Talk:Boolean algebra

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 Definition A form of logical calculus with two binary operations AND (multiplication, •) and OR (addition, +) and one unary operation NOT (negation, ~) that reverses the truth value of any statement. [d] [e]
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Relationship of Boolean algebra and formal logic

Arguably, there is no difference between Boolean algebra and formal logic. But, as far as I know, only mathematicians and computer scientists talk about Boolean algebra per se, and their approach (including the symbols and the typical way of working out the deductive systems) is different from the philosophers' approach. ...And I can't say much more than that. I did add one sentence to this effect, but clearly, a lot more needs to be said in the article somewhere, somehow. --Larry Sanger 01:11, 18 July 2011 (UTC)

Larry: I imagine that Peter Schmitt can be more definitive on this subject. However, my guess is that (i) Boolean algebra is in fact not equivalent to formal logic, but is one of several frameworks, and (ii) high school algebra may have elements in common with Boolean algebra, but algebra in the abstract is a much bigger subject than either of these. John R. Brews 02:10, 18 July 2011 (UTC)
Thanks for the reply. You're surely right, they aren't equivalent. Boolean algebra is definitely a branch of mathematics, using the tools of math to model (maybe that's the wrong word) the sorts of rules and inferences that are covered by formal logic. How to state this with the most accuracy and usefulness to the non-mathematician lay reader would be far beyond me... --Larry Sanger 02:20, 18 July 2011 (UTC)
I have tried to clarify the connection to algebra in general and elementary algebra in particular, and have included a source for further exploration of this topic. John R. Brews 14:49, 18 July 2011 (UTC)
Boolean algebra and formal logic are not the same. Boolean logic is only a special type of formal or mathematical logic corresponding to classical proposition logic. In fact, I think that there should be a general introduction Boolean algebra (rather informal than technical) on its origin and its uses, and more specialized articles on Boolean lattice (or algebra (mathematics), Boolean logic, and Boolean circuits (or Circuit algebra or similar). --Peter Schmitt 22:43, 18 July 2011 (UTC)