This is a guest post by Dr. Daniel Linford. You can find Dr. Linford’s PhilPeople profile here.
“The mind seemed to grow giddy by looking so far into the abyss of time; and while we listened with earnestness and admiration to the philosopher who was now unfolding to us the order and series of these wonderful events, we became sensible how much farther reason may sometimes go than imagination can venture to follow.”
John Playfair, 1797, Biographical Account of James Hutton, p. 35
1. Introduction
Deep Time was discovered in the midst of the Scottish Enlightenment. In the epigraph, Playfair recounts how geologist James Hutton led a group to an outcropping of rock — Siccar Point — where Hutton had realized that the Earth was older than Biblical chronology indicates. Deep Time is now known to extend further back than Hutton, Playfair, or anyone else in their milieu could have realized. Yet, even without the Biblical chronology, there remains the popular notion that the Universe was created by God a finite time ago. According to the Kalam Cosmological Argument (KCA),
P1. Everything that begins to exist has a cause for its beginning to exist.
P2. The Universe began to exist.
C. Therefore, the Universe has a cause for its beginning to exist.
Proponents of the KCA typically understand the Universe’s cause to be God. Nonetheless, the argument does not explicitly mention God and should have broad interest. Most educated members of the general public accept the Big Bang as the origin of the Universe, and so accept premise 2, and most members of the general public accept that things generally require causes for their coming into existence, and so accept premise 1. Unlike most educated members of the general public, I have doubts about both premises. I doubt premise 1 because premise 1 conflicts with a family of theories concerning the nature of causation (causal republicanism) that I find attractive. In my doctoral dissertation and several publications, I have previously defended the view that premise 2 cannot be known given current science. In this post, I consider a metaphysical view of time endorsed by some KCA proponents and discuss why I think, contrary to the view’s proponents, the view blocks scientific arguments for premise 2.
Some philosophically sophisticated proponents of the KCA have argued that beginning to exist requires a tensed theory of time; moreover, they have argued that, in light of the empirical success of relativistic physics, friends of a tensed theory of time ought to accept a Neo-Lorentzian alternative to Special Relativity and an instrumentalist interpretation of General Relativity. In 2021, I published an article in the European Journal for Philosophy of Science in which I argued that those adopting the aforementioned views cannot adequately motivate a scientific case for the KCA’s second premise. Recently, Matthew Damore posted his attempt to dismantle my article to his blog. I was invited by Joe Schmid to write a guest post responding to Damore.
Unfortunately, Damore’s post is riddled with confusions and technical/mathematical errors that make his post difficult to respond to in entirety, particularly given my limited time constraints. However, I harbor no ill will towards Damore; in fact, despite my misgivings with his post and his many criticisms of my own work, I want to encourage him to continue pursuing this difficult subject. My article touches on some of the most mathematically formidable areas of physics, including General Relativity, and is largely outside of the areas in which Damore might be expected to have technical competence. Luckily for Damore, there now exist several books that philosophers can read to come to a better understanding of relativity. (Some examples, at various levels of sophistication, emphasis, and depth, include volume 1 of Sean Carroll’s The Biggest Ideas in the Universe, Tim Maudlin’s Philosophy of Physics: Space and Time, Leonard Susskind and Andre Cabannes’s General Relativity: The Theoretical Minimum, Graham Nerlich’s Einstein’s Genie: Spacetime out of the Bottle, Bertrand Russell’s The ABC of Relativity, Daniel Saudek’s Change, the Arrow of Time, and Divine Eternity in Light of Relativity Theory, and Robert Geroch’s General Relativity from A to B. There’s also a forthcoming textbook on the philosophical foundations of Special Relativity by James Read.) Moreover, I would like to consider Damore a friend, even though we have previously interacted only briefly; Damore explicitly states that his post is a work in progress and invites feedback. This post is intended to provide some feedback. Given how the KCA relates to religious concerns and to perennial philosophical questions, I think many people are likely similarly situated as Damore; they might be interested in what I have to say about the KCA, but lack the technical competence to even begin digesting the issues, let alone judging the issues for themselves. Hopefully, this post provides them with a starting point for going deeper.
For that reason, instead of attempting an exhaustive reply to Damore, for the first time in a public venue, I will try to lay out some of the ideas from my aforementioned article in relatively non-technical terms. I will assume that the reader is familiar with general, undergraduate philosophy of science and that they have at least a high school level familiarity with Big Bang cosmology. In some places, I sketch a technical argument that may be difficult for some readers to understand; in those instances, I will indicate that I do not expect all readers to understand the argument. I will also comment on some of Damore’s replies to my more substantive arguments. (I will not be replying to Damore’s less substantive criticisms, such as his criticisms of my footnotes, citations, or choice in terminology, nor will I comment on most of Damore’s several mathematical/technical errors.) Since this is a blog post written for a more or less general philosophical audience, I hope I can be forgiven for not being completely rigorous.
This post includes three sections. First, I lay out a general schema that one might use to build a scientific case for the finitude of the past. As I will argue, if one cannot satisfy the schema, then there won’t be a way to mount a good scientific inference that the past is finite. The schema requires that we adopt a realistic interpretation of a relevant scientific theory; thus, unless Craig and others who adopt an instrumentalist interpretation of General Relativity can provide an appropriate alternative theory that we ought to realistically interpret, they will not be able to mount a scientific argument for the KCA’s second premise. In the second section, I argue that Craig and company have not adequately defended a measure of past absolute time. While Craig and company have identified cosmic time with absolute time, there is another candidate for absolute time — the York time — that, while answering to many similar motivations as cosmic time, places the Big Bang infinitely far into the past. Furthermore, I identify some reasons that York time might be thought to be a superior candidate for absolute time. Thus, unless Craig and company can adequately motivate cosmic time as an alternative to York time, Big Bang theory provides advocates of absolute time no good reason for endorsing the KCA’s second premise. In a third section, I show that Neo-Lorentzianism invites a form of skepticism that many philosophers will find unappealing and that undermines the use of Big Bang cosmology in supporting the KCA.
2. A General Schema for Scientifically Inferring the Finitude of the Past
According to the view that I defended in my doctoral dissertation and in a subsequent article published in Erkenntnis, showing that the Universe has a finite age is neither necessary nor sufficient for showing that the Universe began to exist. However, Craig and company disagree; on their view, if the Universe has a finite age, then, provided the truth of a tensed theory of time, the Universe did begin to exist. In this post, I will play along and assume their definition.
Most people have heard that scientists have discovered that the Universe is finitely old; according to the commonly accepted wisdom, the Universe originated in the Big Bang approximately fourteen billion years ago. However, although many people, including most philosophers, accept that the Universe has a finite age, they are not able to reproduce the reasoning that physicists utilize in order to infer the Universe’s age. Unfortunately, what most people think they know is simply not true; scientists have not made the inference that the Universe — that is, the totality of physical reality — has a finite age. Instead, scientists have made the inference that the observable universe — that is, the largest spacetime region empirically available to us — has a finite age. For all that scientists have said, there could be spatiotemporal regions that either preceded the observable universe or that are beyond our cosmological horizon; those other regions could be infinitely old, indeterminately old, or otherwise different in age from the observable universe. In my dissertation and in some of my publications, I have developed a general schema that one can use to make an empirically guided inference that either the Universe or the observable universe has a finite age. Let’s briefly review how that schema is motivated and how that schema works.
For the sake of convenience, in what follows, I will use the symbol U to represent the phrase “either the Universe or the observable universe”; the same schema can be utilized in either context, though to differing degrees of success. My schema is motivated by noting that whether U had an origin in the finite past is not directly observable. However, philosophers of science have long maintained that if we are right to adopt a realistic interpretation of a given scientific theory, then we can use that theory, in conjunction with observations, to infer the existence of unobservable entities, relations, or phenomena.
For example, consider a physicist, let’s call them Michaela, living towards the end of the nineteenth century and who is aware of the wonderful experimental vindication of the classical theory of electromagnetism by Faraday, Hertz, Gauss, Lodge, Callan, and others. Michaela is now trying to decide whether to adopt an instrumental or realist interpretation of electromagnetism.
An instrumentalist might say that while the classical theory is empirically adequate — that is, the classical theory is a tool that can be used to correctly predict the outcomes of experiments — we are not justified in endorsing the claims the classical theory makes about unobservables. Importantly, since we cannot directly observe the electromagnetic field, the instrumentalist would tell us that we ought not endorse the actual existence of the electromagnetic field as part of our ontology. Consequently, for the instrumentalist, endorsing a scientific theory has no direct connection to our metaphysical commitments.
The realist would offer Michaela different advice. For the realist, if we are committed to a scientific theory, then we are also committed to claims the theory makes about unobservables. (To some extent, this is an oversimplification; typically, realists will claim that we ought to commit to some of the claims that the theory makes about unobservables but perhaps not all such claims.) Thus, realists might tell Michaela that she should welcome the electromagnetic field into her ontology. For realists, endorsing a scientific theory has a direct connection to our metaphysical commitments.
As I’ve said, whether U has a finite age is not directly observable. But for the realist, this is not necessarily a problem for inferring that U has a finite age. The realist would tell us that we need a well-confirmed scientific theory with the implication that U originated a finite time ago. This, then, provides one of the central ingredients in my schema: To infer that U has a finite age, we need a well-confirmed scientific theory T, such that we ought to endorse a realistic interpretation of T and such that T, together with observations, implies U has a finite age.
