I will share the result of some work I did today on a couple of papers by Alexander Pruss on the PSR.

1. Richard M. Gale and Alexander R. Pruss, 1999. "A New Cosmological Argument".
http://alexanderpruss.com/papers/NewCosmo.html

Here they use "Duns Scotus’s very weak version of PSR":

(W-PSR) For any proposition, p, and any world, w, if p is in w’s Big Conjunctive Fact, then there is some possible world, w1, and proposition, q, such that w1’s Big Conjunctive Fact contains p and q and the proposition that q explains p.

The case can be easily seen using two possible worlds as "w1" and "w" in paper 1.

Theist's world Wt ("w1" in paper 1):

BCFt = BCCFt + BCNFt
BCCFt = BCCFr + q1 = pt = "p1" in paper 1
BCNFt = BCNFr + N1

q1 = free creative decision by NB, necessary and sufficient, in conjunction with N1, to explain pt.
N1 = Necessary Being (NB) exists.

Atheist's world Wa ("w" in paper 1):

BCFa = BCCFa + BCNFa
BCCFa = BCCFr + ¬q1 = pa = "p" in paper 1
BCNFa = BCNFr + ¬N1

It is evident that pa is not explainable in ANY possible world, defined as a maximal, compossible conjunction of abstract propositions, since, due to the requirement of maximality, it contains ¬q1, which is incompatible with the explanatory proposition q1. Therefore an atheist must deny W-PSR. At least, he must deny its applicability to any proposition involving the explanation of a world's BCCF or the negation of that explanation.

Now, since an atheist holds pa as a contingent truth, and it is impossible that pa has an explanation, then an atheist must hold that there are contingent truths that cannot possibly have an explanation, and consequently that W-PSR cannot possibly be true. Thus an atheist must deny WW-PSR as well, as introduced in this blog post:

http://alexanderpruss.blogspot.com/2011/05/weak-weak-principle-of-sufficient.html

2. Alexander R. Pruss, 2002. "Ex Nihilo Nihil Fit: Arguments New and Old for the Principle of Sufficient Reason".
http://alexanderpruss.com/papers/ENNFtalk.html

From the above two worlds and the beginning of the chain of reasoning at the end of paper 2, it can be easily seen that an atheist must deny the weaker version of Brouwer Axiom "If p holds contingently, then it is possible for p to be both possible and false." At least, he must deny its applicability to any proposition involving the explanation of a world's BCCF or the negation of that explanation.

"For suppose that the PSR is in fact false.  Let p be a contingent proposition, then, which has no explanation.  Let q be the proposition that p holds and has no explanation.  Since p is contingent, so is q.  Thus, there is a possible world w at which q is false.  Let us transport ourselves to that world.  In that world, the proposition q is false, <b>but it is still going to be possible.  (This uses the Brouwer axiom which is weaker than S5.</b>"

Relating the terms in this passage to those in atheist's world Wa above:

p = BCCFr
q = BCCFr AND ¬q1
¬q = ¬BCCFr OR q1

Therefore there are 3 possible worlds at which q is false, i.e. ¬q is true:

¬BCCFr, q1 = WG = God, no universe. Explained by a free divine decision not to create.
In WG q is not possible, since contingent beings can exist only by a free divine decision to create them.

¬BCCFr, ¬q1 = W0 = no God, no universe. Quite self-explanatory.
In W0 q is repugnant to reason, since the universe would arise spontaneously out of true nothing (not quantum void).

BCCFr, q1 = Wt = God, universe. Explained by a free divine decision to create.
In Wt q is not possible for the same reason than in WG.

Thus an atheist must deny the weaker version of Brouwer Axiom. Since that version follows from the full Brouwer Axiom, which in turn follows from S5, he must also deny S5. (Notably, as I just noted in a thread in the Religion subforum, a Christian must deny S5 when dealing with the doctrine of the Trinity.)

 

Last edited by Johannes (5/10/2016 4:51 pm)