R.D. Ingthorsson: McTaggart’s Paradox

Kristie Miller

McTaggart's Paradox Book Cover McTaggart's Paradox
Routledge Studies in Contemporary Philosophy
R.D. Ingthorsson
Hardback £115.00

Reviewed by: Kristie Miller (The University of Sydney)

Revisiting McTaggart

Few articles in the recent history of philosophy have yielded as large, and confusing, a literature as has McTaggart’s 1908 the Unreality of Time. Whatever one thinks of the status of the argument contained in that paper—what has became known as McTaggart’s Paradox—there is no denying that it, and the distinctions McTaggart introduces in that paper, have shaped the philosophy of time in many and deep ways. Each of us working in the philosophy of time locates ourselves by appealing to McTaggart’s terminology of the A, B and C series, and by noting the ways in which we agree (and disagree) with McTaggart. Indeed, frequently philosophers’ preferred view in the philosophy of time is heavily influenced by the way they see McTaggart’s Paradox. Had McTaggart known what the future held, and had he, perchance, needed to complete an ‘Impact Statement’ for some kind of quality assessment metric, we can safely say his score would have been excellent. (Fortunately for McTaggart, he died before he ever had to turn his attention to Impact Statements). All of this makes Ingthorsson’s book length treatment of McTaggart’s Paradox in McTaggart’s Paradox, a valuable addition to the literature.

What makes the book of particular interest is that it carefully contextualises McTaggart’s arguments in his 1908 paper in terms of his overall metaphysical picture laid out in his two companion monographs The Nature of Existence I (1921) and The Nature of Existence II (1927). Ingthorsson’s book is a careful explication of McTaggart’s Paradox in the context of McTaggart’s broader metaphysical commitments. Indeed, Ingthorsson compellingly argues that failing to see the argument in these terms can, and has, led to various confusions. One of the many merits of the book is that not only does it present and interpret the argument in context, but, in so doing, provides an account of why the argument has been so very controversial, and why it remains so today. Ingthorsson argues that one of the primary causes of disagreement and confusion have been competing misinterpretations of the argument that have arisen due to viewing it as an entirely stand-alone argument that can be understood and evaluated in isolation from McTaggart’s broader commitments. Whether contemporary philosophers of time share those broader commitments or not, it is valuable to set the argument within the broader context and to see how various interpretations (or misinterpretations) of, and responses to, the argument, sit within that context. To that end, this is an important contribution.

The book is also valuable because it offers an historical overview of the various strands of responses to McTaggart’s Paradox. Ingthorsson carefully shows where contemporary responses have historical precursors, and what those are. That makes it an interesting piece in the history of philosophy. More than that, though, the book does a commendable job of categorizing the kinds of responses that have been made to McTaggart’s Paradox over the years. This is no small feat given the wealth of responses that the argument has garnered. It is much to be admired that someone has managed to sift through the various papers as they appeared from 1908 onwards, with a view to articulating and categorising those responses in a useful manner. This allows the reader to ignore the many small differences in approaches and instead focus on the important philosophical similarities between approaches. For anyone who wants to get to grips with the major threads of thought that developed in response to McTaggart, this is an invaluable resource.

While the book’s principal aim, at least as I read it, is to articulate McTaggart’s argument, place it in context, and then consider the ways in which the argument has been interpreted and responded to, the book certainly ought not be thought of as primarily about hermeneutics or history of philosophy.  Ingthorsson has plenty to say, along the way, about where he thinks responses to McTaggart’s Paradox hit the mark, and where he thinks they do not. He also offers a number of positive arguments of his own about what he thinks the argument establishes, and what he does not. These are also valuable additions to the literature. So there is much that is interesting and rewarding about the book—too much to cover in this review. Instead, in what follows I will consider just two of the issues that jumped out at me as I read, and which I thought deserved particular attention.

In reading the book I was particularly interested in its explication of McTaggart’s account of how it is that it comes to appear to us as though there is a temporal dimension—the appearance as of there being a temporally ordered succession. (Here I suppose that successions have a direction, not merely an ordering, and so the appearance is as of there being a temporal ordering that runs from past, to future). Since McTaggart thinks there is no such ordering (no such temporal ordering that is) he incurs the explanatory burden of explaining why it seems to us as though there is. This is a burden that he takes up. McTaggart’s explanation of these seemings are of particular interest in the contemporary context, since the issue of why things seem the way they do to us, temporally speaking, is one that has become pressing over the last few decades. We find contemporary A-theorists arguing that because it appears to us as though there is an A-series—it appears to us as though events occur in a particular ordered succession and that time itself passes—we have reason (albeit defeasible) to suppose that this is the way things are, and that in fact some version of the A-theory is true.[1] Or, put more strongly, such theorists argue that the best explanation for these appearances are that time is indeed this way.  B-theorists, unsurprisingly, have responded in one of two ways. They have either argued that in fact things do not appear to us this way at all[2] (though perhaps we mistakenly believe that things appear to us this way[3], or they have argued that things do indeed seem this way, but them seeming this way is an illusion.[4] The latter have attempted to spell out how it is that we are subject to this illusion, the former have attempted to spell out how it is that we come to have such false beliefs about the way things seem.