In part VI of Hume’s Dialogues Concerning Natural Religion, Cleanthes suggests that there is evidence for the view that the Earth is finitely old; had the Earth existed forever into the past, Cleanthes suggests, we would have a homogenous distribution of tree species over the Earth’s surface. But explorers find regions where (for example) cherry trees have not yet propagated. Philo replies that the distribution of trees is not convincing evidence for the Earth’s finite age; the fact that we do not find cherry trees growing naturally in some regions may suggest that conditions were different in the past or that cherry trees haven’t always existed. We may have reason to think that there was a past catastrophe and the present distribution could be the result of how trees propagated after that catastrophe. Nineteenth century geology and biology vindicated Philo. The distribution of cherry trees shouldn’t be explained by the Earth’s finite age but instead by the fact that cherry trees haven’t always existed and that conditions were different in the remote past. As James Hutton (1795) remarked, “we find no vestige of a beginning”.
Simultaneously, the development of geology in and beyond the nineteenth century lends support to my account of how we might infer U’s finite age. That is, geologists and planetary scientists developed a general and well-confirmed theory of planetary formation and of the Earth’s history. In adopting a realistic interpretation of that theory, we can welcome into our ontology one of the theory’s metaphysical consequences, namely, that the Earth originated 4.5 billion years ago. Likewise, if we have a well-confirmed theory T of U, ought to adopt a realistic interpretation of T, and T, together with observations, entails that U has a finite age, then we would have reason to welcome into our ontology the implication that U is finitely old.
Science has changed in a much more dramatic way since the eighteenth century. For most of recorded history, there were no particularly good empirical reasons for inferring that U has a finite age. Scientists and empirically oriented philosophers generally thought that there are no relevant differences between any two times, so that no time is a better candidate for U’s origins than any other. (Readers well read in the history of philosophy will recognize that this is closely related to one of Leibniz’s criticisms of Newtonian absolute time in the Leibniz-Clarke correspondence.) Like the distribution of cherry trees, we may find evidence that some processes have only been going on for finite time, but that’s not a good reason to think that something else couldn’t have been going on before the putative origin. This situation changed when the twentieth century saw the arrival of General Relativity.
To be clear, physical theories prior to General Relativity were consistent with U having a finite age. After all, for all that Newton’s physics tells us about our world, U could have begun last Thursday, with you and everyone else coming into existence with memories of times long past that never actually occurred. But this is a kind of skeptical hypothesis no one takes seriously. Christian theologians had reason to posit an origin for the Universe, but they relied upon scriptural or philosophical arguments. Thomas Aquinas argued that the origins of the Universe must be taken as an article of faith and not as the result of demonstrative reason.
With the arrival of General Relativity, physics included a set of differential equations, the Einstein Field Equations, whose solutions were thought to describe possible spacetimes. Time went from being an entity beyond scientific examination to being an object of scientific study in its own right; with time as an object of scientific study in its own right, there opened the possibility that science could infer that time had a beginning. Some of the solutions to the Einstein Field Equations described spacetimes that cannot be continued indefinitely into the past; in turn, we may be able to infer which spacetime we inhabit by surveying the distribution of matter-energy in the universe. In other words, the arrival of General Relativity opened the possibility that, by surveying the universe’s matter-energy distribution, we may be able to infer that there was an earliest period of time; any earlier periods of time are precluded by physical law.
Why are earlier periods of time precluded by physical law? On the assumption that the distribution of matter-energy is exactly homogeneous — i.e., the same at every point in space — and exactly isotropic — i.e., the same in every direction — the Einstein Field Equations simplify to a set of equations called the Friedmann-Lemaitre-Robertson-Walker (FLRW) equations. Some solutions to the FLRW equations describe infinitely old spacetimes, but let’s consider the solutions describing finitely old spacetimes. In those solutions, space, itself, is expanding; if we trace the expansion of space backwards through time, we find that, in earlier periods, the density of matter-energy was higher than it is presently. (Technical caveat: I have assumed that spacetime is maximally extended.) Given the way in which General Relativity ties the matter-energy density to the curvature of space-time, the space-time curvature was likewise higher in the past. (For technical readers, I am referring to the Ricci scalar curvature.) We encounter a time — which we call the Big Bang singularity — when the space-time curvature was unboundedly large; there are no extensions beyond the singularity consistent with General Relativity.
This point is worth spelling out in more technical detail. Consider the function 
I’ve sketched a schema for making a scientific inference that U is finitely old. Additionally, I’ve described how General Relativity, realistically interpreted, in conjunction with various empirical observations, may compel us to accept the view that U is finitely old. Nonetheless, I reject the view that we can satisfy this schema. Without the ability to satisfy the schema, we cannot currently offer a scientific inference that U is finitely old.
There are three reasons to think that this schema cannot be satisfied.
First, I previously mentioned a distinction between the Universe — the whole of physical reality — and the observable universe — the largest spacetime region to which we have empirical access. When we use the observed matter-energy distribution in order to infer which of the solutions to the Einstein Field Equations best approximates the spacetime that we inhabit, we are only able to make a reliable inference concerning the observable universe. For regions arbitrarily far beyond our cosmological horizon, all bets are off. In fact, there are a set of mathematical results (by Malament, Manchak, Ellis, and others) showing that no matter how well observers in a relativistic spacetime determine the structure of the observable portion of their universe, spacetime as a whole can be almost arbitrarily different. For that reason, supposing that we could infer that the observable universe is finitely old, very little would follow for the Universe.
Second, most physicists doubt that singularities are real features of our world. As I’ve said, if we trace the observable universe’s history backwards, according to singular FLRW models, we encounter unboundedly large matter-energy densities and curvatures. To the extent that we should be realists concerning our best physical theories, we ought to think that those theories are approximately true within some domain. But we ought to doubt extrapolations of any scientific theory to domains that are arbitrarily far from the domains in which that theory has been confirmed. I have no idea where the limits of General Relativity’s domain of application might be. But wherever those limits are, we are guaranteed to exceed them if the matter-energy density and curvature can become unboundedly large.
Third, we have strong independent reasons to think that General Relativity cannot be extended to arbitrarily large matter-energy densities. General Relativity is not compatible with quantum field theory; thus, we ought to expect that General Relativity will be replaced with some successor theory. There are good reasons to expect that the successor theory will describe what happens when the matter-energy density is sufficiently high. Without such a theory, we simply do not know what happened in our universe around the time of the Big Bang.
In other words, despite initial appearances, we have no good reason to think the Big Bang is the beginning of the Universe. While some General Relativistic models describe an uncrossable past boundary, we have reason to doubt the application of those models to the Universe. We don’t know what happens beyond our cosmological horizon. We don’t know what happened in our own remote past. So, while we have a general schema for inferring that U is finitely old, we don’t yet have a good way to satisfy that schema.
There is another point worth making before I continue on with this post. Let’s set aside the objections that I’ve considered above and consider the situation with respect to someone who adopts an instrumentalist interpretation of General Relativity. Instrumentalists can take up one of at least two positions. Instrumentalists could say that we simply have no good theory of spacetime. Someone who takes up this position has no way to satisfy the inference schema that I’ve suggested. But instrumentalists could instead say that while we shouldn’t endorse a realistic interpretation of General Relativity, we should adopt a realistic interpretation of a distinct theory of spacetime. On this view, there is hope of satisfying my inference schema — so long as the theory of spacetime that the instrumentalist selects has the appropriate set of features.
To see why the theory selected has to have some appropriate set of features, consider that the FLRW equations do not require General Relativity and can instead be derived in the context of a Newtonian gravitational theory. (This is a standard result presented in most undergraduate cosmology courses. If you want to see the derivation explicitly, you can pick up a standard undergraduate cosmology textbook or watch Leonard Susskind’s cosmology lectures on YouTube.) However, given the Newtonian framework, the FLRW equations have a distinct interpretation than they would have in a General Relativistic context. Instead of describing an expanding spacetime, the Newtonian FLRW equations describe an expanding distribution of matter in an unchanging and eternal spacetime. (That is, so long as spacetime isn’t arbitrarily cut off.) In some solutions to the Newtonian FLRW equations, we can trace the distribution of matter back to a singularity, but the singularity is a point where the matter distribution becomes undefined and not a point where spacetime, itself, becomes undefined. Importantly, in the Newtonian context, the FLRW equations simply do not entail a past boundary for the universe. Like the cherry trees in Hume’s Dialogues, anyone who adopts a realistic interpretation of the Newtonian FLRW equations might have reason to adopt a belief in a past catastrophe, but they would not thereby have good reason to adopt the belief that the observable universe (let alone the Universe) is finitely old.
I am not claiming that a realistic interpretation of the Newtonian FLRW equations is a plausible position. We have observations incompatible with Newtonian gravity, e.g., the recession of the perihelion of Mercury’s orbit, and therefore good reason to reject Newtonian gravity. Nor am I claiming that any of my interlocutors adopt a realistic interpretation of the Newtonian FLRW equations. Instead, I am pointing out that the same empirical observations that suggest a finite age for the observable universe on one physical theory will not generally suggest a finite age for the observable universe on another distinct physical theory. For that reason, the observations we have which might be taken to suggest a finitely old universe — e.g., the recession of distant galaxies, the microwave background, the distribution and relative abundances of elements, and so on — can only suggest a finitely old universe relative to specific physical theories. Our observations are theory laden. The aforementioned data begin to glow afresh and take on new meaning and relevance for the origins of the universe when interpreted in light of specific theories, but not otherwise. For that reason, in order to make an empirical inference that the universe has a finite age, anyone who adopts an instrumental interpretation of General Relativity must not only supply a distinct theory of space-time, but they must supply a space-time theory that demonstrably possesses the right sort of features.
