Unrolled dice and eternal stars…

The point of this post is to differentiate between different kinds of causation and possibility as they figure in debates about God's existence.

Imagine a world that consists entirely of a die-cast mold and some plaster filling that mold. Call this world W_mp. Could such a combination (have) exist(ed) independently for all time? I suppose so. An immediate impulse is to say that a die-cast mold must have been crafted by someone, so this austere scenario seems to require a prior cause. But I'll suppress that impulse for the moment and grant this mold-plaster scenario, for argument's sake.

To make the suppression easier, consider a different world, W_d, which consists entirely of a pair of die in a small bowl. Our impulse once more is to imagine the dice had been rolled, or at least placed, in the bowl, or, at the very least pressed in a machine to make their divots and dimensions. But I don't think it's inconceivable for W_d to exist, so I'll grant it.

Now, both W_mp and W_b would be only dimly causal worlds. In W_mp the shape of the mold gives the plaster its shape, but, then again, the plaster is also what gives the mold its shape qua mold. So there's only a very weak form of mutual causation between them. Further, lacking any other entities, nothing could bring about their separation, which means, once again, causation is basically vacuous in W_mp. The same holds for W_d.

I am pondering these ponderables because of thoughts I had about Doug's presentation of the Scotist modal argument for God's existence (SMA). Here is how Doug presents the argument:

1. A First Cause possibly exists. (Premise)

2. Whatever is possible is either contingent or necessary. (Definition)

3. Whatever is contingent can be actualized. (Premise)

4. A First Cause cannot be actualized. (Premise)

5. Therefore, a First Cause is necessary. (From 1 - 4).

Doug then adds that

…atheistic philosopher William Rowe doesn't dispute any of the premises of Duns Scotus' argument. Rather, what Rowe attempts to do is demonstrate that if this argument were correct, it would lead to all kinds of absurdities:

Surely it is possible for an everlasting star to exist. The stars that exist are presumably not everlasting--for each star, let us suppose, there was a time before which it did not exist and there will be a time at which it ceases to exist. But this seems to be an empirical fact and not a matter of conceptual or logical necessity. The idea of an everlasting star does seem to be a non-contradictory idea, even if no star is in fact everlasting. Let us grant, then, that

i. it is possible for an everlasting star to exist.

Now clearly we must grant that

ii. it is impossible for an everlasting star to come into existence. (If x comes into existence then by definition x is not everlasting.)

Moreover, since if something is produced by something else then there was a time before which it did not exist, we have

iii. it is impossible for an everlasting star to be produced by something else.

[The Cosmological Argument, Fordham University Press, 1998, pp. 52-53.]

Doug responds by saying:

The problem with Rowe's counter-argument is that it assumes a type of modality not necessarily entailed by Scotus. Even a star that is everlasting is being actualized by the matter that composes it. The analogy, then, of a non-actualized everlasting star seems to be incoherent and disanalogous to the SCA. For, the First Cause that Scotus envisages is simply not actualized at all.

I agree, but also added what I think is a subtly different and perhaps even more basic rejoinder. Namely, the problem with conceiving of an everlasting star is that the definition of a star is a) that it is a collapsed planet and b) that it therefore has a finite amount of mass to expend before expiring. A star's definitional parameters for being require not only that it 'descended' or 'emerged' from a prior state of affairs, namely, a planet in collapse, but also that it have a finite amount of energy. Positing an eternal star, therefore, is as incoherent as positing an unborn son or an eternal two-week vacation. So Rowe's objection is––I can't help myself––a non-starter.

Perhaps Rowe, or a Rowe-like objector, would reformulate his position to mean that there is something––call it a star*––which we call "a star" but that is only phenomenally like a star (i.e. bright, hot, large, etc.). This star* would display all the 'behavior' of a star but would not be subject to the prior limitations on what a star actually is. Unfortunately, this only opens the way for further objections. For instance, being like a star entails that a star* pulsates at a specific radiometric frequency and that it recedes from a terrestrial observer at a specific Dopplerized velocity. As such, a star*'s phenomenal constitution intrinsically bears reference to spatiotemporal succession, at least in notion, and therefore includes contingency and change in its own notion.