In this regard, then, the B-theorist is in something like the same boat in which McTaggart found himself. To be sure, the B-theorist does not need to explain why it seems to us though there are temporal relations despite there not being said relations, since unlike McTaggart B-theorists think that the presence of B-relations in the absence of A-properties is sufficient for the existence of temporal relations. Yet the B-theorist does owe an explanation of why it appears to us as though there is an A-series (or why we falsely believe that it seems to us that way) and in this regard she shares a common explanatory burden with McTaggart. Moreover, in that, the B-theorist is not alone. The C-theorist, who thinks that it is sufficient for the existence of temporal relations that there exist C-relations in the absence of B-relations or A-properties, incurs all the explanatory burdens accruing to the B-theorist, and more still. For the C-theorist must, in addition, explain why it seems to us as though there is a B-series: that is, she must explain not only why there appears to be an ordered temporal sequence, but also, why that ordering appears to have a direction when, according to her, it does not.[5] By contrast, since the B-theorist thinks the temporal ordering has a direction (but does not have any A-theoretic flow) she can explain this appearance as veridical. Finally, some contemporary physicists, in their desire to reconcile quantum mechanics with the general theory of relativity, have defended so-called timeless physical theories, according to which there is not even a C-series ordering of events.[6] These theorists incur all of McTaggart’s explanatory burdens, since they need to explain why it seems to us as though there is a temporal ordering, when, in fact, there is none.

Given the extent to which contemporary theorists incur some, or all, of the explanatory burdens McTaggart incurred, the question of how McTaggart discharges that burden is of considerable interest. This is how Ingthorsson describes McTaggart’s approach:

McTaggart suggests that they [the terms in the C-series] are related in terms of being ‘included in’ and ‘inclusive of’ (S566 of NE). Very briefly, the only way he thinks we can explain the appearance of a series of entities related by the earlier than/later than each other is if we assume that, for any two terms in the series (except the first and last is there is a first and last) the one includes the other. The perception of a mental state that includes another can give rise to the misperception that the included content is a part of the content that includes it, and mutatis mutandis for mental states that are included in another. The relations of included in and inclusive of are asymmetric and transitive and so give a sense of direction, and are meant to be able to give rise to a false sense of change, and that in turn gives rise to a false sense of one term being earlier or later than another. (McTaggart’s Paradox pg 59).

Unsurprisingly, McTaggart appeals to the existence of the C-series, alongside certain features of our mental states, to explain the way things seem. This is important, since in doing so McTaggart appeals to the very same resources the C-theorist takes herself to have. So if his explanation is good (or at least, on the right track) then it is an explanation to which the C-theorist can avail herself. If I understand the proposal correctly, McTaggart’s explanation for the appearance as of succession (and with it, change) looks something like what have become known as retentionalist models of temporal experience. According to such models, roughly speaking, the mental state that obtains at one time can, as part of its content, include content from mental states that obtained at other times. So, in theory at least, mental states can have a nested structure, whereby one, as part of its content, includes the content of another mental state, which, in turn as part of its content, includes another mental state and so on. This complex nested structure is precisely the structure McTaggart supposes mental states to have. One might have attempted to explain this nested content in terms of the relations of earlier/later than, by noting that later mental states include content from earlier mental states (but not vice versa). But the proposal, here, would be to explain the appearance as of there being relations of earlier/later in terms of the nesting of mental states by suggesting that the appearance as of a directed succession is given by the existence of these nested states. In particular, since the relation of inclusion is itself asymmetric and transitive, then if mental states have that nested structure along the C-series ordering, then they are ordered by a relation that has the same formal features as the earlier/later than relation.

