Instants, Intervals, and the Reconciliation of Creatio Ex Nihilo with Ex Nihilo Nihil Fit
July 13, 2006 — 14:49

Author: Bill Vallicella  Category: Concept of God  Comments: 8

This post examines Richard C. Potter’s solution to the problem of reconciling creatio ex nihilo with ex nihilo nihil fit in his valuable article, “How To Create a Physical Universe Ex Nihilo,” Faith and Philosophy, vol. 3, no. 1, (January 1986), pp. 16-26. (Potter appears to have dropped out of sight, philosophically speaking, so if anyone knows what became of him, please let me know. The Philosopher’s Index shows only three articles by him, the last of which appeared in 1986.)


I. THE PROBLEM
We first need to get clear about the problem. Given that God creates out of nothing, how is this consistent with the apparent truth that something cannot come from nothing? The latter, the principle of ex nihilo nihil fit, seems to be an intuitively self-evident metaphysically necessary truth. If it is metaphysically necessary, it is not a truth over which God has any control. The truth in question is interpreted by Potter in terms of the following Principle of Creation by Compounding:
PCC. For any object O and time t, if O comes into being at t, then there exist some objects out of which O is composed and those objects existed prior to t.
Potter sees the problem as one of reconciling (PCC) with the following principle:
ENP. God created contingent objects in such a way that there was a time t1 at which contingent objects came into being, although there was no time prior to t1.
On the face of it, (PCC) and (ENP) are logically inconsistent.
II. POTTER’S SOLUTION
Potter attempts to evade the inconsistency by distinguishing between two senses of ‘a time’ as it figures in (ENP). The phrase can be taken to refer to an instant, or to a finite interval. (ENP) thus splits into two principles:
ENP1. God created contingent objects in such a way that there was an instant t1 at which contingent objects came into being, although there was no instant prior to t1.
ENP2. God created contingent objects in such a way that there was a finite interval t1 during which contingent objects came into being, although there was no interval prior to t1 and no instant during t1 at which contingent objects failed to exist.

It is clear that (PCC) and (ENP1) are inconsistent. But (PCC) and (ENP2) are not inconsistent. To appreciate this, one must realize that an interval of time need not have a first instant. It may be that the first interval of time was ‘open in the earlier direction,’ or ‘past-open,’ or as Potter puts it, “open-ended at its beginning.”
If we take the concept of an instant as undefined, we may define an interval of time to be a set S containing at least two instants such that (i) every member of S is an instant; (ii) between any two members of S there is a third member that comes before one member and after the other; and (iii) any instant that comes before one member of S and after another member of S is a member of S.
Clause (ii) of this definition insures that an interval is an infinite set of instants: if between any two there is a third, then between any two there are infinitely many. The members of S are densely ordered in that they are packed together like the rational numbers. Given that an interval so defined is open in the earlier direction, it follows that for any member of the interval, there is some other member of the interval that comes before it.
It follows that there can be a first interval of time, an interval that precedes every other interval, without there being a first instant of time. To say that interval S wholly precedes interval T is to say that every member of S comes before every member of T.
The reason there can be a first interval without a first instant is because the interval is open in the earlier direction. Now if there was a first interval of time, a first year some fifteen billion years ago let us say, but no first instant of time, then God can create the physical universe without violating (PCC). For at any instant during the first interval, there will already exist contingent beings that God can operate upon in order to create further contingent beings.
Thus God creates out of nothing in the following sense: God creates contingent beings in such a way that there was a time (an interval of time) that was not preceded by any interval of time. And this creation out of nothing is logically consistent with ex nihilo nihil fit because there is no instant of time within the first interval at which contingent beings do not exist.
III. A QUESTION ABOUT POTTER’S SOLUTION
Potter’s solution is ingenious, but the very move he makes — the distinction bretween a first instant and a first interval — may perhaps be used against him by the atheist. For what could prevent the atheist from arguing that the physical universe causes itself to exist? For if the first interval of time contains no first instant, then the atheist can maintain that what exists at each instant is caused to exist by what exists at earlier instants. If so, then there is no instant at which there exists something that requires something external to the physical universe as its cause.
Thus to Potter’s claim that God at every instant has contingent beings available upon which to operate, the atheist can respond: “But if that is the case, then why posit God as cause of the universe’s beginning to exist?” The atheist’s point is that the existence of a temporally finite universe can be explained internally or immanently by construing the temporally first interval as open in the earlier direction such that every state of the universe is caused by earlier states. If every state has a physical cause, then there is no need to invoke God.
Ex nihilo nihil fit is an intuitively obvious principle that threatens both the theist and the atheist. It is a problem for the atheist since, if the universe began to exist, it could not have come out of nothing, and so appears to require a cause of its existence. It is a problem for the theist, since if the universe began to exist, it presumably did not come out of God, but was created by God as distinct from God. Not coming out of God, it came out of nothing — but how is that possible?
Potter’s solution removes the sting of ex nihilo nihil fit for the theist, but unfortunately gives aid and comfort to the atheist who can make the Potterian moves to argue that the universe caused itself and so does not need a divine explanation.
For more on whether the universe could cause itself to exist, see this paper of mine published in Philosophy, the journal of the Royal Institute of Philosophy. See also this post over at Maverick Philosopher, the posts chained to it, and the associated comment threads.