Thus, while a star* could be posited ad hoc to have just "been there" from/for all time, its stellar specificities as a cosmic sub-entity render it decisively unlike what God is. An infinitely large star coextensive with the cosmos is incoherent, since a star must at least phenomenally shine against some non-star background. If Rowe and Rowesque objectors go for broke by saying the star––now call it Star!––is immobile, unchanging, infinitely powerful, timeless, purely luminiscent, devoid of any interfering or transmitting medium, etc., they will be dangerously to mounting an atheist case for God. The more this Star! takes on divine attributes, the less it enjoys properly stellar attributes, until eventually Rowe's objection just becomes a species of the "flying spaghetti monster" argument. At which point we must invoke St Thomas: "Sapientis enim est non curare de nominibus" (Wisdom does not treat of names).

Rowe's everlasting star and my everlasting W_mp and W_d are all counterintutive but nonetheless conceivable. Now here's the point I want to make about differing kinds of possibility in these arguments.

Let's say something is possible¹ iff nothing in the notion of the thing entails an intrinsic contradiciton. A square circle would not be possible¹.

Now let's say that something is possible² iff it is possible¹ and possible¹ for it to exist with accidental variations. For example, as an American, it is possible¹ for me to be a citizen of Idaho but only possible² for me to be a citizen of Idaho after 1890 (when Idaho was admitted to the Union). It is likewise possible¹ for N. and K. (the individuals who became my parents) not to have had me, but it is not possible² for me not to have had N. and K. as my parents. Who I am intrinsically depends on my being the child of my parents. My proper parameters for being preclude an alternate parentage is possible².

Lastly, something is possible³ iff it possible¹ but not possible². This means that a state of affairs S:a is conceivable (possible¹) but it is inconceivable (~possible¹) for S:a to exist in any other way, under any other circumstances, by any different means, in any other sense, with any other parameters for being, and so on.

This notation is totally provisional and may be terribly faulty, but, hey, this is a blog, so let me show how they apply to my larger point. I realize that the more conventional terms are "conceptual possibility" (possible¹), "metaphysical possibility" (possible²), and "analycity" (possible³), but for some reason I want to avoid those terms in this train of thought. I would like to say that something possible¹ is weakly possible, or enjoys weak possibility; something possible² is strongly possible, or enjoys strong possibility; and something possible³ is integrally possible, or enjoys integral possibility.

W_mp is possible¹ and possible², but not possible³. Here's why: As I've granted, W_mp is possible¹ but it is also possible¹ for W_mp to exist in slightly different ways. For instance, imagine there were numerously variable pock marks in the surface of the plaster that allowed for 'air' to exist between the mold and the plaster. Or imagine no such gaps existed, and the interior of the plaster mold was perfectly hermetically smooth. Or imagine the many possible shades of the plaster, or what metal the mold is made of, and so on. The variables are endless, yet they don't compromise what W_mp is as a whole S:a. This is because there is nothing in the definition of a die-cast model and/or of a mass of plaster that either preclude its possible¹ existence or exhaust its possible² features. The same holds for W_d. The size, smoothness, glint, separation, etc. of the dice can vary indefinitely when considered in possible² terms.

Now contrast this with the SMA, which argues that if an Unactualized Actualizer (UA) is possible¹, such an Actualizer is necessary. (The UA is "unactualized" by virtue of not being subject to anything which essentially makes it actual. It is simply actual, not actualized.) The UA is possible¹, since it is not intellectually repugnant like a square circle or a married bachelor or an unborn son. But is the UA possible²? I say it is not. For the very definition of the UA is not to be subject to variations in its conditions of existence, such variations being the way a thing is possible². Unlike W_mp and W_d, the UA could not exist in any other way, could not be subject to any other qualifications, and still remain what it is by definition. Making the UA possible², therefore, amounts to asserting that the UA is not possible¹. By supposing the UA could be actualized based on, or according to, numerous other factors or under numerous other conditions––and could be "de-actualized" by other unsuitable factors/conditions (à la me and Idaho and 1889)––, the suppositions would subject the UA to an existential conditioning precluded by its definition (as a weakly-possible). Unlike W_mp and W_d, and like a circle, there is no way to 'tweak' how the UA exists without denying the possibility that the UA exists altogether. The UA is possible¹ only in the way it is presented as being possible¹, which means it is possible³. Like W_mp, the definition of the UA entails that it is possible¹ but precludes that it is possible². Insofar, therefore, as the UA is possible¹ and not possible², but is possible³, and its possibility conditions include its necessary existence, then the UA is actually existent (again, by virtue of it remaining a coherent first-order possibility).