Explain to me why the word "lattice" has to be mentioned in an article called "Boolean algebra" at all. For Chrissakes, Boole isn't even mentioned in the article! Sheesh! --LMS, who would have to go back to his books to set things right.
Because that's what a Boolean algebra is - a kind of lattice. Which would be more important in a page on platypuses - to mention they were discovered by sir so-and-so, or to mention they are a type of monotreme? Not that we shouldn't have both, but we aren't normally that impatient.
Well, Boole himself probably wouldn't understand the article about Boolean algebra in its present form. And it omits all sorts of totally essential information to understanding what Boolean algebra is. Have a look at this, and compare the article in its present form. I can have read Boole's formulation of Boolean algebra and understand it, without understanding our present BooleanAlgebra article. I think there's something wrong with that, particularly in an encyclopedia that attempts to explain concepts. This is, as always, MHO! --LMS
Boole would definitely understand the article once he heard the definition of Lattice. The fact remains, however, that the abstract definition given here has much less intuitive flavor for somebody not interested in abstract mathematics than a more concrete definition. Of course, that is exactly the point of the abstract definition: it is not limited to a particular example. Most importantly, the ideas embodied in Boole's original algebra are far more limited than the abstract definition. It is important to make it clear that there are an infinite number of Boolean algebra's and that the one with just the elements 0 and 1 is only the simplest one. On the other hand, it helps beginners enormously if the simple and concrete case is explained a bit more fully.
So anyway, does my addition to the entry help make this clear?
Clearer, but not as clear as an encyclopedia article should be. The first paragraph or two should be introductory--something that someone who has had a basic course or two in logic ;-) should be able to understand, anyway. I am a fan of making difficult concepts clear, which is what is needed in an encyclopedia (and which can be difficult to do, of course).
Why not see other encyclopedia articles about B.A. online and see what they do? --LMS