So, in all the books on propositional logic, I feel unsatisfied with the "intuition" about the meaning of the implication connective. I completely understand how the mechanics work via truth tables, but whenever an anecdote is given in natural language, I completely do not follow.
For example, in my current book, they give the atomic formulae:
p = the moon is red q = the moon is made of cheese
And the compound formula:
p => not q
And they state,
obviously p => not q is true.
This is not obvious to me. I understand that the following truth valuations of p and q induce the implication to be true:
p q not q --------- 1 0 1 0 1 0 0 0 1
So, the author thinks that one or more of the above cases is obvious? Can someone walk me through this?
The author then changes p and q for the statements:
p = My telephone is ringing q = Someone is calling me
The author then claims
p => not q is obviously false
However I can think of many cases of why the telephone is ringing (p=1) and someone is not calling me (q=0). E.g. I'm fixing a phone, or I'm setting a ring-tone, etc.
Can someone help me understand this "obviousness"?