4 October 2006 (UTC)

PhD student of mathematics here. We are teaching 'proof by contrapositive' to all our first year university students (University of Warwick). For reference, I mean (P $\implies$ Q) $\iff$ (not-Q $\implies$ not-P). Thus we need to split off a 'Contraposition (mathematical logic)' page, otherwise there will be a lot of confused mathematicians. As an aside, I have to agree that this page seems *very* hard to read. I've taken philosophy courses and worked my way through basic logic books, and this section seems to be trying to make the topic as incomprehensible as possible. Can anyone rewrite this page? Kalkyrie

I agree the section on modern logic does need to split off. By "proof by contraposition" I assume you mean by "P $\implies$ Q) $\iff$ (not-Q $\implies$ not-P" as what philosophers such as myself refer to as the rule of transposition (logic) and not transposition (mathematics). A confusion of readers that I have had to deal with in editing this article. I have linked to both concepts of transposition in the article in an attempt to quell those editors in their trying to dispell the traditional form of Aristotelian logic. I am not a mathematician. I am a philosopher and logician. As for the section on traditional logic, I see nothing hard to read here. If you want to read something "hard" refer to some of the various math articles here at Wiki. They are no more for the layman than this article is. Up to the section on modern logic, which I would like to see go elsewhere, the article is pretty much verbatim Copi. After the modern logic part is removed and contraposition in mathematics is created, I can edit this article back to its original form dealing with the original traditional form up until the end of the 18th century.Amerindianarts 01:39, 24 October 2006 (UTC)

For the sake of clarity I would like to add that philosophers of logic such as Prior and Blumberg use the phrase "law of contraposition" as a class consisting of the traditional concept of contraposition in dealing with categorical statements, and as the rule of transposition in symbolic logic which includes material implication and the disjunctive. The square of opposition, despite its flaws, is based upon the copula (predicate as a term of grammar rather than predicate (logic)). When not dealing with categoricals, the term contraposition is dropped in favor of transposition (If p then q, if and only if, not q then not p) and neither "transposition or "contraposition" is a term used by philosophers referring to the concept in class algebra or set theory. Texts of logic by Copi used in first year as well as advanced symbolic logic classes for philosophy make this distinction. The processes are "absorbed by rules". It is my thinking that "proof by contraposition" has no need for the copula. The traditional form for contraposition, as well as conversion, deal with the reasoning processes of natural language, as the tables in the articles illustrate. Tables which are verbatim the texts by Copi and Stebbing (philosophers).Amerindianarts 02:13, 24 October 2006 (UTC)

This page is awful

No offense meant to anyone--I'm well aware that things can very easily get carried away. This encyclopedia is NOT aimed at college students. Contrapositives are a very, very basic concept in logic and absolutely crucial to understanding logic and mathematics (how could one understand, say, an indirect geometric proof without knowing how contrapositives work?)... and it's a sad thing that Wikipedia doesn't have a decent explanation of it. This page is SO high-level as to be worthless to anyone who's not (at least) knee-deep into college-level math and logic classes.

So, I'll wait a few days, then if no one objects, I'll kill the redirect from contrapositive and write a little stub in its place. I'm no expert on logic, but I know what a contrapositive is well enough to make other people's quests for contrapositive-related knowledge a bit easier. Matt Yeager ♫ (Talk?) 23:14, 30 November 2006 (UTC)

I'm an expert in the use of contraposition in traditional logic and it is not the same concept as used in mathematics. The term in an indirect proof in logic is the "rule of transposition". So, no you're not an expert and I'll revert any redirect. Contrapositive is already redirected here. I suggest you research the concept in mathematics and do something. In philosophical logic the term "contraposition" is rarely used in symbolism, and is commonly used as the process described in Aristotelian argumentation by means of natural language. This article is based upon a freshman level text book, so any deficiencies are on your part. Your assumption that Wiki is not directed toward towards college student is entirely off the wall and a misconception. Most of the better contributors have gone beyond that level and Wiki DOES in their guidelines try to actively recruit experts in different fields.Amerindianarts 04:39, 1 December 2006 (UTC)

Obviously you intend for this article to be on traditional logic. (Which somewhat violates, say, WP:OWN, but we shall let that slide.) This has little or nothing to do with the contrapositive in mathematics, so I have moved this article to a space where it will not be confusing to anyone. Good day. Matt Yeager ♫ (Talk?) 02:15, 22 December 2006 (UTC)

Yes, you moved it to a page on contraposition in mathematics and if you view the talk page there everybody is confused by it.Amerindianarts (talk) 09:33, 2 May 2009 (UTC)

This page is almost completely inaccessible

At least the lede should be accessible to a general audience, even if the body is not. The table seems to contain irrelevant E and I statements. And the distinction between contraposition and the contrapositive in mathematics is not clearly addressed. I know a little math, very little logic, came here to clarify something, and was disappointed. Jd2718 (talk) 20:44, 8 May 2011 (UTC)