J. R. Lucas’ Indeterminism and Temporal Realism
Part of a Series on the Philosophy of History
Wednesday 18 June 2025 is the 96th anniversary of the birth of John Randolph Lucas (18 June 1929–05 April 2020), better known to posterity as J. R. Lucas, who was born in Guildford in Surrey, on the outskirts of London, on this date in 1929. Lucas was another philosopher who discussed the philosophy of time but who isn’t usually associated with philosophy of history. Similar to Lucas in this respect I’ve profiled Hans Reichenbach and, most recently. G. J. Whitrow, and to this list I could add Kurt Gödel, Adolf Grünbaum and a few others, including Einstein himself.
Another thing common to these philosophers is most of them — not all of them — come from a background of analytical philosophy, and as such their approach has the same kind of thoroughgoing naturalism that we find in natural science. Often these philosophers take scientific conceptions of time as their starting point, and drawing out the philosophical implications of the ideas that the scientists who proposed them often didn’t notice. Einstein’s theory of relativity gave these naturalistic philosophers a lot to discuss. But it wasn’t only Einstein. It was all the work that built on Einstein, sometimes as surprising and as counter-intuitive as the theory of relativity itself.
One of the most surprising elaborations of the theory of relativity was the work of the logician Kurt Gödel, who was a close friend of Einstein when both were at the Institute for Advanced Study. Gödel formulated a cosmological model consistent with Einstein’s general relativity in which time travel would be possible. It’s important to point out that this cosmological model does not describe our own universe. Gödel’s cosmological model isn’t expanding and it’s rotating somewhat rapidly, but the philosophically important point here is that our universe is only contingently different from Gödel’s cosmological model.
Gödel’s rotating universe is contingently different from the spacetime structure of our universe, but he didn’t see the two cosmologies as differing in terms of laws of nature. Part of Gödel’s argument involves the claim that the same laws of nature would hold in his rotating cosmological model as hold in our expanding universe, and he made this argument because he wanted to show that, as in the works of the idealistic philosophers he studied, like Leibniz and Kant, time is ideal, and not real. In a recent paper, “Can Rotation Solve the Hubble Puzzle?” by Balázs Endre Szigeti, István Szapudi, Imre Ferenc Barna, Gergely Gábor Barnaföldi, the authors explicitly cite Gödel’s rotating universe as an inspiration, but their model avoids closed timelike curves, and was intended to resolve the Hubble tension, that is to say, the difference in measurements of the Hubble constant made by different methods. In short, their universe rotates too slowly to sufficiently tilt a light cone into a closed timelike curve, but I think Gödel would have been interested to know that his cosmology continues to be an influence and an inspiration.
I said that the scientific philosophers I’ve mentioned in connection to the philosophy of time have been naturalistic thinkers. Gödel obviously can’t be counted among their number. But it’s not that Gödel was non-naturalistic in the traditional sense, by which I mean that he didn’t deny the reality of the physical world studied by the natural sciences, though he did deny the reality of time. His method was naturalistic to the point that he mastered the natural sciences of his time and used his mastery of these bodies of scientific knowledge to argue for unexpected and counter-intuitive positions.
In Gödel’s later years he was a careful reader of Husserl, frequently citing Husserl in his writings. I’ve mentioned in my Husserl episodes that Husserl did have an explicitly non-naturalistic outlook, and this was increasingly an influence on Gödel. My previous episode on G. J. Whitrow prompted me to read Palle Yourgrau’s A World Without Time, which focuses on Gödel’s work in relativistic cosmology and his denial of the reality of time. It’s difficult for me to give a fair sketch of this book since there are parts of it with which I am enthusiastically in agreement, and I’m pleased to see someone discuss these things explicitly. On the other hand, I sharply disagree with many of the conclusions drawn. In any case, I recommend the book. It’s well written, it’s an easy read, and the argument is interesting.