Someone might object that the instrumentalist can use General Relativity to make predictions, because the instrumentalist agrees that General Relativity is empirically adequate, and so the instrumentalist can use General Relativity to predict that U is finitely old. This view is mistaken. Again, instrumentalists do not accept the unobservables entailed by a given scientific theory. For that reason, anyone who accepts an instrumental interpretation of General Relativity should not accept the unobservable consequences of General Relativity. Whether U has a finite age is not an observable consequence of General Relativity. Ergo, empirical adequacy does not provide the instrumentalist with a reason to accept that U has a finite age.
Before closing out the section, I offer an important disclaimer. I am not arguing against the adoption of an instrumentalist interpretation of General Relativity. For everything that I’ve said here, there may be good reason to adopt instrumentalism. Instead, what I have argued is that one cannot both adopt an instrumentalist interpretation of General Relativity and utilize General Relativity to infer that the universe has a finite age. Without offering a fleshed out alternative theory, we lack the grounds for making a scientific inference that U has finite age.
3. The Problem of York Time
Up to now, I have been writing as if we can unproblematically consider the state of the Universe at a time. This is the intuitive view of the Universe maintained by most non-physicists; according to this view, there is a fact of the matter about what’s happening right now on Mars or in the Andromeda galaxy. You, Mars, and the Andromeda galaxy exist together in three-dimensional space; in the next moment, there will be another three-dimensional space co-inhabited by you, Mars, and the Andromeda galaxy. To put the point another way, there is an objective fact about what is happening on Mars simultaneous with your reading this sentence. The arrangement of objects in space is an arrangement of mutually simultaneous goings-on.
Relativity, realistically construed, provides an entirely different picture of our world. Relative to any entity’s state of motion, there are distinct facts about which goings-on are simultaneous with which other goings-on. So, there may be a fact, relative to you, concerning what is happening on Mars simultaneous with your reading this sentence. But, relative to an entity in motion relative to you, there will be a distinct set of facts concerning what is happening on Mars. Relativity, realistically construed, tells us that we cannot speak unproblematically of history broken up into a series of three dimensional spaces.
According to presentists, only present entities exist. Since relativity makes the notion of The Present problematic, presentism might be in trouble. In light of relativity, there are a few options that presentists might take up; in the following, I will review some (not all) of the possibilities to sketch why someone like Craig might think that his proposed solution is superior to others. (For a more exhaustive discussion of the available options, see, e.g., Gilmore, Costa, and Calosi 2016.) Here’s a first possibility. Presentists might say that the only thing that exists is a single spacetime point, that is, the here-now. Let’s call this view spacetime solipsism. I confess that I don’t understand why anyone would adopt spacetime solipsism. For example, assuming that some version of physicalism is true, I am a spatiotemporally extended entity. For example, if I am my brain, since my brain has spatial extension, I have spatial extension. But spacetime solipsism says that only a single space-time point exists. In that case, my brain doesn’t exist and so I don’t exist. Regardless of whether you adopt physicalism, this seems a bridge too far for most to cross; surely, more than a single spacetime point exists. Here’s a second possibility. Presentists might say that since facts about simultaneity are relative and, since the present is a collection of mutually simultaneous goings-on, facts about what exists are relative. Let’s call this view fragmentalism. Typically, I think that fragmentalism, at least when conjoined with presentism, is utterly bizarre; how could it be that what is real for me is not what’s real for you? Worse, how could it be that what’s real for one part of my brain is not what’s real for another part of my brain? But, occasionally, I enter into moods where fragmentalism begins to look more attractive. Before encountering relativity, we might have thought that what exists is relative to a time. Dinosaurs do not exist now but did exist in the past. Given how relativity mixes and intertwines space and time, we might think that space comes to have a feature we used to think only time could have; what exists is not only relative to our location in time, but also to our location in space. In that case, reality would be different at here-now than at there-when. Nonetheless, I think that most philosophers will want to resist fragmentalism and so will want to adopt another view.
Here’s the possibility that Craig prefers. Perhaps relativity, though empirically adequate, is not actually true, or at least not true in the sense that realists would endorse. Despite what relativity appears to tell us, there is an absolute fact about what is present, and so an absolute fact about what is happening on Mars simultaneous with your reading this sentence.
How could there be absolute facts about simultaneity even though relativity is empirically adequate? Poincaré famously proposed the following thought experiment in order to argue that no physical measurement can mandate the view that space has any specific geometric structure. Consider a population of creatures, inhabiting a three dimensional space, and who carry rulers that they want to use to survey their world’s geometry. Unbeknownst to the creatures, the creatures inhabit the interior of a sphere, and there is a temperature gradient from the sphere’s center to the sphere’s surface. The temperature gradient causes the rulers carried by the creatures to change size as the creatures approach the sphere’s boundary. Supposing that the rulers shrink to zero size as the creatures approach the boundary, the creatures might mistakenly surmise that their world is infinitely large.
Astute readers might make an immediate objection. Although ordinary objects change in size with temperature, different materials undergo different responses to the temperature. So, by selecting materials with different coefficients of thermal expansion, Poincaré’s creatures might come to realize that their world is not actually infinite in size. In order to hide the true geometry from Poincaré’s creatures, we have to postulate a set of forces, let’s call them universal forces, that act the same way on all of the matter in the world that the creatures inhabit. By carefully selecting universal forces, we can postulate a world with almost any geometry we’d like, but which, to internal observers, will appear to have almost any other geometry we’d like.
Poincaré maintained the view that two apparently different states of affairs that do not differ in terms of any possible observation are actually one and the same state of affairs. Thus, Poincaré understood his thought experiment to support geometrical conventionalism, that is, the view that there really are no geometrical facts. Instead, what we call “geometrical facts” are mere conventions that we adopt. By adopting a different set of universal forces, we adopt a different set of geometrical facts. Today’s philosophers reject Poincaré’s view that two states of affairs that do not observationally differ are not actually distinct. For that reason, today’s philosophers would not be convinced that Poincaré’s thought experiment supports geometrical conventionalism. Nonetheless, Poincaré’s thought experiment does support the view that, by carefully adopting a set of universal forces, we can accommodate almost any set of observations given almost any metaphysical hypothesis about the structure of spacetime.
Here, then, is some (albeit tongue-in-cheek) advice for Flat Earthers. You don’t need to say that humans have never seen the Earth from space. You can instead say that some strange set of universal forces act on light in such a way as to make the Earth appear spherical, even though the Earth has an entirely distinct geometry. (Circumnavigating the “globe” can likewise be accommodated if we allow for, e.g., teleportation in addition to universal forces.)
Likewise, we have a strategy for presentists to pursue. By a careful selection of universal forces, we can accommodate an apparent (but non-real) relativistic spacetime alongside a metaphysical hypothesis in which space and time have an entirely different structure. For example, by a careful selection of universal forces, we can return to Newton’s absolute space, absolute time, and the accompanying universal reference frame. We can say that objects foreshorten as they approach the speed of light because there are universal forces that act on any object in absolute motion. We can say that two clocks, in relative motion, record different durations of time because there are universal forces that act on any moving clock. Thus, through a careful selection of universal forces, we can accommodate the empirical adequacy of relativity with the metaphysical reality of absolute simultaneity. With the return of absolute simultaneity, we can unproblematically return to presentism.
This strategy may seem ad hoc, but the strategy predates Einstein’s publications on relativity. In the nineteenth century, physicists generally thought that waves could propagate only in a material medium. For example, water waves are features of the surface of a body of water. The idea that water waves could propagate in empty space and without water seemed incoherent and incomprehensible. Light was understood as a wave and so physicists postulated a material medium — the luminiferous ether — whose undulations were identified with light. At the turn of the twentieth century, physicists attempted to measure the Earth’s motion with respect to the luminiferous ether. If the Earth is moving relative to the luminiferous ether, then the measured velocity of light should be different in different parts of the Earth’s orbit. A crisis appeared when the measured velocity of light was found to be the same in all directions and in all parts of the Earth’s orbit. One proposal was that measurement devices — and so rulers and clocks — are subject to a conspiracy of forces whose consequence is that light is always measured to have the same velocity.
Oliver Heaviside offered a simple argument that appeared to suggest the foreshortening of moving rulers and that would explain the apparent constancy in the velocity of light. Heaviside considered a spherical distribution of charge that is put into motion. When the distribution is at rest, the distribution produces a radially symmetric electric field; placed into motion, the field changes. Supposing that the charges within the distribution relax into the new equipotential lines of the newly established field, the spherical distribution will foreshorten along the direction of motion. At the turn of the twentieth century, interatomic and intermolecular forces were not well understood. No one knew whether the forces that act on atoms or molecules are electromagnetic forces. But there was nothing obviously wrong with the suggestion that the atomic or molecular constituents of rulers are subject to forces sharing some features with electromagnetic forces; if so, there was nothing obviously wrong with the suggestion that the null results of experiments meant to measure the Earth’s motion with respect to the luminiferous ether were due to a set of forces that, like electromagnetic forces, would foreshorten moving rulers in precisely the amount required to reproduce the null results. When Einstein proposed Special Relativity in 1905, Einstein derived similar equations but with an entirely different motivation and interpretation. (For a discussion of this history and its philosophical upshots, see, for example, Brown 2006.)
