Feser on Koons on relative actuality

In a recent blog post, Edward Feser outlines a problem he sees with Rob Koons’ usage of relative actuality/potentiality to explain how an Aristotelian B-theorist might explain the reality of change. If you want to see Koons’ proposal then take a look at section 6 of his paper or take a look at Feser’s brief summary of it on his blog post; I will assume a general familiarity with it in this post. The objection is as follows:

Suppose someone suggested that time was nothing more than a spatial dimension.  I reject this view, and Rob wants to avoid it too.  One problem with it is that it also seems incompatible with the existence of real potentialities in the world.  If past, present, and future events are equally real in exactly the same way that the spatially separated hot and cold ends of a fireplace poker are (to borrow a famous example from McTaggart), then it seems that they are equally actual, just as the hot and cold ends of the poker are equally actual.  There is no real potentiality in a spatialized conception of time, and thus no real change — and thus, really, no time either.

But suppose our imagined spatializer of time defended his view by saying that there is potentiality of at least a relative sort on his conception of time.  Suppose he appealed to the poker analogy, and suggested that we could say that relative to the left side of the poker, the poker was actually cold but potentially hot, whereas relative to the right side, it was actually hot and potentially cold.  Suppose he suggested that there was therefore a kind of “change” in the poker from left to right.  And suppose he suggested that a similar kind of relative actuality and potentiality could be attributed to things and events at his spatialized points of time, and that a similar kind of change could therefore be attributed to them too.

In my view this would be clearly fallacious, involving little more than a pun on the word “change.” … I imagine Rob might agree, since, as I say, he too wants to avoid spatializing time, or at least denies that the B-theory need be interpreted as spatializing it.  But I fail to see how Rob’s notion of relative actuality and potentiality captures real potentiality, and thus real change, any more than my imagined spatializer of time does.

Feser’s point here is that the relativization of actuality/potentiality doesn’t help the spatializer to account for change, and he struggles to see how it could be comparatively any better for Koons. But I think he misdiagnoses the problem with the spatializer’s suggestion, and in fixing the diagnosis the difference between the spatializer and the Aristotelian B-theorist becomes clear.

As the last sentence of the quote makes clear, Feser thinks that the problem with the spatializer’s account lies in the fact that there are no real potentials anywhere, and so there can be no real change. But in the poker example, there surely are real potentials in the picture: the cold end is actually cold and potentially hot, whereas the hot end is actually hot and potentially cold. Anyone who accepts the Aristotelian account of change will affirm this, since we all know that pokers can change from hot to cold and back again. And they will likewise tell you can’t deny the presence of potentials simply because of the presence of actualities. Thus, if we suppose that time is spatially spread out like the poker, then the mere fact that all events are actual doesn’t prevent them from including various real potentials. Moreover, these real potentials and actualities seem to be adequately demarcated by using the notions of relative actuality and potentiality, so the problem isn’t there either.

The true problem with the spatializer’s answer is not that there are no real potentials, but that the potentials and the actualities are not connected in such a way so as to constitute change. Change, after all, is the actualization of a potential, it is not the spatial coincidence of a potential with an actuality. We can think of it like this: one reason someone might spatialize time is in order to explain why time is extended rather than collapsing into a single moment — it is extended, they say, for the same reason that space is extended, whatever that reason happens to be. But, of course, the extension of space doesn’t depend on the actualization of potentials, and therefore we know that simply pointing at spatially separated potentials and actualities doesn’t give us real instances of change. The problem, then, is that the spatializer spatializes time, and in doing so removes the possibility of an actuality ever being the actualization of a potential.

By contrast, the Aristotelian B-theorist need not spatialize time in order to explain its extension, because they have a ready alternative: the extension of time is explained by the actualizations of potentials. That is, the fundamental reason why things exist through multiple moments is that at earlier moments they have potentials which are actualized in order to bring about later moments. Of course, we’ve explained before that this is only the beginning of the account, since things can also move through time because of their real relations to other things. But even after we fill out all the details, the extension of time will always ultimately be explained with reference to the actualization of potentials — which, you will notice, is another way of stating the Aristotelian position that time is the measure of change.

So, then, the difference between the Aristotelian B-theorist and the spatializing B-theorist is that the former accounts for the extension of time in terms of the actualizations of potentials, whereas the latter has no room for the actualization of potentials because of how they account for the extension of time.

Eternity’s relation to time

A few months ago, reader Ante asked this question on my What I Believe page:

I am very much struggling how to combine a presentist account of time (like the A-theory for example) and the view that God is outside of time, in a Thomistic sense.

I would be very thankful for your help, since it seems to me that I am hitting a wall regarding this issue, since I cannot accept a B-theory of time, but at the same time the view of St. Thomas regarding God’s eternity is much more plausible than the other philosophical alternatives (especially open theism!).

For those unfamiliar with the relevant terms, we begin by briefly explaining what the A-theory and B-theory are, how they relate to presentism, and what this has to do with God’s eternity.

The distinction between A- and B-theory of time was introduced to analytic philosophy by McTaggart in his paper The Unreality of Time. Briefly, the A-theory of time holds that there is some objectively privileged moment of time we call the present, relative to which other moments of time can be categorized into past and future (called the A-series). By saying it is objectively privileged we mean that the fact of which moment is present is not a matter of perspective, but is rather a feature of reality prior to any considerations from us. The B-theory, by contrast, denies that there is such an objectively privileged moment of time, and holds that the only relations between moments are those of earlier than and later than (called the B-series). We can still speak of the present, but it must always be understood from the perspective of a particular moment under consideration. The most we can say, for instance, is that from the perspective of the 3rd of March 2018, the 2nd of March is in the past and the 4th is in the future.

