Continual recreation

(This is a question that arose out of a talk given by Tad Schmaltz here at Wash U on the 11th.) Could it be said, given Cartesian conceptions of time, etc., of a substance that it existed just for an instant?
NB (20 Nov). Tad Schmaltz has commented on this entry in email. See the addendum.
One reason to say no is this: An instant is the analogue for time of a point in space. A point is usually said to be the terminus of an interval, and ontologically speaking a mode, meaning that if the interval did not exist its termini would not exist either.
The duration of a substance is an interval (of time). Call that interval AB. Descartes says the duration of a thing is just the existence of a thing; and the existence of a thing is just the thing itself considered as actual (or something like that) -- in any case not distinct (not even modally) from the thing itself. If we take an interval CD contained in AB then the existence of the thing in or at the instant C is the left-hand terminus of its existence (i.e. the existing thing itself) in the interval CD. It is a “mode of a mode” (i.e. a mode of the duration of the substance, which is itself a mode of the substance). On this account it doesn’t make sense to speak of existence at an instant except for a thing that exists through some interval.
Figure 1
But perhaps we can make sense of existence at an instant as a limiting case. We want to show how it is possible for God to create a substance, call it Adam, such that for some instant, which we designate by ‘A’, Adam exists at A, and for no other instant distinct from A does Adam exist at that instant -- or rather such that if Adam exists at an instant B then B is identical to A.
Start with an interval OA. Define B as the right-hand terminus of the left-hand segment defined by bisecting OA, C as the terminus etc. The point O is the common terminus of all such intervals. Descartes knows you can define objects in this way. Now we say: it is possible that God should create Adam so that Adam exists at O, considered as the left-hand (and right-hand) terminus of the "limit" of the nested intervals OA, OB, etc. The right-hand terminus of the limit is to the left of all the points A, B, C etc. But the only such point in OA is O. So we have an interval OO which is identical to its termini .
A point, then, is a degenerate case of an interval, one whose termini coincide. (Similarly a line is a degenerate surface, a surface a degenerate volume.) For Adam to exist "at one and only one instant" would be for Adam to exist only during a degenerate inteval OO.
All the tools for thinking of a point in this way are available to Descartes. What was not available, I think, was any way of constructing the line from points as is done now in real analysis. Our version of the “continuous quantity” of Aristotle is the real line, i.e. the set arrived at as the completion of the metric space of the rationals, either by the Dedekind’s method of cuts or by the Cauchy-Weierstrass method, together with the "standard" metric d(a,b) = |a - b|. Here the "points", i.e. the pairs C, D of a Dedekind cut or the sequences x1, x2, x3 … of rationals, exist as an actually infinite collection in their own right; intervals are defined as sets of points ( [0,1] = {x : 0 ≤ x ≤ 1}, etc.). If you grant that the set-theoretical constructions involved in defining the reals confer existence on the things constructed (via the existence axioms of set theory, e.g. the axiom that gives you {x, y} given x and y), then the point x = √2 exists independently of the intervals of which it is a terminus. It is not a mode of those intervals in the Scholastic or Cartesian sense.
The context of the question was the interpretation of the doctrine of continual re-creation that some people foist on Descartes: at each instant God creates the world anew, i.e. with an act distinct from the act with which he creates the world at any other instant. (I think Descartes holds the more common view that conservation is “continued” creation, i.e. that the act by which God conserves my soul today is numerically identical to the act by which he created me, where “create” means “cause to exist”, with, as Suárez says, the connotation that the thing caused to exist did not exist before the instant of creation -- whereas ‘conserve’ has the connotation that the thing caused to exist did exist before the instant or moment in which it is conserved).
To say that God re-creates the world at each instant is to say that for each point of time that we can designate there is a distinct act by which God brings the world into existence. The emphasis here is on ‘distinct’. How do we individuate divine acts? The usual means of individuation are (i) the agent (you and I cannot perform numerically the same act, unless by “you and I” is meant an individual composed of you and me); and (ii) the object (in the present case the thing created; creating Adam and creating Eve, if those are distinct individuals, are distinct acts). There may be other criteria (e.g. the intention with which the act is performed, the power that brings it about) but I don’t think any of them would come into play here.
The principal basis on which people attribute the doctrine of continual re-creation to Descartes is his claim that my existence in each of its (temporal) parts is independent of my existence at any other part. If you take parts to be intervals (in Descartes’ vocabulary, “moments”), and grant the construction of instants as degenerate intervals, then you can get from this the claim that my existence at each instant is independent of my existence at every other instant. You can’t get distinct acts from this unless you infer that "Dennis at t0" is somehow a distinct individual from "Dennis at t1"; and I should probably say actually distinct (because otherwise you need a distinct creative act for every point of a body, which isn’t a doctrine I think any one wants to attribute to Descartes). That is, you need to think of the “time-line” of my duration (= my existence = me) as an actually infinite collection of “time-points” or instants, and that I, as a substance enduring through time, am an actually infinite collection of instantaneous me’s.
