Talk:Boolean algebra (basic concepts)

Intent of this article

This article is intended to cover the basic, common usage of the term "Boolean algebra". This is the one taught in middle school and high school to everyone, not the more complex "Boolean algebra" theory which mathematicians take in college. Therefore, please don't add any material on "homomorphism", "isomorphism", "rings", "ideals", "filters", "axiomatic bases", "duality" or "lattices" here, those belong in the other article. StuRat 02:14, 15 September 2005 (UTC)

This article may also contain certain simplifications to make it more accessible to a wider audience. Think of these as similar to the Dalton model of the atom, which had finite spherical electrons in circular orbits. While not technically correct, that model does allow a nice intro to electron shells for those not yet able to understand the more complex probability functions which conform to modern atomic theory. StuRat 16:57, 15 September 2005 (UTC)

To add

I would like to add examples of subsets, proper subsets, supersets, and proper supersets. I would also like to add examples with Venn diagrams of 3 or more sets. I couldn't find any suitable illustrations for these concepts, so will need to make my own, which could take a day or two. I would also like to add specific applications examples, such as database queries and search engine parameters. StuRat 02:14, 15 September 2005 (UTC)

Other planned additions include the common English language uses of Boolean terms and the use of Boolean logic to describe domains and ranges for inequalities. StuRat 18:02, 15 September 2005 (UTC)

I struck-out items already addressed. StuRat 16:16, 16 September 2005 (UTC)

I struck out the remaining item (Venn diagram of 3 or more sets), as it has now been added. I would like to work more on the transition from section to section, but that will need to wait a few days as I will be busy for a bit. Meanwhile, I will place this article under Boolean logic and see if anybody besides the PhDs complains. StuRat 12:35, 18 September 2005 (UTC)

Boolean logic

So I don't entirely agree with Pmanderson's systematic change to "Boolean logic", which is apparently a correction to Aristotelean logic obtained by allowing vacuous truth. See Boolean logic. The wording will need to be tweaked, but I'm not sure that's the right tweak, and I think we should probably let StuRat finish. (I think making sure the dab notice says something sensible is fair game, though.)) --Trovatore 15:55, 15 September 2005 (UTC)

This is because Boolean logic is not a very good article. This one is much better, and should replace it. Septentrionalis 13:54, 16 September 2005 (UTC)

Well, where do we put the material about Boole's syllogistic, then? I confess I'd never heard of it before I read the current Boolean logic, so for all I know the article could just be wrong, but assuming it's not it probably belongs here. (BTW the notice at the top claiming that it's closely related to propositional calculus seems to be just wrong--the syllogistic described involves quantified statements, which PC doesn't.) --Trovatore 15:14, 16 September 2005 (UTC)

I would think you would be the best person to verify the legitimacy of that article's claims. OTOH, if it's so obscure that a PhD is set theory never heard of it, I personally think we could live without it. However, if you insist on keeping it, we can move it to a new name, perhaps "Boole's syllogistic" ? StuRat 16:29, 16 September 2005 (UTC)

Perhaps more importantly, I don't think we should be making up names for things. We might prefer that the topic of this article (exclusive of the algebra-of-sets stuff) were called "Boolean logic", but it's not; it's called "Boolean algebra". An attempt to change that wouldn't be a bad idea, but I don't think it should start in WP. --Trovatore 15:14, 16 September 2005 (UTC)

You need to discuss this issue with Oleg Alexandrov, who is also a PhD in mathematics, and appears to disagree with you. I suggest going to his talk page, since he rarely responds to this talk page. StuRat 16:34, 16 September 2005 (UTC)

I agree that you, and other mathematicians, should edit the "dab" here, to get it the way you like. I will expect the same coutesy, however, so that I, and everyone else in the world who isn't a mathematician, should have the right to edit the "dab" which points to this article. For example, I don't want it called "count noun/mass noun" or "propositional calculus" or anything like that which the non-mathematician audience will not understand. In short, a "dab" should be written for the audience of the article to which it points, not for the audience in which it is placed. StuRat 16:52, 15 September 2005 (UTC)

I wouldn't think of calling it "mass noun"; that was an attempt to get people to understand my point when I couldn't think of a more-direct wording. But "basic concepts" isn't really right either; it suggests that the study of the algebraic structures called "Boolean algebras" is a "more advanced" version of the topic treated in this article. I hope you've understood by now that that is not the case. --Trovatore 17:02, 15 September 2005 (UTC)

