Friday, December 20, 2019

Cundy on relativity and the A-theory of time

One of the many topics treated in Aristotle’s Revenge is the relationship between Aristotelian philosophy of nature and contemporary debates in the philosophy of time.  For example, I argue that, while at least the most fundamental claims of an Aristotelian philosophy of nature might be reconciled with the B-theory of time, the most natural position for an Aristotelian to take is an A-theory, and presentism in particular.  Thus was I led to defend presentism in the book – which requires, among other things, arguing that the presentist view of time has not been refuted by relativity theory.  Nigel Cundy disagrees.  A physicist with a serious interest in and knowledge of Aristotelian-Thomistic philosophy, he has posted a detailed and thoughtful critique of this part of my book at his blog The Quantum Thomist.  Cundy thinks that presentism cannot be reconciled with relativity, and that other A-theories of time at least sit badly with it.  What follows is a response.

Cundy’s article is very long, but it has to be in order to set out the case Cundy wants to make.  It is well worth reading and you may want to take a look at it before proceeding, so that you have the entire context.  There are six main parts of his article.  The first is an introduction, and in the second he sets out the physics of space and time.  In the third, he evaluates the A-theory and B-theory in light of the physics.  In the fourth, fifth, and sixth sections, Cundy addresses my criticisms of the B-theory, my treatment of relativity, and my defense the A-theory.  I’ll comment on each of these parts in turn.

The physics of space and time

Cundy’s second section puts forward an admirably lucid exposition of the methodology and content of modern physics’ account of space and time.  One of the themes I consistently hammer on in Aristotle’s Revenge is the highly abstract character of physics’ description of nature, and Cundy’s exposition beautifully conveys that.  I want to pull out several key passages from his discussion, because they are essential to understanding Cundy’s main points and the points I will make in response.  Cundy writes:

We perform a mapping to a geometrical space, which is an abstract object. So every point in physical space time corresponds to a point on the geometrical space, and vice versa. We have a great deal of freedom in choosing the geometrical abstraction, but not total freedom… We then perform a second mapping from the geometrical space time to a coordinate space, i.e. we assign a number to every point in the geometrical space. Again, this is a one to one mapping, and there is even more (but not total) freedom in how we do this… This freedom should not affect our predictions concerning physical space time. Wherever we place the origin of our coordinate system, we should make equivalent predictions. There are not many possible theories which pass this criteria, and one of the driving forces behind contemporary physics is that we are restricted to just those theories. Indeed, this is one of the key principles behind the theory of relativity.

End quote.  This is followed by a description of how this approach to representing space and time gets worked out in the case of special relativity.  Cundy then writes:

This geometry provides a background on which physics takes place. It is not all there is to physics. Additionally, we require an additional set of abstract objects which represent the matter (or perhaps our knowledge of material states). This second abstraction builds upon the representation of space time, since we say that there is a certain likelihood (or amplitude) that a particular particle exists at a particular place, and the representation of matter thus depends on the coordinate system being used. When we perform a coordinate transformation, we must also at the same time transform the details of how we represent a material object. So the representation of matter is linked to the representation of space time, but contains additional information.

We can also introduce natural coordinate systems for each observer, i.e. where the observer is at the origin of their coordinate system… So two observers A and B each have their own coordinate system with themselves at the origin.

End quote.  Now, a representation is abstract to the extent that it focuses on certain features of the thing represented to the exclusion of others, and the specific mode of abstract representation utilized by modern physics is mathematical.  What Cundy is pointing out so far is that space, time, matter, and the observer are represented in special relativity in a way that is doubly abstract.  It isn’t just that they are represented geometrically, but that the geometry in turn is represented in an abstract coordinate system.  Cundy continues:

The statement of relativity is that coordinate systems must be relative to each other, and that there is no absolute coordinate system. This I take to be so deeply enshrined in physics that I don't think that anybody can rationally challenge it. It also makes philosophical sense: there is no right way in which to construct the abstraction. We have to pick one, but ultimately we are free to choose. "Absolute space" is interpreted to mean that there is some preferred frame of reference, and with regards to describing the locations and times of physical objects this is not the case.

End quote.  Cundy then moves on to a discussion of symmetry.  But before we turn to that we need to pause, because it seems to me that Cundy is inadvertently gliding over a crucial issue here.  Let’s concede for the sake of argument that the relativity of coordinate systems is indeed “so deeply enshrined in physics that I don't think that anybody can rationally challenge it.”  Why is it so deeply enshrined?

As philosophers of science sometimes point out, it is hard to avoid the conclusion that the reason has to do with the verificationism that famously guided Einstein as he first hammered out special relativity, and that was so influential in physics and philosophy at the time.  The sense in which there is no preferred frame of reference is simply that there is no empirical test that can justify a preference for one frame rather than another. 

Now, the problem this poses is this.  Verificationism can be read either as a philosophical position or as a methodological constraint.  As a philosophical position, it is the thesis that no statement is meaningful unless it is either analytic or empirically testable (where mathematics is put on the analytic side of this divide).  In the present context, this would have the implication that talk of an absolute frame of reference is, since neither analytic nor empirically testable, strictly meaningless.  That is to say, it literally has no intelligible content.  Special relativity coupled with philosophical verificationism would thus have the dramatic metaphysical consequence that it is in principle impossible for there to be a privileged reference frame.  The trouble with this interpretation, though, is that verificationism has been refuted about as decisively as a philosophical thesis can be.  The problems with it (which I summarize at pp. 139-45 of Aristotle’s Revenge) are many and grave, and they led to its almost complete abandonment within philosophy of science by the middle of the twentieth century.

Better, then, to read verificationism as a mere methodological constraint.  Here the idea would be that even if statements that are neither analytic nor empirically testable are not strictly meaningless, physics is simply not concerned with them.  Physics, on this view, ought to confine itself to what is susceptible of what Jacques Maritain called an “empiriometric” analysis, viz. the use of mathematical representations to organize data about what is directly empirically detectable.  While there may or may not be aspects of reality that are beyond empirical testing and/or mathematical representation, they are simply not within the ambit of physics.

Now, whereas verificationism as a philosophical thesis has radical metaphysical implications, verificationism as a methodological constraint has, by itself, no metaphysical implications at all.  Hence the absence of an absolute reference frame from special relativity, when interpreted in light of merely methodological verificationism, by itself does not entail that there is no absolute reference frame in objective reality.  The failure of a method to reveal some thing X gives you reason to think that X does not exist only if you already have independent grounds for thinking that the method would have revealed X if X did exist.  In the present case, the absence of a privileged reference frame from the physics of relativity would entail that there is no such frame in objective reality only if we have an independent philosophical rationale for thinking that the physics would reveal it if it were there.  And in that case it would really be the philosophical rationale, and not the physics, that is doing the main work.

The trouble is this.  This distinction between philosophical implications and merely methodological constraints is, it seems to me, constantly blurred in discussions of the metaphysical implications of relativity.  Rightly impressed by the inherent beauty and brilliance of Einstein’s theory and by its spectacular empirical successes, people jump to the conclusion that the physics of relativity has established some dramatic metaphysical claim – that presentism is false, that time is an illusion, or what have you.  But the physics has done no such thing.  It would have such implications only given philosophical verificationism, or given some other philosophical argument in defense of the thesis that the methodology of physics provides an exhaustive description of its subject matter.  And in that case it would, again, be the philosophical arguments, and not the physics, that are doing the metaphysical heavy lifting.  You won’t ever pull more philosophy out of physics than you first put in.

Since Cundy’s view seems to be that relativity of itself rules out presentism and threatens other versions of the A-theory as well, this should raise a red flag.  But Cundy has a lot more to say, so let’s return to his exposition.  He turns next to an explanation of symmetry, and he relates this to the notion of structural realism.  He writes:

Professor Feser himself adopts structural realism, where the reason that the abstract representation used by physics is successful is that it maintains the same relationships between the representations of the objects as exists in reality. I quite agree with him that this is crucial…

Now identifying a symmetry relies on two principles, the transformation or relationship between different points (or potentia in things), and the statement that two physical configurations are equivalent. As a structural realist, Professor Feser would agree that there must be something corresponding to the transformation in physical reality if the physical description is accurate. Equally, if two configurations are equivalent in reality, if it is to be in any way accurate, they must also be so regarded in the abstracted representation (and if they are not equivalent, they must be distinct in the representation). Thus if we need to construct the representation with a particular symmetry in order to make it line up with reality, then that symmetry must also be present in reality. So if you give the idea of structural realism to a contemporary physicist, part of what he will do to break it down into something he can work with is to demand that both reality and the physical abstraction should respect the same symmetries.

End quote.  Now, here we need to pause again.  The kind of structural realism I defend in Aristotle’s Revenge is, specifically, epistemic structural realism.  This is a middle ground position between instrumentalism on the one hand, and scientific realism of the usual sort on the other.  It holds, against instrumentalism, that physics is not merely a useful tool for making predictions and developing technologies, but really does reveal to us something that is objectively there in nature.  But it also holds, against the more familiar sort of scientific realism, that what this something is is merely the mathematical structure of the natural world.  In particular, physics reveals mathematical relations, but does not tell us about the intrinsic nature of the entities related by these relations.  (Or to be more precise, we can have much less confidence in anything physicists have to say about the relata themselves than we can have that the mathematical relations that relate them are real.)

Cundy is astute to emphasize this view of mine, because it is an absolutely crucial component of the overall argument of Aristotle’s Revenge.  Some readers seem to jump straight to whatever part of my book deals with some particular topic they are especially interested in, and to read that part in isolation from the rest of the book.  This can lead to serious misunderstandings.  Epistemic structural realism is not some incidental part of the book.  It is central to the way I deal with a number of topics, especially topics in physics.