What doesn’t make a great deal of sense to me would be to say that God re-creates numerically the same substance at each instant. What could the ‘re’ mean? The best I can do is something like this: think of created things as needing a “boost” from God if they are not to subside into nothingness (a view which you can pull out of Descartes’ definition of substance in Principles I). The thought then would be that God, in giving existence to an enduring substance, at each instant gives it (the same it) a new boost (like an impulse engine, only continuous, not discrete). If he didn’t give it a boost at some instant, it would not exist at that instant. The act of boosting at each instant is an act distinct from the act of boosting at any other instant, but the object boosted may be the same object in distinct acts of boosting. If to boost is to create (“cause to come into being from nothing”) then God re-creates the object at each instant.
This yields a causal reason to hold that my existence at each instant is independent of my existence at any other instant. God’s boosting me now is independent of his boosting me at some other instant. It can be used, moreover, to make sense of what Descartes says in demonstrating the second law of nature (the “tendency to move on a tangent” law).
Indeed the case of a body in curvilinear motion (where its “tendency to move” differs at each instant provides the best argument for supposing that God gives each existing substance a new boost at each instant of its existence. Otherwise I don’t see why we should multiply boosts.
The logical independence of the body’s existence through each interval from its existence at every other (disjoint) interval is not a strong reason to attribute the doctrine of continual re-creation to Descartes. If I hold up a paperweight for thirty seconds, it is logically possible that I should cease to hold it up at any time short of thirty seconds; but I don’t see any reason to affirm that there actually is a distinct act of holding for each instant during the interval through which I hold it up. (“Holding up” was one of the analogies used to explicate the claim that creation and conservation are distinct only in reason: the act by which God conserves me in existence is just the same act as that by which he created me—it is a “continued” creation.)
But in the case of a body whose motion (i.e., whose trajectory in relation to some nearby body taken to be a rest) is a curve, the “determination” of its “tendency to move” changes at each instance; & if that tendency—its “force of motion”— is given to it by God immediately, then God’s act of giving it force must change at each instant. If you take that force to be simply the “continuing to exist in the same state” proposed in Descartes’ first law of motion, then with a little more legerdemain, you can extract the doctrine of continual re-creation from Descartes’ argument for the second law. But only for bodies in curvilinear motion. Not for bodies at rest or for minds: what would be the mental counterpart of curvilinear motion?
Addendum I: Individuating actions. I said that acts may be individuated by their agents. Tad notes that in concurrence distinct agents (God & creature) operate together to produce the same act. As he suggests, I should have said “causes of the same order”. A look at Suárez confirms that I was indeed too hasty.
In his disputation on actio, Suárez concludes that all actiones, even so-called “immanent” ones (like seeing, considered as an action), have not only causal principles, but termini. In generation or creation, the terminus is the patient itself; in other cases the terminus is some quality of the agent or else its quantity. The question then is whether the principle or the terminus is “more essential to the act”, and thus to determining its species (Disputationes metaphysicæ 48§3). Suárez records four answers: (i) the principle alone; (ii) the terminus alone; (iii) both; (iv) both, together with the modus agendi. I won’t go through the arguments; I note only that Suárez settles on the second.
In his disputation on the concursus or co-operatio of the first cause with second causes, Suárez notes an argument against concurrence which begins from the fundamental claim that two agents cannot “immediately concur in the same action, unless each of them is imperfect and only partial, which cannot be said of God” (22§1no4, Opera 25:802). We could infer from this that acts could be individuated by their agents in those cases where the causality of the agent is not imperfect or partial. Suárez, however, dismisses that argument as entirely one of words rather than things (no16, 25:805).
Specification and individuation are distinct. Things of different species cannot be identical individuals, but the converse is of course false (except for angels and God). The question remains: how are actions individuated, especially actions of the same agent? In the case at hand—the creation or re-creation of the world—we have one object (or one for each instant), one terminus (or one for each instant), one agent. It still seems to me that the only way to construe continual re-creation is as the creation of a numerically distinct world at each instant: how else do you get distinct acts? But then all talk of the “duration” of a substance must be, for Descartes, a mere façon de parler.
Addendum II. For a thorough airing of the issues around continual re-creation, see Geoffrey Gorham, “Cartesian causation: continuous, instantaneous, overdetermined”, Journal of the history of philosophy 42.4(2004):389–423. (The link is to the subscription-only Project Muse site.) Gorham examines, under the name ‘continual creation’, the view that whenever a created thing exists, God causes it to exist—the conservation of the thing by God is the sole cause of its existence for as long as it exists. This is continual (or continued) creation because Descartes accepts the dominant Aristotelian view that conservation and creation are distinct only in reason. Gorham treats in some detail the reasons Descartes had for maintaining continual creation, and examines some consequences for Descartes’ theory of human freedom.

LinkNovember 13, 2004 in History of Philosophy