Is There a Null World?

November 22, 2006

A while back–roughly 18 yrs ago to be precise–Brian Leftow had articulated what might be a plausible account for how necessary abstract entities (the Platonic horde! as Richard Davis calls it) depend on God.  Leibniz had insisted that the ‘essences or possibles’ absolutely depend on God such that not only would they not have existed if God did not exist, but that they would not have even been possible.  Leftow takes inspiration from this to construct a semantics of ‘impossible worlds’ as he calls it.

In Religious Studies 42 (2006): 371–391, Richard Davis puts this view under scrutiny and finds it wanting.  I intend here to take a breif look at one point that Davis finds puzzling in Leftow’s account.

Davis points out that Leftow professes to be an actualist.  On this view, all that exists, exists in this world.  The entire set of concrete and abstract entities exist in this world, which we will call C.  Among C’s members are worlds or sets of atomic propositions.  There are non-null worlds–maximal sets of atomic propositions such that for every proposition p, either p or –p.  A possible world is a non-null world who’s members are capeable of being true conjointly or individually.

Now according to Leftow, C contains not only possible worlds, but also impossible worlds.  There are non-null impossible worlds–worlds where there is at least one proposition p such that both p and –p are included in that world.  But then, Leftow says, there are also impossible worlds that are null worlds, or worlds with the null set of propositions–a set with exactly 0 members.  In fact, there is exactly one null-world, the world in which God does not exist.  God’s non-existence occurs if and only if the null world obtains.  In his Liebnizian Cosmological Argument, there is a burning question here however that Leftow tries to anticipate:

That God’s non-existence occurs in the null world does not entail that the proposition ‘God does not exist’ exists in the null world.  It does not exist there.  In the null world, no propositions exist, and so none are true (or false).  God’s nonexistence is a logical ‘black-hole’, sucking all the propositions of a world into itself.

But is Leftow convincing here?  One would think that if there is a world in which God does not exist, then doesn’t the proposition “God does not exist”, exist in that world, right?  Leftow tries to solve the problem using Adams’ in/at distinction according to which there a propositions about possible worlds that are true not in those worlds, but at or of them.  But I confess that I do not understand what it means (sorry John) for a proposition to be true of the null world and that proposition not be true in it.  Davis offers an argument that seems to me intuitively true:

(1) Necessarily, if God did not exist, then the null world would have obtained.

(2) Necessarily, the null world obtains if and only if nothing exists.

(3) Necessarily, nothing exists if and only if it is true that nothing exists.

And now from (1)–(3) we can infer:

(4) Necessarily, if God did not exist, then it would have been true that nothing exists.

(5) Necessarily, if God did not exist, then the proposition ‘Nothing exists’ would have been true. 


EPS 2006 Conference

November 21, 2006

We just got back from the annual Evangelical Philosophical Society conference in Washington D.C. and I thought I’d share a few highlights

First, questions on Molinism kept coming up.  Steve Cowan (a good friend of Keith’s) and professor of Apologetics at my alma mater read a paper: Molinism, Christian Belief, and Luck.  I beleive he intends on having it published.  According to Cowan, while the grounding objection has recieved much attention, another equally weighty argument can be leveled against the theory of Middle Knowledge.

Cowan points out that on Molinism, God is able to control the course of history by actualizing that possible world where free creatures, do the things that God wants them to do.  But of course, God has no control over which counterfactuals of creaturely freedom are true, so he cannot just actualize just any possible world that he might want.  Now we must suppose that God, logically prior to scientia media, has a particular plan for how he would like history to turn out.  As it turns out, however, God might be unlucky.  That is, there might be no possible worlds God would actualize that would match his plan.  Cowan concludes that any theory of providence which entails God’s being ‘lucky’ is theologically unnaceptable.  Moreover, such a theory means that the probability of God getting the world that he wants to actualize is either low or inscrutable.

Next, Trenton Merricks of the University of Virginia read as the keynote speaker.  In his paper, Grounding and Subjunctive Conditionals: A Defense of God’s Middle-Knowledge, Among other Things, Merricks attempted provide a defeater for the Truthmaker thesis, and along the way, undercut its usefulness as an objection to Molinism (the grounding objection can be seen as a particualr construal of the truthmaker thesis).  According to the Truthmaker thesis, every truth has a truth-maker, some fact (Russell), state of affairs (Lewis), or whatever, that makes the proposition true.  Truthmaker theorists (save Armstrong), however want to exempt negative existentials from this maxim.  Take the negative existential:

(1) Cerberus does not exist

Many would insist that (1) does not need a truthmaker. 