The meat of Yourgrau’s book can be found in chapters 4 and 7, respectively titled “A Spy in the House of Logic” and “The Scandal of Big ‘T’ and Little ‘t’,” and which are respectively concerned with Gödel’s incompleteness proofs and his rotating universe cosmology. I think we can safely say that Gödel’s cosmology is radically different from the world that we live in, but his point was that his cosmology pointed to a denial of the reality of time, and this conclusion constitutes a step beyond what relativity theory taken alone entails. If we only take the first step of relativistic cosmology, and don’t take the second step, which was Gödel’s step, we still have a universe with time, even if we’re forced to revise our intuitions about time. But there’s a tendency to over-state how radically relativity theory requires us to revise our conventional views of time.
Einstein himself isn’t guilty of this, and in fact I wrote a blog post years ago in which I characterized Einstein’s conservative claims for the theory of relativity in relation to its radical consequences, and I contrasted this to the radical claims for other theories that have relatively conventional consequences. Einstein didn’t need to engage in the theoretical equivalent of attention-seeking since he understood how fundamental his results were. Interestingly, Yourgrau credited a similar attitude to Gödel. Yourgrau wrote that:
“…in his published writings he aimed for maximum precision and minimum controversy, stripping down his contributions until only the bones were left — that is, until all that remained was what was most amenable to rigorous demonstration and unavoidable philosophical interpretation.” (p. 183)
However, Einstein did favor thought experiments, and sometimes thought experiments can suggest interpretations of ideas that have been otherwise given a conservative exposition. Thought experiments can be powerful — Daniel Dennett famously calls them “intuition pumps” — but this cuts both ways. Thought experiments can powerfully advance our thinking, but they can also powerfully mislead us. A lot of people don’t know, for example, that the Schrödinger’s Cat thought experiment was introduced to show that quantum theory is ludicrous, and now the Schödinger’s Cat thought experiment is invoked as though it were intended to justify quantum theory.
Einstein used the thought experiments of moving trains and lighting strikes on the embankment of the train tracks, suggesting that at this level of human observation we could see a potential reversal of the time order of events due to the relativity of simultaneity. But it’s only possible to observe the reversal of the temporal (or historical) order of events when these events are “spacelike separated,” to use the language of relativity theory, and nothing along a railway line is spacelike separated. Indeed, nothing within the Hubble sphere is spacelike separated. The Hubble sphere is a construct related to the idea of the observable universe, but the two aren’t exactly the same thing. The Hubble sphere is a bubble around every observer defined by the maximum distance from which the observer can receive light. If follows from the definition of the Hubble sphere that everything within the Hubble sphere is causally connected, in at least the minimal sense that the past light cone of any event within the Hubble Sphere overlaps with the past light cones of other events in the sphere.
In this way, events in the distant past of the universe can still be rippling outward into the cosmos and affecting us all billions of years later, meaning that we are causally connected even to very distant events. Only causally disconnected events, that is to say, events whose past light cones don’t overlap, can be perceived as having a different temporal (or historical) order. Here’s where the Einstein train thought experiments can be misleading. No two observers could communicate their different observations of the order of events, so that asserting that observer A sees x precede y while observer B sees y precede x is a construction as ideal as a claim of the same two observers sharing in a universal simultaneity.
I’m not saying that relativity theory is wrong, I’m only saying that the train thought experiment can be misleading, but we can do thought experiments of our own to try to correct this misimpression. We can start to gain an intuitive sense of the spectacularly counter-intuitive result of the relativity of simultaneity and the relative order of events in time by engaging in a thought experiment. Suppose we imagine ourselves as being so enormous we could hold the entire Hubble sphere in our hand, like a snow globe as large as the universe, only, instead of snow swirling inside, it’s stars swirling inside the Hubble sphere. Imagine you’re holding the Hubble sphere, and it’s like a crystal ball in your hand, and you can see inside it — assuming you have four dimensional vision — all the events that make up the history of the universe. You look into the Hubble sphere turning it this way and that, and as you turn it you see the events in the Hubble sphere from radically different perspectives, so that sometimes events seem to have a certain sequence and from other angles the same events seem to have another sequence. But you can only do this if you’re so far outside the Hubble Sphere you can view it in this way.