Cundy not only does not make the mistake of overlooking this, he cleverly tries to use this broader philosophical commitment of mine as a way to force me into precisely the sort of interpretation of relativity that I am using structural realism to avoid.  (Though as an aside – and to forestall a foolish ad hominem objection I am sure some hostile reader will try to raise – I do not adopt structural realism for the purpose of avoiding such an interpretation of relativity, in an ad hoc way.  As the book shows, I have ample independent grounds for adopting structural realism.  Indeed, I’ve been a structural realist since before I was a Thomist, way back in my atheist days in the 1990s when I first got interested in the work of the later Bertrand Russell.  It is a standard option in philosophy of science that is typically defended for reasons having nothing to do with debates over presentism, Aristotelianism, etc.)

Cundy’s strategy is going to be to argue that even if what physics reveals is structure, if symmetries in the mathematical representation of nature mirror symmetries in nature itself, then we should conclude that there must be in nature something corresponding to the structure represented in the physics of relativity.  And since the latter treats past and future events as on a par with present ones, we should conclude that past and future events really are no less real than present ones – which is, of course, precisely what presentism denies.

As I say, this is a smart strategy, but I don’t think it works.  The reason is that the structure affirmed by the usual formulations of structural realism (including mine) is much more abstract than Cundy’s argument requires.  Take, for starters, Russell’s version of structural realism.  As I discuss in the book, Russell’s initial version of the view held that what physics reveals to us is in fact only the properties of the relations holding between the entities to which it refers, as captured in the language of modern formal logic.  This is extremely abstract – it tells us only that the entities to which physics refers bear relations to one another that have properties such as transitivity, reflexivity, and the like.  It opened Russell up to an objection raised by the mathematician M. H. A. Newman, according to which Russell’s position made the knowledge afforded by physics entirely trivial.

Now, a structural realist need not take Russell’s approach, and in Aristotle’s Revenge I reject it.  The point is just that there are various things “structure” can mean, and the more abstract one’s conception of the structure revealed by physics is, the less metaphysical bite physics can have.  Now, the version of structural realism I defend in the book is closer to that of the contemporary philosopher of science John Worrall.  Worrall’s view is that what tends to be preserved through theoretical revolutions in physics are mathematical equations.  A favorite example of his is the equations that survived the transition from Fresnel’s account of the nature of light to Maxwell’s account.  Now, though they use the same equations, Fresnel thought of light in terms of an elastic solid ether, whereas Maxwell thought of it in terms of a disembodied electromagnetic field.  That illustrates just how metaphysically thin the knowledge of objective reality provided by the equations is.  The truth of the equations does not by itself tell in favor of one or the other of these very different conceptions of the nature of light. Only considerations distinct from the equations can do so.

In the case of special relativity too, the mathematics is compatible with a variety of possible metaphysical interpretations.  One could, of course, adopt a B-theory of time.  But as William Lane Craig emphasizes, one could instead accept the mathematics and nevertheless adopt Lorentz’s conception of space and time rather than Einstein’s.  Or one could take Dean Zimmerman’s view that there is a privileged slicing of the four-dimensional spacetime manifold that corresponds to the present, but that physics is simply unable by its methods to identify it and must be supplemented by metaphysics.  Or one could endorse Michael Tooley’s attempt to marry special relativity to a “growing block” version of the A-theory.  Or one could take yet some other option. (I discuss all these in the book.)

It is crucial to understand exactly what I am saying here.  I am not endorsing Craig’s neo-Lorentzian position, or Zimmerman’s or Tooley’s or any other interpretation.  That’s not the point.  The point is that the mathematics by itself (which, for the structural realist, is all that the physics gives us confidence in) doesn’t tell you which of these views, with their radically different metaphysical implications, is correct.  Mathematical structure is simply too abstract for that.  Hence physics interpreted in a structural realist way is not going to have the metaphysical bite that Cundy seems to think it does.  And so it cannot refute presentism or the A-theory more generally or any other metaphysical position regarding time.  There may or may not be other reasons that decisively refute one or more of these positions, but if so they will have to be reasons additional to the mathematical representation.

Coming back to Cundy’s exposition, let us now consider what he says about the relationship between space and time.  He writes:

Would the symmetry then just map points next to each other in time, and not require the whole four dimensional space? But if we say that the symmetry only maps the neighbouring points of time means that only those neighbouring points exist, then we ought to conclude the same thing about space. Nobody denies the existence of points far from me when considering a space-space rotation. We should conclude the same thing when considering a rotation between space and time.

End quote.  Cundy’s argument here appears to be that since relativity treats past and future points in time in a way that is analogous to the way it treats distant points in space, to be consistent we should regard them as ontologically on a par.  In particular, since we regard distant points in space as no less real than near ones, we should regard past and future points in time as no less real than the present one. 

Naturally, this invites the retort that Cundy is fallaciously reading into physical reality features that reflect only the mode of representation rather than reality itself – in particular, that he is supposing that since the mathematics effectively spatializes time, time itself must be something like a spatial dimension.  But Cundy has a reply to this objection.  Alluding to some points he had made earlier in his exposition, he writes:

Just because we are treating space and time as contained within one four dimensional block does not mean that time is just the same sort of thing as space. I want to highlight three differences. Two I have already mentioned. The first is that minus sign in the metric; that is of significant importance. The second is the need for time ordering in the calculation of the amplitude: this is an admission that we cannot ignore the causal sequence. The third is related to energy and momentum. In quantum physics, momentum is a measure of how likely a particle is to move in space, or, on average, how fast it moves. Energy is the corresponding quantity relating to time; it tells us how quickly the particle's internal clock moves... But while momentum can be either positive or negative – particles can move forwards and backwards in space – energy is always positive. This means that particles can only move forwards in time.

The first of these differences is well acknowledged by the philosophers who favour the tenseless theory of time, but the second two, arising from relativistic quantum field theory rather than special relativity alone, are perhaps less well known. Together, they mean that a) there is a direction in time, from past to future, and b) moments of time follow one after another. These differences apply to time but not space.

End quote.  Now, in Aristotle’s Revenge I explicitly acknowledge (at pp. 275-76) that modern physics does not in fact treat time exactly as it does space, and certainly it does not assimilate time to the commonsense notion of space.  So this is a bit of a red herring.  What is really going on, I argued, is that mathematical representations of the sort Cundy has been describing essentially desiccate both time and space.  It’s not that they drag time down into the world of concrete spatially located objects, making movement through time literally like forward movement through space.  It’s rather that they raise space and time alike up into eternity.  They make of space-time a kind of Platonic abstract object that is spaceless no less than it is timeless, or at any rate is like neither time nor space in the ordinary conceptions of those things.

The features identified by Cundy don’t show otherwise.  Directionality and succession do not suffice for time, or for space for that matter.  Number series exhibit both, but they are neither temporal nor spatial.  After 1 comes 2, after that comes 3, then 4, and so on.  Numbers get larger as you go forward in the series just as you get older as you go forward in time, and the numbers can’t change places in the series any more than events can.  But again, number series are not temporal.

No doubt Cundy will say that it is the causal relations between events in a series that makes them temporal.  But the problem is that it is also hard to see what remains of the ordinary notion of causality when the ordinary notions of space and time are both replaced by coordinate systems of the kind Cundy describes.  If points in time are as equally real as points in space, then a stick’s going from rest to motion is like it’s being red at one end and green on the other.  The latter is not a change but just the having of different attributes at different spatial parts, and it is hard to see how the former amounts to a true change either, as opposed to merely the having of different attributes at different temporal parts.  And if we replace our ordinary notion of space no less than our ordinary notion of time with the idea of points in an abstract coordinate system, the result is something even less like change in the ordinary sense.  But without change in the ordinary sense (which, Cundy agrees, entails the actualization of potential) what becomes of causality in the ordinary sense?  We don’t seem to be talking about change or causality at all as we consider the coordinate systems Cundy is describing, but simply noting different aspects of a kind of Platonic object.

As the philosopher of physics Lawrence Sklar points out, a persistent source of fallacies when discussing the metaphysical implications of physics is the circumstance that the physicist often uses the same words as common sense does, but attaches to them radically different meanings.  This generates the illusion that the physicist and the man on the street are talking about the same thing, when in fact they are not.  When the link of analogy between “time” in the ordinary sense and “time” as the physicist uses the term has been broken, the continued use of the same term invites a fallacy of equivocation.  Sklar writes:

If what we mean by ‘time’ when we talk of the time order of events of the physical world has nothing to do with the meaning of ‘time’ as meant when we talk about order in time of our experiences, then why call it time at all?  Why not give it an absurd name, deliberately chosen to be meaningless (like ‘strangeness’), and so avoid the mistake of thinking that we know what we are talking about when we talk about the time order of events in the world?  Instead let us freely admit that all we know about ‘time’ among the physical things is contained in the global theoretical structure in which the ‘t’ parameter of physics appears.  And all the understanding we have of that global structure is that when we posit it, it constrains the structure among those things presented to our experience in a number of ways.  And that is its full cognitive content. (“Time in experience and in theoretical description of the world,” pp. 226-27)

What Sklar says about “time” is no less true of words like “space,” “change,” and “cause.”  Because the physicist continues to use these words, it can seem like he is talking about the same things as the man on the street and the Aristotelian metaphysician are when they use those terms.  But that is not the case, because the elements of the world that are constitutive of time, space, change, and causality in the ordinary and Aristotelian senses have been drained out of the mathematical representation utilized by the physicist.  Hence Cundy seems to me in danger of exactly the sort of equivocation that Sklar is warning of.

