Hi, folks. I'm sure this ends up being a philosophical question regarding logic—and I'm hoping someone can point me to an appropriate philosopher, logician, or better: book/paper/website. I want to say that I'm looking for Ludwig Wittgenstein (my reading regarding formal logic is fairly limited), but I'm not entirely certain. This semester I found that I'm not as well-versed at mathematics as I should be, so I started independently reading some books. Currently I'm going through a book entitled "An Introduction to Mathematical Reasoning" which contains this proof: The book proves both the [itex]\Rightarrow[/itex] statement and the [itex]\Leftarrow[/itex] statement—and it seems, at first, like a very simple proof. My qualm is this: If someone were to claim, "ab = 0 implies a = 0 or b = 0"—how can using the properties of 0 prove the statement? Isn't that circular, because what we want to prove in the first place is a statement of a property of 0 itself?