From the Mailbag: Modality and Perfection

Daniel C. writes,

A quick remark on your recent possible worlds post. 

You only mention it in  passing but one thing possible worlds talk surely does throw into sharp relief is the issue of the modality of modal statements i.e. if a certain proposition is possibly true is it necessarily possibly true or merely possibly possibly true? To the best of my knowledge most pre-modern metaphysicians simply presumed the truth of the Brouwer axiom (Leibniz and Scotus) or of S5. Far be it from me to challenge these venerable principles but as far as I know very few thought of disputing them before the question could be phrased in terms of accessibility relations between worlds.

Your general point is important and correct: possible worlds talk allows for the rigorous formulation of questions about the modal status of modal statements, which in turn hinges on accessibility relations between worlds.  But I hope you are not suggesting that the Brouwer axiom is the same as the characteristic S5 axiom. I am not a logician, but my understanding is that they are not.

 

Brouwer Axiom: p --> Nec Poss p. That is to say, if a proposition is true, then it is necessarily possibly true.

 

Characteristic S5 axiom: Poss p --> Nec Poss p. That is, if a proposition is possibly true, then it is necessarily possibly true.

Also: On the contrary, I say that God's status as a necessary being follows from His perfection rather than simplicity (although the former may entail the latter as Anselm certainly thought).

I take it that a perfect being is one that possesses all perfections. The Plantingian gloss on 'perfection' seems good enough: a perfection is a great-making property. So a perfect being is one that possesses all great-making properties and the maximal degree of those great-making properties that admit of degrees. 

Now A. Plantinga famously denies the divine simplicity while upholding the divine perfection. I take it we all agree that God is a necessary being.  That than which no greater can be conceived cannot be a mere contingent being. But what makes a necessary being greater than a contingent being? On a possible worlds approach, it will presumably be the fact that a being that exists in all worlds is greater than one that exists in some but not all worlds. It is a matter of quantity of worlds.

But then I will press the question: what makes it the case that God exists in all possible worlds?  What grounds this fact? My answer: the divine simplicity, which implies the identity in God of essence and existence.  Divine perfection is not enough. For God could be perfect in Plantinga's sense while harboring a real internal difference between essence and existence. But this leaves open the question as to why God is necessary.

If you say that God is necessary because he exists in all worlds, then you give a bad answer. It is true that God exists necessarily iff all world-propositions say he exists. But it doesn't follow that God is necessary because all world-propositions say he exists. It is the other way around: he exists according to every world-proposition because he is necessary!

Mundane example. Am I seated because the proposition BV is seated is true? No. The proposition is true because I am seated. The truth-maker is what makes the truth true; it is 'bass ackwards' to say that truths make states of affairs exist.  

Same with God. It is the divine necessity that makes it true that God exists in (i.e., according to) every possible world, and not the other way around. But to be necessary in the unique way that God is necessary, a way he does not share with garden-variety necessary beings such as the number 9 and the set of prime numbers, God must be metaphysically simple.