The logic is valid -- the contrapositive of a true statement is also a true statement -- but the syllogism is unsound because not all the premises are true.
e.g.
1) If God does not exist, moral knowledge does not exist;
2) The contrapositive is also true, therefore, if moral knowledge exists, then God exists;
3) Moral knowledge exists:
C) Therefore God exists.
That's valid, but because #1 isn't true, the conclusion isn't valid.
e.g.
1) If God does not exist, moral knowledge does not exist;
2) The contrapositive is also true, therefore, if moral knowledge exists, then God exists;
3) Moral knowledge exists:
C) Therefore God exists.
That's valid, but because #1 isn't true, the conclusion isn't valid.
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