A similar strategy was later pursued by some early quantum gravity theorists, particularly those with a particle physics background. As General Relativity is typically interpreted, General Relativity postulates that matter-energy couples to space-time in such a way that the presence of matter-energy accompanies spacetime curvature; the more matter-energy we squeeze into some space-time region, the greater the resulting curvature. In turn, the spacetime curvature couples back to matter-energy. Objects fall or go in orbits because they are following paths set for them by the structure of spacetime itself. In contrast, in Special Relativity, matter-energy does not couple to spacetime and spacetime does not couple to matter-energy. Special Relativity is said to be a theory in which space-time is a “fixed background”. Squeezing more matter-energy into a region of a Special Relativistic spacetime leaves the curvature unchanged. Both theories describe spacetime using a mathematical object called a metric tensor; you can roughly think of the metric tensor as a kind of four-dimensional analogue of the Pythagorean theorem. If you want to know the four dimensional interval between two spacetime points, you use the metric tensor. In the 1960s through 70s, some physicists, including Richard Feynman, considered an alternative interpretation of General Relativity, in which the General Relativistic metric tensor is interpreted as a gravitational field, and the background spacetime is assumed to have a Special Relativistic metric tensor. (Additionally, see the several articles by J. Brian Pitts on this topic that I cited in my original article.) If the resulting view were correct, General Relativity would correctly predict the outcomes of any measurements we could ever make, but, despite appearances, spacetime curvature would not really exist. Instead, gravitational interactions, mediated by a physical field, would be responsible for General Relativistic phenomena.
Here, then, is a strategy for presentists. There could be a set of universal forces that conspire to make our world merely appear relativistic. Just as some physicists considered a view on which the General Relativistic metric tensor is interpreted as a gravitational field superimposed on to a fixed Special Relativistic spacetime, so, too, presentists can interpret the General Relativistic metric tensor as a gravitational field superimposed on to a fixed Newtonian absolute space and absolute time. Any theory of that sort will reproduce all of the predictions made by General Relativity and so will be empirically indistinguishable from General Relativity. In my article, I suggested that this is how the Neo-Lorentzian strategy, pursued by William Lane Craig and friends, ought to be applied in the cosmological context. (Damore misdescribes how this is supposed to work, e.g., Damore talks about laying the General Relativistic metric tensor on top of a gravitational field and confuses the Einstein tensor with the metric tensor, but nevermind.)
If we follow the Neo-Lorentzian strategy, what happens to the inference that U has a finite age? On the Neo-Lorentzian strategy, there are two different ways that we can talk about time. On one hand, there is time as measured by physical clocks; let’s call this parameter physical time. Physical time is the time used in one standard expression of the General Relativistic metric tensor and not the time associated with the underlying Newtonian absolute time. And since physical time is merely an apparent time, without any underlying metaphysical reality, whether physical time is finite to the past has no direct relevance for the KCA. Whether U is finitely old — in the sense that does have relevance for the KCA — should be understood as a question about whether U has finite age with respect to the underlying Newtonian absolute time.
Craig and company are not alone in adding absolute time to relativistic physics. Although the view that there is an absolute time is not popular among physicists, some physicists have seriously defended absolute time. For example, Roser and Valentini have defended the view that a parameter called York time should be understood as absolute time. (For citations of Roser and Valentini’s work, see my original publication.)
Spacetime is represented in both Special and General Relativity as a four dimensional block. (Note that I said “represented as”. The former sentence should not be read as a metaphysical commitment to four dimensionalism.) We can “cut” that four dimensional block into three dimensional slices in various ways; any given cutting of the four dimensional block is called a foliation. Advocates of absolute time think that there is a single best foliation, where each three dimensional slice corresponds to a moment of absolute time. And there are various theoretical reasons to think that a particularly good candidate is a slicing into hypersurfaces of Constant Mean (extrinsic) Curvature, that is, what’s been called a CMC foliation. (For a non-technical introduction to the CMC foliation, see Laycock 2005, pp. 118-121. At one point, Damore claims that the hypersurfaces in an FLRW spacetime should be understood as hyperplanes: “From what I understand, that particular kind of ‘slicing’ is why some call this a ‘hypersurface’, even if, mathematically speaking, it’s a hyperplane.” This is confused in two ways. First, a hyperplane is a kind of hypersurface. Second, the CMC hypersurfaces are not generally flat, even if we make the restriction to FLRW spacetimes and even if we say that only one (“present”) hypersurface is actual.)
Mathematicians distinguish between two different kinds of curvature. When we inflate a balloon, anything we’ve written on the balloon stretches. This sort of curvature is called intrinsic curvature. When we roll a piece of paper into a tube, we do not stretch the paper. This sort of curvature — the kind that might be associated with bending through higher dimensional embedding space — is called extrinsic curvature (see, e.g., Laycock 2005, p. 118). Each CMC hypersurface is a three dimensional cross section of spacetime identified by the average value of the extrinsic curvature on that hypersurface.
Generally speaking, a given relativistic spacetime can be sliced into a CMC foliation in multiple ways. For that reason, the CMC foliation is not generally unique. If friends of absolute time want to tell us that the hypersurfaces in the CMC foliation correspond to moments of absolute time, they will need to provide us with a procedure for selecting which CMC foliation is the correct one. But let’s set that issue to one side. Let’s suppose that we either have such a procedure or that we are considering a spacetime model in which the CMC foliation is unique, such as a closed FLRW model. Once we have the desired foliation, we need to label the hypersurfaces in the foliation with a time parameter.
By way of analogy, suppose that I hand you a canister of movie film. And let’s suppose that this is the kind of old fashioned movie film used in a hand cranked camera. I don’t tell you how fast I cranked the film. Your job is to label each frame with the time at which that frame was captured. Depending on how familiar we are with what the film contains, this job isn’t terribly difficult. For example, we can tell when footage of a person walking is played back too slowly or too fast. But if the film contains a ball rebounding off of a wall, and we are not familiar with the ball’s composition, then we have less of an ability to correctly label each frame. And if the film contains footage of some obscure phenomenon with which we have no familiarity at all, then we will be at a total loss to correctly label each frame with a specific time. We won’t be able to tell whether the film is run too fast or too slow.
Likewise, given a foliation of a relativistic spacetime, we are tasked with identifying the absolute time that corresponds to each hypersurface in the foliation. In an expanding FLRW spacetime, we can imagine a set of observers — called “fundamental observers” — who are carried along with that spacetime’s expansion. We can suppose that each observer carries a clock. We can construct a CMC foliation such that, on each hypersurface, all of the fundamental observers have clocks that are synchronized with one another. This time parameter kept by each of their clocks is called the cosmic time. And now the proposal, made by Craig and company, is that the cosmic time ought to be identified with absolute time. (Damore argues that we should understand cosmic time as approximating absolute time. Fair enough; if the reader would like, they can reinterpret my former sentence as stating that cosmic time ought to be identified with an approximation of absolute time.)
However, the aforementioned labeling of the hypersurfaces in the CMC foliation is not unique. There are an infinite number of ways we can label the hypersurfaces in one and the same CMC foliation and each of those labelings are possible candidates for the absolute time. One candidate that enjoys many of the same advantages as cosmic time is the York time, that is, the value of the average extrinsic curvature itself; moreover, as I will explain below, some would argue that the York time is a better candidate for absolute time. I do not endorse absolute time myself and I am currently undecided on whether York time actually is the superior candidate. Instead, my argument is that, insofar as I can tell, there is no particularly strong reason why proponents of absolute time ought to favor cosmic time nor have they provided an adequate response to arguments for the view that York time is the superior candidate. Without having adequately ruled out York time, they haven’t succeeded in mounting a scientific case for the KCA’s second premise.
Here’s the trouble. Consider one of the singular FLRW models and let’s suppose that we’ve identified one of the CMC foliations as the one that correctly cuts the model into moments of absolute time. While the cosmic time might tell us that the singularity is finitely far into the past, so that the Universe, so depicted, is finitely old, the York time labels the singularity as infinitely far into the past. So, unless we have a reason that adequately breaks the symmetry between cosmic time and York time as candidates for measures of absolute time, we cannot tell whether, according to absolute time, the Universe has a finite or infinite age. Thus, we cannot tell whether the Universe began to exist.
3.1 Two technical asides
There are two technical asides that I need to make here. Since both asides are “technical”, some readers may not grasp every detail. Don’t let that bother you. Read through the asides, grasp what you can, and move on; feel free to ask questions in the comments section.
Let’s turn to the first. A symmetry breaker will need to be adequately strong in order to suffice. The probability of a conjunction 
Even though the view that absolute time is measured by York time is not probable, the possibility that absolute time could be measured by York time would still provide us with reason to not accept the KCA. Moreover, if there are considerations that count in favor of cosmic time over York time, but other considerations that count in favor of York time over cosmic time, then, even though we might have some asymmetric considerations, it will still be possible that none of those considerations provide us with adequate reason for favoring cosmic time over York time. Friends of the KCA who are also proponents of absolute time have a difficult job to do. I do not envy the situation that they are in.
Now the second technical aside. Damore seems to be confused about what, exactly, the implications of York time are for the Big Bang singularity. While I wrote in my article that York time relegates the Big Bang singularity to infinitely far into the past, Damore explains that he “was under the impression that York Time, as it functions in the Hamilton-Jacobi formulations of Einstein’s equations, gets rid of the singularity altogether, not that it puts it at ‘negative infinity’.” Damore goes on to say that he’d “like corrections here if needed. I think the singularity stays in certain contexts, like if we’re dealing with Schwarzschild space-time, but that wasn’t mentioned.” The first thing to notice is that the Hamilton-Jacobi formulation of the Einstein Field Equations is mathematically equivalent to the standard formulation of the Einstein Field Equations. Thus, if Damore were right that the York time somehow removed the Big Bang singularity without relegating the Big Bang singularity to negative infinity, my job would be really easy; in that case, the Big Bang singularity would only be a artifact of a notational choice and not a real feature of the world. Damore should know that things are not so easy for me.