Merricks argues however, that dispositional conditionals of the kind

(2) If G were struck, then G would shatter,

appear to entail negative existentials of the sort

(3) There is no sorcerer who would keep G from shattering, were G to be struck

But if (2) entails (3), then one cannot object to it using the truth maker thesis.  Similarly, counterfactuals of creaturely freedom are dispositional conditionals.  Hence

(4) If Curley had been offered a $35,000 bribe, he would have freely taken it

is a true counterfactual and this would be immune to the truthmaker thesis and thus the grounding objection.  During the question session, Michael Rea got into an argument with Merricks on one of the finer points of his argument.  The whole time, I couldn’t help but think, ‘man, I really need to learn more logic.’  To be honest, I knew what they were talking about was important somehow.  I just didn’t know what they were talking about.

R. Scott Smith of Biola University read another interesting paper, A Few Issues for Craig’s Fictionalism and Conceptualism.  Smith takes note of Craig’s rejection of the Platonic view of abstract objects and his favorable treatment of Fictionalsim and Conceptualism in his Creation out of Nothing .  He makes some good arguments against the Fictionalist view.  Roughly, Fictionalism denies the existence of abstract objects.  What we concieve of as abstract entities are actually useful fictions we use to describe the world.  Smith suggests that the problem reconciling God and abstract entities this way is not promising.  Similarly, he argues against Craig’s conceptualism which appears to collapse into a kind of nominalism or at best founders on how exactly God’s concepts (say the concept of redness), is related to the property redness in a red box.

Smith suggests a sort of modified platonism akin to Thomas Morris and Christopher Menzel’s view, according to which properties are created by God.  During the question time, Craig pointed out the well known flaw in modified platonism.  If God created properties then whence his own?  Did he create them?  Smith, suprisingly, appeared to be taken off guard by that objection.  I don’t understand why, since this is the standard objection to Morris and Menzel’s view.  See Plantinga, Leftow, et. al. (I even make the same objection in my master’s thesis…to brag a bit).  Nevertheless, this is an area of metaphysics that needs a lot of work.  Many of the attempts at resolving the problem of God and abstract objects appear to come with some sort of baggage:  Fictionalism seems theologically unnaceptable , modified Platonism appears to get hoisted on its own petard, Divine Simplicity might do the trick but most analytic theists reject it for other reasons, and Conceptualism appears to collapse into nominalism or Platonism, depending on how you take it.  This is exciting stuff!

Speaking of God and abstract objects, Richard Davis of Tyndale University College read an interesting paper in that vein, God and Counterpossibles.  Brian Leftow’s account of counterpossibles–his attempt to explain just how propositions and other abstract objects depend on God–is put under scrutiny.  Counterpossibles are counterfactuals whose antecedents are impossible.  For example:

(5) If God were to cease existing, then p would not exist

(6) If God were to cease existing, the p would still exist

Here, (5) would be trivially true and (6) trivially false.  Davis points out that, among other things, counterpossibles such as (5) and (6) do not appropriately capture the dependence of propositions on God.  Along the way, Davis suggests some emmendations to Leftow’s view.  One of his radical suggestions is that we not think of propositions as necessary beings at all.  In fact, he says, propositions might be seen as contingent entities such that there are possible worlds where no propositions exist. 

Davis’ God and Counterpossibles is published in Religious Studies 42 (2006): 371–391.  Leftow offers a response in the same issue, Impossible Worlds, Religious Studies 42 (2006): 393–402.  This is the stuff of metaphysics.

All in all, great conference. 

New Christian Worldview Magazine Hits Shelves

November 6, 2006

I subscribe to a lot of Christian periodicals. Faith and Philosophy, JETS, Chronos, First Things, Books and Culture, Areopagus Journal, Philosophia Christi—the list goes on. As far as I’m concerned, these (give or take a title) represent the cream of the periodical crop.

Now, given the sort of work I do, I’m kind of privy to new publications. Some are good; most, well, not so good (just being honest!). One of the good ones really good ones has just come across my desk: Salvo . Read the rest of this entry »