The A-theory and B-theory in light of physics

Let’s turn now to the section of Cundy’s article which applies the physics to the dispute between the A- and B-theories of time.  Presentism is the version of the A-theory that I favor, but Cundy judges that it is flatly incompatible with the physics of relativity.  He writes:

It should be immediately obvious that presentism violates Lorentz symmetry. It requires that only one moment of time, the same moment throughout the universe, is real, and there is a distinction between the past and future on one hand and the present on the other. The geometrical and coordinate representations contain points for all of past present and future. This means that we can map between the present in reality and one time slice in the representation, but there isn't anything to map to the locations in the representation which represent past and future events. This means that the representation would have Lorentz symmetries, mixing time and space, but reality can't… Thus, if presentism were true, the representation would have a greater degree of symmetry than reality. As stated above, this is impossible (if the predictions of the abstract representation are to accurately match the real world, and the real world is complete and doesn't have any missing causes).

End quote.  Cundy goes on to make critical remarks about the “growing block” and “moving spotlight” versions of the A-theory too (albeit not quite as critical since these views do not claim that the present alone is real). 

Now, once again it seems to me that Cundy is underestimating how extremely abstract the information contained in the mathematics really is.  He seems to be implying that one can read off the equal reality of past, present, and future events from the mathematics itself.  And that is simply not the case.  You might as well say that you can read off the falsity of presentism from the truth of the sentence “I was in the kitchen a minute ago, am now in my study, and will be in the garage in another minute.”  Of course, it does not follow from the truth of this sentence alone that the states of affairs of my being in the kitchen, my being in my study, and my being in the garage are all equally real.  To show that, one would need additional, metaphysical argumentation to the effect that the truth of the sentence cannot be accounted for in a presentist way.  But the same thing is true of the mathematics of special relativity. 

This is precisely why positions like Craig’s neo-Lorentzian presentism, Tooley’s growing block interpretation, etc. can get off the ground at least long enough to require detailed criticism from opponents of the A-theory.  The critics typically don’t say that Craig, Tooley, et al. simply fail to understand the implications of the mathematical representation, and then quickly dismiss their positions on that basis.  Rather, the critics allow that Craig, Tooley, et al. offer possible interpretations of the mathematics, but then accuse them of having to make ad hoc assumptions, of putting too much stock in independent metaphysical considerations, etc.  Again, the point isn’t to endorse any of the specifics of the interpretations defended by Craig, Tooley, et al., but just to emphasize how little the mathematical representation by itself settles. 

However, I would certainly endorse the view of Craig, Tooley, et al. that it is perfectly legitimate to allow independently motivated metaphysical considerations to guide one’s interpretation of the mathematics.  Again, I would say that that is what all sides of the debate – the critics of the A-theory no less than its defenders – are doing, and have to do.  Like Dean Zimmerman, Arthur Prior, and other defenders of presentism, I would say that the most that special relativity rules out is a privileged reference frame that is empirically detectable.  But that makes the notion of a privileged reference frame objectionable only if one assumes verificationism or some other brand of scientism – which are philosophical positions rather than anything required by the physics, and positions which (I argue) we already have ample reason to reject whatever we think of special relativity.  On alternative philosophical positions (such as the Aristotelian one I endorse) we have independent metaphysical grounds to affirm presentism, and it is no less legitimate for the A-theorist to be guided by these grounds when interpreting relativity than it is for critics of the A-theory to interpret relativity in light of their own philosophical assumptions (verificationism, scientism, or whatever).

Nor, contrary to Cundy, does adopting presentism entail that there are aspects of the mathematical representation that correspond to nothing in reality.  For there are more ways in which the representation might correspond to reality than the one Cundy supposes.  As I note in Aristotle’s Revenge at pp. 269-70, one could say that only the present exists, but that there are in the collection of presently existing objects taken as a whole potentialities for generating future outcomes, including the range of observations that might be made by different observers, of the kind represented by the mathematics of special relativity.  That’s a pretty thin kind of realism, to be sure, but as I keep saying, the realism defended by the structural realist is pretty thin in any event.

It is also important to keep in mind that an aspect of a mathematical representation can both correspond to reality in one respect while in another respect being a mere artifact of the mathematics.  A simple and common example would be a statistical claim to the effect that there are 2.5 children in the average family.  Such a claim is grounded in reality insofar as if families today had as many children as families tended to have a century ago, the number would have been higher.  But at the same time, there is, of course, no family with 2.5 children.  That the average number of children per family comes out to be 2.5 is an artifact of the mathematics.  In the same way, the empirical success of relativity’s mathematical representation of space and time does not entail that all the points in time it represents are equally real in the way that all the points in space it represents are.  The appearance that they are equally real might, for all the utility of the representation shows, merely be (and in my view actually is) an artifact of the mathematics.

Since Cundy puts such emphasis on symmetry and invariance, it is worth pointing out that here too we can have something that is really just an artifact of the representation rather than of physical reality, even when the representation is in some sense grounded in physical reality.  As Cundy points out, physics’ representation of space is constructed in two stages.  There is a first mapping from physical space to geometrical space, and then a second mapping from geometrical space to coordinate space.  Now, consider Euclidean geometrical space.  Obviously it has tremendous utility in most everyday contexts, which is why people assumed for so long that it was the correct geometry of physical space.  Moreover, there are features of Euclidean space (such as the distance between two points) that remain invariant under different coordinate systems.  They show that Euclidean space has a structure that is independent of choice of coordinate systems.  Does this invariance coupled with the utility of Euclidean geometry show that the structure of physical reality must correspond to the structure of Euclidean space?  Of course not, as every student of relativity would be the first to tell you. 

And yet for all that, it remains true that Euclidean geometry wouldn’t have the utility it has if it didn’t capture something about reality.  It isn’t just made up out of whole cloth, and wouldn’t work so well if it were.  So we aren’t left with instrumentalism, exactly.  But the realism we are left with is still extremely thin.  Structure tells you something about reality, but not a whole lot, since the correspondence between the structure of a mathematical representation and the structure of reality can be pretty loose.  Hence structural realism simply cannot underwrite attempts to read strong metaphysical conclusions off of the mathematical representations employed in physics.

Turning to the B-theory, Cundy disputes my claim that it implies a Parmenidean world that is devoid of change or the actualization of potential.  On the contrary, says Cundy, “the four dimensional view allows for actualisation.  At one time, state A is actual and state B exists potentially.  At a slightly later time, state B is actual and C is potential.”  But to appeal to an example used earlier, this is like saying that a stick that is red at one end and green at the other must by virtue of that fact alone be changing its color, since it is potentially green at the first end and actually green at the other.  In fact, of course, there is no change at all, because it is not going from red to green but actually is red and green at the same time in different parts.

But the B-theory makes the attributes a thing has at different times essentially like this, and this is so whether or not it spatializes time full stop.  For on the B-theory, potentiality does not give way to actuality any more than it does in the stick example.  There is no process, but the eternal co-existence of different states.  In other words, the B-theory fails to capture real change and real causation for the same reason that, as I argued above, the physicist’s abstract space-time coordinate system, considered by itself, fails to capture them.  It eternalizes the series of events and thus strips it of change.  There is no actualizing in it, for everything in it is already actual.

Cundy tells us that his own position is neither an A-theory nor a B-theory, but a third sort of view.  The reason he is not a B-theorist, he indicates, is that he thinks that time does have a direction, that moments of time do succeed one another, and that tensed language still has utility even though “the notions of nowpastpresent and future are not objective, but observer dependent.”  But B-theorists wouldn’t necessarily deny any of this, so it isn’t clear to me from these remarks how Cundy’s view really is different from a B-theory.

Responses to my arguments

In any event, Cundy does defend the B-theory against some of the criticisms I raise against it.  Unfortunately, some of his responses rest on misunderstandings of what I wrote.  For instance, when discussing the question whether the B-theory objectionably spatializes time, Cundy accuses me of several errors.  He writes:

[Feser says that] The spatial dimensions differ profoundly from time [insofar as] You can rotate in space to convert width to height, but not convert a spatial dimension to a temporal one [and] You use a ruler to measure length and a clock to measure time, but not vice versa.

Both of these statements are false. As mentioned, a Lorentz transformation is the exact analogue of a rotation, mixing time and space coordinates: the differences in the mathematical expression arise solely from that minus sign in the metric…

Secondly, you can use clocks to measure distance. One can, for example, fire a pulse of laser light, have it bounce off a mirror at the end of the target, time how long it takes to make the round trip, and calculate from that and the known speed of light the length of the object. Coupled with an interferometer, this is, in fact, the most precise and accurate way of computing distances.

End quote.  The trouble with this is that Cundy has overlooked the context in which I made these remarks.  I explicitly said that I was describing “our pre-theoretical or commonsense notions of time and space” (p. 274, emphasis added).  So the fact that rotation of the sort in question is possible on relativity’s theoretical model of space and time is irrelevant to the specific point I was making.  Furthermore, while you can use clocks as a method for inferring distance, that too does not conflict with what I said, which is that on the commonsense conception of time, you cannot measure distance with a clock in the sense in which you can do so with a ruler.  That might seem too obvious to be worth mentioning, but that too is precisely the point.  What I was trying to describe is precisely what seems obvious to common sense.

Nor was I saying that the fact that any of this reflects common sense suffices all by itself to show that it is true.  The point is just that, before you can determine the extent to which physics either captures, revises, or abandons our ordinary conception of time, you first need (naturally) to determine exactly what our ordinary conception of time involves.  That’s what I was doing in that section.  Whether physics is or ought to be consistent with our commonsense conception of time is, of course, another question.  But the further physics departs from it, the greater is the danger Sklar identifies, viz. that of falling into a fallacy of equivocation when drawing metaphysical conclusions about the nature of time from the physics.