To see why the York time relegates the Big Bang singularity to negative infinity, I will sketch how the mathematical argument proceeds. As I’ve said, for each hypersurface in the CMC foliation, the York time is proportional to the average value of the extrinsic curvature for that hypersurface. We can compute the average of the extrinsic curvature 
In turn, the Hubble parameter is given by the ratio of the time derivative of the scale factor to the scale factor, i.e., 
If one imagines going back in time and approaching the Big Bang singularity, then one would find that 
And thus:
Therefore, the York time does relegate the Big Bang singularity to the infinite past. But since the Big Bang singularity is an open boundary, there is no point at negative infinity included. As I will explain below, this effectively removes the beginning altogether. Hence, the correct statement is that the York time removes the Big Bang singularity by relegating the Big Bang singularity to negative infinity.
What about Damore’s other comment? Does the singularity remain in certain contexts, e.g., with a Schwarzschild black hole? The answer here is that precisely the same thing happens; for almost any spacetime in which the York time can be defined, including Schwarzschild’s model of a black hole, the York time maps curvature singularities to positive or negative timelike infinity. (I say “almost any” because there are some known exceptions. For example, Eardley and Smarr (1979) showed that some Tolman-Bondi spacetimes involve a sufficiently rapid collapse to a singularity that is not mapped to positive or negative timelike infinity.) The fact that York time does typically map singularities to positive or negative infinity is part of why York time is often deployed in computer simulations of General Relativistic phenomena. Curvature singularities are difficult to deal with in computer simulations, but, since simulations do not include infinitely distant points, simulations written in terms of York time avoid having to deal with curvature singularities altogether.
Now that I’ve expunged with both technical asides, let’s return to our regular programming.
3.2 A Return to Our Regular Programming
Perhaps, some readers will object, even if the Big Bang is placed in the infinite past, the Universe, so depicted, would still have a beginning. Perhaps they imagine that the Big Bang is the Universe’s beginning and so the Universe would have a beginning no matter how long ago the Big Bang took place. A beginning that takes place infinitely long ago is still a beginning. But this objection is no good.
To see why, consider the real line. The real line has no beginning and no end; real numbers stretch forever into the negative direction and forever into the positive direction. We can think of the real line as a collection of points, where each point is labeled by a real number. But now suppose that I keep the points while removing the labels. Without the labels, the line still has no beginning, that is, no first point, and no end, that is, no last point. But without the labels, there is no fact about how long the line is. Let’s use L to denote the line that results from removing the labels.
Suppose that I take the segment of the real line from 0 to 1, not including either 0 or 1. The resulting open interval can naturally be thought of as having the length 1. But suppose that I remove the labels. The resulting segment has no first point and no last point. Again, with the labels removed, there is no fact about how long the segment is. Let’s call this unlabeled segment L’.
Question: how does L compare with L’? First, notice that, since there is a one-to-one correspondence between the interval between 0 and 1 and the entire real line, there is a one-to-one correspondence between the points in L and the points in L’. For any point in L, we can find a corresponding point in L’, and vice versa. Second, notice that both L and L’ lack a first point and a last point; both are open intervals. Third, notice that L and L’ have the same topological structure. For example, for any point p in L, I can construct an open interval around p containing only points in L and the same is true for any point q in L’. Both L and L’ are dense; for any two points r and z in L, there exists a third point s between r and z, and likewise in L’. In fact, there simply is no property that L has and which L’ lacks; by construction, L and L’ are indistinguishable. Our ability to distinguish the two was destroyed when we removed the labels. (If I were someone like Leibniz, who endorsed the identity of indiscernibles, then I would say that L and L’ are not distinct; they are one and the same entity under two different names.)
There is a strong intuition that if time is like the interval from 0 to 1, then time has a beginning, but if time is like the entire real line, then time has no beginning. Singular Big Bang models are like the interval from 0 to 1 in that the singularity is an open boundary; each point in the interval can be taken to represent a hypersurface in a CMC foliation. Thus, whether singular Big Bang models depict the Universe as having a beginning apparently depends upon how we label the hypersurfaces in the preferred foliation. If absolute time is correctly identified with cosmic time (or if one is a close approximation of the other), then the Universe (barring other objections) has a beginning. But if absolute time is instead identified with York time, then the Universe is beginningless.
Damore has objected that, for Craig, the notion that the Universe has a beginning is defined in terms of how many isochronous intervals can be placed into the past. (I don’t accept this definition myself, and describe why in my dissertation and in a recently published article, but set that issue aside.) In his consideration of whether the past intervals of York time are isochronous, Damore considers a fork; either the intervals of York time are discrete, and so isochronous, or form a continuum, and so are not isochronous. Here, Damore has apparently confused two independent sets of issues; whether past time can be broken into a finite or infinite collection of isochronous intervals of York time is independent of whether time is continuous. Furthermore, General Relativity does not include a notion of discrete time. For that reason, when we represent an FLRW spacetime in terms of York time (or cosmic time, for that matter), time is represented as a continuum. For all I know, time could be discrete, but, since discrete time has no General Relativistic representation, I will set that possibility aside.
When Damore turns to the possibility that time, when represented in terms of York time, is a continuum, Damore claims that I am “trading on an ambiguity”. Damore apparently thinks that if we label the hypersurfaces in the CMC foliation with the York time, then the intervals will not be isochronous and so we will not be able to escape the verdict that the Universe had a beginning. He thinks that the sense in which the singularity is infinitely distant from the present is innocuous and irrelevant; Damore thinks this is the same sense in which my birth is infinitely distant from the present since I can “endlessly halve intervals separating my present existence from the date of my birth”. Had Damore been right, then the York time would be irrelevant for whether the universe is infinitely old, since the intervals considered would not be isochronous. But this is a complete misunderstanding of what friends of the view that York time is absolute time would say. They would say that the duration of past York time can be subdivided into isochronous intervals and it is with respect to those intervals that the universe is infinitely old.
Obviously, isochronous intervals of York time are not isochronous intervals of cosmic time. But I don’t understand why this should matter. Friends of the view that York time measures absolute time would point out that isochronous intervals of cosmic time are not isochronous intervals of York time. For that reason, Damore is simply begging the question against friends of the view that York time measures absolute time. In other words, provided that I understand his objection correctly, Damore is illicitly assuming that cosmic time measures absolute time in order to reject the view that York time measures absolute time. If we apply Craig’s definition to a singular FLRW model described in terms of York time, we would conclude that the resulting model does not include a beginning.
4. Possible Symmetry Breakers
In this section, I take up two tasks. First, I describe some of the reasons why one might support York time as a candidate for absolute time. Second, I will describe and respond to some of the ways in which Damore suggests we break the symmetry between cosmic time and York time as proposals for absolute time.
Before turning to the reasons why one might support York time as a candidate for absolute time, I turn to three preliminary comments. As a first preliminary comment, note that Craig and company are not the only advocates of absolute time. Among philosophers who advocate for absolute time, many take up York time as their preferred candidate for absolute time. For example, Callendar and McCoy (2021) write that York time is an “especially popular” choice for absolute time. Craig and company implicitly deny the identification of York time with absolute time — because they think the reality of the Big Bang singularity would mean the universe is finitely old — but have not explicitly argued against the identification of York time with absolute time. Those of us who are skeptical of the KCA do not bear the burden of showing either that absolute time is York time or that absolute time isn’t cosmic time. Instead, skeptics can point out that they have been offered no good reason to accept the identification of absolute time with cosmic time or to reject York time as a candidate for absolute time. Insofar as the KCA requires absolute time, skeptics have no reason to accept the KCA.
The second important preliminary observation is that, at least in the context of FLRW spacetimes, the York time and the cosmic time can be used to label one and the same CMC foliation. I think this was an issue on which Damore was confused, since he repeatedly writes about identifying the correct foliation instead of about identifying the correct labeling of that foliation.
In FLRW spacetimes where the CMC foliation is unique, there is a bijective map between the cosmic time and York time. Why? Precisely because every CMC hypersurface labeled by cosmic time is also labeled by York time. Any three dimensional cross section of an FLRW spacetime identified as an instant of cosmic time will also be an instant of York time and vice versa. For that reason, any argument for the identification of absolute time with cosmic time that counts only in favor of the CMC foliation will not be adequate for preferring York time over cosmic time.
To be fair, in my original article, I do mention that the CMC foliation is unique only for some FLRW spacetimes and not for others. Since the CMC foliation is not generally unique, an issue could be raised concerning which CMC foliation is the one that we ought to think corresponds to absolute time. But I don’t think this issue would force us into skepticism concerning the total duration of past absolute time and so I don’t think this issue is relevant for my disagreement with Damore.
As a third preliminary comment, Damore sometimes wonders why I interpret Craig as discussing a preferred foliation in places where Craig instead discusses a preferred reference frame. (There are other places where Craig does explicitly discuss the CMC foliation.) In Special Relativity, we can unproblematically define a reference frame for the entire spacetime. However, things differ in General Relativity, where a global reference frame cannot generally be defined. The reason that reference frames cannot generally be defined globally in General Relativity has to do with how coordinate maps are assigned to curved surfaces. When coordinate maps are assigned to curved surfaces, we define coordinates locally, in terms of how the region around a given point can be approximated by a plane tangent to the surface, and in terms of a mathematical object that describes how the local coordinate maps are connected one to another, i.e., the connection. In General Relativity, inertial frames can be expressed in terms of the local coordinate map; the fact that the same one coordinate map cannot be continued throughout spacetime turns out to be another way to describe gravity; in turn, the connection turns up in the equation describing the trajectories bodies undergo when subject only to gravity. In any case, in FLRW spacetimes, there exists a foliation of the spacetime into CMC hypersurfaces where the reference frame of each fundamental observer locally coincides with the CMC hypersurface. Since, strictly speaking, one cannot generally define a universal reference frame in a General Relativistic context, I think Craig should be charitably read as defending a preferred foliation.