Each of these theories has a number of models, which are concrete proposals for the nature of time that satisfy the requirements of the theory. Confusingly, these models are also sometimes called “theories.” A-theoretic models include presentism, which holds that only the present moment of time is real, while the past moments were once real and the future moments have not yet become real; the spotlight theory, which holds that all moments of time are equally real but only one ever has the property of “presentness”, which leads to us visualizing time as a spotlight gradually moving over a fixed timeline; and the growing block theory, which holds that once a moment is real is stays real, resulting in all past moments being equally real and forming a “block” of time, with the present being on the edge of this ever-growing block. B-theoretic models include four-dimensionalism, which treats time like a sort of spatial dimension, holding that objects have temporal parts spread across the fourth dimension of time just like they have spatial parts spread across the first three dimensions of space; and eternalism, which we will here take to be the model that all moments of time are equally real without any having the status of being objectively present, but not necessarily construed as temporal parts of objects either.

As for God’s eternity, the Thomistic view is that eternity and time represent fundamentally different modes of being. Eternity is not merely about existing without beginning or end, since this would be consistent with existing in time as long as we stipulate that (1) either time itself has no beginning or end or (2) God entered time upon creation.1 The Thomistic view can be seen as a consequence of Boethius’ definition of eternity, which says that it is “the complete possession, all at once, of illimitable life.” Such an existence is incompatible with being in time, since temporal existence requires that we have our life bit by bit rather than having all of it at once. Accordingly, God’s eternity means that he must be outside of time, and the problem of eternity has to do with the relationship between an eternal God and his temporal creation.

Thomistic and analytic approaches to time

Now, for us Thomists who are familiar with the analytic distinction between A- and B-theory, it is natural to wonder how it applies to God’s eternity and his relation to time. What is not always realized, however, is that there is an important difference between the Thomistic and analytic approaches to questions of time. The Thomistic approach is Aristotelian, and therefore starts with an analysis of change. Aristotle starts by asking questions like whether change is possible and what it consists in, and considers examples like that of a person becoming educated and an object moving location. By contrast, the analytic approach — by which I mean the approach of those in the analytic tradition broadly following McTaggart — starts with the ontology of the passage of time. The main point at issue in the debate over A- and B-theory is whether the passage of time “flows” from past to future. On the A-theory it flows as the present moves from moment to moment, while on the B-theory it is in some sense static.

We saw the analytic approach in action during our discussion on McTaggart’s paper, wherein he switches between questions about changes to reality (which is change in the everyday sense of the word) and questions about changes to the time series, as if these were interchangeable. On the Thomistic approach, time is just the measure of change,2 and it makes little sense to speak of the time series itself changing, as if this could be decoupled from the change to reality which it measures. Indeed, from a Thomistic perspective the analytic approach can seem to treat time as a sort of quasi-substance, which is certainly the impression one gets from McTaggart’s talk of moments of time merging into one another or changing properties.

We can illustrate the difference between the two approaches by considering how they would attempt to answer the question of whether temporal becoming is an objective feature of reality.

For the Thomist, temporal becoming is the feature of things when they change, as when an uneducated person becomes educated or a physical object moves from one place to another. Every change involves a coming-to-be of what was not before, and in this case the becoming is of things and in time. Given this sense of temporal becoming, we can determine whether it is an objective by determining whether change is real. And since change is evident to our experience, all we need is an account of it that shows its possibility, and therefore that our experience of it need not be an illusion.

On the analytic approach, things are less clear, because temporal becoming sometimes takes on a different sense and because the two senses are not always clearly distinguished. It’s difficult to avoid talking about changes to everyday things like people and physical objects, but with a primary concern for the ontology of time this talk gets mixed up with talk about changes to the passage of time itself.3 We are no longer simply interested in whether someone who is uneducated can become educated in the future, but also whether that future moment itself is something that can become present. This is not simply a becoming in time, but a becoming of time itself. The result is the conflation of temporal becoming with the A-theory, since only the A-theory involves the passage of time being in flux. Given this sense of temporal becoming, in order to determine whether it is objective we need to determine whether the A-theory is true, and that our experience of the passage of time itself (which is much less evident than our experience of change) is not an illusion.

So these two approaches give us two senses of the notion of temporal becoming, namely becoming in time and becoming of time. The former arises from considerations of change in the Aristotelian sense, as when an uneducated person becomes educated, and a physical object changes place. The latter arises from considerations of how the moments of time itself might change, as when a future moment takes on “presentness.”

The compatibility of (Aristotelian) change with B-theory, and its irrelevance

The upshot of all of this is that the analytic debate over theories of time is irrelevant to Aristotelian and Thomistic concerns. Both A-theorists and B-theorists recognize the reality of time with its peculiar feature of being ordered according to before and after, which is all the Aristotelian needs. As Aquinas said, “time is nothing else than the reckoning of before and after in movement” (ST I Q53 A3 corp).