The first two sentences in the article now contradict each other. StuRat, please understand, this article is not about the concept called "Boolean algebra", it is about a particular Boolean algebra, namely, the Boolean algebra of subsets of a given set. Oleg Alexandrov 17:44, 15 September 2005 (UTC)

To mathematicians, that is true. But, this article is written for non-mathematicians, and they don't know, or care, that this is one type of all the other "Boolean algebras". Think of it as the same as the relationship between the words "God" and "god" or "Dad" and "dad". Depending on the context, the words refer to different things. You wouldn't insist that a priest refer to "the god we worship under Christianity", rather than just "God" or that a child say "the dad which is my father", rather than just "Dad". Similarly, from the pt of view of the intended audience for this article, there may be other "Boolean algebras", but that doesn't mean they can't refer to the one they are familiar with as "Boolean algebra". StuRat 18:22, 15 September 2005 (UTC)

I tweaked the opening lines a bit, is that better ? StuRat 18:30, 15 September 2005 (UTC)

Better maybe; still not good enough. The algebra of subsets of a given set is not a special case of Boolean algebra; it's a special case of a Boolean algebra, and much of the article is not actually about it.

I still haven't seen any clear indication that you understand the distinction. I would be willing to propose a 48-hour cease-fire while you go learn it (it's really not that hard, and I'm willing to help). Of course I couldn't enforce it for anyone else, but most people are reasonable. --Trovatore 18:54, 15 September 2005 (UTC)

I see how it's relevant to the mathematician's article, but not how it matters to non-mathematicians. As for halting devlopment of this article, I don't want to do that, as I've already seen two people try to change this into a clone of the mathematician's article, and the longer I leave it unattended the more damage will be done here. At this point I am focusing on adding content, I will look it over for "tweaks" after I finish that phase. StuRat 19:05, 15 September 2005 (UTC)

What's the first thing you need to know, to train a dog? More than the dog. An elementary understanding of the algebraic concept would vastly improve your presentation, even if aimed at people who don't want to know about the algebraic concept.

The other thing is, your "audience" concept works for textbooks, not so much for an encyclopedia. If you expect mathematicians to stay out of the article (long-term) even if you say things that aren't true, things that would actually hinder someone from understanding the mathematical concept, that's not going to happen. There's a serious need for the article you're writing and we'll owe you a debt of thanks, but it needs to be written correctly. You'll have a much better shot at doing that if you gain just a slightly broader understanding. --Trovatore 19:13, 15 September 2005 (UTC)

I disagree that knowing all the complexities will make explaining the simple part easier. In fact, I've seen just the opposite. PhD's frequently can't relate to students who lack their level of understanding, and say things like "that should be obvious" when asked a question they consider stupid. For example, Einstein was apparently a poor lecturer. My Dad (or should I say "the dad which is genetically my father") attended a lecture of his at Princeton. As a computer programmer, I've often found it useful to have non-programmers review my documentation, which tended to contain programmer jargon. Even with a concerted effort, is it often difficult to tailor documentation for the intended audience, rather than for yourself. If the author is a member of the intended audience, this problem is greatly reduced. StuRat 19:56, 15 September 2005 (UTC)

It's not a question of knowing complexities; the distinction involved is not really particularly complex. Understanding it, just at a very basic level, would save you from some blatant errors. --Trovatore 20:06, 15 September 2005 (UTC)

Well, that's true for sections "Terms" through "Properties"; it doesn't seem to be true of the rest of the article. That incoherency needs to be fixed, but maybe we should give StuRat a little space to do so, given that there's been a clear need for an article like this for some time and at least he's giving it a shot.

OTOH StuRat, I can't agree with your notice about minor inaccuracies. If you were teaching a high school course, maybe you could get away with little lies in the service of the bigger pedagogical picture, but this is an encyclopedia; whatever you say should be true. --Trovatore 17:55, 15 September 2005 (UTC)

Using that logic, we can't have any mention of Newtonian physics, since it's technically not correct, in that it ignores effects of relativity, etc. We also can't include Dalton's model of the atom, or any chemical bond notation, since all are "incorrect" two-dimensional approximations of the true 3D bonds. Globes must also be banned, as the Earth isn't really a sphere made of paper with a metal pole through the center.StuRat 18:06, 15 September 2005 (UTC)

Without attempting to deal fully with the general case, I will simply point out that there is no analogue of Newtonian physics under consideration here. Or if you find one, we'll discuss it when it comes up. --Trovatore 18:13, 15 September 2005 (UTC)

Sorry, I don't have time to debate Newtonian physics with you now, I have an article to finish writting. StuRat 18:22, 15 September 2005 (UTC)

New example

I've replaced the "dehydrated red apple" example with an example using integers and sets of even numbers, multiples of 3, and multiples of 5. I may create a suitable illustration using a universe of integers from and including 0 to and including 30. It may not be needed, though. What do you guys think ? StuRat 23:13, 15 September 2005 (UTC)

Progress

No question about it, things are looking better. But there's still a serious missing transition in the middle of the article. What's the connection supposed to be between the sections from "truth tables" on, and the algebra-of-sets stuff that constitutes the first half? Needs to be made clear.

