Talk:Contrapositive
I am just wondering why there is a link to combustion from contrapositive. If you're knowledgeable about logic and know some sort of combustion that is not related to heat/oxygen/fuel, please fix the combustion page; otherwise, remove the link.
- The link is there to demonstrate that the proposition "If there is fire here, then there is oxygen here." is indeed true. And the combustion article does indeed state that there is no fire without oxygen. (20040302)
- I would like to open a discussion about this page and the page on Contraposition. 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. The obvert contrapositive is immediated inferred from the contrapositive. Contraposition as an immediate inference is actually only one step in the method of deriving the tautology stated here and on the contraposition page. So, the contrapositive as stated is wrong in name, and the proof is lacking in steps. This page on the "contrapositive" seems to follow the example of the page on contraposition. My example is in Aristotelian Logic.
| Original Proposition | Obversion | Contraposition | Obverted Contraposition |
|---|---|---|---|
| (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 09:20, 7 September 2005 (UTC)
- Hi (I trust you don't mind I reformatted your table) - I guess the solution here is that within different contexts the term has subtly distinct flavours, or meanings. The Oxford dictionary tells me that Contraposition/Contrapositive means "conversion of a proposition from all A is B to all not-B is not-A". This does not mean that you (or your training) are wrong, just that the term has inherited more than one interpretation. So - we can easily make sense of this in the following manner - if you can provide the article with sources for your exposition (what university/texts/whatever defines contraposition as you understand it), then there is a place for it in the article. I am sure that you can see that there is no 'one true meaning' of any word, and that language depends very much upon the context within which different communities use it. (20040302 08:35, 8 September 2005 (UTC))
- One thing I learned as a student of philosophy is that the Oxford is a great dictionary but it usually wasn't very good for citing definitions within the discipline, for example the use of the term "conversion" by the Oxford is its everyday usage, but "conversion" is a method of immediate inference within philosophy which has nothing to do with contraposition. Just like any other discipline, or science, philosophy has its unique definitions of its terms, and they usually are different than those used in common, everyday discourse. I am currently at a remote location and will check further sources when I return to my desk, but the source I was citing was an intro to logic book by L. Susan Stebbing. When I get back to my desk I will check Frederick Copi (both Aristotelain logic and quantification theory), and the Encyclopedia of Philosophy. From surfing Wiki it appears that situations like this are usually handled through a disambiguous page where one can distinguish between common usages and conceptions of a term and its technical applications, e.g. creating a link "Contraposition (philosophy)", or "Contraposition (logic)". Amerindianarts 18:07, 8 September 2005 (UTC)
- Well, a discipline isn't necessarily able to govern common usage of the terms it invents - and dictionaries do their best to concern themselves with common usage, first and foremost. I don't really feel that contrapositive needs to be disambiguated - just a good explanation of the different definitions is probably enough. Disambiguation is primarily used for homonyms of one sort or another. (20040302 21:34, 8 September 2005 (UTC))
- Disambiguation is probably not necessary, but I'll research the term and see if it is simply wrong. Contrapositive and contraposition are a terms of logic, math, and philosophy. It's common usage is to state opposition and really doesn't require the formulation as stated in the contraposition article.Amerindianarts 21:49, 8 September 2005 (UTC)
It has been over twenty years since I had any logic classes, so I had to retrieve my old texts from the attic. What is referred to on the contrapositve and contraposition pages is wrong. The proof is correct, but the type of immediate inference stated is incorrect. The proper rule for the proof is "transposition", and transposition doesn't apply to traditional logic except for the step by step of the table which the rule of contraposition is limited to. The table above is correct except for the argument for the E proposition (second row). It is valid with limitations (per accidens). The importance of this besides stating the wrong rule and type of inference is that the table above roughly conforms to Aristotle's grammatical arguments in his Analytics. He did not present them in symbolic form, but presented the inferences step by step. The argument on the contrapositive and contraposition page is for the obversion (you can check the stub I expanded at obversion) of the contrapositive. Also, The symbols used in the proof are for "not", and the rule of Contraposition deals with "non", a difference which is roughly that of the difference between a contradictory and a contrary statement. I am a professional philosopher, but if you doubt my research you can check Irving M. Copi's Intro to Logic and his Symbolic Logic as well as Stebbing's book that I cited and volume five of the Encyclopedia of Philosophy. Probably any intro to logic book will do however. As soon as I find time I will try to make some changes with as few disruptions as possible.Amerindianarts 18:55, 9 September 2005 (UTC)
- Rather than edit the page on contrapositive I started a page on transposition and expanded obversion. Amerindianarts 23:28, 11 September 2005 (UTC)
- It looks like good stuff, AIA - I won't stand in your way. Thanks for taking the time to explain it :-) (20040302 07:52, 12 September 2005 (UTC))
Discussion on merging contrapositive and contraposition[edit]
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 18:06, 24 November 2005 (UTC)