Failure to recognize the different senses of temporal becoming has led some to conflate views they shouldn’t.4 The B-theory, for instance, is sometimes labeled “Parmenidean,” as if these two views are even remotely similar. Parmenides denied the existence of any distinctions in reality whatsoever, which leads to the denial of change and therefore the denial of any meaningful distinction between before and after. But the B-theory presupposes a distinction between before and after, since this is built into the relations earlier-than and later-than.

Another claim is that the B-theory excludes the possibility of change, and is therefore at odds with the Aristotelian commitment to its reality. Why does the B-theory preclude change? Well, the argument goes, if all moments of time are equally real, then the earlier moments when someone is uneducated are equally as real as the later moments when they are educated, and so they never become educated. But this clearly equivocates the two sense of becoming we’ve been discussing. The Aristotelian concern is whether someone who is uneducated at some time t1 can become educated by some later time t2, not whether t1 and t2 can somehow change their properties of “presentness.” All the Aristotelian needs is that a person can persist through time while varying in their educatedness, which the B-theory happily provides. What the B-theory does not provide — but which is irrelevant to the Aristotelian — is that this happens together with a change to the moments of time themselves. Again, the Aristotelian is concerned with becoming in time, not becoming of time.

Once we recognize the difference between Aristotelian temporal becoming and analytic temporal becoming, we can see that Thomists can happily hold to either the A- or B-theory. The analytic debate just isn’t something we have a stake in. But here’s the kicker: this doesn’t help us in any way with the problem of eternity! It is tempting to think that the B-theory would give us an automatic explanation of the relationship between the eternal God and his temporal creation, but it doesn’t. Why? Because at the end of the day, the B-theory is still a theory about time.

Let me explain.

We’ve said that time is the reckoning of before and after in the process of change, but what we haven’t mentioned is that before and after can be reckoned to something on account of a change to something else. This is an instance of what’s been called “Cambridge change,” which Feser describes as follows:

Here, building on a distinction famously made by Peter Geach, we need to differentiate between real properties and mere “Cambridge properties.” For example, for Socrates to grow hair is a real change in him, the acquisition by him of a real property. But for Socrates to become shorter than Plato, not because Socrates’ height has changed but only because Plato has grown taller, is not a real change in Socrates but what Geach called a mere “Cambridge change,” and therefore involves the acquisition of a mere “Cambridge property.”

There’s a certain ambiguity in this that we’ll discuss later, but for now consider the example he gives. Socrates remains the same height while Plato grows, and on account of this we can reckon before and after for Socrates: before he was taller than Plato and afterwards he was shorter than Plato. Thus, there’s a sense in which the change of other things can bring us along with them through time. Since this results from our being able to reckon before and after through changes to things in time, and since both the A- and the B-theory give us this, this will apply on both theories.

The real problem of God’s eternity, then, isn’t about whether the nature of time is such that all moments are equally real, but about how our movement through time doesn’t bring God along with us. And since this happens for both A- and B-theories of time, neither of them is capable of solving the problem.

Starting over with relations

Rather than a theory of time, what we need is a theory of relations. The reason Plato brings Socrates along with him through time is that Socrates is really related to Plato in some respect. In the above example it is that they are really related in regards to their height, but it could equally have been their relative location, color, age, or whatever. Conversely, if Socrates were not really related to Plato with respect to some feature of Plato that changes, then there would be no way of reckoning before and after for Socrates in terms of a change in Plato.

Aquinas worked out a detailed theory of relations, and we will summarize the relevant parts here. First, relations are divided into real relations, which obtain in reality prior to any consideration by an intellect, and logical relations, which result from such consideration. Socrates being taller than Plato is a real relation, but Socrates being to the left of Plato is logical since it is dependent upon how one considers their relative positions. When something has a real relation to another thing we say that it is “really related” to it. In English, the word “really” is often used to mean “truly” — as when we say something “really happened” — but in our present case “really” just indicates the nature of the relation. Socrates being to the left of Plato is not a real relation, but it is nevertheless true that Socrates is to the left of Plato.

Now, a relation between two things is not some separate reality floating outside of those things, but is instead grounded in them. When we have some relation R between A and B, it is therefore technically more precise to speak of R as a pair of relations, R1 from A to B and R2 from B to A. Socrates is taller than Plato (R1) and Plato is shorter than Socrates (R2). Each relation has a foundation in the thing it relates from, and this foundation grounds how that thing relates to others. For instance, Socrates has a certain height H, by virtue of which he will be shorter than things with heights taller than H and taller than things with heights shorter than H. This generic relational fact comes to be “resolved” to one of the alternatives when considered with respect to a particular individual: Plato has a height shorter than H, and so Socrates is taller than Plato. Notice that since the relation from Socrates to Plato will depend on both their heights it can change without Socrates ever changing, as when Plato changes his height while Socrates remains the same. It is this change in the relation from Socrates to Plato that brings Socrates through time when Plato changes.

We can also talk about the type of relation, which is derived from the type of its foundation: the taller-than relation is based on height while the brighter-than relation is based on color. In addition to the foundation in A, a real relation from A to B requires something in B of the relevant type, which we might call the relation’s co-foundation. It makes little sense, for instance, to say that Socrates is taller or shorter than an immaterial angel, since a relation of height from Socrates to another thing requires that that thing have a height as well. There is no co-foundation of the relevant type in the angel.

