[This is the third installment of my worrying a certain bone. In the first portion, I presented the claim that the Einsteinian theory of special relativity (ESR) entails certain oddities which compromise either the veracity of truth or the realism of ESR. In the second portion, I elaborated on this position and explained why, in conjunction with Einsteinian general relativity (EGR), I think it presents a major problem for materialism. In this third but––don't get your hopes up––probably not final portion, I revisit some rough spots in my argumentation thus far and sharpen my claim that the universal truth of ESR-EGR undermines materialism or itself in a materialist metaphysics. In short, the speed of truth is faster than the speed of light.]
I am a naïve boy from a reclusive, Stone-Age tribe; you are a scientifically informed child of a leading astronomer in Manhattan. One day we enter that age-old debate: “Does the light stay on inside the refrigerator when we close the door?” In my ignorance, I assert that it does not turn off. After all, right up to the moment we close the door, we see the light shining. We both agree that there is no “gremlin” in the fridge to turn the light on and off. Based on your knowledge of the theory of electricity and switches (ignoring for now, for the sake of analogy, our ability to find the switch and depress it while the door is open), you confidently deny the light turns off when the door closes. I ask you how you know that is true. There is no way, after all, of looking into the fridge while the door is closed; we in one frame of reference are empirically forbidden such vision into another frame of reference. One of us is right and one of us is wrong simply because at the moment we make our respective claims, there are grounding conditions inside (and about) the refrigerator which validate, or invalidate, one of our claims. One of us is actually right only if those grounding conditions (viz., the door is depressing a trigger in the refrigerator which breaks the circuit and deactivates the bulb) are actually the case at the very moment we make our competing claims.
I want to apply this scenario to ESR this way: A naïve observer assumes the Sun we see (the phenomenal Sun, call it p-Sun) just is the Sun itself, das Ding an sich. A scientifically informed observer, however, denies that p-Sun portrays the actual condition of the Sun when we imagine it in outer space (i.e., the objective Sun, or o-Sun). The closed refrigerator door parallels our inability in our frame of reference (frP) to observe directly the o-Sun “up close” in its own frame of reference (frO). The depressed switch and the theory of electrical circuits corresponds to time dilation and ESR.
The grounding conditions for the truth of our deflation of p-Sun in frP (based on our theoretical knowledge of o-Sun in frO) must 'be the case' in both frP and frO––and hence, during a coterminous span of time in relativistically divergent frames of reference––in order for our claim about p-Sun to be true when we assert it. If there is a 'theletic lag', similar to the 'photic lag' which accounts for the empirical divergence between p-Sun and o-Sun, then our deflation of p-Sun would not be true when we assert the truth of p-/o-Sun divergence on ESR. If the grounding conditions for our deflation of p-Sun were not simultaneously 'the case' at the moment of deflation in frP (call this time td-P), then our deflation would be objectively ungrounded, and thus untrue, when we assert it. The grounding conditions cannot be verified empirically, and we can't say they haven't happened “yet” (i.e., outside our frP), for if we had to wait for them to be true when we made our deflation of p-Sun at td-P, then the deflation would be true only once the grounding conditions had so to speak caught up with the grounding conditions for our perceptions in frP; in which case our deflation in frP would be not yet be true when we assert it. Any further revision of our claims about o-Sun, even if serially repeated hundreds of time a second (like a “streaming” online video based on the latest available input), would still not be true at td-P, since there would always be a relativistic lag, or saptiotemporal disparity, between the actual grounding conditions in frO and our description of them in frP.
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[Now for those of you who think I never have a “dark night” of the intellect, and am oblivious to difficulties in my own position(s), check out what I wrote a couple days after posting the first two portions of this argument:]
Upon further reflection, I am reluctant to say truths like 'A is A' or 'A is not not-A' are incompatible with materialism, since the ontic identity of any object with itself is, by definition, a material reality; or at least it is a truth which is just as true everywhere in material reality as it is in abstraction. … Does not that, then, allow for analytic truths to be similarly materialized? Hmmm, this might be the Achilles heel of my argument as it stands: any analytic truth can be actualized in material reality––after all, we find them all the time in 4DST––so material reality can and does instantiate such truths at all points in 4DST. Until I sort this out better, I need to stick closely to Adler's and Ross's arguments about the incapacity of the physical exhaustively to instantiate pure functions, universals, and abstract truths. …
[I faced a similar objection in the comment box of the second portion, an objection which led to the quandary above. Granted, this perplexity did not stop me from moving ahead with some adjustments:]
But as I reflect even further, perhaps this is not a decisive problem for my argument. My argument is that certain kinds of truth require 'being the case' and having proper grounding conditions at all points in the spacetime continuum. This means that some grounding conditions in actual 4DST must be the case all at once everywhere, which, however, is an impossibility on a materialist reading of ESR-EGR. The only way for one set of universal grounding conditions to be the case––and thus to validate the spatiotemporal universality of certain truths––is for them to be the case instantaneously in all frames of reference (i.e., wherever the truth could be said to hold and does hold). The universality of some truths requires their being instantiated (actualized by relevant grounding conditions) spatiotemporally as widely and coterminously as they hold propositionally. Some truths, in other words, unify the spatiotemporal prevalence of their grounding conditions with the conceptual breadth of their propositional content.