If you’re inside the Hubble sphere, you can’t take this perspective on events within the Hubble sphere. And because you’re causally disconnected from this perspective from outside the Hubble sphere, and no signals can be exchanged between those inside and those outside the Hubble sphere, you can’t communicate with an observer who has this perspective, and the observer who has this perspective can’t communicate with you. So that’s a little digression on the weirdness of relativity theory, and the even greater weirdness of using relativity theory to argue for the non-reality of time, as Gödel did.
Interestingly, J. R. Lucas is also something of an exception to the naturalistic rule of analytical philosophers of time. Again, like Gödel, he’s not openly non-naturalistic. Like Gödel, he is thoroughly conversant with natural science, and in fact many parts of his book A Treatise on Time and Space is rather more technical than G. J. Whitrow’s A Natural Philosophy of Time. He delves deeply into relativity theory, though he doesn’t come to the same conclusions as Gödel, that is to say, he doesn’t deny the reality of time. One of the reasons I wanted to talk about Gödel’s interpretation of relativity in this context is to contrast his views to those of Lucas, to highlight the clash of philosophical traditions that was going on especially in the twentieth century.
While Gödel’s denial of the reality of time seems eccentric to us today, it is, in fact, the default view of most Western philosophy until quite recently. I mentioned the influence of Leibniz and Kant on Gödel, but the denial of the reality of time in Western philosophy goes back at least to the pre-Socratic philosopher Parmenides, and it receives its most famous and its most influential formulation in the philosophy of Plato. One of the most distinctive features of Plato’s philosophy is its denial of the reality of time. Plato called time “the moving image of eternity,” and held that the Forms, the only things that are truly real, are outside time. The cost of this maneuver is to erect a distinction between reality and appearance, and time and everything temporal is held to belong to mere appearance, and not to reality, thus the distinction between reality and appearance has been one of the great themes of metaphysics in Western philosophy.
This tradition remained almost intact up until the end of the nineteenth century, and it still had its representatives in the early twentieth century. Bertrand Russell in his 1914 lectures published as Our Knowledge of the External World called this the “classic tradition” in philosophy. Of this classical tradition Russell said: “The classical tradition in philosophy is the last surviving child of two very diverse parents: the Greek belief in reason, and the mediaeval belief in the tidiness of the universe.” His primary target was F. H. Bradley, perhaps the best known of the British idealists at the time. Bradley’s chief work was titled Appearance and Reality, and in consonance with the classical tradition, it denied the reality of time. His contemporary J. M. E. McTaggart, whom I profiled last year, built much of his metaphysics around the denial of the reality of time. Russell also, many years later, wrote:
“Gödel turned out to be an unadulterated Platonist, and apparently believed that an eternal ‘not’ was laid up in heaven, where virtuous logicians might hope to meet it hereafter.” (Autobiography, Volume II)
But Russell himself, despite having criticized what he called the classic tradition as well as having ridiculed Gödel for his views, still retained something of the devaluation of time that we find so often in Western philosophy. Russell wrote:
“…there is some sense — easier to feel than to state — in which time is an unimportant and superficial characteristic of reality. Past and future must be acknowledged to be as real as the present, and a certain emancipation from slavery to time is essential to philosophic thought.”
I previously quoted this in my episode on G. J. Whitrow since it’s such a perfect evocation of a philosophical disdain for time that reaches far beyond the classical tradition. I’ve said that both Gödel and Lucas departed from some of the expected positions of philosophical naturalism while not being out-and-out non-naturalists. Where they differ, among other positions, is that Gödel was part of what Russell called the classical tradition, and Lucas was not. Lucas represents a growing willingness to take time as reality, and not as mere appearance. This reconciliation of the tradition of Western philosophy with the reality of time has been slow and gradual. Today we have philosophical works that are frankly metaphysical, but which instead of using metaphysics as a tool to deny the reality of time, as in the classic tradition, they use the tools of analytical metaphysics for the exposition of time as a fundamental reality of the world. I have a couple of books like this in my library. For example, Past, Present, and Future by Irwin C. Lieb and A Survey of Metaphysics by E. J. Lowe.