Indeed, something like this picture seems to be a precursor of contemporary C-theoretic explanations for the appearance as of temporal direction in terms of, inter alia, asymmetries of memory, knowledge, and deliberation.[7] In fact, something very close to McTaggart’s proposal is to be found in the work of contemporary timeless theorists. Those theorists, of course, do not have recourse to the existence of a C-series as a partial explanation of the way things seem. So they appeal entirely to unordered (temporally unordered, that is) nested mental states to explain why it seems to us as though there is an ordering (the appearance of ordering is, as it were, the product of the nesting) as well as why that ordering appears to have a direction.[8]

The explanation cannot, of course, end there. It might be right that this nested feature of our mental states gives rise to the appearance as of temporal succession where there is none. But there remains the question of why our mental states have this feature at all: why do some mental states include others? Given the rich resource of McTaggart’s thought, it would be of significant interest to pursue the question of what more he has to say about why mental states have these features. Of course, contemporary philosophers of time will typically point, at least in part, to features of increasing entropy to explain why mental states exhibit this ‘nesting asymmetry’; but it would be of interest to investigate McTaggart’s own views on this.

Interestingly, what all this tells us is that the gap between McTaggart and the C-theorist is, in fact, quite slender. McTaggart agrees with the C-theorist that what gives rise to the appearance as of a temporal succession is the existence of the C-series, combined with certain (asymmetric, transitive) relations (i.e. inclusion) that obtain between our mental states. Where they disagree is in whether the C-series, absent any B- or A-series, is properly called temporal or not. And there, of course, we come back to the issue of whether such a series can give rise to ‘genuine’ change. For the reason that McTaggart concludes that the C-series is not temporal is that in the absence of an A-series, there would be no genuine change, and genuine change is necessary for an ordering to be temporal. Thus neither a C-series nor a B-series, absent an A-series, could count as a temporal series. Both B-theorists and C-theorists reject the claim that there can be no genuine change in the absence of an A-series, and Ingthorsson takes up this issue in chapter 7. There, he argues that McTaggart was right in at least the following way: the B-theory is incompatible with genuine change, since genuine change requires enduring objects—objects that are wholly present at each time they exist rather than being merely partly present as are perduring objects—and the B-theory cannot accommodate such objects.

The reason endurantism is suppose to be the only view of persistence that captures genuine change, is that it entails that persisting objects are numerically identical over time, so that one and the same object exists at multiple times, and at those times instantiates different properties. Thus persisting objects endure through changes, rather than change being a matter of persisting objects having parts with different properties at different times (as per perdurantism). The idea that the B-theory is incompatible with endurance, then, is an interesting (and important) claim, and one that it is worth further consideration. For if time does require genuine change, and if genuine change requires endurance, then McTaggart was right all along: if all events, objects, and properties exist (if eternalism is true) then there exists a C-series and perduring objects, but there does not exist any temporal ordering of the objects in the C-series.

Let’s set aside the issue of whether genuine change requires endurance, and whether, if it does, genuine change is, in turn, required for an ordering to be temporal. Instead, let’s just focus on Ingthorsson’s contention that the B-theory is incompatible with endurance.

Ingthorsson argues that endurance requires temporal passage at least in the sense that enduring things have to move from one time, to another. But there is no way for them to do that given the B-theory. Another way to put this is that what it is to be wholly present is to be entirely at one time, and to be nowhen else (that’s why enduring objects move, being first at one time, and later at another). But B-theorists are committed to what Ingthorsson calls the temporal parity thesis—the view that all objects events and properties that ever did, do, or will, exist, exist simpliciter (i.e. co-exist). (The temporal parity thesis is the view that is sometimes known as eternalism). If that thesis is true then enduring things co-exist with themselves at many times. So in what sense are said objects wholly present, given that each of them exists not only at the time in question, but also outside of it. Ingthorsson writes that

…the very idea of an enduring particular, in the sense I initially described it, is as of a three-dimensional thing that exists wholly and exclusively at one time at a time i.e. not multiply located in time any more than a football that crosses the pitch is multiply located at all points of it spatial trajectory. (McTaggart’s Paradox, 102)

The idea is that just as the football sweeps across the field, and is at no time at multiple places on the field (but rather, at each in succession) somehow the same ought be true of enduring objects.

It is worth noting that this argument, if it succeeds, succeeds against views that accept something weaker than the temporal parity thesis. It succeeds against any view that says that there exist a least two times t and t*, such that whatever objects, properties and events exist at t, and whatever objects, properties and events exist at t*, all of those objects, properties and events co-exist (i.e. exist simpliciter). Presentism denies even this weak thesis, but other non B-theoretic views such as the growing block and moving spotlight theories do accept that weaker thesis. If the argument succeeds, then, it shows that every view of temporal ontology is incompatible with endurance (and hence, perhaps, with genuine change and with temporal relations) aside from presentism.[9] That’s because Ingthorsson’s view about what it would take for an object to be wholly present, and hence to endure, requires that said object exists at only one time, and nowhen outside that time. But if any other times exist than the present one, then this would flout that requirement.

