bmiller wrote:

But then it seems the argument is actually about ontology in the first place.
Theists maintain that God is essential for things to exist.  Atheists maintain that God is not essential for things to exist.  The arguments contradict each other so Fred could not rationally hold that both are true.  Parsimony would only tighten up each argument to be more concise. 

H2 is God, but H1 doesn't have to be atheism. It could be another god hypothesis. Say a unitarian god. It's just an example anyway. H2 could be something entirely different (viz. non-theistic). The point is that if H1 is simpler, and H2 non-essential, and yet the person already accepts H2 on other grounds but not H1, then choosing H1 would involve an expansion to their ontology.

bmiller wrote:

OK.  May I ask if what you are getting at is: 
1) Brute facts the simplest explanation for anything
2) Parsimony dictates that we should accept the the simplest explanation
3) Therefore we should accept that existence is a brute fact.

Is this the gist of your inquiry?

No. Something more like this:

1) Not expanding our ontology always takes precedence over expanding it
2) N is already part of our ontology
3) S is not already part of our ontology
4) E is sufficiently explained by S
5) E is non-essentially explained by N
6) Explaining E by N does not involve an expansion to our ontology (from 2 and 5)
7) Explaining E by S does involve an expansion to our ontology (from 3 and 4)
8) Therefore, we should attribute E to N (from 1, 6 and 7)

Jason wrote:

I do not think that this argument can work since for A/T God is the reason we even have our ontology in the first place. So to say that God expands our ontology does not even make sense. Involving God in our ontology does not expand it but explains it.

The argument isn't about God. It's a general argument. I gave the example of God since this is a classical theism forum.

surroundx wrote:

How much stock do forum members put in the Principle of Parsimony?

It seems to me that, even if you somehow accepted it as a metaphysical first principle, it's application would still be contingent to some degree upon one's current (meta-)ontology.

I think that the principle of parsimony is a good principle, but it's an epistemic rather than a metaphysical principle. It's not that the universe is, and surely not that it must be, such that simpler explanations are true. Often they aren't.

surroundx wrote:

Take Fred, who is trying to decide which of two competing hypothesis is the best explanation of some phenomenon. Call them H5 and H10 respectively, alluding to the number of assumptions/commitments that each requires. Let us further say that there is no overlap of the assumptions/commitments that constitute H5 and H10. Assuming that all other things are equal (cf. ceteris paribus), then clearly Fred should choose H5. However, if Fred already accepts 6 of H10's assumptions/commitments and none of H5's, then clearly (or so it seems to me) Fred should really choose H10 since that only burdens him with 4 extra assumptions/commitments. Thoughts?

So far the situation is insufficiently described. Fred may have no reason, or bad reasons, for accepting the 6 of H10's assumptions which he already accepts. Then the fact that already accepts them has no significance for his choosing between H5 and H10.

The dogma of reductionism survives in the supposition that each statement, taken in isolation from its fellows, can admit of confirmation or infirmation at all. My countersuggestion ... is that our statements about the external world face the tribunal of sense experience not individually but only as a corporate body. H5 and H10 are competing explanations of some phenomenon B. B is not the only phenomenon. Fred, say, accepts 6 of H10's assumptions because he is also trying to explain some other phenomenon, A. And strictly, Fred is not presently trying to find the explanation for B. He is trying to find the explanation for A and B. If H10 explains A and B, but H5 only explains A and B if it is conjoined with 6 distinct assumptions from H10, then H"5" really involves 11 assumptions, and not 5, and is less parsimonious than just accepting H10.

Greg wrote:

I think that the principle of parsimony is a good principle, but it's an epistemic rather than a metaphysical principle. It's not that the universe is, and surely not that it must be, such that simpler explanations are true. Often they aren't.

Simpler explanations often aren't true because they're too attenuated. In virtue of the fact that the simplest explanations could be said to be epistemic rather than ontic (e.g. "there is nothing to explain"). If you agree that there is something to explain then the simplest explanation is false. That doesn't negatively affect the PoP.