Comment by dietrichepp

My problem here is that I distinguish between multiplication and addition by seeing which one distributes over the other.

  a * (x + y) = (a * x) + (a * y)

However, the reverse doesn’t work…

  a + (x * y) =? (a + x) * (a + y)

Why is this a problem?

  a ∧ (x ∨ y) = (a ∧ x) ∨ (a ∧ y)
  a ∨ (x ∧ y) = (a ∨ x) ∧ (a ∨ y)

Both are true. So, who are we to say that one corresponds to multiplication, and the other corresponds to addition? The two operations are too similar to each other.