We say that the co-foundation must be of a “relevant” type rather than the “same” type because sameness is not always required. The height relation is an example that requires the co-foundation to be the same type, but consider what happens when I come to know a material object. In this case I take on its form in my mind, which serves as the foundation for a real relation from me to it and which has the object’s own form in itself as the co-foundation. But these two forms have different types: the form in my mind is intentional while the form in the object is entitative; the form in my mind does not turn my mind into that object whereas the form in the object’s matter does.

Knowledge is also an example of what is called a non-mutual relation. We have said that my real relation to the object has its foundation in the intentional form in my mind and its co-foundation in the entitative form in the object. This works because of the intentional form by its very nature refers to the object of the intention. But the entitative form is about constitution rather than reference, and so does not refer back to the intentional form in my mind. It can serve as the foundation of relations to other things by comparison to their entitative forms, but that’s about it. This means that there is no corresponding real relation from the object to me that has its entitative form as foundation and the intentional form in my mind as co-foundation. This asymmetry in foundation and co-foundation is what makes the relation non-mutual. When a real relation from A to B is can be turned into a real relation from B to A simply by flipping the foundation and co-foundation, then that relation is mutual.

If this were not complicated enough, consider what happens with active and passive powers. Here we have an agent with an active power (ability to influence others) and a patient with a passive power (capacity to be influenced by others), and when the agent actually does influence the patient then we have action and passion. The active power of an agent is grounded in some actuality (actual feature) of the agent, like motion, size, intentions, and so on. Any relation that arises from the active power, then, will have this ground as its foundation, which will determine which co-foundations are relevant. The passive power of a patient is slightly different in that it is grounded in the potential of the patient to be influenced in a particular way. This potential will be the foundation of the relations that arise from the passive power, and the co-foundations will be any actuality that can actualize it.

There is an important asymmetry here, in that the conditions for an agent to really relate to the patient are different from the conditions of the patient to really relate to the agent. For a patient, all that is needed is something capable of actualizing it, but for the agent, the conditions will depend on the ground of the active power. It could happen, then, that a patient is really related to an agent by a non-mutual relation. Consider, for instance, a saw cutting through wood. We might say that the active power of the saw is grounded in the sharpness of its serrated blade, while the passive power of the wood has to do with its potentiality for being split. Certainly there is a real relation from the wood to the saw because of this passive power, but as for the active power the wood is not really comparable in terms of sharpness or serratedness. The wood is really related to the saw, then, with a non-mutual relation. Of course there are other real relations between the two that have to do with active and passive powers and which are mutual. The saw might be used to push the piece of wood, for instance, in which case the ground of the active power (the motion of the saw) has a relevant co-foundation in the wood (the motion of the wood).

The problem of eternity

With this we can state the Thomistic answer to the problem of eternity: God is not really related to creation, and is therefore not brought through time by our changes.

This arises from applying what we’ve said about relations to the nature of God. For Thomists, God is a being of pure actuality, with no potentiality in him whatsoever. This makes him radically unlike anything else in reality, all other things being made up of a combination of potentiality and actuality. Furthermore, since potentiality is what allows for the diversity of actuality within a thing, it follows that God’s purely actual substance is the only possible foundation for real relations from him to others. But since pure actuality is so different to anything else in existence, it follows that there can be no relevant co-foundation to this purely actual foundation, and that therefore God cannot be really related to anything else.

Creation is still really related to God, mind you, but this relation is non-mutual. We are really related to God by virtue of our dependence on him for our being, and by virtue of being ordered toward him as the ultimate final end (cf. ST I Q44). Both of these arise from us being patients of God’s activity, and it is because of the potentialities in us that we can be really related to him — although pure actuality might be very different from us, it is nevertheless capable of actualizing all the potentials in us. Conversely, since God has no potentiality in himself there can be no chance of him really relating to us by virtue of us acting on him in some way.

Not only does God’s pure actuality exclude real relations from him to us or our acting on him, but it also excludes the possibility of change within him. All change involves the actualization of a potential, after all, and so without a potential there is no possibility of change. This notwithstanding, he is the source of all actualizations of potentials, including all instances of change. Thus God is called the Unmoved Mover, or Unchanged Changer, or more generally the Unactualized Actualizer. It might sound a bit strange to say that something could cause change without itself changing, since in our experience these tend to coincide. But it is a consequence of the fact that action and passion arise by an actuality of an agent actualizing a potential of a patient.5 This does not require that the agent’s actuality itself be the actualization of a potential, even if that happens with all the material agents we experience in the world.

Now, we might wonder why God would not be really related to us by virtue of knowing us. God is omniscient, after all, and earlier we mentioned that a knower is really related to the object of their knowledge. Here we must again appreciate the difference between God and ourselves. We come to know things outside ourselves through inquiry and exploration, by means of which we acquire the intentional version of its form in our mind. The entitative form in the object stands as a measure to our conception of it, and it is to the extent that our conception fulfills this measure that it is said to be true or accurate. With God, things look very different. His act of knowing reality is the same act whereby he creates and sustains everything in reality, and so he has no need of inquiry or exploration. He does not discover anything and has no need to acquire new knowledge by means of taking on the intentional forms of things. Since it is by his activity that all things continue to have their being, and since his act of knowing is the same as this activity, it also follows that God’s knowledge is measure of things rather than the other way around. All of this means that God’s knowledge does not make him really related to us like our knowledge makes us really related to the objects of our knowledge.