Lucas preceded these works, and, in a sense, made them possible by making the philosophical analysis of time as a reality respectable. This I characterize as the naturalistic aspect of Lucas’ thought. But one aspect that distinguishes Lucas’ work from the pervasive philosophical naturalism of our time is his theological interests. His book A Treatise on Time and Space both begins and ends with theological concerns. The book opens thus:
“Time is more fundamental than space. Indeed, time is the most pervasive of all the categories. Some theologians say that God is outside time, but it cannot be true of any personal God that he is timeless, for a personal God is conscious, and time is a concomitant of consciousness. Time is not only the concomitant of consciousness, but the process of actualization and the dimension of change.”
Here Lucas not only immediately introduces us to a relationship between his philosophical inquiry and theology, he also sets the tone by introducing time as fundamental, even more fundamental than space. In terms of the classical tradition, this is heresy, but it’s Lucas’ starting point. And Lucas concludes A Treatise on Time and Space with a discussion of eternity. This also reveals his heterodoxy vis-à-vis the philosophical tradition, what Russell had called the classic tradition. Lucas notes that a distinction is often made between understanding eternity as an infinite extension of time and understanding eternity as timelessness, but he wants to go even farther than this, asserting that eternity is even beyond timelessness:
“Eternity is not timelessness. For eternity is an attribute of God, and God is a person, a conscious personal being, and time is an inevitable concomitant of consciousness (see § 2, pp. 8–9). To say that God is outside time, as many theologians do, is to deny, in effect, that God is a person.”
Lucas’ interest in eternity, then, seems to reflect a desire to show a condition that lies beyond time but which is not timelessness because a personal being involves temporality. God as a personal being who is also eternal requires a definition of eternity distinct both from infinite time and from timelessness. Lucas further develops his theological themes in his book The Future: An Essay on God, Temporality, and Truth. This book began as the 1981 Margaret Harris Lectures on Religion. Lucas makes many interesting arguments in this book, as his A Treatise on Time and Space. The first chapter, “Time and Reality,” is, again, an openly metaphysical discussion of time as a fundamental reality. But there’s an interesting wrinkle here — for example:
“It is a deep metaphysical fact that though in our bodies we are time-bound, in our thoughts we are not. I, my mouth, my body, my hand, am imprisoned in the twentieth century. But my mind is free to range over all time. I can imagine myself having a nasty encounter with a dinosaur in the Jurassic age, viewing the battle of Marathon, listening to a speech by Pericles, addressing the United States Congress in 2020 AD, witnessing the final inauguration of peace upon earth, having difficulty in explaining myself on the Day of Judgement. I am in my mind’s eye a spectator of all time, and therefore all time, when I contemplate it philosophically, must, it might seem, be on a par, every part of it possessing the same philosophical properties.”
Lucas also writes, further elaborating this theme:
“…although I am in my mind’s eye a spectator of all time, this is not to say that all time is, either in my view or sub specie aeternitatis, the same, but that each needs to be viewed not just from my standpoint, but from its, and in its own particularity.”
A charitable interpretation of the Bertrand Russell quote I cited earlier is that this is, in essentials, what Russell meant when he said that, “…a certain emancipation from slavery to time is essential to philosophic thought.” Be that as it may, Lucas’ claim that, in thought, we are free from time, gives him a way to set aside the seemingly deterministic implications of the theory of relativity, especially as interpreted by Gödel. Methodologically, what Lucas is doing here is quite close to Yourgrau’s line of argument in his book on Godel’s world without time, since Yourgrau several times points out the importance of keeping the intuitive grasp of anything distinct from its formal capture in mathematics or science. Yourgrau wrote:
“Gödel’s overarching ambition throughout his career consisted in the attempt to establish, by formal means, the limits of formal methods in capturing intuitive concepts.”
I completely agree with this, and I see Lucas as doing the same thing, though calling it by a different name, but, more importantly, drawing the opposite conclusion from that of Gödel and Yourgrau, and I have to say that, on this, I’m on board with Lucas’ interpretation of the implications of the methodology to which both parties appeal. It seems to me that the obvious application of Yourgrau’s claim when it comes to the theory of relativity is the need to establish the limits of formal scientific theories, like the theory of relativity, to capture our intuitive concepts of space and time. I think Yourgrau held this view, too, but, again, he took it in a very different direction than did Lucas, in his different formulations.