Cundy also seems to me to read some of what I wrote a bit uncharitably.  For example, speaking as if he were informing me of something that I didn’t know, he writes that “there is far more to geometry than just lines and planes” and that while “Euclid started defining his geometry from a set of axioms involving lines and circles… we have moved on since then, and now think of geometry in different ways.”  Naturally, I am well aware of that.  I would have thought it obvious from the context that I was using simple examples as the clearest way to introduce the idea that the mathematical representations utilized by the physicist abstract from concrete reality.

In response to the charge that “the four dimensional view of space time collapses the distinction between time and eternity,” Cundy says:

On the contrary, it maintains it. Time passes for things within the universe, eternity is for those outside it. Temporal beings have a subjective notion of the present, as from inside a B theory universe. The eternal being sees all of reality together, as one would expect from something outside a B theory universe.

End quote.  But this not only does not refute the claim that the four-dimensional view collapses time into eternity, if anything it reinforces it.  For it seems to amount to nothing more than the point that even if the B-theory is true and all points in time are equally real, time will still appear to pass and there will appear to be a unique present from the subjective point of view of the observer.  But nobody denies that much!  The question is whether this appearance corresponds to anything in reality outside the subjective point of view of the observer.  If you are worried that you are merely hallucinating the pink elephant you think you see in front of you, it is no comfort if I assure you that from your subjective point of view it really does seem to you as if there is a pink elephant there.  What you want to know is whether there really is a pink elephant there, not whether there seems to you to be one (you already know that much).  Similarly, what is at issue in the debate over the B-theory is whether time really would collapse into eternity on such a theory, not whether it would seem not to.

Cundy’s last two sections respond to my remarks on the implications of relativity, and my reasons for affirming the A-theory.  I have already addressed the first of these two topics in my comments above about the metaphysical implications (or lack thereof) of the mathematical representations employed in physics. 

In response to the A-theorist’s claim that there are truths that cannot be captured in the tenseless terms favored by the B-theory, Cundy says:

I accept that tense is a real part of the four dimensional universe, but argue that it is subjective rather than objective. Thus for everything within the universe (which includes us), there is indeed a present, past and future. But it is still not an objective feature; which moment is the present depends on when you are in time

End quote.  Once again, it seems to me that Cundy is missing the A-theorist’s point.  What is at issue between the A-theory and the B-theory isn’t whether tensed language is necessary in order to describe the way the world seems to us, subjectively.  What is at issue is whether tensed language is necessary in order to describe the way it really is, objectively.  And Cundy seems to think that such language is not necessary to do the latter job – in which case he does not after all “accept that tense is a real part of the four dimensional universe.”

In Aristotle’s Revenge, I argue that even if we could eliminate the notion of temporal passage from our description of mind-independent reality, we cannot coherently eliminate it from a description of the mind itself.  Hence the notion of temporal passage is ineliminable.  Cundy responds:

I think that Professor Feser's argument is compelling to show that the passage of time is a real feature of the world. So this argument works well against those formulations of the B theory which he criticises. But I have been arguing is that there is an alternative four dimensional viewpoint which does accept change and temporal passage. The argument from experience says nothing against this.

End quote.  In other respects too, Cundy says, he agrees with my analysis of the experience of time.  Here it seems to me that Cundy is not really replying to the A-theory but rather precisely backing himself into a version of the A-theory, namely the “moving spotlight” version that he elsewhere claims to reject.  His main reason for rejecting it, he tells us earlier in his article, is that it seems to him an ad hoc and unnecessary addition to the picture of the world given by the B-theory.  But it seems to me that Cundy’s acceptance of the ineliminability of temporal passage gives him a non-ad hoc reason to endorse it. 

Cundy’s position is therefore ambiguous.  On the one hand, his affirmation of the equal existence of past, present, and future moments of time and his characterization of tense and presentness as “subjective” seem to imply a B-theory.  On the other hand, his Aristotelian-Thomistic commitment to the reality of change as the actualization of potential and his affirmation of the ineliminability of temporal passage seem to point to an A-theory.  It appears to me, then, that Cundy may really be a “moving spotlight” theorist without realizing it, or at least that adopting a version of the moving spotlight theory might be the best way for him to make his various commitments cohere.

A lot more could be said, but this post is long enough as it is.  I will end by noting that the briefest way to sum up my own position would be as follows.  We cannot coherently deny the reality of change and temporal passage, but the B-theory implicitly denies these by effectively collapsing time into eternity.  So we should adopt an A-theory instead.  Furthermore, given its methodological verificationism and the abstractness of its mathematical representations, physics simply gives us way too thin a description of the world to have much in the way of metaphysical implications.  In particular, by itself it gives us no reason to prefer the B-theory to the A-theory.  Meanwhile, versions of the A-theory like the growing block theory and the moving spotlight theory make needless and ill-advised concessions to the B-theory, which lack motivation once the problems with that theory are exposed.  So, the version of the A-theory we should adopt is presentism, which makes no such concessions. 

For the detailed exposition of these lines of argument, see Aristotle’s Revenge.  I thank Dr. Cundy for his serious engagement with the book, and in particular for setting out such a clearly reasoned, well-informed, thorough and constructive critical response.


  1. I wonder if Cundy will find the time to respond to this. He's mentioned that, as a physicist, he really wants philosophical experience.

  2. "to forestall a foolish ad hominem objection I am sure some hostile reader will try to raise"

    Somehow that reminds me of the comments in a recent thread. I wonder why.

  3. Not to toot my own horn, but I would really encourage readers to read (and Dr. Feser to comment on) my exchange with Dr. Cundy in the comment section of that blog. Comments 2 thru 6 (between Scott Lynch and Nigel Cundy) to be precise. It seems like Dr. Cundy’s view is ontological presentism with an epistemological eternalism. He even goes on to say that if the speed of light were infinite, it would invalidate all of his objections to Dr. Feser.

    That is to say it seems he is saying that presentism is ontologically true in any given person’s reference frame, but when we transform to different reference frame, things look a lot more murky. That is to say past and future (from an epistemic point of view) are observed relative. I make the point that the intellect’s ability to abstract all material conditions make it so that an alien 10,000 light years away can speak ontologically of Socrates dying in the past even though epistemically (apart from Divine Revelation) the event is in the future for him (that is he cannot be causally affected by it for 8,000 years because of the light cone).

    1. Scott: He even goes on to say that if the speed of light were infinite, it would invalidate all of his objections to Dr. Feser.

      But the speed of light isn’t infinite, so that’s surely irrelevant.

    2. I don’t think it is irrelevant. His interpretation of the way we make transformations between coordinate systems seems to suggest that the speed of light affects what is past, present, and future, depending on your relation to a specific event. But if the speed of light affects that, then it seems like elements of eternalism are a mere artifact of the light cone which is primarily an epistemic reality, not an ontological one. Why should the speed of information have an affect on the reality of past present and future of things in themselves?

    3. Well, the Theory of Relativity states that it isn’t just an epistemological difference. In order to explain the experiments that have been done, there does have to be something (structurally) real about time-dilation. If the universe were different in certain ways, such that the speed of light were infinite, then it would also have to be different in being “flat” instead of curved spatiotemporally. In that case, we wouldn’t have the evidence Cundy uses to argue against Feser; that wouldn’t prove Cundy was wrong, just that he would have to make his case without recourse to physical evidence. But since the actual speed of light is finite, we have that evidence, and our metaphysics has to account for it somehow.

  4. I've been waiting for this since reading Cundy's post. Didn't disappoint! Great post Ed.

    I wonder if you are aware and have ant thoughts on how some Aristotelian philosophers square change and causation with the B theory. I'm thinking of people like Trent O'Dougherty and Alex Pruss (I think Rob Koons may be open to it as well).

    The gist would be that all causation in a 4d block would be of the simultaneous causation that Aquinas describes with the hand moving the stick which moves the stone.

    Let's say I throw a baseball to Ed. Ed swings a baseball bat and hits the ball after which Nigel catches the ball. If I get the idea right, all events would exist *actually* but there's dependence. This would in affect (to borrow Ed's language) to reduce all linear causation into hierarchical causation?

    I'm sceptical but the idea of dependence between events seems to make make room for causation than a general 'events ordered in a specific way' ontology b theorists typically go with.

    1. That could work but more would need to be said. Just what sort of thing potency is and how such dependence is to be analysed?

      Contemporary discussion about different analysis of powers and dispositions might be important here.

  5. The point about the B theory 'eternalising' time is absolutely crucial in theological debates.

    I've already mentioned Pruss and O'Dougherty, both see a 4d universe as straightforwardly allowing an eternal, immutable God to interact with the temporal world.

    As Ed points out, what typically happens is that the temporal world really becomes eternal. David Bradshaw is an Eastern Orthodox Christian who sides with Palamas' E-E distinction. One criticism he has of the West is precisely this tendency to either eliminate the temporal (like Pruss) or eliminate eternity (like Open theists do) in order for the two different spheres to interact.

    I actually think both sides (Pruss and open theists like Swinburne) have a point. But, I don't think the issue is settled. Eleonore Stump had probably given the best account for how a classical theist can have an eternal God on the one hand and a temporal world on the other, have both interact without one being reduced to the other.

    I think she is right on the money that unless her E-T ET-simultaneity broadly correct, Aquinas was wrong and you have to choose between Pruss and Swinburne.

    (Of course Pruss would probably object that he is perfectly consistent with Aquinas!)

  6. Really good post. Would like to more exchange between you two, even a co-authored work seems like a great idea.

  7. Hi Ed,

    You write:

    "What is at issue between the A-theory and the B-theory isn’t whether tensed language is necessary in order to describe the way the world seems to us, subjectively. What is at issue is whether tensed language is necessary in order to describe the way it really is, objectively...

    In Aristotle’s Revenge, I argue that even if we could eliminate the notion of temporal passage from our description of mind-independent reality, we cannot coherently eliminate it from a description of the mind itself. Hence the notion of temporal passage is ineliminable."

