Subsection 2.6.1 Boolean Logic Isn’t English
English is a much more expressive language than Boolean logic is. The meanings of most English sentences can’t be captured naturally in Boolean logic. For example:
“All powers of 10 are even numbers.”
“Most English sentences are hard to represent exactly in Boolean logic.”
“I think that you’re lying.”
“After you eat your dinner you can have dessert.”
In the first of these sentences, the problem is that we want to make a single claim but have it apply to an infinite set of objects. There’s a straightforward way to solve this problem; we’ll see it when we move on to predicate logic and introduce quantifiers. The problems posed by the other examples are harder and require additional mechanisms that are mostly beyond what we’ll be able to cover in this class.
So, if Boolean logic can’t solve all of our problems, why are we spending so much time on it? Two reasons:
It does solve a lot of practical problems. We’ve mentioned circuit design and search engine querying. We’re about to look at some more examples.
It is the basis for extensions that solve some harder problems. So we need to understand it before we can move on to them.