Hi Richard, thanks for joining us and welcome to CZ.
Speaking as an author and not as Editor-in-Chief, I know that logicians love to write their books and articles with a maximum amount of rigor, formulas, and whatnot, and a minimum of woefully imprecise ordinary English, but I think it would help considerably if you could add some useful explanatory prose surrounding the definitions. You don't just have to make definitions, lay out axioms, and prove theorems. You could also try to opine about why relations are important in logic, what some important theorems or facts about relations are, who published important articles about relations--things like that. I'm not instructing you what to do at all. I'm just pointing out that, since CZ is a general encyclopedia and its audience is just college-educated, some explanatory prose might be helpful. Frankly, someone who needs an article titled "relation (mathematics)" might well not be able to understand this article, which would defeat the purpose, it seems to me. Take me as a potential audience member for this article. I've read a few logic books and had an advanced symbolic logic course in grad school, but mostly I was your basic philosopher. I'm afraid I can't make heads or tails of the article in its present form. Maybe I'm just declaring that I'm logically illiterate; I'll let you do with this what you will.
Let me give you an example of something that puzzles me. Your definition has logical relations as relations between sets. But can't other ontological categories be mathematically related? Can't mathematics describe the relation between, say, me and you? I'm a set, I guess you'll say. Also, I've no doubt clearly you've shown they can be defined this way, and I'm sure they are sometimes defined this way, but are they usually so defined? Do they have to be? Is this your personal definition and approach, is it one leading way, or is it the only accepted way in 2008 for logicians to define "relation" (I find that a little hard to believe). I don't know the answers to any of these questions, which is why I ask. I don't even know if this is a problem, perhaps not, but for what it's worth, I personally found it puzzling. --Larry Sanger 20:46, 3 November 2008 (UTC)
- A fair comment. At present there are huge gaps in the mathematics coverage and so I'm putting in some skeletons to clarify what articles are likely to be needed and implicitly sketch out a possible sequence in which they might be added. It's a balance between getting something down about a wider range or fewer more polished articles. I'm doing what I find most congenial. I am very far from claiming that these articles are finished!
- About logical relations: this is an article about mathematics not logic. It's not quite correct, but nearly so, to say that in 20th century mathematics there had been a programme to ensure that "everything" is a set (see for example the comment I made in ordered pair). Logic and philosophy may make a claim to deal with a wider universe of discourse. Richard Pinch 21:01, 3 November 2008 (UTC)
Thanks very much. This makes perfect sense.