    Four quick questions:

    1. Are "subjective" and "objective" the only categories? What about "inter-subjective," a category popularized by Professor Yuval Harari in his bestseller, Sapiens: A Brief History of Humankind (2014)? This intermediate category describes things that don't exist in the natural world, but are agreed to exist by human beings, such as laws, money and nations. Does change belong in this category?

    2. If the only thing we cannot eliminate temporal passage from is our description of the mind itself, then in what sense can change be called an objective fact? Surely at best, it's merely inter-subjective.

    3. Supposing for argument's sake that change is confined to the mind itself, can Aquinas' First Way be reformulated accordingly? Is it obvious that a psychological change requires an external cause? Why couldn't it be internally driven?

    4. Is change real to God? If so, why?

    1. "This intermediate category describes things that don't exist in the natural world, but are agreed to exist by human beings, such as laws, money and nations. Does change belong in this category?”

      How is that meaningfully distinct from being subjective proper?

    2. "Is change real to God? if so, why": eternity, aeviternity, the present, and access to tensed states. All these are as I just suggested states. The temptation is to think of them as sorts of completely obligatory normative conditions that are enforced by God. however, this is incorrect as pointed out by your above reductio ad absurdum. If God does not live in the state being enforced, change cannot be real to him. However, they are states. So, their ontologies are self sufficient or naturally actual, [I'm playing fast and loose with the term natural here, but what I mean is to give a subtle gloss on them being potentially substantial forms rather than saying God does not need to actualize them. In the same way prime matter I would argue is a substance but doesn't exist on it's own.] rather than actualized by some external force, even if some are more privileged than others, as the present is more privileged than the past and the future, which exist in a quasi virtual state. This means that the state derives it's existence from another (the present) and has no existence on its own.

      Side note: saying a state is not in some way substantial is like saying that existence in no way affects reality. It is part of a state's ontology to be substantial. Just like it is part of being to affect reality

    3. This intermediate category describes things that don't exist in the natural world, but are agreed to exist by human beings, such as laws, money and nations. Does change belong in this category?

      Vincent, I fail to see how this presents a distinct category. If by "natural" you mean "does not occur in a world without humans", then it is true that human positive laws are not natural. But if what you mean is that laws are a sort of quasi-real things that are sort of objective and sort of subjective, this fails. It is a real part of the world that Congress approved by a majority a new provision of the U.S. Code last week. In that sense the new law is as objective as the paper it was written on - at a minimum, it has that kind of reality that comes from the fact that it was written on paper. It is irrelevant, for that purpose, whether "law" is in some sense not "objective" because (under some theories) the bindingness and obligation to observe it are due solely to mutual agreements to observe these sentences in the imperative mood. Whether law is real in that sense matters not at all to whether Congress passed a change to the U.S. Code. All Prof. Harari is identifying is the issue of whether law is "real" in the moral sense, not whether it is "real" in the sense that it has existence only to the extent that mind regards it so. Even if all human minds ceased to exist, it would still be true that Congress had approved a change in the U.S. Code.

  8. Is backward causation possible for A-T?

    Some physics experiments such as the Double Quantum Eraser experiment were considered likely evidence of things in the future causing something in the past.

    Can Aristotelianism theoretically countenance this type of backward causation - like it can theoretically countenance B-theory, or not?

    1. You should ask that question Cundy, too. Maybe there is also a different interpretation. The way I see it, what I have heard is that the vast majority of physicits regard genuine time travel as impossible. If physics prohibits that, it follows that backward causation is impossible ,too.

    2. Joe, you might interested in this post by Sean Carroll on quantum-erasure.

      The problem with “backwards” causality is trying to figure out what it could even mean. Time-travel seems to presuppose that time is some kind of “thing” that can be travelled in. But if time is just the measure of change, what could it possibly mean to “change backwards”?

      When we imagine something travelling backwards through time, what we are doing is, say, imagining watching a movie played in reverse. But we are still moving forward in time, our imagining is a forward-imagining of a movie being played backwards. The spool of film (or videotape, etc.) is moving in a different direction, but the playback itself happens by means of normal forwards-pointing causality. We aren’t really visualising reverse-causality, just things “moving backwards”.

      Consider an electron moving backwards in time: it moves — from its backwards perspective — away from another electron. But if we play a movie of that happening in the forwards direction, the backwards-electron appears to move towards the other electron, as though it were attracted instead of repelled. Now we could think of it as a negatively-charged particle moving backwards through time, but it would be more natural to think of it as a positively-charged particle moving forward through time. So it seems to me that anything that we try to set up as backwards-causality would make metaphysical sense only as merely a different kind of thing with forwards-causality.

    3. @Mr Green,

      Yes, my question was more theoretical, rather than depending on specific examples like the Quantum Eraser. Heck, in the past there were even psychic experiments done to try to determine the alleged retrocausal influence of the mind - results of a random number generator were collected before the subject actively tried to manipulate it with his mind, and so positive results would be seen as confirming retrocausality.

      What I take to be important here, then, is that retrocausality itself doesn't seem to make sense - how can something in the future exert causal influence to something in the past?

      Backwards causality / retrocausality are closely connected to time travel - they both presuppose that time is some sort of medium that one can exert influence across. And if time is just the measure of change, of potency to act, then talk of backwards / retrocausality and time travel quickly seems to lose coherence.

      I would however add that the examples of the Quantum Eraser and other potential retrocausal examples aren't exactly like playing a movie backwards - the cause in the future doesn't play anything back, but somehow reaches backwards in time to cause something in the past. So the objection that this is just a more exotic variety of forward-causality won't work.

      What do you think?

    4. Hi JoeD,

      While it is common to interpret the Delayed choice Quantum Eraser experiment (involving two entangled particles) as showing retrocausality in time, that is not a necessary interpretation of the experiment. It can be seen as correlation at work in that experiment, instead of any backward causation at work. Nature never forgets the entangled relationship between the two related particles.

    5. JoeD: And if time is just the measure of change, of potency to act, then talk of backwards / retrocausality and time travel quickly seems to lose coherence.

      Right. If something were travelling backwards in time, it couldn’t change what already happened in the past (like in a bad sci-fi story); if we sent an electron back through time, it couldn’t move another electron if the other electron hadn’t already moved in the necessary way. But that just means that we would see all the effects caused by the backwards electron as we moved forwards through time — i.e. the effects would look like the result of normal forward-causes… in which case we would just say what we were seeing was a normal forward-travelling positron. I don’t think there’s any way to say, “No, backwards causation would look different from that” without running into a contradiction.

      >[…] the cause in the future doesn't play anything back, but somehow reaches backwards in time to cause something in the past.

      What I wanted to get at is that we don’t really have any idea of what reverse-causality would mean. We might think we do, because we think we can imagine what it would be like — but really, we’re just playing scenes backwards in our memories, or something similar. I can walk backwards down the street, but that doesn’t give me any genuine insight into moving backwards through time (if there were such a thing, and so far I don’t think we have any reason to suppose that there is). So I would agree with Carroll that although examples like quantum erasure are supposed to be about backwards causation, that’s only an interpretation; and not one we should adopt.

      On top of that, Aristotelians already have a better way to understand this sort of purported “cause from the future”: a final cause is something that determines how an effect will play out in the future. The finished statue is a cause of the sculptor’s actions; but not because the future-statue is reaching back through time. The final cause exists now (it’s just not in the statue now — it’s in the sculptor’s mind). I think final causality is the right way to approach this sort of QM puzzle.

    6. @Mr. Green,

      So Aristotelians would already have a different explanation for so-called occurences of retrocausality?

      Say you have a result Z that is only caused by X influencing a charged Y directly in a controlled manner, and this time you decide to test for retrocausality and you measure the same result Z on a charged Y several days before X is present. Then later on you put X in front of a non-charged empty Y, and X tries to influence Y (but that fails due to it being a non-charged Y, and X was brought in so that it could try to exert an influence, but that influence was already exerted in the past).

      Could such an example be explained via final causality, for instance?

    7. Joe D: Your scenario would need to be spelled out in more detail, but from my forwards-looking perspective, it sounds as though what I observe is that at some point a charged system Y decays, emitting an uncharged Y and an antiparticle X’. Perhaps it’s some sort of spontaneous quantum indeterminacy. Certainly it could be explained in terms of final causality — indeed, final causality will have to figure into the explanation somehow, because any explanation without all four causes will be incomplete. That doesn’t mean simply crying “final causality” is the best or sufficient explanation; the apple didn’t fall because it was in its nature to suddenly starting moving downwards — it fell because the earth’s gravity was acting on it (and apples have as part of their final causality the tendency to be acted upon by bodies that exert a gravitational pull).

      But just saying, “Event Z happened because it’s just in the nature of Y’s to suddenly act that way” is still a better explanation than “an X was travelling backwards in time” — especially since we still don’t know how to give an actual meaning to those words.

  9. The idea of subjective time is interesting. If there could be multiple “presents”, such that each person (or indeed, each substance) had its own “timeline”, that would easily solve any problems with the physics. Now it might seem incoherent — how could something be, say, present to me, but past to you if only the present is real and the past not? But everything is in some sense “present” to God while still existing only at each of its own present moments; perhaps this notion could be extended.

  10. A region of space can be occupied by one thing, then vacated by it, and occupied by another thing. Time is not like that.

    I don’t think this is right. Time is not like what? The way it’s phrased implies that we’re talking about space in a way that one could not (reasonably) talk about time. But the sentence is talking about time too — it’s just implicit in the verb “vacated”. If we say the same thing making “time” and “space” explicit, we get something like: “The same space can be occupied by different things at different times” — which of course is easily transposed to “The same time can be occupied by different things at different spaces.” And of course that latter sentence is as true about time as the former is about space.