So, God does not change and is not really related to things that change. This means that there is no way of reckoning before and after for him and that therefore he is not in time. This notwithstanding, he is still the creator and sustainer of everything, and by virtue of this we are really related to him. Just as God is an unchanged changer, so too is he the non-temporal cause of things in time. We must remember, of course, that being really related to something is not the same as being truly related to it. Despite not being really related to us, God is still truly related to us as Lord, Creator, Knower, and so on; it’s just that these true relations are based on logical relations from him to us rather than mutual real relations between him and us.

Now before we conclude, we said earlier that there is an ambiguity in the notion of Cambridge change, and we are finally in a position to see why. Sometimes Cambridge change is proposed as a solution to the problem of God’s eternity, but of itself this is insufficient. To say that God only undergoes Cambridge change is to say that he does not undergo any change within himself. This is fine so far as it goes, but it doesn’t explain why he isn’t brought through time by changes to other things — as we saw in the example of Plato and Socrates we used to introduce Cambridge change. This further step requires the approach we’ve outlined in this post. The upshot of this is that either we should say (1) that God doesn’t even undergo Cambridge change, or (2) that Cambridge change must be divided into instances that bring us along through time and instances that don’t. In this second option, the two species of Cambridge change are distinguished by whether there are the relevant real relations in place or not.

Conclusion and further reading

So, Ante, thanks for the question and sorry for taking so long to reply. As I see it, the Thomistic approach to time is largely indifferent to the analytic debate over A-theory and B-theory, and the problem of eternity is not caused or solved by embracing either of these. What we need for a solution is an account of when and why things are brought through time, and an explanation for why this does not apply to God. To this end, the Thomistic account of relations provides us with a promising start. I hope what I’ve managed to outline here helps.

On the topic of relations, Mark Henninger’s Aquinas on the Ontological Status of Relations and David Svoboda’s Aquinas on Real Relation are both excellent discussions on the account of relations laid out by Aquinas. From Aquinas himself, perhaps the most important place to start is his discussion in question 7 of the De Potentia, especially articles 9–11. His discussions on God’s knowledge through his substance and the divine relations in the Summa Theologica are also noteworthy, since they push the account of relations to its limits when applying it to God.

More broadly, Edward Feser’s Classical Theism Roundup is a great resource for thinking through issues like eternity. Moreover, while I think Thomists don’t have a stake in the analytic debate between A-theory and B-theory, that is not to say that we don’t have interesting contributions to make. A case in point is Elliot Polsky’s Thomistic Special Relativity, which provides a three-dimensionalist account of length contraction and time dilation using a Thomistic framework that is different from other A-theoretic approaches I’ve seen.

  1. This is the view of William Lane Craig. See, for instance, his God, Time and Eternity. I also discussed it in my pre-Thomist days in an earlier post.
  2. Or, more accurately, it is the numbering of change according to “before” and “after”. (ST I Q10 A1 corp.) We’ve discussed before the connection a measure must have with what it measures.
  3. I’m not the only one who sees this. According to the SEP article on Being and Becoming in Modern Physics, “What emerges from the McTaggart literature is, first of all, a tendency to identify the existence of passage or temporal becoming with the existence of the A-series (that is, to think of becoming as events changing their properties of pastness, presentness or nowness, and futurity) and hence the tendency for debates about the existence of passage to focus on the merits or incoherence of the A-series rather than examining alternative accounts of becoming.” Note that the “events” mentioned in the parenthesis should be taken to mean “event-slices,” since an event in the everyday sense is something that spans multiple moments of time, and not all slices of it will be present (or past, or future) simultaneously. Again, this is a usage that we see in McTaggart’s paper.
  4. I stumbled upon a recent example of this while writing this very post.
  5. See my earlier post Lonergan on Aquinas on Causation for a discussion of this in Aquinas, as well as the essential agreement between him and Aristotle despite a terminological difference.

McTaggart and meta-time

There is what I take to be an error common among my fellow Thomists regarding change and certain theories of time. Put tersely, this error says that the B-theory of time is committed to the Parmenidian denial of change. I had decided to write something about it, but after doing a bit of research, it occurred to me that a form of this error goes all the way back to the start of the contemporary debate about the nature of time. That is to say, a variant of this error is present in John McTaggart’s paper The Unreality of Time. Before I can write about the error of my fellow Thomists, then, it seems appropriate to first say something about McTaggart’s mistake. And that is the aim of this post.

As the name suggests, McTaggart’s paper puts forward an argument that time is unreal. In the course of doing this he introduces a distinction that is now commonplace in philosophy of time, namely the distinction between the A-series and B-series:

For the sake of brevity I shall speak of the series of positions running from the far past through the near past to the present, and then from the present to the near future and the far future, as the A series. The series of positions which runs from earlier to later I shall call the B series. The contents of a position in time are called events. The contents of a single position are admitted to be properly called a plurality of events. (I believe, however, that they can as truly, though not moretruly, be called a single event. This view is not universally accepted, and it is not necessary for my argument.) A position in time is called a moment.

The A-series is indexed by tensed terms like past, present, and future. The B-series, by contrast, is indexed by tenseless terms like earlier than, and later than. Both of these series index the same time into a time series (or timeline), but they do so differently: in an A-series there is a privileged moment we call “present,” and other moments are called past or present through reference to this moment. In a B-series, by contrast, there is no such privilege and all moments are, in a sense, on an equal footing.