Lucas concludes his book on the future by explicitly drawing out the theological implications of God being a personal God, with personhood entailing some kind of temporality. The last chapter is titled, “The Vulnerability of God,” which is as counter-intuitive as anything claim made by Gödel. In it Lucas writes:
“God is temporal, though not merely that. Although we can properly say that God is more than merely temporal, that He transcends time, and to that extent is beyond and outside time, we cannot say that He is timeless, or that for Him there is no difference between future and past.”
He knows that he’s arguing against established tradition, and he explicitly takes up the challenge in arguing his position. I have no idea how orthodox or heterodox Lucas is in relation to contemporary theology, but what he’s arguing lies far outside the tradition of philosophical theology, and is points to how far Lucas was willing to go in integrating time into fundamental reality.
One of the interesting unconformities in Lucas’ thought is that one of the most influential papers he wrote was about Gödel — “Minds, Machines, and Gödel” (1961) — but it wasn’t about Gödel’s rotating cosmology, much less about the use of relativity theory to argue for the denial of time. This paper was about applying Gödel’s incompleteness theorems to the view that the human mind is a mere mechanism. At the end of the paper Lucas doesn’t hold back, drawing out what he sees as the moral implication of Godel’s incompleteness theorems:
“…now, though many arguments against human freedom still remain, the argument from mechanism, perhaps the most compelling argument of them all, has lost its power. No longer on this count will it be incumbent on the natural philosopher to deny freedom in the name of science: no longer will the moralist feel the urge to abolish knowledge to make room for faith. We can even begin to see how there could be room for morality, without its being necessary to abolish or even to circumscribe the province of science. Our argument has set no limits to scientific enquiry: it will still be possible to investigate the working of the brain. It will still be possible to produce mechanical models of the mind. Only, now we can see that no mechanical model will be completely adequate, nor any explanations in purely mechanist terms. We can produce models and explanations, and they will be illuminating: but, however far they go, there will always remain more to be said. There is no arbitrary bound to scientific enquiry: but no scientific enquiry can ever exhaust the infinite variety of the human mind.”
Lucas thus uses Gödel’s incompleteness theorems to argue for the indeterminism of human thought as a manifestation of free will, and human free will requires an indeterministic universe, thus the antithesis of what Gödel argued in regard to relativity and cosmology. So although Lucas saw himself as unraveling one philosophical dilemma — the dilemma of deterministic science versus autonomous moral agents — he has effectively introduced a new philosophical dilemma, and that is between Godel’s indeterministic incompleteness theorems and his deterministic cosmology. There is at least one way out of this dilemma, which would be to argue for what is known as compatibilism, that is, that free will is compatible with determinism. I’m not going to talk about the compatibilist view, except to say that I don’t think that either Gödel or Lucas was a compatibilist.
As we’ve seen, Lucas is what we could call a temporal realist, while Gödel denied the reality of time. On this point, they occupied antithetical philosophical positions. But Lucas drew on Gödel to offer a rigorous demonstration of his indeterminstic worldview. Lucas’ paper on Gödel was widely read and widely attacked. For example, Paul Benacerraf wrote an almost equally influential paper against Lucas, “God, the Devil, and Gödel” in which he says: “I come to a rather different conclusion from Lucas concerning what implications Gödel’s incompleteness theorems have for mechanistic philosophy.” There’s an enormous literature surrounding this paper, so if it sounds interesting to you, by all means dive in, but I won’t attempt to survey it now.
Is there any way that we can bring together the apparent indeterminism of Gödel’s incompleteness theorems as they bear about human free will, if indeed they do, with the strong determinism of Gödel’s deterministic cosmology and denial of the reality of time? I don’t know, but it would be an interesting problem to pursue, and it has implications for philosophy of history on many levels, as we always find when we look at philosophies of time. Here we have philosophies of time mixed up with cosmology, determinism, free will, and the nature of the human mind. All of these are fundamental philosophical concerns, and all of them are relevant to philosophy of history. Their interaction both deepens and complexifies philosophy of history.
