But now consider a different example. You say to me, 'You can be my friend if you love logic or chocolate'.
Then, as before, it turns out that I love both.
In this situation you're not going to deny me friendship. You're not going to say I haven't meet the criterion you specified.
No, if I love both then I'm doubly your friend.
This tells us that an English sentence involving 'or' is true when the two sentences
conjoined are both true. That is, the English 'or' is inclusive.
But now we seems to have contradictory urges. One case urges us to say that the English 'or' is exclusive
(false when the things conjoined are both true), the other case urges us to say the opposite.
Now the truth is probably that the English 'or' is neither inclusive nor exclusive but much more complex still.
The point of introducing a formal language is to avoid all this complexity.
Not because there's anything wrong with the English 'or'--on the contrary, it's complexity is a wonderful thing for communication.
But our concern is not communication but logic.
Now if we define our symbols just by invoking the meanings of English words, we won't succeed in avoiding the complexity of
natural languages like English. We will have merely replaced one sign with another.
This is why we need more than the rough guide