Question

There is an old joke that goes something like this: “If God is love, love is blind, and Ray Charles is blind, then Ray Charles is God.” Explain, in the terms of first-order logic and predicate calculus, why this reasoning is incorrect. If the person who told you this joke was your grandmother, how would you respectfully explain this to her?

Answer 1

If a then b is not the same as If b then a.

For example, If it rains today then I will carry my umbrella is not the same as If I carry my umbrella then it will rain today

In your problem a=God is Love and B=Love is Blind

We then have if "God is Love" Then "Love Is Blind"

which is not the same as

If "Love is Blind" Then "God is Love"

A simple truth table will show that these two are not equivalent, since If a then b is logically the same as "a or not b"

Answer 2

Correction to the above: If a then b is not a or not b
http://en.wikipedia.org/wiki/Material_conditional
Here's the corrected truth table


But for grandma, the umbrella explanation would be better.

Answer 3

Correction #2: If a then b is equivalent to "not a or b"