Let’s turn to the first reason why someone might support York time as a candidate for absolute time. For models of the observable universe, there is a way of foliating spacetime into hypersurfaces in which the matter-energy distribution is approximately uniform and in which observers would see the cosmic microwave background as approximately uniform. This is the CMC foliation. The York time labels the hypersurfaces in this foliation. Unfortunately, this reason would favor any parameter that labels the hypersurfaces in the CMC foliation, including cosmic time, and so is not a reason that breaks the symmetry between cosmic time and York time.
Let’s turn to a second reason. The laws of physics are typically expressed either as differential equations or as recipes for differential equations. For example, if I want to predict the trajectory of a rocket, I can write down a differential equation describing all of the forces acting on the rocket. The equation’s solution describes the rocket’s trajectory; given the state of the rocket at the time that the rocket is launched and any time during the rocket’s flight, the solution outputs the location of the rocket at that time. Mathematical problems where we are provided the initial state of a system and our goal is to predict subsequent states using a differential equation are called initial value problems.
Initial value problems arise in General Relativity. There are relativistic spacetimes — for example, spacetimes that include time travel — in which the initial value problem cannot be solved. Although some presentists do endorse the possibility of time travel, many do not; I think there is a clear intuition that if presentism is true, then time travel is not possible. (After all, if non-present times do not exist, there is nowhere for time travelers to go.) Moreover, there is a natural connection between initial value problems and presentism. If time truly passes, one moment producing the next, then laws describing temporal evolution describe how each moment necessitates the next.
Thus, if presentism is true, then the relativistic spacetimes for which the initial value problem is not well-posed might not be real physical possibilities. For that reason, let’s focus on relativistic spacetimes in which the initial value problem can be solved.
Relativistic spacetimes for which the initial value problem can be solved have the following feature: they can be cut into hypersurfaces, analogous to the different times in the rocket’s trajectory, and then, given information on one hypersurface, we can calculate the contents of the other hypersurfaces. Any spacetime that can be cut up in that way is said to be globally hyperbolic and the resulting hypersurfaces are called Cauchy surfaces. For example, a computer simulation of two colliding neutron stars might begin with two neutron stars on one Cauchy surface. The simulation will then calculate approximate states on subsequent Cauchy surfaces in which the neutron stars approach each other and eventually collide. Since the hypersurfaces in the CMC foliation are Cauchy surfaces, the York time labels Cauchy surfaces. Since the presentist should find plausible the notion that moments of time are identified with Cauchy surfaces, the presentist should find plausible the identification of CMC surfaces with moments of time.
Unfortunately, in the context of FLRW spacetimes, this argument would favor any parameter that labels the hypersurfaces in the CMC foliation and so is not a reason that breaks the symmetry between cosmic time and York time. However, York time can be defined for a far broader class of spacetimes than cosmic time and is related to the mathematics of initial value problems in a way that cosmic time is not.
Technically sophisticated readers will know that the initial value problem in General Relativity is closely related to the Hamiltonian formulation of General Relativity, i.e., the Arnowitt-Deser-Misner (ADM) formalism. In turn, the relationship that the York time has to the Hamiltonian formulation of General Relativity helps to motivate the role that York time plays in (some) quantum gravity proposals, particularly the canonical quantum gravity program. And given the role that York time plays in quantum gravity proposals, we ought to have seemings in favor of the view that if absolute time exists, then York time measures absolute time. This is a reason that does favor York time over cosmic time, since cosmic time has no similar relationship to the Hamiltonian formulation of General Relativity and cosmic time does not play this role in any quantum gravity proposal.
Let’s turn to a third reason. While the cosmic time can be defined for all FLRW spacetimes, we know that the observable universe is only approximately FLRW. While the FLRW equations demand that the matter-energy distribution is completely uniform on every hypersurface labeled by the cosmic time, the matter-energy distribution in the actual observable universe is not completely uniform. Thus, the cosmic time can only be approximately defined for the observable universe; local clocks can undergo almost arbitrarily large departures from the cosmic time. (Consider, for example, a clock sitting on a neutron star or falling into a black hole.) In contrast, as far as anyone can tell, the York time can be defined exactly for the observable universe. Damore thinks that this is not a strong reason to prefer York time over cosmic time. As he points out, on the view that Craig and Damore share, cosmic time is only intended to approximate absolute time. However, as I described in a previous section, nearly all bets are off concerning the structure of spatiotemporal regions beyond our cosmological horizon. There is no good reason to expect that spacetime as a whole approximates an FLRW spacetime. For that reason, we have no good reason to think that cosmic time can be defined, even approximately, for spacetime as a whole. Since the York time can be defined for a broader class of spacetimes than the cosmic time, this is one reason to prefer the York time over the cosmic time as a candidate for absolute time.
In my original paper, I pointed out that if inflationary cosmology is correct, then we should not expect spacetime to be well approximated as an FLRW spacetime in regions beyond our cosmological horizon. According to Damore, I conclude a section with “speculations about the inflationary multiverse” and about “the cosmological horizon”. Damore seems to have missed the point entirely. For all we know, regions beyond our cosmological horizon are not well approximated as FLRW. This fact does not require inflationary cosmology or any other specific cosmological model. However, there are live proposals — such as inflationary cosmology — on which the portion of spacetime beyond our cosmological horizon is likely not well approximated as FLRW. Since cosmic time cannot be defined for spacetimes in general, we have no good reason to think that cosmic time can be globally defined for the entire Universe.
Here’s a fourth reason, albeit not one that I considered in my original article. Barrow and Tipler (1978, p. 458), motivated by some earlier comments by Misner, note another argument for favoring York time (or a similar parameter) as a candidate for absolute time and for disfavoring cosmic time. Suppose we adopt a relational conception of time, on which time is the measure of change. Looking back in time, close to the Big Bang singularity, according to the cosmic time, changes occur more and more rapidly. But if we “stretch” out time — or, in other words, describe the universe’s history according to York time — then changes do not happen more rapidly “close” to the Big Bang singularity than they do in subsequent history. I am not sure what I think of this argument, but I mention the argument here as a consideration that some have found plausible.
Here’s a fifth and final reason, albeit, again, not one that I considered in my original article. Craig has previously signaled his preference for Bohmian mechanics and, in a variety of places, has argued that quantum non-locality provides evidence for absolute simultaneity. But if so, we have some reason to think that absolute time is measured by York time. This reason is technical, but may be of interest to readers with a technical background. As Roser (2016) notes, hidden variable approaches to quantum cosmology are easier to construct if we assume York time than if we assume many other possible time parameters, including cosmic time. Due to the well-known violation of the Bell inequalities, any hidden variable interpretation of quantum mechanics, such as Bohmian mechanics, must be non-local. In turn, in attempting to construct a quantum mechanical successor to General Relativity, non-local features are well represented on the metric’s configuration space only if spacetime is non-singular. Since York time removes singularities by relegating them to past or future infinity, formulating one’s theory in terms of York time allows one to more easily construct a hidden variable quantum cosmology.
Are these reasons convincing? I don’t know. I’m not making the claim that York time does measure absolute time. Instead, I claim that Craig and company have not adequately ruled out the possibility that York time does measure absolute time and I have argued that there are reasons that count in favor of York time that some find convincing. Without having adequately ruled out the possibility that York time measures absolute time, Craig and company have not provided adequate justification for the view that Big Bang cosmology supports the KCA’s second premise.
Momentarily, I will turn to considering some of the symmetry breakers that Damore suggests. Before doing so, I turn to a consideration that some authors have thought counted in favor of cosmic time as a candidate for absolute time, but which might instead be argued to count in favor of York time as an absolute time candidate. As such, the following consideration should not be considered a symmetry breaker counting in favor of cosmic time. Since Newton onwards, proponents of absolute space or absolute time have held that good candidates should make the laws of physics particularly simple to express. For example, in classical mechanics, there exist a distinguished class of reference frames — which we call inertial frames — in which dynamics can be expressed in a particularly simple form. If one assumed that a non-inertial frame corresponded to absolute space and absolute time, then one would need to postulate a large number of additional laws describing so-called “fictitious” forces, such as centrifugal forces. On the grounds that the laws do assume a particularly simple form in inertial frames, Newton held that one of the inertial frames corresponds to absolute space, even though we cannot determine which inertial frame. Likewise, post-Einstein, one might claim that dynamics will have a particularly simple expression in terms of the variables that most closely correspond to absolute space and absolute time. The claim has been made that dynamics has a particularly simple expression in terms of cosmic time. If that were so, then we’d have a reason to prefer cosmic time as an absolute time candidate. However, as York (1972) and subsequent authors have made clear, dynamics has a particularly simple expression in terms of York time; as Laycock (2005, p. 120) describes, “York has shown that we can achieve a striking simplification in the equations governing the dynamics of the universe.” And as should now be clear, York time can be used to describe a broader class of spacetimes than cosmic time.
Let’s turn to considering some of the symmetry breakers Damore suggests in his post. I should mention that I found Damore’s post difficult to read and to interpret; for that reason, I may have misinterpreted some of the points that Damore makes as attempted symmetry breakers. I am open to correction if any of the following were not intended as symmetry breakers.
First, Damore suggests that we ought to think the clocks of (most) local observers approximate cosmic time, since (most) local observers are approximately at rest with respect to the universe’s expansion. Provided local clocks seem to measure absolute time, we have a seeming that absolute time is measured by cosmic time.
