Start with:
- (Premise) Possibly, an unlimited being exists.
- (Premise) Necessarily, for every proposition q that is possibly true, there is a state of affairs p(q) such that p(q) grounds the possibility of q.
- (Premise) Necessarily, if s grounds the possibility of x not existing or the possibility of x being limited, then s limits x.
- (Premise) Necessarily, nothing limits an unlimited being.
- (S5) If something is possibly necessary, then it is necessary.
It follows that there is an unlimited being. For suppose
w is a world that contains an unlimited being
u. Suppose it is true at
w that
u possibly does not exist. Then by 2 and 3, something at
w limits
u, which violates 4. So it is true at
w that
u necessarily exists. Suppose it is true at
w that
u is possibly limited. Then by 2 and 3, something at
w limits
u, which again violates 4. So, at
w it is true that
u exists necessarily and is necessarily unlimited. So, by S5,
u exists necessarily and is necessarily unlimited.
The most controversial premises, I think, will be 1 and 2.
1 comment:
It seems to me (and I have very little training in philosophy, so I may be way off) that possibility is the rational default. So, I don't know why people debate premises like your P1 (very similar to Plantinga's premise in his version of the Ontological Argument). Possibility is just openness, in the absence of some impossibility being demonstrated. It's not as though there's a third option ("agnosticism" or "undecidedness" in this case would be incoherent, since it would leave the possibility open, but "possibility" is one of the two options).
It seems to me that any premise that just says "X is possible" ought to be accepted in the absence of any defeaters or reasons to think X is impossible.
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