  11. Hello,

    I have seen one of absolutely best empirical evidence, which you may knows as fine tuning argument, but before you think it is old, I have something new into it.

    In recent academic paper, Man Ho Chan answers almost all traditional objections to it, systematically compare different hypothesis with mathematical analysis, and shows that theistic explanation is best.

    And if you think, this is just some other paper, it is very comprehensive paper with more than 120 references, which is reviewed and approved by reputable University. It is somewhat long, but worth it.

    Here's direct link to paper:

    The best empirical evidence may comes from something which is all around us, like the way nature behaves, and as evidence suggest, probably nature being directed by God because of which life, DNA, and Universe all such as it.

    Let me know your thoughts on it.

    1. Fine tuning argument,
      One major problem with the argument is that if a fine tuning argument counts as evidence for theism, so does an extremely coarse tuning.
      The paper argues that the Omega constant is extremely finely tuned so that if it is less than 0.99999999999999 or greater than
      1.0000000000000001, the conditions for life would not occur. Given the infinitude of theoretically possible values omega could have, this is meant as evidence for theism.
      However, suppose that life could occur if Omega were anywhere between 0.0000000000000000001 and 1,000,000,000,000,000,000. This is still a tiny range given the infinitude of theoretically possible values Omega could take and would also count as evidence for theism if the argument were valid.

    2. @Tim Finlay,

      I don't see how that makes the point. If a constant actually could take on an infinitude of values and only a narrow range allows anything beyond thin energy-soup, this would only mean that it is infinitely finely-tuned itself.

      It would be like a pool with infinitely many balls having only a finite quantity of cubes and the rest are spheres - the probability you would pull up a cube is extremely small, no matter how large the finite value is.

    3. Precisely, JoeD.
      It means that the fine-tuning observations are not doing any work in the argument. The argument would work with extremely coarse tuning in comparison.

    4. If the advocate of the fine-tuning argument could show, on other grounds, that Omega had to be in the range 0.5 to 1.5, for example but that for life to occur Omega had to be in this incredibly small range, then the fine-tuning observations would be doing some work. But if fine-tuning advocates make those sort of claims, I have not seen them. They certainly are not prominent in most formulations of the argument.

    5. Fine tuning argumentDecember 23, 2019 at 7:55 PM

      @Tim Finlay

      Author has answered coarse tuning objection in section 3.6.2 and other traditional objections in paper.

      Please see it.

    6. Fine tuning argument,
      As far as I can see, in section 3.6.2. they still produce no estimates for A subscript W, which is what is needed for the argument to have actual probabilities.

    7. Unless you have some sort of bound on the total parameter space (A subscript W in their terminology), the coarse tuning argument does as well as the fine tuning argument.

    8. Fine tuning argumentDecember 24, 2019 at 1:05 AM

      @Tim Finlay

      You are right that some bound needed. But to shows it, we only need to show that any parameters is not actual infinity.

      And we have good reasons to think it. Author has given reasoning like:

      "However it is possible that Aw is not an actual infinity. In the Hilbert’s Hotel paradox, even though the hotel has no vacancies, a large number of guests can be accommodated by having everyone move up a fixed number of rooms. Any countable number of guests could just as easily be fit into this “full” hotel.109 However, it is a contradiction that a “full hotel” can still be occupied by many more guests. Craig thinks that the Hilbert’s Hotel paradox proves that actual infinities do not exist. The view is that infinity (∞) is merely a mathematical device but not physically real in nature. If actual infinities do not exist, then the probability defined in Equation (3.5) can be
      possible because the probability is normalizable."

      And think about gravity. If gravity has constants larger than certain value, Universe just collapse after forming or may not even form. Or some parameters if go beyonds certain value, Universe may not exist or some fundamental limitations can arise, which gives us reasons to think that value of parameters should not actual infinity.

      And as author has gives some other ways to differentiate between coarse tuning and fine tuning by relations and certain parameters as defined in paper, it helps us to differentiate between two, by which fine tuning still there.

    9. Fine Tuning Argument,
      It is insufficient to show that Aw is not an actual infinity. Regarding the Ω constant, for example, if it could be shown that the range for Aw was between 0.5 and 1.5, the fine tuning observations work and coarse tunings would not. However, if the range for Aw was between 10 to negative 50 and 10 to positive 50, then coarse tunings also work.
      Your paragraph about fundamental limitations on some parameters for the universe even to be possible offers a way forward. Fine tuning argument advocates need to do the hard work of establishing a reasonable Aw for Ω and the other constants relevant to the argument.

    10. The issue with infinite ranges is probably the "best" objection to the argument. But I think it is a bad one, in the end, and there have been many responses over the years:

      In addition, there is also Luke Barnes's reply (google Luke Barnes probability fine-tuning), which is basically that the same issue would also affect much of physics and cosmology in general, not just fine-tuning, yet we nevertheless do make sensible probability judgments with these theories, and he goes in depth about this.

    11. Fine tuning argumentDecember 24, 2019 at 9:10 AM

      @Tim Finlay

      This is exact problem author has addressed in paper.

      For it, we can define certain parameters by which we can evaluate whether there is fine tuning or not even when total parameter space is large.


      First, degree is seriousness S, which is inversely proportional to area of life permitting regions.

      If S is large, problem is serious. Next, author has defined parameters:

      "Moreover one can ine a ratio R, which is defined as the ratio of possible variance Δ�� (the variation of the life-permitting range) to the mean measured value ε0:

      R =
      . (3.7)
      For example, for our universe, Δe = 0.001 and ��e = 0.007 for life-permitting. Therefore, the ratio is R = 0.142. We know that S would be large if R is small. We can now relate the probability of getting the fine-tuned value by using R such that P ∝ R. Although we do not have the actual value of P, we can
      qualitatively describe the fine tuning problem by using the value of R. Therefore, when we say that the probability (rational degree of belief) of getting the life-permitting range is small, that means the variable range is small, and thus the ratio R is small too. In general, we can have the following relation:
      P ∝ R ∝
      ∝ A .

      From the above relation, it is not necessary for us to consider the Aw and the actual value of P. More importantly, instead, we should consider how small the variance of the anthropic value is."


    12. Fine Tuning Argument,
      That is the portion of the paper that I could not understand. Perhaps it is sound, but I could not understand it.

    13. Here is cosmologist Luke Barnes's response to the normalizability objection:

    14. Atno,
      This would take me way too long to work my way through. Over thirty years ago, I wrote a 60 page paper comparing proofs of the Prime Number Theorem. Two years ago, I tried to reread my own work and after a month's very hard work, I understood 5 and a half chapters, but the other chapter and a half was beyond my grasp.
      I don't have the time to go through Luke Barnes's article.

    15. @Tim Finlay

      If we see it in simple way, author has defined some parameters from which we don't need to know all space constants or conditions can takes, and we don't need to know actual probability to consider whether there is fine tuning or coarse tuning, or whether particular fine tuning parameters is serious or how much serious, etc.

      In short, author has gives way by which we can differentiate between fine tuning and coarse tuning and how serious is it without knowing all parameter space.

    16. @Tim Finlay

      To summarize, I think Barnes's point is that the issue of assigning probabilities to large or even infinite numbers of possibilities, although complicated, is not unique to fine-tuning. It affects pretty much every theory in physics, but nevertheless we obviously can and do make sensible probability judgments in physics. So this shouldn't also deter us when it comes to fine-tuning.

      He goes in detail about how the probability issues can be technically avoided in different physical theories, and how the same methods could work for fine-tuning, etc.

      This is just a very brief summary, though.

    17. Atno and Fine tuning argument,
      As to this argument, I have no particular dog in the fight. I used to think that it worked, because atheist physicists were clearly troubled by just how finely tuned some constants were; and they demonstrated their trouble by arraying ad hoc arguments (e.g. multi-verse) or poor arguments (e.g. the constants had to have this tuning or else we would not be having this conversation). I went to a lecture by an atheist and he went through all his reasons to reject the fine tuning argument, like those above, but the one that gave me serious pause was the one I discussed above.

    18. Atno and Fta, continued,
      I did not know until reading the articles you mentioned that the coarse tuning objection had been given by the Magrews, whom I highly respect and who had apologetic reasons to support it, if they considered it sound.
      Perhaps you two are right that this objection can be overcome. Compared to the cosmological argument, however, it has at least two deficiencies.
      1) It is only probabilistic, rather than being logically deduced from non-probabilistic premises.
      2) It does not show that a being with the property of aseity exists, i.e. it cannot by its nature establish the God of classical theism.

    19. How is 1 a deficiency? Probabilistic arguments can be very strong and we use them all the time in ordinary life, science, and more. Sure, strict logical deductions are technically better, but probabilistic arguments are still very strong.

      Abductive and inductive teleological arguments have existed for millenia before the fine-tuning argument. It just so happens that the FT has significantly strengthened them in recent years, with impressive hard data. Probabilistic arguments are good; you do not need absolute mathematical certainty in order to know that something is true, even beyond a reasonable doubt.

      2) Granted, the fine-tuning argument by itself does not show aseity. But frankly, that's a small issue. We would conclude that the universe was created/designed by an intelligent supernatural creator. This is perfectly compatible with Classical Theism; it's not like the argument dictates anything less than that. And by itself it also significantly raises the prior probability of (for example) a miracle like Jesus' Resurrection. So, in practical terms, we still get very close to CT anyway.

      In any case, the FT argument can be easily combined with classical cosmological arguments to give us classical theism. In fact, it is a great contribution to Stage 2 of cosmological arguments (establishing that the First Cause is God). Once we have established that contingent reality has a Necessary, purely actual First Cause, we can then consider the orderliness and fine-tuning of contingent reality, which makes it very, very plausible that the first cause is intelligent/personal.