McTaggart divides the time series into “moments” and calls the things at these moments “events.” Now, we need to clarify something here, because it’s key to understanding McTaggart’s mistake. We typically think of events as existing in reality and persisting across moments, as when I wave my hand for a few seconds. And at least initially McTaggart seems to talk in terms of change of reality, which aligns well with this typical way of thinking. However, he quickly switches to talking about change of the time series itself, which is what leads him into all manner of strange places. What do I mean by this? Let’s say I waved my hand from 12 to 12:05 and then stopped. Did the event of my waving go out of existence? Surely it did once 12:05 came along. But what if I asked whether the event happening at 12:02 went out of existence? On a typical reading — in which reality is the thing that changes — the answer would be the same, since I’ve just reworded the same question. But if we read it in terms of the time series rather than reality, then the question becomes whether me-waving-at-12:02 went out of existence. Do you see the difference? We are no longer asking about the event that spanned 12:02 (together with some other moments), but rather the particular slice of the event at 12:02 (rather than the slices at other moments).

As I said, in the course of his discussion McTaggart switches from talking about the event to talking about slices of the event. The confusing thing is that he refers to the latter as the event too. This is something important to keep in mind as we proceed.

With this in hand, we can formulate McTaggart’s argument as follows:

  1. Change is essential to time.
  2. Change is impossible if the moments of time are ordered only by the B-series.
  3. Therefore, the moments of time are at least ordered by the A-series.
  4. Being ordered by the A-series involves a contradiction.
  5. Therefore, the reality of time involves a contradiction.
  6. Therefore, there is no reality of time.

The relevant points here are (2) and (4). In defending both of these points, McTaggart makes unmotivated (and strange) assumptions about the nature of change and the interpretation of his distinction between the A- and B-series.

In discussing (2), he starts off well enough but quickly makes the switch that was discussed above:

If, then, a B series without an A series can constitute time, change must be possible without an A series. Let us suppose that the distinction of past, present and future does not apply to reality. Can change apply to reality? What is it that changes?

Could we say that, in a time which formed a B series but not an A series, the change consisted in the fact that an event ceased to be an event, while another event began to be an event? If this were the case, we should certainly have got a change.

But this is impossible. An event can never cease to be an event. It can never get out of any time series in which it once is. If N is ever earlier than O and later than M, it will always be, and has always been, earlier than O and later than M, since the relations of earlier and later are permanent.

The question in the first paragraph is about the application of change to reality. But by the time we get to the second paragraph he’s switched to talking about events as slices of real events. He correctly notes that if the slice of the event ceased to exist or came into existence, then “we should certainly have got a change.” But he incorrectly assumes that this change would be of the reality he was talking about in the previous paragraph. That he’s thinking in terms of slices becomes very clear in the third paragraph, when he evaluates the suggestion in the second. He says, for instance, that “An event can never cease to be an event. It can never get out of any time series in which it once is.” Now for a normal event to go out of existence, all that is required is for it not to exist at a later time. As soon as we start talking about getting out of the time series, then we’ve moved to talking about slices of events rather than real events. And once we start talking about that, then we’ve moved away from talking about change in reality toward talking about change of the time series.[1]

So we have that McTaggart intends to account for change in reality by reference to change in the time series. But now we have a problem, for this account seems to really only push the question of change up a level: from reality to the time series. What, then, accounts for the change in the time series? If we were to apply McTaggart’s account again, then we would have to posit a meta-time series which tracks the change of the time series. Changes in the time series would be accounted for by reference to changes in this meta-time series. But now we have the same problem again, for which we’d need to posit a meta-meta-time. And so on. Eventually we’d need be led to an infinitely nested collection of times and meta-times, and we wouldn’t have gotten any closer to accounting for the change we started with. In other words, McTaggart’s account of change leads to a vicious infinite regress.

This conclusion comes up in the paper a number of times in different forms, but it’s not clear to me whether McTaggart realizes that they’re all instances of the same problem. In the present section he rejects the possibility of the time series changing in this way (“the relations of earlier and later are permanent”), and thereby rejects the adequacy of the B-series given his account of change. Indeed, the same conviction continues through his entire rejection of the B-series being able to account for change. Consider, for instance, the paragraphs that follow:

Or shall we say that one event M merges itself into another event N, while preserving a certain identity by means of an unchanged element, so that we can say, not merely that M has ceased and N begun, but that it is M which has become N? Still, the same difficulty recurs. M and N may have a common element, but they are not the same event, or there would be no change. If therefore M changes into N at a certain moment, then, at that moment, M has ceased to be M, and N has begun to be N. But we have seen that no event can cease to be, or begin to be, itself, since it never ceases to have a place as itself in the B series. Thus, one event cannot change into another.

Neither can the change be looked for in the numerically different moments of absolute time, supposing such moments to exist. For the same arguments will apply here. Each such moment would have its own place in the B series, since each would be earlier or later than each of the others. And as the B series indicate permanent relations, no moment could ever cease to be, nor could it become another moment.

This entire discussion is predicated on the confusion between the change of reality and the change of the time series. Needless to say I think his criticism of the adequacy of the B-series to track change misses the mark, and this becomes fairly clear once we fix up this confusion. All one needs for change is that things can have different properties at different times, and nothing about this requires that we talk about these times in terms of past, present, and future (that is, the A-series). If time t1 is earlier than time t2, and I have different properties at these times, then I have changed. The B-series, then, is more than capable to track change.

