p implies q is equivalent to ~q implies ~p.
Agreed
I'm sure we all agree with that ...
Not sure that we all agree. I can't speak for others.
... Craig probably believes that if not objective moral values and duties, then not God.
This is reasonable, but it's irrelevant since it's not a premise of the argument that Craig uses in this case (he may use it elsewhere, I suppose).
You agree (as do we all) that the syllogism takes a valid form ...
Yes, I do. Take out the content and it works perfectly. Put in the content, as Craig does, and it is logically valid. Within the limitations of logic, it continues to work perfectly. Nonsense in, nonsense out.
but you don't like the way it's structured because to deny objective moral values in this case is to affirm the consequent and to affirm the antecedent would probably be question begging.
What? No. Perhaps this is someone else's objection. But it would be wrong. The problem has nothing to with the two fallacies you mention. Affirming the antecedent isn't a fallacy, just in case someone is misremembering "denying the antecedent" (a fallacy that is hinted at, but isn't the actual problem either).
Did I sum it up correctly?
Not for me, no. Perhaps for someone else, but I hope not.
Neo,
I wasn't mentioning affirming the antecedent was a formal fallacy. Just that affirming the antecedent “God does not exist” in the argument as a defeater of the argument is just to deny the conclusion and is question begging to assert it as a defeater.
Do you take this syllogism to have a “cloaked” premise and a twisted structure:
(1) If cars do not exist, then car shops do not exist.
Cloaked:
(1) If car shops do exist, then cars exist (sneaky bastard)
WAIT!!!!!!! (The lightbulb struggling to flicker shines brightly with incandescence at its epiphany)
The cloaked premise in my example syllogism and your Craig syllogism aren't the equivalent of the actual premise.
In your Craig's cloaked premise, you've got the consequent and antecedent backwards.
It goes from:
(1) If God does not exist, then objective moral values and duties do not exist.
Proper cloaked:
(1) If objective moral values and duties exist, then God exists.
Mine:
(1) If cars do not exist, then car shops do not exist.
Proper cloaked:
(1) If car shops do exist, then cars exist.
So, how did you arrive at your cloaked premise?
If you take issue with Craig's argument, then you should take issue with mine because they're both “twisted”.