Let me restate that for emphasis and clarity: I recognize that some truth claims, probably most (?), are propositionally 'one' with the spatiotemporal occurrence of their grounding conditions. My only objection to a wholly materialist theory of truth is that, since there is no way for material grounding conditions to be “everywhere all at once” according to ESR-EGR, while there is obviously a way for some truths to be true everywhere all at once, the universality of truth, and our grasp of it, is universally present in a non-material way. Insofar as the curvature of 4DST is a function of its 'contained' matter, the instantiation of some truths as wholly material realities would require an 'invariant' deformation of 4DST by all matter, which is impossible on ESR-EGR.
[I realize I really need to read R. Nozick's Invariances for a sophisticated look at this very issue. In time, in time, Deo volente…]
For a truth to be the case everywhere in the cosmos requires enveloping the entire cosmos in one ultimate frame of reference frΩ, otherwise it could not be observed as a materially real event in 4DST. We would, in other words, have to be able to step outside the bounds of 4DST in order to view the grounding conditions of certain universal truths as holding throughout all of 4DST. This is of course impossible to accomplish materially. But since we can in fact 'observe' (i.e., conceive of) the universality of grounding conditions for certain universal truths, we manage to step outside the bounds of 4DST in a non-material way. For if matter were able to 'escape' the confines of 4DST, it would no longer be the determinative factor for the curvature of 4DST 'around' it, and thus EGR would be false. Insofar however as some truth––notably, ESR-EGR––is 'observed' in this way, we seem to have access to frΩ, in defiance of our own spatiotemporal finitude. Grasping the truth of ESR-EGR both requires and enables us to transcend its materialistic implications.
Let me present one of the numerous corroborative quotations I am preparing for the fuller, and perhaps some day final, version of this essay. On page 45 of The Quantum Enigma, Wolfgang Smith writes, “If it be the case… that mathematical forms are not existentiated in the physical domain with “absolute fidelity”, it does not follow by any means that they are not existentiated therein at all. … If the physical universe did not somehow embody or reflect mathematical forms, it would be simply unintelligible, and physics would not exist.”
Smith's point here serves as an analogous reply to the objection that immaterial acts and truths cannot be materialized, or, if they are materialized, then such acts and truths are eo ipso material. A controversial but now well recognized feature of physics is that mathematical physics is idealized (cf. Cartwright, Ellis, et al.): matter never wholly or perfectly “performs” mathematical functions, and yet mathematical truth does manifest itself in the physical scope. For example, while it is true that E=mc^2 and F=ma, these functions are never perfectly realized in nature, since a perfect conversion of matter into energy “leaks out” due to entropy and friction retards perfectly smooth acceleration, respectively. Likewise, while the intellect is not wholly materialized, and thus escapes the complete 'grasp' of matter, as idealized laws do, yet it is active in the material world similar to the way the truth of physical laws escape being wholly 'grasped' in 4DST. Indeed, the physically incomplete presence of mathematical truth seems to find its partner, or rather, catalyst, in the physically transcendent agency of intellection. The intellect is thus nothing less than the partially-physical power in human nature by which we wholly grasp the partially-physical immanence of mathematical truth. Were there no such agency, we would have no power to grasp such truth, since, again, matter itself does not perfectly existentiate pure theoretical truth. “The 'thing-in-itself' is for the atomic physicist, if he uses this concept at all, finally a mathematical structure.” (W. Heisenberg, Physics and Philosophy, p. 91, as cited in The Quantum Enigma, p. 72.) I explored this train of thought recently in this post.
Let me close with one more quotation from Smith (Enigma, p. 79):
“With the advent of Einsteinian relativity, … the space-time continuum carries a geometric structure which both affects and is affected by the distribution of matter it is said to contain. Space and time, therefore, prove to be inextricably connected with the material entities and events which make up the physical universe; in short, content and container have lost their independent status, and it now appears that space, time and matter… do but constitute distinguishable aspects of one and the same reality. It follow, moreover, that the reality as such is neither space, time nor matter, nor indeed can it be contained in space or time; for it is ultimately the reality itself that in a sense “contains” space-time––even as a cause may be said to “contain” its effects. … As Henry Stapp has expressed it, “Everything we know about Nature is in accord with the idea that the fundamental process of Nature lies outside space-time… but generates events events that can be located in space-time.” [cf. footnote 4]
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In the first portion, I alluded to James Ross's essay [PDF!] about the annihilation of the cosmos in St. Thomas Aquinas' doctrine. Ross argues that there could be no “moment” in which the universe was annihilated, since there is no absolute time in which the annihilation of the universe could be chronicled. This does not, however, mean the universe could not be annihilated as a whole, only that such an annihilation would be a non-temporal (and thus non-natural) event. But surely this is just to recall that cosmic annihilation, like cosmic creation, is nothing less than a divine and supernatural action. Just as creation did not take place in tempore, so annihilation will not take place in time, at some single moment. All that the doctrine of eschatological annihilation requires is that every point in 4DST be effected together, under one causal 'heading,' as it were, albeit in a temporally immeasurable manner. For the annihilation of the spacetime continuum means nothing less than the annihilation of time; therefore it could not even in principle afford a temporal measurement, the conditions for temporal quantity being nullified in the very act of supernatural annihilation.