Thursday, September 14, 2006

Scotus' New and Improved Onto-Cosmological Argument

Edit: This argument is being left up mainly for historical purposes. Even the pared down version which I present below leaves out an important step, and even without this flaw doesn't have the force of the argument which I initially thought I had.

*Danger: Modal Logic Warning*

I've been reading through Scotus' argument for the existence of God, and given the strong modal tendencies of it, I figured I would try to find a version amenable to modern modal logic (not that medieval and modern modal logic are the same, though possible world semantics may be able to be traced back to Scotus' thought). His argument goes essentially like this (greatly simplified - Scotus was always one for details):

  1. The are orders of causes in which A causes B to cause anything (essentially ordered causes, as opposed to accidentally ordered causes in which A may cause B in some way but then B can act on its own).
  2. It is possible that there is a primary essential cause (there is no contradiction in asserting this).
  3. Such a cause would be uncaused.
  4. Anything that is uncaused and possible must exist.
  5. This primary essential cause must exist.

That at least is the short version. Based on the above, and inspired by Plantinga's version of the ontological argument, I have developed the following

  1. It is logically possible that if p is contingent, the contingency of p could imply that necessarily p could (materially) imply G. That is, it is logically possible that given a contingent thing, it would not exist when God does not.
  2. If p exists actually and is contingent, then G exists actually.

It seems to have ever so slightly more force than Plantinga's argument. At very least, the main premise here is more confusing and thus provides more stalling time in searching for another argument. However, it still suffers from the defect of not saying much about God. I'll most likely work on a stronger version of the argument to supplement this.

For those who want to see the inner workings (where P indicates possibility, N indicates necessity, and -> indicates material implication):

By reductio:
1) P( (Pp & P-p) -> N(p -> G) ),0 (that is, at world 0) (by hypothesis; though I'm working on an argument for it. I thought I had something, but I had mixed up a P with an N. I wonder how God feels about falling prey to a typo?)
2) p, 0 (by hypothesis)
3) P-p, 0 (by hypothesis)
4) (Pp & P-p) -> N(p -> G), 1 (by possiblity of 1)
5) -G, 0 (reductio hypothesis)
Now, either (N-p v Np), or N(p -> G). If N(p -> G) = N(-p v G), then:
6a) N(-p v G), 1
7a) -p v G, 0
both of which lead to contradictions (by 2 and 5). Next, let us look at (N-p v Np). First, N-p:
6b) N-p, 1
7b) -p, 0
which leads to a contradiction by 2. Finally, Np:
6c) Np, 1
7c) -p, 2 (by 3)
8c) p, 2
Another contradiction. Therefore, if there is anything which exists and is contingent, and it is logically possible that there could be something which always exists when something contingent exists, then that thing actually exists. Put more strongly, if it is logically possible that God would exist whenever something contingent exists, then God exists.

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