I have two replies. To start, supposing that Neo-Lorentzianism is true, I don’t see why we should have the seeming that local physical clocks have any connection with absolute time. According to Neo-Lorentzianism, local physical clocks measure physical time; in turn, physical time is supposed to come apart from absolute time. For example, in Poincaré’s thought experiment, the apparent geometry, as measured by rulers, comes apart from the actual geometry; if we follow Poincaré, we end up skeptics about our ability to measure our world’s true geometry. Likewise, if we commit to Neo-Lorentzianism, I see no way to escape the same skeptical conclusion concerning our measurements of time. I understand that Craig and company think that the local clocks of fundamental observers approximately measure absolute time, but, provided Neo-Lorentzianism is true, why would local clocks measure absolute time? But let’s suppose that we do (for some reason that I don’t see) have a seeming that the clocks of (some) local observers measure absolute time. We also have seemings from, e.g., research in quantum gravity that York time measures absolute time. And I’m not convinced that one set of seemings are all that much stronger than the other.
Let’s turn to another one of Damore’s proposed symmetry breakers. Damore notes throughout his post that the Neo-Lorentzian can endorse an instrumentalist interpretation of York time. Nothing that I (or others) have written suggests a reason to deny an instrumentalist interpretation of York time. In reply, let me begin by agreeing that I haven’t argued against an instrumentalist interpretation of York time. But so what? Any Neo-Lorentzian who commits to the KCA will want to endorse an instrumentalist interpretation of York time. But, equally, Neo-Lorentzians who deny that the Universe is finitely old may want to endorse the view that York time is absolute and an instrumental interpretation of cosmic time. Damore has not provided us with a good reason to think that someone with that view is wrong.
I don’t shoulder the burden of proof of ruling out the instrumentalist interpretation of York time. Instead, proponents of the instrumentalist interpretation of York time need to provide us a good reason why we ought to adopt their instrumentalism. Equally, it’s not my job to show that absolute time is measured by York time. Instead, it’s Damore’s job to rule out that view or at least to show that that view is sufficiently improbable. (In fact, Damore’s job is more difficult than that; he needs to show that the cosmic time is a much more probable measure of absolute time than any other proposal.)
In a closely related attempt at a symmetry breaker, Damore claims that the York time is a mere mathematical construct with “absolutely no real-world consequences at all” and certainly not any “ontological consequences that would actually imply a past-eternal universe”. Well, sure. I know that’s what he’d like to claim. But proponents of the view that York time measures absolute time will say exactly the reverse, namely, that it’s cosmic time that has absolutely no real world consequences at all and no ontological consequences that would actually imply a past-finite universe. This attempted symmetry breaker is simply question begging.
In another attempted symmetry breaker, Damore thinks that those who take up an Aristotelian understanding of temporal continua, like Craig, have reason to prefer cosmic time over York time. I have to confess that I did not follow why Damore thinks that this is so. In any case, I see nothing that bars Neo-Lorentzian friends of York time from adopting an Aristotelian conception of temporal continua. Recall the analogy that I made between the CMC foliation and the real line. In that analogy, I utilized a Cantorian conception of continua. But if Aristotelians would like, they can reconstruct my analogy in terms of the Aristotelian continuum.
Here’s another attempt at a symmetry breaker. Damore writes that partisans of cosmic time might “think that while York Time could be instrumentally applied and defined on local levels, a cosmic time parameter must be defined globally, so any and all potential observers that are privy to the CMC slicing that Cosmic Time identifies will agree on what the time is.” But this is precisely backwards, as I stressed in my article. The cosmic time can be defined globally only on some very specific cosmological models, namely, FLRW models. The cosmic time cannot be defined globally for models which are not globally homogeneous and isotropic, even though the York time can be. So, if the advocate of absolute time wants a candidate for absolute time in which local observers distributed throughout all of space agree on what time it is, they ought to prefer York time over cosmic time.
In another attempted symmetry breaker, Damore argues that considerations of spatial isotropy should count in favor of cosmic time over York time: “the isotropy shouldn’t only imply that cosmic time is the same in all directions, but that it is the same for all observers.” This won’t do for distinguishing cosmic time from York time as candidates for absolute time. At least in FLRW models, surfaces of constant cosmic time are also surfaces of constant York time. Consequently, both candidates imply the same conclusions for whether time is the same for all observers. In non-FLRW models, the cosmic time cannot even be defined, even though the York time can be. Thus, for a broader class of spacetimes, the York time would allow one to say that the time is the same for all observers.
In another attempt, Damore thinks that considerations about the global structure of spacetime should count in favor of cosmic time as a candidate for absolute time. He writes that, “partisans of Cosmic Time agree about monotonicity, but that it should be in terms of global, rather than local, properties of the globally expanding universe, which would then imply the indispensability of considering those parts of the universe that are distant.” Again, this doesn’t distinguish cosmic time from York time. To start, we simply don’t know whether spacetime is globally expanding. If we do assume that spacetime is globally expanding, so that spacetime is globally approximated as one of the FLRW models, both cosmic time and York time label the same hypersurfaces and so both can be defined in terms of the same global properties. In some non-FLRW models, the cosmic time can only be defined as a local approximation. For example, if spacetime consists of a number of local regions, where each region is undergoing expansion, as in an inflationary multiverse, then a cosmic time can be approximately defined within each expanding region, but cannot be globally defined, even approximately. In other non-FLRW models, the cosmic time cannot even be locally approximately defined. Only the York time can be defined globally in all spacetimes with a CMC foliation.
In yet another attempt, Damore appears to claim that there is a general “consensus” among physicists that cosmic time ought to be preferred over York time. (Damore writes that a “majority” are “persuaded by the metric of Cosmic Time and its present implications”.) But what is cosmic time preferred for? There certainly are contexts in which physicists do prefer York time, e.g., in the context of numerical relativity. In context, Damore presumably means that physicists prefer cosmic time as a candidate for absolute time. But then this cannot be described as a consensus, since most physicists deny absolute time altogether. For those physicists who do subscribe to absolute time, I don’t have survey results for how many prefer either York or cosmic time as measures of absolute time; I submit that Damore does not either.
We do have one piece of evidence, namely, the role that York time plays in canonical quantum gravity and the absence of any similar role for cosmic time. But this bit of evidence supports the view that York time is the preferred candidate for absolute time.
Still elsewhere, in describing the parametrization of FLRW models in terms of the cosmic time, Damore writes, “The [FLRW] metric describes a natural foliation, but that natural foliation (the constant time surfaces) can then be used to describe the universe in terms of Cosmic Time, and then Cosmic Time can then be used to label the CMC foliation.” Damore goes on to write: “From the previous concept, it’s really easy to see how Craig can arrive at the privileged status of Cosmic Time using the natural foliation given to us by the spacelike hyperplanes of constant t [that is, constant cosmic time]. The special group of ‘preferred observers’, the fundamental observers, clearly define a privileged cosmic time, a ‘real cosmic time’.”
I think Damore is confused about the order of explanation, but set that aside. Damore is right that we can write the FLRW metric in terms of the cosmic time. We can also write the FLRW metric in terms of the York time. After all, the same hypersurfaces that can be labeled by the cosmic time can also be labeled by the York time. In fact, a slight variant of the argument Damore describes, albeit without reference to fundamental observers, can be posed in terms of York time. For that reason, Damore has not provided us with a reason for preferring cosmic time as a candidate for absolute time. In fact, given that the Hamiltonian evolution of a relativistic spacetime is more naturally expressed in terms of the York time than the cosmic time, there is a strong sense in which the universe’s evolution is better expressed in terms of York time.
(Technical aside. Here’s a sketch of an argument for the conclusion that the FLRW metric can be expressed in terms of the York time. Supposing that the bijective map between the cosmic time 
Lastly, Damore provides a block quote where I deal with a possible objection, namely, the objection that physically embodied observers whose clocks measure cosmic time are easier to come by than physically embodied observers whose clocks measure York time. I reply that on Craig’s view, following Newton, local clocks do not coincide with God’s absolute time. Damore finds this reply “underwhelming”. Why? Because Craig asserts over and over again that the proper time of the local clocks of fundamental observers who are co-moving with the universe’s expansion “very nearly approximate Absolute Time”. Right, of course I know that this is what Craig asserts. But I want to know why we ought to believe that what Craig says is true. Damore doesn’t help matters by merely quoting Craig.
5. Neo-Lorentzianism Invites Skepticism
Throughout his post, Damore accuses me of being overly skeptical. On some occasions, he simply misunderstood the role that skepticism plays in my arguments. For example, I presented some standard and well known arguments for why physicists reject truncated spacetimes as unphysical and tend to only consider maximally extended spacetimes. According to the argument that I discussed, we ought to avoid truncated spacetimes because truncated spacetimes lead to skeptical consequences. For reasons that I don’t completely understand, Damore takes my comments to endorse some wild form of skepticism for which Damore apparently has no patience.
On other occasions, Damore overplays what sort of inferences intuition can license; since I don’t think intuition can do what he thinks intuition can do, he thinks that I am much more skeptical than I ought to be. For example, in response to my point that the observable universe is consistent with spacetime, as a whole, having any one of several different global features, Damore replies that we can rely on what seems to us to be the case. I take it that Damore is making a similar move to the one phenomenal conservatives make in reply to brain-in-the-vat scenarios. That is, even though my experience might be indistinguishable from the experience of a brain-in-a-vat, until provided adequate reason to doubt my experience, I should think that my experience is precisely what it seems to be, viz, the experience of a real external reality. Unfortunately, I simply have very few, if any, seemings about the global structure of spacetime. Insofar as I can tell, the best that we can do is to survey the matter-energy distribution in the observable universe and then use General Relativity to infer the contents of regions beyond our cosmological horizon; unfortunately, there are good mathematical reasons for thinking that this sort of inference cannot be successfully made. So, the two scenarios do not appear to be analogous.