McTaggart continues with his confusion when moving to discuss the A-series:

Since, therefore, what occurs in time [event-slices] never begins or ceases to be, or to be itself, and since, again, if there is to be change it must be change of what occurs in time (for the timeless never changes), I submit that only one alternative remains. Changes must happen to the events of such a nature that the occurrence of these changes does not hinder the events from being events, and the same events, both before and after the change.

Now what characteristics of an event are there which can change and yet leave the event the same event? (I use the word characteristic as a general term to include both the qualities which the event possesses, and the relations of which it is a term — or rather the fact that the event is a term of these relations.) It seems to me that there is only one class of such characteristics — namely, the determination of the event in question by the terms of the A series.

Here he envisages what we might call a “spotlight” theory of time. The ordered events permanently exist in the time series, and the present moment has a temporal spotlight shining on it. This enables us to track the progression of time by following the progression of this spotlight. Dropping the metaphor, this means that each of the event slices has one of three properties: it is past, it is present, or it is future. Only one such event slice is present, everything earlier than it is past, and everything later than it is future. McTaggart is forced into this because (1) he assumes change of reality involves change of the time series, and (2) he is convinced from preceding argumentation that this change cannot consist in the creation or destruction of event slices in the time series. Thus, his proposal: moments remain permanent without being created or destroyed, and the march of time consists in them merely changing their properties.

But this A-series proposal, just like the B-series proposal above, requires that there be some kind of meta-time. What, after all, would track the changes of the time series represented by the spotlight moving along it? Or, without metaphor, what would track the changes of the time series that occur when the event slices change their properties?

After much discussion about this McTaggart realizes that the way he’s construed things entails that there will be an infinite regress of times and meta-times. We might summarize the process as follows: we sought to give an account of change, and so we proposed the spotlight account. But this requires that we postulate a meta-time to track the change of the spotlight. If our original proposal was correct, then in order to account for this meta-time we need to propose a meta-spotlight. But this will in turn require a meta-meta-time. And so on. So we have a vicious infinite regress on our hands.

As far as it goes this is a valid conclusion, and one McTaggart could have raised when discussing the B-series earlier had he seen the implicit dependence upon meta-time there. As we’ve already said, however, instead of taking this as a reason to reject his account of change (in terms of the change of the time series), he takes it to mean that neither the A-series nor the B-series can be real. And since these are exhaustive options for time, he concludes that time cannot be real.

In fact, the problem isn’t with either the A-series or the B-series. As we did earlier, we can frame the infinite regress argument directly against McTaggart’s account of change without ever mentioning either series.

To summarize, then, McTaggart’s mistake was in confusing change to reality with change to time. Once this error is corrected, neither the A-series nor the B-series precludes the possibility of change, since both can track things having different properties at different times. And neither series necessarily leads one into an infinite regress.


  1. Initially McTaggart raises it as a hypothetical (“Could we say that…?”), and so long as it remains option that might admit of alternatives there is no problem in his argument. The only caveat would be that he cannot conclude to the unreality of time if he limits himself to only one option among others. The problem is that this is exactly what he does conclude.

Craig’s timeless moment sans creation

William Lange Craig’s model of how God relates to time can be stated succinctly: God is timeless sans creation, and temporal since creation.[1] The reason we word it like this is obvious: he can’t be timeless before creation, since before-ness is a temporal relation and creation includes time itself. Craig holds this view largely because he is a presentist,[2] believes that time is relational,[3] and that the past is finite.

Ok, now let’s talk about “states.” Let’s say that a state is constituted by a collection of things exemplifying properties, and that an event is a change from one state to another.[4] We’ll say that a state is maximal if it is not properly contained within any other state. We’ll use the word moment as synonymous with maximal state. Finally, we’ll call the moment of God existing sans creation the timeless moment.

The central problem of this post comes when we try and answer the question, “What makes a state temporal?” Or, in different words, what is a moment of time? One is tempted to say something like the following:

1. The moment S is temporal if and only if there is another moment T such that S is causally prior to T or T is causally prior to S.

There’s an interesting consequence of (1): combined with finitism (of the past), relationalism, and presentism, it entails that God began to exist. To see this, picture the scene: God exists and nothing else exists. We’re in the timeless moment, call it t1. God creates something, bringing about the first change, and therefore the first event, and therefore time itself. Let t2 be some moment later than the beginning of this first event. How are t1 and t2 related? Well, there have been a series of changes that lead from t1 to t2, so either they’re the same moment, or t2 is later than t1. They’re not the same, so t2 must be later than t1. But, given (1) it follows that t1 is a moment of time. And because God didn’t exist before t1 (since there is no “before”), it follows that God’s existence is completely contained within time. And since the past is finite, God’s existence (extended temporally backward) is finite, and thus he began to exist.[5]

Such a conclusion is certainly worrying for theists. But regardless of whether one is a theist or not, surely it’s absurd to think that the timeless moment is temporal, or that it somehow went from being timeless (sans creation) to temporal (since creation)!