Technorati Tags: ex nihilo, nihil, physical universe, fit, god, compounding, philosopher, apparent, consistent, philosophy, faith, creation

Technorati Tags: ex nihilo, nihil, physical universe, fit, god, compounding, philosopher, apparent, consistent, philosophy, faith, creation

Comments:
  • Bill, this is very interesting. Let (n,m] be the first interval, closed at m and open at n. The greatest lower bound on (n,m] (viz., n) is not an instant in the first interval, so there are no contingent objects at n. But for every instant after n there are created contingent objects, and there is no earliest instant after n. But then you say,
    “For at any instant during the first interval, there will already exist contingent beings that God can operate upon in order to create further contingent beings”.
    That’s pretty clever. But here’s my worry. It is impossible that God creates contingent objects at the first instant of the interval (n,m] since there is no first instant. So at whatever instant t in the interval God chooses to begin creating contingent objects, there will be a previous instant in the interval at which there are no created contingent objects. So we have the same violation of ex nihilo.
    Here’s another way to put it. God creates contingent objects in the first interval, not prior to the first interval. Anything that happens in the first interval, happens at some instant t in the interval. For every instant t in that interval there is a previous instant t’ earlier than t. So at whatever instant God begins to create contingent objects, there will be a previous instant at which there object does not exist.
    Solution: well, why not assume that God creates contingent objects from the very first instant?
    Reply: That is impossible, since there is no first instant. Necessarily, for any time t at which he *begins to create* anything, there is a t’ earlier than t at which creation has not yet begun. So again a violation of ex nihilo.

    July 14, 2006 — 8:40
  • Tim Pawl

    Bill,
    This is a neat post. I don’t agree with Potter’s understanding of ex nihilo nihil fit (ENNF). I’ve always thought it meant:
    E) It is not the case that something could have started to exist without an efficient cause. (nothing without an efficient cause)
    I never took it to be:
    M) It is not the case that something could have started to exist without a material cause (nothing without a material cause).
    Am a wrong about this? Does anyone know a reason why I would have to interpret ENNF as M) rather than E)?
    Notice, if we can understand ENNF as E), we have no problem with the two doctrines.
    Also, think of PCC in the world where God only creates immaterial beings (say, an only-angel world). Of what are the angels composed? One may want to constrict PCC from “any object” to “any material object”. But, then I think that PCC is sounding more like my M), which I don’t yet have a reason to affirm.

    July 14, 2006 — 8:54
  • Kevin Timpe

    I had a slighly different worry about Potter’s understaning of (ENNF), though I think that it is related to Tim’s comment above. I though that the principle described how things operate in the natural order. But taking the principle in an unrestricted way, as Potter appears to, seems to rule out the possibility of certain sorts of miracles. Now perhaps Potter’s idea is that the unrestricted application of (ENNF) shows that miracles such as creating out of nothing are logically impossible. But I doubt that much of the tradition has understood (ENNF) in this way.

    July 14, 2006 — 10:49
  • Mike,
    Thanks for the challenging comments. I see what you are saying. But you are assuming that God can create only by acting at an instant. Suppose instead that God acts timelessly to bring about a finitely old universe whose first interval is past-open. Thus he brings about a universe in which every state has an earlier state. Thus no state arises out of nothing, each arises from an earlier state. The universe as a whole arises out of nothing in the sense that there is no interval before the first interval.
    This is perhaps not an adequate response, but I plead Phoenix’s 115 degree temp. today. My brain is fried. The Dog Days of summer are upon us.

    July 15, 2006 — 17:56
  • Timn,
    Very good comment. Since God is an absolute, self-existent being, one possessing aseity, his creating cannot be an acting upon something that does, or could, exist apart from him. Otherwise, he would be a demiurge. So I’d say the sense of ENNF is that God creates, but not out of, or by acting upon, something distinct from himself.
    As for angels, they are not composed of form and matter, but they are presumably composed of essence and existence and act and potency.

    July 15, 2006 — 18:07
  • Kevin,
    I don’t have the energy to respond properly, but are you suggesting that creation out of nothing is a miracle? If a miracle involves the suspension of nat’l laws, and natl’ laws are gruunded in dispositions of natural things, then prior to the creation of space-time-matter there are no nat’l laws to violate, hence no miracles.

    July 15, 2006 — 18:12
  • Bill, you say,
    “Suppose instead that God acts timelessly to bring about a finitely old universe whose first interval is past-open”.
    I confess to having no idea at all what it might mean to ‘act timelessly’, to do something that takes no time. And I doubt that the phrase is meaningful simpliciter. No matter. The logic of the problem does not require meaningful talk. It is still true that timelessly creating contingent objects is creating them in a way that also violates ex nihilo. For there are no contingent objects prior to the timeless creation of contingent objects. How could there be? So you have this dilemma: if the creation of contignent objects is timeless, then there is a violation of ex nihilo and if the creation of such objects is at some instant in the interval (really, the only interpretation that makes any sense) then we again have a violation of ex nihilo. So there is no avoiding the ex nihilo problem.
    Incidentally, the same problem plagues Quentin’s argument. The realization of contingent objects on his view also must begin at some instant k in the interval (n,m] such that k is earlier n and there is some l such that (n is earlier than l is earlier than k). So his naturalistic solution to this problem is not going to work either.

    July 15, 2006 — 21:03
  • “must begin at some instant k in the interval (n,m] such that k is earlier n and there is some l such that (n is earlier than l is earlier than k). So his naturalistic solution to this problem is not going to work either.”
    I’m sorry, I meant some k such that k is *later than* n . . .”

    July 15, 2006 — 21:07