Ironically, Neo-Lorentzianism, itself, leads into skepticism. Neo-Lorentzianism is committed to the view that all of the experimental tests of Special and General Relativity that we can carry out yield illusory results. Although all of our experimental tests seem to vindicate Special and General Relativity, both are actually false; instead, Neo-Lorentzians maintain that an alternative is true, in which universal forces conspire to produce all of the observational consequences of Special and General Relativity.
Both Special/General Relativity and Neo-Lorentzianism predict that, e.g., muons will live longer (on average) when in motion relative to us than when they are rest, that atomic clocks will record less time on airplanes than a counterpart that remains situated on the ground, and that the clocks on satellites will not keep time with ground-based clocks. But the explanation that either theory proffers will be distinct in important respects. For Special and General Relativity, each clock records how much time passes for that clock. In other words, on Special and General Relativity, what clocks seem to measure — how much time they record passing — is what they really do measure. In contrast, for the Neo-Lorentzian, clocks simply do not measure what they seem to measure. Instead, any clock that is in motion with respect to the universal reference frame is subject to universal forces that result in that clock producing spurious readings. The degree to which the readings of any given clock differ from the true time is a function of how fast that clock is moving with respect to the universal reference frame. Faster moving clocks produce worse results because they are subject to greater universal forces. If the Neo-Lorentzian is right, many of the clocks used in contemporary physics laboratories are subject to universal forces that result in illusory readings. If we cannot identify how fast we are moving with respect to the universal reference frame, we cannot be confident that any clock measures what that clock seems to measure.
Note that, in the contexts in which Special Relativity is typically thought to apply, we simply have no way to determine whether we are at absolute rest or how fast we might be moving with respect to the universal reference frame. On this point, all parties agree. Thus, in the Special Relativistic context, we have a nearly complete defeater for any seemings we might have for the rate at which time passes.
By way of analogy, suppose that I bring you into a room where there appears to be a red piece of fruit on a table. Since you seem to see red fruit, you are thereby justified in believing that there truly is red fruit in front of you. But now suppose that you learn that the lights in the room have been replaced by red lights. No matter the fruit you are presented with, that fruit will appear red. You now have a reason to lose your confidence in your seemings concerning the color of the fruit in the room. Worse, imagine that you are presented with a bowl of fruit and asked to identify which fruit is truly red and which fruit merely appears red. You would have no principled way of doing so. Likewise, suppose that you are presented with a clock. Since you seem to see a clock you are thereby justified in believing that time is passing at the rate indicated by the clock. But now suppose that you learn that there are universal forces that act on nearly all clocks to distort the rate at which they read time. No matter the clock you are presented with or the universal forces that clock is subject to, that clock will appear to read the rate at which time passes. Pondering on this issue, you realize that you have an internal clock and that there is a rate at which time seems to pass for you. Perhaps you can determine whether the clock you have been presented with correctly reads the rate at which time passes by comparing that clock with your internal clock. But, like any other clock, internal clocks are potentially subject to universal forces that distort their readings; supposing that the clock you are presented with and your internal clock disagree, all that you can rightfully conclude is that at least one of the two must be wrong. You now have a reason to lose your confidence in your seemings in the rate at which time appears to pass. Worse, imagine that you are presented with a collection of clocks and asked to identify which clock, if any, tells the true rate at which time passes. You would have no principled way of doing so.
Perhaps things are different in the contexts in which General Relativity is typically thought to apply. In that context, Craig has presented an argument for the conclusion that we can determine how fast we are moving with respect to the universal reference frame. We observe a specific kind of anisotropy in the cosmic microwave background and this, Craig claims, indicates that we are moving with respect to the universal reference frame. This argument is difficult to understand because General Relativity does not include a universal reference frame and yet is completely consistent with the observed anisotropy. For that reason, the observed anisotropy does not rule out General Relativity. Moreover, without a fleshed out Neo-Lorentzian alternative to General Relativity, I have a difficult time seeing why the observed anisotropy should be expected given Craig’s view. For that reason, there doesn’t seem to be a relationship between the epistemic probability of absolute simultaneity and the observed anisotropy.
Set all of those misgivings aside. Let’s suppose that the observed anisotropy does suggest a universal reference frame and that the observed anisotropy suggests we are moving with respect to the universal reference frame. Since we are moving with respect to the universal reference frame, our clock measurements are spurious. But not all spurious results are illusory. As Damore would point out, the difference between the rate at which ordinary clocks tick and the rate at which absolute time passes is (perhaps) not significant; so long as the rate at which we experience and measure time passing is a very close approximation to the actual rate, the fact that our experienced rate differs from the actual rate has no skeptical consequences. Can we determine how fast we are moving with respect to the universal reference frame? Once more, consider that, in an FLRW space-time, our observations of the cosmic microwave background make no difference to whether we understand cosmic time as (an approximation to) absolute time or whether we understand York time as (an approximation to) absolute time. If we combine either assumption with the observed anisotropy, then we will come up with distinct answers for the Earth’s absolute velocity. There isn’t going to be a way to settle the degree to which the readings of ordinary clocks are illusory without first settling which clock, if any, measures or approximates absolute time. Consequently, we are left with our original defeater.
Note that the set of universal forces postulated by the Neo-Lorentzian do not, and by construction cannot, act differently on different kinds of matter. No matter how we construct a clock, that clock, if in motion with respect to the universal reference frame, will be subject to universal forces that alter how much time that clock records as having passed. If this were not so, then Special and General Relativity would not be empirically adequate.
Note, too, that Craig, and other friends of Neo-Lorentzianism, leave entirely mysterious what those universal forces are or how they couple to matter. We are offered no explanation whatsoever for how clocks, with entirely different constructions, could produce the same spurious results. We are provided no information at all concerning the universal forces other than that they need to be postulated so as to reproduce the predictions made by Special and General Relativity. We have no Lagrangian, no field equation, no equation of motion. Nothing. On what grounds can we then say that some set of clocks provide us with approximately correct answers? How could we possibly check whether any given clock satisfies the conditions to yield spurious results?
This issue is particularly salient in cosmology. On the assumption that both the stress-energy tensor and the cosmological constant are zero, General Relativity reduces to Special Relativity. There is a standard undergraduate level exercise to derive the Lorentz transformations from the metric tensor. In the General Relativistic context, where we do not assume that the stress-energy tensor and the cosmological constant are zero, we use the same procedure to derive a more general set of transformations from the metric tensor; a variety of General Relativistic effects are then concluded using those transformations. Consequently, if Neo-Lorentzians claim that the Lorentz transformations ought to be understood in terms of universal forces, so, too, they should understand a variety of General Relativistic phenomena, which have a similar derivation from the metric tensor, as the result of universal forces.
Here, we return to the problems posed by instrumentalism that I discussed near the outset of this post. Consider the elementary school experiment in which sprinkling iron filings around a magnet reveals the magnetic field around the magnet. The bits of iron line up with the magnetic field because, as described by the Lorentz force law, the magnetic field exerts a force on the iron. In turn, the magnetic field is described by Maxwell’s Equations. Someone could deny that the magnetic field exists and adopt an instrumental interpretation of Maxwell’s Equations. They would say that Maxwell’s Equations are empirically adequate — they enable us to successfully predict the motion of bits of iron, for example — even though the magnetic field they describe has no metaphysical reality. What they cannot do is to say that, at the level of fundamental metaphysical description, there is a region where the magnetic field becomes unboundedly large.
Likewise, on standard interpretations of General Relativity, matter tries to take the “straightest” path between any two points, but, as described by the geodesic equation, the “straightest” path is curved. Spacetime, itself, is then described by the Einstein Field Equations. The geodesic equation has a role analogous to the Lorentz force law and the Einstein Field Equations a role analogous to Maxwell’s Equations. Just as the iron filings reveal the magnetic field to us, the motion of objects reveals the curvature of spacetime. To say that spacetime is singular, at least in the sense relevant for the Big Bang, is just to say that there is some spacetime region where the curvature becomes unboundedly large. Thus, just as with electromagnetism, to infer that spacetime is singular requires that we take up a realistic interpretation of the geodesic equation and Einstein Field Equations — that is, that we reject the instrumentalism recommended by the Neo-Lorentzian.
The consequence of pursuing the path Craig and company have laid out for us is that Big Bang cosmology has no clear relevance for whether the Universe began to exist.
Author: Daniel Linford
References
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Gilmore, C., Costa, D., & Calosi, C. 2016. “Relativity and three four-dimensionalisms”. Philosophy Compass 11(2), pp. 102-120.
Hutton, J. 1795. Theory of the Earth with Proofs and Illustrations. https://www.gutenberg.org/cache/epub/12861/pg12861-images.html
Roser, P. 2016. “An extension of cosmological dynamics with York time”. General Relativity and Gravitation 48(42), pp. 1-15. https://link.springer.com/article/10.1007/s10714-016-2037-2
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Hey peeps! This is Joe now. I hope you enjoyed the guest post! Many thanks to Dan for writing it. If you’re interested in this blog post, you’ll almost certainly be interested in my book Existential Inertia and Classical Theistic Proofs (Springer, 2023, co-authored with Dan), as well as my Kalam playlist on YouTube. 🙂
Majesty of Reason 