For that matter, the intro suggests that the whole article is about the algebra of sets, which first of all isn't true, and if it were true it would mean this isn't the article we've been needing (it would be a candidate for a merge with algebra of sets).

A smaller point: Is the algebra of sets really "sometimes called Boolean logic", as the intro claims? Not a usage I'm familiar with. --Trovatore 23:45, 15 September 2005 (UTC)

Well, I'm still working on merging the material I "stole" with the new material I added. What we do with the intro somewhat depends on where we end up putting the article. My suggestion is that we place it under Boolean logic. If you agree, please add your support to the talk page there. Regarding whether the algebra of sets is really "sometimes called Boolean logic", I suggest you discuss that with Oleg Alexandrov, since he put that in. I will let you mathematicians slog that one out, LOL. StuRat 15:03, 16 September 2005 (UTC)

What you wrote at the beginning of the article was about the Boolean algebra made up of sets. All I did, is call things by proper names.

Now, whether this article is at all necessary, that is what I don't know. Oleg Alexandrov 00:35, 17 September 2005 (UTC)

Progress or Regress

It now seems to me that this article should be split up among

• algebra of sets
• Truth tables to somewhere in logic
• "Boolean terms" sections to elsewhere in logic, or a separate subject (they need to be defined, anyway).
• Applications to a separate article

With disambiguation pages from Boolean algebra and Boolean logic.

Arthur Rubin 00:14, 17 September 2005 (UTC)

I originally came to Boolean Algebra because of the "too complex" tag (somebody has since removed it). What I'm trying to do is provide a basic intro to all the Boolean concepts for somebody who knows nothing about any of it. Surely a place can be found to put that in one article. Breaking it up into multiple articles would make things as hard to understand for newbies as it is now, maybe even worse. StuRat 00:45, 17 September 2005 (UTC)

Your intention is admirable. :) However, this article is an incoherent amalgam of a lot of things. The first part is about union and intersection of sets, operations which were baptized "or" and "and". The second part deals with "or" and "and" for real, as elements in a logical table; these are not sets anymore. Then, what follows is the English usage of "and" and "or", which is again, something different.

This article should be renamed to

the fairy tale about "or", and "and", their friends and adventures.

Oleg Alexandrov 05:21, 17 September 2005 (UTC)

Providing a "less technical" version so that the "technical" tag could be removed, was never quite the right motivation, and this is at the heart of many of the misunderstadings here.

In fact, slapping a "technical" tag on Boolean algebra was never justified; it could justifiably have been removed immediately. No one would put a similar tag on Group (mathematics). Presumably the reason it was put there in the first place was that visitors were expecting a different concept, one taught in other places as "Boolean algebra".

And we do need an article on that concept, whatever it is. To be honest I'm not sure just what the boundaries of that concept are. But it should be thought of as an encyclopedia article on that concept, not as an introductory course. It will be naturally more accessible, simply because the concept is more accessible. --Trovatore 17:57, 17 September 2005 (UTC)

I'd add that if someone wanted to write an entry-level article about the study of Boolean algebras, I wouldn't be opposed to that on principle, though I'm not sure why you wouldn't start with a simpler structure, say groups. But it would be a very different article from the one I think StuRat is trying to write. --Trovatore 21:11, 17 September 2005 (UTC)

(and also very different from the one people are looking for under "Boolean algebra", when they're shocked to find this one instead) --Trovatore 21:16, 17 September 2005 (UTC)

Note of move

This article was moved by StuRat to Boolean logic, with that one moved to Boole's syllogistic. Just thought I would let people know. Oleg Alexandrov 15:47, 18 September 2005 (UTC)

I thought the redirect was sufficient to point them to the new article, but I suppose stating it explicitly can't hurt. StuRat 17:05, 18 September 2005 (UTC)

You did not post an edit summary when you did your redirect. Nobody would have been aware of what you did. Oleg Alexandrov 20:22, 18 September 2005 (UTC)