02 Jul '05 17:34>
Now, since M is itself a state of affairs, either M is logically possible or logically impossible.Let's look at the basic assumptions of the system you are talking about:
Suppose M is logically possible.
If so, then it is logically possible that God cannot cause X to obtain.
Thus, it is logically possible that X is logically impossible.
Thus, X is logically impossible.
Alternatively, suppose M is logically impossible.
If so, then it is logically im ...[text shortened]... oth[/b] M and X). This is your mistake, and it has nothing to do with my argument.
Cheers.
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(a) God can cause any logically possible state of affairs to obtain.
(b) <Some assumption I'm making about M/X>
Your claim is that, by making assumption (b), I am deliberately introducing a proposition that is inconsistent with (a). Correct so far?
Originally posted by bbarr
M = ‘God cannot cause X to obtain’
Presumably, the variable ‘X’ in M just denotes some state of affairs or other.
Now, there is no reason to suppose that X cannot be M itself. Clearly, whatever system of logic we are using is capable of having states of affairs that refer to other states of affairs (otherwise, we would not be able to define M as you did above). By the same token, the system of logic is capable of expressing/defining self-referential states of affairs as well.
Hence, if we consider the state of affairs such that the M and X we are talking about are identical, this state of affairs (M/X) can be properly expressed in the system of logic we are using.
So, what is the assumption I am making?
(b) X is logically possible (impossible) iff X is logically possible (impossible)
which is a tautology.
If (a) and (b) lead to a contradiction; and (b) is a tautology, then it follows that (a) must be a falsehood.