    20. Atno,
      I agree that abductive and probabilistic arguments are extremely important where there is no other method--as for example in the central issue of Christ's resurrection.
      But we can do better than that with regards to the existence of God.
      With regards to the second point, the fta does not get very close to CT. It allows for something like a demi-urge that is itself dependent on a higher cause or a chain of such causes.

    21. "But we can do better than that with regards to the existence of God."

      Great, but the more arguments, the better.

      "With regards to the second point, the fta does not get very close to CT. It allows for something like a demi-urge that is itself dependent on a higher cause or a chain of such causes."

      It does not dictate that it must be a demiurge. It could be God instead. The argument establishes that there is an intelligent creator or designer of the cosmos. This is perfectly consistent and consilient with Classical Theism. Someone could also instead conclude a demiurge, but there's no reason for favoring it over theism. Insofar as the argument establishes the existence of (say) a minimal deity, it already gives us many relevant consequences, such as raising the prior probabilities of miracles (such as Jesus' Resurrection).

      But one can easily complement the argument with Classical Theism. "Since there is an intelligence behind the whole universe, this intelligence must either be contingent/dependent or necessary and purely actual... so we eventually reach a necessary, intelligent, purely actual creator".

      As I said, the argument is great for complementing cosmological arguments. Once we establish there is a necessary, purely actual First Cause, we then notice fine tuning and the order of the universe and conclude this First Cause very probably has intelligence etc. Which is what a lot of analytical thomists do (Robert Koons, Alex Pruss, etc). It considerably strengthens the classical theist case.

  12. All time exists simultaneously. Therefore, ALL events are fixed and knowable in advance as well as during and after the fact of their apparent happening.
    Even so, the knowledge of any event depends on the ability to enter into the plane or moment of that event. Therefore, knowledge of events outside of conventional memory and perception depends on our native ability to transcend the body-mind in its present space-time state, configuration, or definition. And true knowledge of what is not contained in the present space-time limits of our experience depends on self-surrender, deep consciousness, ecstasy or self-transcendence and resort to that Condition of Being that transcends all past and present knowledge. In fact, then, the same requirements exist as a condition of perfect memory, foreknowledge, and total knowledge that exists as the Ultimate Condition of Ecstasy or God-Realization. Such is the Paradox or Equation of Reality. The same condition pertains at Zero, Everything, and Anything.

    1. I think your speaking about eternity which is non-tensed time which is different than presentism. Also not sure if troll.

  13. You won’t ever pull more philosophy out of physics than you first put in. To disagree with this thesis I propose a thought experiment. Suppose physics were one day to discover that you could have a conversation with yourself while experiencing the solidity of past events in one self and the the flux of the present in another self. And say it is in the absence of memory for the duration of the conversation for the present self. In the absurdly unlikely event of this happening it would surely provide extremely rich philosophical ammo. Now an objection might be raised that philosophical ammo is not what this thesis talks about because it is not essentially part of philosophy. However, I would argue that while quantitatively philosophical ammo is not essential, some form of the substance is.

  14. For everyone: On December 23rd there will be an episode of the Classical Theism Podcast with Nigel Cundy

    1. Yes, unfortunately, this was recorded several weeks ago and I hadn't a chance yet to dig into Cundy and Feser's remarks on time. Yet, I think the podcast will serve to show how Cundy thinks about various issues.

      For those who don't have time to listen, one of my big take-aways from Cundy: The mechanistic, anti-Aristotelian picture may have felt at home for a while (e.g. from Galileo to early 1900s). BUT, with the advent of Quantum Field theory, Aristotle is back with a vengeance and the mechanistic picture just doesn't work out like many thought it would.

      So, while they undoubtedly differ on specifics, Feser and Cundy both think Aristotle is having his revenge!

  15. The mind does not exist in space. The mind only exists in time. But the mind arises in the Transcendental Being or Consciousness, which is prior to time.
    The body does not exist in time. The body exists only in space. But the body arises in Infinite Energy, which is prior to space.

    Just as the body exists in space, the mind exists in time. The body-mind, therefore, exists in space-time, and it demonstrates all of the paradoxes of space-time phenomena.
    The mind through association with the body, enjoys the modes of movement or change in space. The body,through association with the mind, enjoys the modes of movement or change in time. But the body-mind inheres in the Divine Being or Infinitely Radiant Self. Therefore, the Being Who is the Self of the body-mind always transcends time, space, and space-time, or all the phenomena and paradoxes of experience.
    All conditions in time may be conceived or inspected in the mind's permutations. All space may be perceived in the body's mutations or planes of manifestation. All space-time may be known in the states of the body-mind, if the body-mind is surrendered in Transcendental Ecstasy, or inherence in the Infinitely Radiant Being.

  16. For those interested, I recently recorded a podcast with Dr. Cundy on his book What is Physics? A Defence of Classical Theism.

    You can find it here:

    1. Awesome! I'm going to give this a listen tonight if I have the time.

  17. "AnonymousDecember 22, 2019 at 3:27 PM
    The mind does not exist in space. The mind only exists in time. But the mind arises in the Transcendental Being or Consciousness, which is prior to time."

    Utter drivel.

    What is called "the mind" is brain function, a sequential process of material changes through time, brain state changes over time.

    But by all means, please do prove me wrong, yes, a mind absent a physical being, the evidence, the example, please provide, tick tock...

    1. Remember all, don't feed the troll.

    2. Gee, when somebody calls me a "troll" they usually at least identify themselves.

      Perhaps (blank) can explain how "consciousness that is prior to time" is anything other than incoherent?

      How would that work, to be prior, yet absent time? I suppose you might argue that the term "prior" means ontologically prior, not temporally prior, but how does that work? Doesn't ontologically prior also require temporally prior or simultaneous? So, if simultaneous then wouldn't that make material existence as eternal as god?

      And how does consciousness work without time? How can a being think thoughts without time? How is it at all coherent to assert a timeless static unchanging entity somehow thinks thoughts?

      Theists commonly feel as though they have solved a logical problem by asserting that "god exists outside of time". In fact they have only succeeded in uttering an incoherent statement.

    3. Don't feed the trollsDecember 24, 2019 at 10:34 PM

      Feser banned you, get lost troll.

    4. Gosh (blank), rather uncharitable of you, especially in light of this season of reconciliation and good will.

      This post by Feser is perhaps the most rational and lucid writing of his I have yet to read. I wholeheartedly agree with his advocacy and reasoning for the A theory of time.

      I think the B theory of time will go the way of the notion that GR mandates the universe began as a singularity that was the beginning of material existence, a naive misapplication of GR that was nevertheless widely expressed by eminent physicists who really should have questioned some of their own fundamental rational methodologies more closely.

      I especially appreciate the differentiation between verificationism as a philosophical position or as a mere methodological constraint. While we cannot complete the process of the scientific method without some sort of verification we can at least begin it with a hypothesis and a search for its verifiable implications, as opposed to simply giving up before the start due to a present day lack of verification method.

      So much so, that from time to time I think about how good it would be if Dr. Feser were to return to his rationalist roots, this subject seeming to resonate with that aspect of his personal journey, hinted at with this "Indeed, I’ve been a structural realist since before I was a Thomist, way back in my atheist days in the 1990s when I first got interested in the work of the later Bertrand Russell." It is unfortunate that in later years Dr. Feser chose to reprint a gross mischaracterization of Russell in Five Proofs, as I have detailed and referenced elsewhere on this site. In the spirit of reconciliation that is integral to the tradition of this season I invite Dr. Feser to re-examine how the sentence from On the Notion of Cause Bertrand Russell Proceedings of the Aristotelian Society, Volume 13, Issue 1, 1 June 1913, Pages 1–26, "In the motions of mutually gravitating bodies, there is nothing that can be called a cause, and nothing that can be called an effect; there is merely a formula." was proof read and turned into a strawman by the author Dr. Feser reprinted.

      This fine post by Dr. Feser is admirably dogged in its grounding in realism above abstraction, and I found myself agreeing with every incisive word he has written here, slicing with scalpel sharpness through the physicist’s fallacy of affirming the consequent, clearly elucidating that while we recognize that the nature of the underlying reality progresses with great regularity, which can in principle be described mathematically, that in no way means that every feature of some highly successful mathematical model must be existentially realistic. It seems a testament to the segmentation of the human brain that such a great work of realistic reasoning comes from the same brain that also adopts Thomistic Christianity, which is of course utterly riddled with gross errors of premises, analysis, incoherent terms, and logical fallacies.

      So, we atheists can consider that the Ed Feser of the 1990's is perhaps our finest prodigal son, and remain ever hopeful he will find his way back from the intellectual wilderness of Thomism.

      Merry Christmas!

  18. Dr. Michael Huemer explains that science is to explain how things are--not to claim only what science knows is what can exist. So the fact that (so far) it is hard to tell what is special about "now" as different from the future, that does not mean that there is no difference. And Dr. Kelley Ross has also suggested that the Kant-Leonard Nelson approach can help but I am not sure how.
    Mainly what we see in Quantum Mechanics is that things do not have values in space or time until measured. So time does seem to be an odd kind of entity. Kant calls it a "ding an sich". (Which Dr Ross explains as meaning that it exists but we do not know how.)

  19. There might be two arrows of time that meet to make the "now" different from the future or past [since it is the intersection of both arrows]. Feynman had such a paper. It did not produce at the time any great results but if you combine it with two arrows of entropy it does come with amazing results.

  20. So the first plank in all this is not Thomism but structural realism? Pity. It's shaky ground, as is anything which seeks to explain the universe without the Thomistic method of constantly referencing back to revelation, the only true form of "verificationism", as St. Thomas Aquinas states.

    1. Don't feed the trollsDecember 26, 2019 at 1:27 PM

      Notorious troll number two. Don't feed this one either folks.