So, what’s wrong? It seems to me that the entire approach to time seems to start in the wrong place. On relationalism, time is understood as a relation between events, not states.[6] Furthermore, it seems that a necessary condition for a moment being a moment of time is that there be an event occurring at that moment. After all, surely it always makes sense to ask what is happening at a given moment of time? Moments are temporal, then, only by virtue of being “part of” or “contained within” an event.[7]

Now, go back to our timeless moment. Certainly, no events are happening at this moment: things only start happening at the first moment of creation, and surely the moment sans creation is not the same as the first moment of creation. So the problem doesn’t arise once we start in the right place. However, I’d still like an account of what makes a moment temporal, in terms of just moments (like we had in (1)). This time, of course, taking into account the fact that in reality it is their relation to events that makes moments temporal. Assuming that “instants” of time are merely potential,[6] and that in reality all temporal intervals are open, the following might work:

1′. The moment S is temporal if and only if there is another moment T such that S is causally posterior to T.

That is, there is a series of changes that lead from T to S.

There’s another interesting perplexity that is solved by starting the right place is this: the timeless moment is causally prior but not temporally prior to creation. This does seem strange at first glance. I suspect it seems strange because we try to make sense of this cause as an instance of event-event causation. But, obviously, since the timeless moment is timeless, it is not contained in any events, and so we simply can’t make sense of this as an instance of event-event causation. And of course, since the effect is an event, we can’t make sense of this as an instance of state-state causation. What we need is some sort of state-event causation, and this is what leads Craig to introduce agent-causation as the solution.Actually, thinking of agent-event causation as an instance of state-event causation can be quite helpful: the state in question is the agent being impressed by various reasons for an action combined with the causal powers they possess in that state, and the event in question is the agent freely choosing to act in accordance with some of these reasons.[8]


  1. Here we are including time and all reality apart from God in the notion of “creation” and ignoring concerns about Platonic abstract objects.
  2. Presentism is the A-theoretic view that only the present exists. That is, the past no longer exists, and the future hasn’t but will exist.
  3. The relational view of time holds that events or change is explanatorily prior to the passage of time. Thus, if there were no events, there would be no progression of time.
  4. This definition allows for states to be constituted by events: the state of me waving my hand consists of the event of me waving my hand.
  5. “Having one’s existence completely contained within a time range finitely bounded in the earlier-than direction” is, for me, a defining characteristic of “beginning to exist”. A cool paper to read about defining “beginning to exist” is Adolf Grunbaum and the Beginning of the Universe by David Oderberg.
  6. Indeed, the whole idea of thinking of events as collections of instantaneous moments seems wrong, for Zeno paradox-like reasons. I’d refer the interested reader to another of David Oderberg’s papers, Instantaneous Change Without Instants, particularly section 3.
  7. I might need to be a bit more precise than this: considering that in note 4 we said that states can be constituted by events, it’s also possible for a moment to be temporal insofar as an event is part of it. This nuance is not relevant to the upcoming discussion, so I’ve left it here as a sidenote.
  8. This suggestion is highly influenced by Timothy O’Connor’s paper Agent Causation, and Alexander Pruss’ paper Divine Creative Freedom (particularly section 4).

A Case for Chronons

Chronons are the discrete quantum of time. In other words they are the smallest (or indivisible) length of time. Naturally, if we think chronons exist, then we must hold that time is discrete.

Admittedly, if we say chronons exist we have the following weird result: Two balls, each with a 10cm diameter, are moving in opposite directions each at the speed of 10cm per chronon.

The two balls at some time, t1

It’s possible, then, that the two balls pass each other without ever being next to each other.

The two balls one chronon later, at t2

Because the balls moved between these two positions at the speed of a chronon, there wasn’t point between t1 and t2 at which A and B were next to each other. We’ll call this the “strangeness argument” for later reference.

Consider the following argument in favour of the existence of chronons based off the following 2 premises:

  1. Time is continuous, not discrete. In other words, time is infinitely divisible (there isn’t any minimum span of time that cannot be further divided).
  2. Let t0, t1 and t2 be points in time with t0 before t1 before t2. If we were a time t0 and are now at time t2, then at some point we were at time t1

Now assume we’re at some point in time, tn. Let tm be some point in time after tn. Since time is continuous (by 1. above) there exists some time tk with tm after tk after tn. By 2. we need to pass tk before we get to tm. But since tm was some arbitrary point after tn, it follows that we can never move forward in time past tn, since we’d always have to pass another point in time first. In other words, there isn’t any next point in time, so we can’t move to it in order to move forward in time.

Now of the 2 premises I think the first is the least likely to be true. Either way, if we deny the second premise, we keep time continuous, but it may as well not be. Let me explain.

Assume 1. is true and 2. is false. So we skip points in time when moving through it. In fact, we must always skip some range of points every time we move through time, because if we didn’t, 2. would be true for that range and then we wouldn’t be able to move through that range. Let’s even assume, for generality sake, that we don’t always skip by the same amount every time we move. But now, assuming 1 and not-2, time is almost indistinguishable from discrete time isn’t it? To see this we can note that the strangeness argument still applies. Say the balls are diagonally next to each other (like in the first picture above) at tn and the next point (the point we skip to) in time is tm. Now assume that the balls travel at 10cm per tm-tn moments of time. Then we have the same strange outcome we did when time was discrete. So rejecting 2. hasn’t done anything to remove the strangeness of discrete time.

It might be said that if we exist at ranges of time instead of points in time we might remove the problem. However, when the range is moving we still need to know how to move it’s boundaries which raises exactly the same problem (with a single point) we originally had. So that won’t help.

One of the premises must be false if we are to move through time, but both are susceptible to the strangeness argument. Although, because not-2 is slightly more strange than not-1 I think we should deny 1. Which means chronons exist!