From my other episodes you may know that my own interest in philosophy of history is naturalistic, and I see the whole of human history telescoped within natural history, and natural history cannot stop short of cosmology. Therefore, the problems of cosmology we find in Lucas and Gödel aren’t merely problems for natural science and the philosophy of science. The philosophy of the natural history of the cosmos is the ultimate context of human history. We can find this in the past, when we look to the cosmological conditions that made it possible for the species like us to evolve on Earth, and we can see it in the future for the legacy we may someday have, or which a species like us, if not us, will have for the universe at large.
From a cosmological perspective, human history is dead simple. This is despite the fact that human history is one of the most complex phenomena of which we know, to the point that there is little agreement among historians on the interpretation of history. But this complexity supervenes on an underlying simplicity of the structure of time relevant to human beings on their homeworld. Everything that has happened has happened within the inertial frame defined by the Earth. When astronauts accelerate away from Earth, they and their spacecraft define a new inertial frame of reference, although, to date, all astronauts have returned to Earth, and none have traveled fast enough for time dilation to be apparent. We have devices of sufficient precision that we can measure time dilation, and we’ve had these instruments for decades.
In 1971 the Hafele-Keating experiment measured time dilation by installing atomic clocks on commercial airliners, and found time dilation measured in nanoseconds — not enough to be noticed by a conscious observer, but enough to be registered by atomic clocks. If astronauts were to continue accelerating away from Earth, unlike all astronauts to date, the new inertial frame of reference they define would begin to diverge from Earth’s inertial frame of reference. In my essay, “The Coming Coeval Age,” about which I also produced an episode of the same title, I discussed scenarios of spacefaring expansion for humanity in which multiple centers of civilization separated by relativistic travel maintain inertial frames of reference derived from Earth at their time of departure. My point is that, if our civilization endures and continues to develop technologically for a period of time sufficient to produce technologies allowing human beings to expand throughout the cosmos, the simple unilinear history that has characterized human history to date will cease to obtain. Human history, or the history of human successors, or the history of human peers, once scattered through the universe and subjected both to extremes of acceleration and gravity, could someday reflect the complexity of the universe itself.
A philosophy of history in which time is as tangled as a ball of string, and when there are multiple human (or post-human) histories in different inertial frames of reference, will no longer be a history that can be related in a unilinear continuum. This will challenge our intuitions about history, and this challenge will force us to attain a more comprehensive conception of the history of the universe and human history within the universe. We saw that Lucas argued that, “There is no arbitrary bound to scientific enquiry.” If the development of technology is similarly subject to no arbitrary bound, we can’t event rule out the possibility that our descendants might someday transcend their universe of origin and take an external perspective on the universe as in the thought experiment I suggested earlier of holding the Hubble sphere in one’s hand. This would be an overview like no overview any human being has experienced, and it might give the observer of such a sight an intuitive if not a visceral grasp of the relativity of simultaneity — something that we will never experience if we remain on Earth and go extinct.
There are also claims in Lucas’ temporal realism that I think we will need to transcend. For example, in The Future Lucas wrote:
“…the present is peculiarly significant for the existence of time. Unless we can connect a time sequence with the present, it ceases to be real: if our only answer to the question ‘when?’ is the studiously vague ‘once upon a time’, we are not talking about real facts at all, but only fiction. Time is in this respect different from space. It is perfectly intelligible to envisage a space in which we are not located: we can understand a geometer when he draws on the blackboard, and there is no question of any point’s representing ‘here’, but not a historian who puts up a date chart on which there could be no date that is ‘now’. The fact that we cannot conceive of a time totally divorced from our own temporal existence is the converse of time’s being a necessary condition of consciousness and experience, whereas space is not.”
I don’t say that this is entirely wrong, but it requires further elaboration and clarification. I think that there is, or that there will be, cases in which it’s perfectly intelligible to envisage a time in which we aren’t located, but to spell this out in detail will be a task for another day.