    2. Wow. An incontrovertible philosophical argument, and one more reason why we need the Thomistic method. PC labeling won't help anyone here and ideas which endanger the Faith are not a joke either. By all means take an aspirin if your head hurts, because the Faith will be defended, like it or not.

    3. Miguel, the Thomist is most naturally a structural realist. Aquinas argued not from revelation but from observation and rational deduction, presaging the modern scientific method.

      "The first and more manifest way is the argument from motion. It is certain, and evident to our senses..."

      From that observational starting point Aquinas attempts to form a sound logical argument to discern the true nature of the underlying reality. The author of the above linked site put in the effort to attempt a translation of the words of Aquinas into syllogistic form, declaring (falsely) that the argument is logically valid.

      After establishing that his method is to be based on what is "evident to our senses" Aquinas uses sensory observations of fire, hot, cold, hand, and staff integrated into his (failed) attempt at a logical argument for the existence of god.

      At no point in his arguments for the existence of god does Aquinas cite revelation as his basis for concluding that god exists in reality.

      It is these features of Aquinas arguing from rational analysis of sense observation that allows the atheist materialist and the Thomist to at least have a common language for meaningful discourse. So much so that I thoroughly agree with and appreciate the careful and sound reasoning Dr. Feser has put forth in this fine post.

  21. "You won’t ever pull more philosophy out of physics than you first put in."

    That's the whole crux of the matter right there: you can't get metaphysics out of a tape measure. And yet, they will not hear it.

  22. The world seems to be full of chatroom trolls who say that their opponents thoughts are nothing but a particular chemical reaction, but they know their opponents have the "wrong" chemical reaction because they apparently have access to some transcendent standard that tells them this special and private revelation. Ironically, they call themselves "atheists".

  23. To throw a spanner in the works: it seems to me that there are serious problems with the whole Einsteintian physics and subsequent world-view. He himself said that there should be only one "singularity", yet physicists are finding lots of them. To me that points to flaws in the whole theory. His theories have caused so many problems and solutions to which it resembles pretty much the "wheels within wheels" complexity of the ancient astronomical theories. We have lost "simplicity". All modern physics is in a mess! So I don't think metaphysicians should take too much note of objections to Aristotelian views of time and space.

  24. To illustrate my point: many years ago now an astronomer in a reliable astronomical magazine (with illustrations to prove) pointed out the visible relationship between a bright star and a galaxy seeming to spin off from that star. He pointed out hundreds of occurences of this visible phenomena. The implication was thoroughly denounced by all other professional astronomers because according to them, there was no correlation of distance between the star and the galaxy, all measurements acccording to the "doppler red shift", which all rely on. Yet the visible evidence is startling. But the doppler shift can itself be questioned, if there is indeed an inter-space substance which would slow the speed of light down and equally account for the shift. And of course, make the speed of light varriable. That old theory has been raised occasionally, but Einstein reigns supreme in the eyes of all. So, on one particular theory, the cause of the "doppler shift" the whole of modern astronomical physics is based. We need a shift in physics.

  25. By the way, Feynman, the last of the greats, at the end of his life, expressed serious doubts about the whole Einstein framework. So I am in good company here.

    1. Simple, good old fashioned intellectual humility would go a long way to solving the dearth of progress in physics. In the last century we made a lot of great discoveries and found out we were good at measuring things. We're so good at measuring that we now think we're good at metaphysics. Just last week a physicist told me that we know the multiverse in the same way we know gravity. Zing! How do you argue with someone like that? Scratch him off the list of people who might someday discover something great; I tell you, he has already received his reward. Such hubris definitely cancels the wonder required for discovery.

      Perhaps I should grant him more credit: we don't actually know that much about gravity (metaphysically speaking), but at least we can see it, and that used to count for something.

  26. The Lonely ProfessorDecember 31, 2019 at 9:31 AM


    I'd like to discuss a little more the issue of coordinate systems, relativity, and absolute space. I think fobbing this off as "verificationism" is a little too glib. Just because A isn't strictly disproven doesn't give us a good reason for believing A really is the case.

    "Let’s concede for the sake of argument that the relativity of coordinate systems is indeed “so deeply enshrined in physics that I don't think that anybody can rationally challenge it.” Why is it so deeply enshrined? As philosophers of science sometimes point out, it is hard to avoid the conclusion that the reason has to do with the verificationism..."

    I think you misinterpret Cundy here. This has nothing to do with verificationism and everything to do with the fact that changing the coordinate system doesn't change the physics (i.e. you get the right answer regardless of which system you use), which is what is meant by "relativity of coordinate systems" and no, no one can really rationally challenge that. That is a physics question and not a philosophical or metaphysical one. That is the point he is trying to make.

    Regarding a preferred reference frame: A coordinate system is an abstraction, and one abstraction is preferable to another one only insofar as it better represents the part of reality one is attempting to represent. Thus, all coordinate systems are on an equal footing, as all perform equally well insofar as representation of physical reality.

    Now Cundy does say ""Absolute space" is interpreted to mean that there is some preferred frame of reference, and with regards to describing the locations and times of physical objects this is not the case." He is right; this frame of reference is simply not preferable to any other insofar as describing the location and times of physical objects.

    So, if you want to make the case for a preferred coordinate system, it has to be preferred on some other ground than the physics - what other aspect of reality does it represent better? It's true physics doesn't, and can't, have an answer here.

    1. What does a preferred coordinate system have to do with the question of wither or not the present is real or not?

      I mean if the present was local we could still have a form of presentism and still not have a preferred coordinate system.

  27. Dr. Feser,

    My apologies for being so far behind on this, but I am genuinely curious how the A theory of time reconciles time dilation. For the B theory, it's as simple as saying when you depart from the geodesic, you move through less in the time dimension while moving through more in the space dimension.

    I look in the SEP on-line and a couple of other resources, but one addressed time dilation in terms of A theory or B theory. If you address this in Aristotle's Revenge or some other book, I will track that down and read, or if you know of any other source, that would also be good. If not, what do you think is happening during time dilation?

  28. One Brow wrote (April 20, 2020 at 6:19 PM):
    > [...] curious how the A theory of time reconciles time dilation. For the B theory, it's as simple as saying when you depart from the geodesic, you move through less in the time dimension while moving through more in the space dimension.

    This seems to have wrongly conflated two individually correct statements:

    - If your trip duration from one event to another is less than the maximum duration (which some other traveller may have attained, a.k.a. the Lorentzian distances between these two events) then you weren't travelling geodetically.


    - If A and B were and remained separated at rest wrt. each other, then a nonzero distance AB may be attributed to them;
    and if you had moved geodetically (a.k.a. "straight and uniformly") from A to B then your trip duration τYou[ _A, _B ] and the (constant) speed v_AB[ You ] which A and B would determine of your motion wrt. them are related as:

    τYou[ _A, _B ] = AB * √{ 1/v^2 - 1/c^2 } < τA[ _P, _simultaneous_to_B_P ] = AB / v.

    The former statement is (arguably) in terms of B theory, namely in the sense of dealing with ("invariant") geometric relations between events;
    while the latter statement is (arguably) in terms of B theory, namely in the sense of dealing with geometric relations between members of selected frames of reference (and, event by event, not with the entire event as an indivisible whole, but merely with the share which the particular participating member of the selected frame has of this event).

  29. Frank Wappler wrote (November 16, 2020 at 8:06 AM):
    > [...] Also:
    The former statement is (arguably) in terms of B theory, namely in the sense of dealing with ("invariant") geometric relations between events;
    while the latter statement is (arguably) in terms of B theory

    ... should have been:
    while the latter statement is (arguably) in terms of A theory

    [sorry; the comment preview didn't seem to work with my browser] ...

    > [... A theory], namely in the sense of dealing with geometric relations between members of selected frames of reference (and, event by event, not with the entire event as an indivisible whole, but merely with the share which the particular participating member of the selected frame has of this event).

    The share which one particular participant has of one particular event (in which generally several other participants may have been coincident, each having had an individual share of this same event, too) may suitably be called the "indication (of this participant, at this event)";
    corresponding to the German word "Anzeige (dieses Beteiligten, an diesem Ereignis)", which in turn matches and generalizes Einstein's usage
    >>> »[... dass] ich an Stelle der "Zeit" die "Stellung des kleinen Zeigers meiner Uhr" setze.«
    >>> [... »my substituting "position of the small hand of my clock" for "time."]«

    Since the formatting of "the time dilation equation of the special theory of relativity (variant A theory)" in my previous comment didn't quite turn out as desired, too, here another attempt:

    > [...] - If A and B were and remained separated at rest wrt. each other, then a nonzero distance AB may be attributed to them;
    and if you had moved geodetically (a.k.a. "straight and uniformly") from A to B then your trip duration τYou[ _A, _B ] and the (constant) speed v_AB[ You ] which A and B would determine of your motion wrt. them are related as:

    τYou[ _A, _B ] = AB * Sqrt[ 1/v^2 - 1/c^2 ] <
    τA[ _You, _simultaneous_to_B_You ] = AB / v.

    Note also that (obviously)

    τA[ _You, _simultaneous_to_B_You ] =
    τB[ _simultaneous_to_A_You, _You ] = AB / v,

    where this equal duration of A as well as B may perhaps be referred to as "the duration of track AB being occupied by you"
    in distinction from "your duration of the trip from A to B)",
    τYou[ _A, _B ].

    > τYou[ _A, _B ] = AB * Sqrt[ 1/v^2 - 1/c^2 ] <
    > τA[ _P, _simultaneous_to_B_P ] = AB / v.

    I wrote "τA[ _P, _simultaneous_to_B_P ]"
    instead of "τA[ _You, _simultaneous_to_B_You ]"
    because I had intermittently thought of "You" as "projectile P" ...
    (which I hope You don't mind. ... ;)