Tuesday, June 29, 2010

Some sound theistic arguments

Argument 1:
  1. Possibly, the Principle of Sufficient Reason (PSR) is true.
  2. Necessarily, if the PSR is true, then there is a causally efficacious necessary being.
  3. Therefore, possibly, there is a necessary causally efficacious being.
  4. Therefore, actually, there is a necessary possibly causally efficacious being.
Argument 2:
Let @ be the actual world. Say that a being is omnipotent* provided it is omnipotent at at least some explanatory point in the history of the world (so omnipotence* is prima facie compatible with giving up omnipotence).
  1. Possibly, there is an omnipotent being.
  2. Necessarily, if x is omnipotent, then x exists at @.
  3. Necessarily, any omnipotent being is essentially omnipotent*.
  4. Therefore, there is an essentially omnipotent* being.
Premises (2) and (3) need support. First, necessarily, a being is only omnipotent if it could create me (directly or mediately). But by essentiality of origins I could be created by a being only if I am created by the being. Therefore, if there is a being that could create me, that being creates me at @, and hence exists at @. Thus, (2). Also, plausibly, an omnipotent being could be the First Cause in any possible world. Hence, an omnipotent being must be a necessary being, and hence exist at @. Thus, (2).
What about (3)? Well, an omnipotent being could exercise its omnipotence to put itself in any state possible to it. Suppose it's possible for an omnipotent being to fail to be omnipotent*. Then the omnipotent being could make itself be non-omnipotent* by exercising its omnipotence. But then the being would be omnipotent at some explanatory point in that world where it makes itself non-omnipotent*, and hence it would be omnipotent* there. So absurdity arises. So it's not possible for an omnipotent being to fail to be omnipotent*.

Argument 3:
Say that x knows* p iff x knows p or knows some proposition of which p is a conjunct.
  1. Possibly, there is a being x such that for any proposition p that could be true, x could know p.
  2. Therefore let w be a world and x a being such that x exists at w and for any proposition p, if p could be true, x could know p.
  3. Therefore, if w* is any possible world and p be any proposition true at w*, then x could know that w* is actual and p.
  4. x could know that w* is actual and p only at w*.
  5. Therefore, if w* is a possible world and p is true at w*, then x exists at w* and knows* that p at w*.
  6. Therefore, there is a being that exists at every world and knows* every truth at every world.

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