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Thomas E. Vaughan
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I wonder whether you might find interesting a peculiar idea that is related to identity and perhaps even to the matter of self-identity. Your post reminds me specifically of an idea from the interface, in physical theory, between quantum mechanics and statistical mechanics: That two physical things might be so radically indistinguishable as for their being swapped not to count as a different state of the system of which they are part. For example, suppose that in a certain system there are two marbles and three locations, each of which can hold a single marble. The system is such that, in the absence of intentional interference, each marble will quickly fall into one of the three locations and linger nowhere else. How many stable states are possible for this system? Let the marbles be M1 and M2, and let the locations be L1, L2, and L3. Then we have the possible states S1, S2, S3, S4, S5, and S6. S1 = M1 at L1 and M2 at L2. S2 = M1 at L1 and M2 at L3. S3 = M1 at L2 and M2 at L1. S4 = M1 at L2 and M2 at L3. S5 = M1 at L3 and M2 at L1. S6 = M1 at L3 and M2 at L2. In classical mechanics, even if M1 and M2 were intrinsically indistinguishable, so that nothing intrinsic to M1 or to M2 could be used to tell them apart, there would still be six possible states. After all, one could distinguish M1 and M2 by something extrinsic, such as their initial locations. In this case we might arrange the marbles so that one is at L1 and the other at L2. Then we distinguish between S1 and S3 by reaching in a hand, grabbing the marble at L1, reaching in another hand, grabbing the marble at L2, and then manually swapping their positions. By keeping an eye on the system as it continuously changes configuration during this process, one knows that S1 and S3 are distinct states. However, treating this system as it would be in quantum mechanics, one finds that, if there be particles that are intrinsically indistinguishable, then there is also no extrinsic way in which to distinguish them: There are only three different states. What classically are the distinct states S1 and S3 are indistinguishable in quantum mechanics. So, too, for S2 and S5; and for S4 and S6. Instead, quantum mechanically, there are only three states, QS1, QS2, and QS3. QS1 = M at L1 and M at L2. QS2 = M at L1 and M at L3. QS3 = M at L2 and M at L3. If M were an electron instead of a marble, then in a quantum-mechanical description of a system, every electron is so absolutely identical to every other electron as that exchanging the location of any pair whatsoever does not count as a different configuration of the system. Now one might be tempted to ask, Why should one care about this obscure detail of quantum mechanics? An answer is that the observational results of thermodynamics can be predicted by way of statistical mechanics only if one assume that identical fundamental particles are radically identical. The number of states available to a system is a key concept upon which many a result from statistical mechanics rests; in fact the theory agrees with real-world measurements only under the assumption that fundamental particles like electrons are radically indistinguishable. Maybe I'm hung up on nothing, but, to this day, I am still struck by the apparent insanity of the quantum-mechanical idea. I still remember my sudden realization of this, when I was a second-year graduate student. I was sitting at a desk in the peace and quiet of the physics library in the Spring of 1992. I was reading a passage in which the author was discussing the history of statistical mechanics. When I came to the part about how the theory's success hinged on the assumption that the exchange of two ("identical") particles did not count as a different state of the system, my jaw dropped. It's as though there must really be only one electron, somehow mysteriously multiplied to occupy different locations in the system. On the one hand, there seems really a numeric plurality, for, according to the theory, the total electric charge in the system due to the electrons is as it would be if there were many, but, on the other hand, there seems also to be the lack of a fundamental sense of plurality, as if in a sense there is really not a distinction between one electron and another in the system.
BV, Yes, it seems that there is too much in what I labeled "1" above. I suppose that one will never be able to produce an argument rationally compelling by your standard, but this is a fun exercise. Here is a different, second argument (A2, perhaps). Among all whatnesses, consider B, actual being itself. Every non-B whatness W has one of three relationships to B: A whatness Wn is necessarily joined with B, so that a thing of type Wn must actually be. A whatness Wp is potentially joined with B, so that a thing of type Wp might or might not actually be. A whatness W0 could never be joined with B, so that a thing of type W0 could never actually be. Whatever has parts joined together has a cause of composition. Of type Wn or Wp, a thing that actually exists has a cause. (2, 3)
BV, Here is an argument. [0. What has being of itself cannot fail to be.] 1. Anything contingent in the sense of D2 does not have being of itself but rather either receives being, if it exist, or else does not receive being, if it exist not. 2. The universe is contingent in the sense of D2. 3. The universe exists. 4. Therefore, (by 1, 2, and 3) the universe is the recipient of being. 5. Whatever receives being is caused by what gives it being. 6. Therefore, (by 4 and 5) the universe is caused.
BV, You wrote to Elliot that "modal contingency does not entail existential dependence". I'm trying to understand what you mean exactly. If your first quote from Garrigou-Lagrange were rendered, "every contingent[, actual] thing, even if it should be ab aeterno, depends on a cause which exists of itself", then would the addition of "actual" change his claim at all? I think that it would not, for he is implicitly speaking only of actual, contingent things when he insists that each of them must have a cause.
BV, Right. Starting from your definition of contingency, one does not deduce that there is a distinction between essence and existence. I did not mean to suggest that deduction, but your reading of my poor wording was a fair interpretation. What I was rather trying to get at is this: If one begin (as Garrigou-Lagrange presumably begins) from the principle according to which every actual thing apart from God is a composite of essence and existence, then D2 implies that every contingent, actual thing has a cause, for the only kind of thing that can satisfy D2 is one whose essence might or might not be composed with an act of existence and if a thing be so composed (and therefore actual), then it has at least the cause of this composition as its cause (though it might have other causes as well). It seems to me that Garrigou-Lagrange's claim just boils down to this. A wider claim that he would seem likely to make, for the same reason, is that every actual thing apart from God has a cause. Among actual things apart from God, there might be some necessary things as well as some contingent things. Even if the universe were so unified as to render the apparent distinctions among things in the universe illusory---so that the universe need not have a cause of composition to unite the things that appear to the senses as distinct actualities---the universe's contingency would still imply (for one who starts from the distinctio realis) that the universe must have a cause. So it seems as though you're really poking at whether the distinctio realis implies things (such as that every contingent being must have a cause) that you might not buy. Is that a fair reading of what (among other things) you are doing here?
Is not D2 really the same as saying that every contingent thing is the composite of an essence and an act of existence? If it actually exist, then, as contingent it might not have existed, as what binds essence and existence together might not have done so. If it do not actually exist, then it corresponds to an essence that is in potential to an act of existence. Viewed as necessarily a composite of essence and an act of existence, every contingent thing must have a cause that brings unity to its parts. There could on this view perhaps be things that are dependent and yet not contingent. For example, if there were a necessary composite of act and essence, then it would not be contingent, but it too must be caused, for the same reason according to which a contingent thing must be caused: Composition requires a cause; otherwise the parts would not be composed.
Thomas E. Vaughan is now following Bill Vallicella
Jun 14, 2012