To be sure, if being wholly present means being at one time, and nowhere else, then it must be the case that endurance is incompatible with any view but presentism. But ought we think this is so? Of course, in the case of the moving football—what we might call the spatial case—what it is to move through space (very roughly, setting aside issues of relativity) is to exist at different spatial locations at different times. Hence at any one time one will see the football at a single position along its trajectory: we will see it at one place on the field, and at no other. But if one ‘sees’ all times, one will see that object at each location along its trajectory: that is, in fact, what a worldline is, in Minkowski space-time. So one sees a whole set of co-existing three-dimensional objects, each of which is the football at one time. Why should that be puzzling? Why should it show that the football is not, in any good sense, wholly present at each spatial location at which it is located at each time?  What is the sense in which the ball is wholly present at each of those locations, given that, quite clearly, it is present at more than just one location? It is the sense in which at each time, what exists is all of the ball—all of the three-dimensional object that is the ball, as opposed to there existing some three-dimensional object that is a mere part of the ball.

To be sure, what we see when we look at the full four-dimensional representation of the ball’s movement across the field is that the ball fills a four-dimensional region of space-time (namely its four-dimensional trajectory through space-time). But that doesn’t make the ball four-dimensional, since one way of accomplishing this filling of space-time is for the ball to endure, and to fill that region by being wholly located at each of the three-dimensional regions. The ball moves across the field, and it does so by existing at different places at different times, not by existing only at a single time, and by different times themselves existing sequentially.

Ingthorsson is aware of such a view, noting that, many contemporary endurantists (those who think persisting objects endure) think that endurance is compatible with the temporal parity thesis. Such endurantists hold that we should understand what it is to be wholly present in terms of a multi-location thesis spelled out in terms of different location relations that objects bear to regions of spacetime. [10]  To be sure, they say, the enduring ball is located at different times (all of which are equally real) but it endures nonetheless, since it is the very same, numerically identical, three-dimensional ball, that exists at each of those times.

Ingthorsson, however, thinks that such a view falls foul of the problem of temporary intrinsics. Does it? I don’t see why. If the ball is, indeed, multiply located then there is just one ball, located in many places. It doesn’t sweep through time, to be sure, but the entire ball is located at each time, and each such three-dimensional object is one and the same thing. That ball has a single complete set of properties—the properties that completely characterise the ball—which mention how it is at each of those times. One might worry, as Ingthorsson does, that this makes the instantiation of properties into disguised relations to times, since the ball must instantiate properties such as being dirty at one time, and being clean at another (let’s suppose the ball picks up dirt as it traverses the field). But it’s hard to feel the force of this worry, given the picture on offer. If it turns out that objects persist by being multiply located along the temporal axis, then they do so by bearing location relations to each of the three-dimensional regions they occupy. A single persisting ball bears a series of location relations to a series of such regions. But in that case one might expect that at each of such region, the ball will instantiate properties relative to that location. It’s not as if this is an ad hoc proposal borne of the need to reconcile change with Leibniz Law (a la the problem of temporary intrinsics); rather, it seems to be the natural thing to day for someone who endorses this picture. No doubt, however, there is much more to be said here, and McTaggart’s Paradox sews the seeds for such discussion.

Whatever one makes of the arguments, the book is a rich source of argumentation and discussion of a number of core issues in the philosophy of time, and for that reason is well worth a read.


Barbour, J. (1999). The End of Time.  Oxford; New York: Oxford University Press.

Baron, S., Cusbert, J., Farr, M., Kon, M, & Miller, K (2015). Temporal Experience, Temporal Passage and the Cognitive Sciences. Philosophy Compass. 10 (8): 56—571.

Baron, S and K Miller (2015). “What is temporal error theory?” Philosophical Studies. 172 (9): 2427-2444.

Baron, S and K Miller (2014). “Causation in a timeless world”. Synthese. Volume 191, Issue 12, pp 2867-2886 DOI 10.1007/s11229-014-0427-0.

Braddon-Mitchell, D (2013). Against the Illusion Theory of Temporal Phenomenology. CAPE studies in Applied Ethics volume 2  211-233.

Gilmore, C. (2014). “Location and Mereology”, The Stanford Encyclopedia of Philosophy (Fall 2017 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/fall2017/entries/location-mereology/>.

Eagle, A., (2010a). “Perdurance and Location”, in D. Zimmerman, ed., Oxford Studies in Metaphysics, vol. 5, pp. 53–94.

Hoerl, C. (2014). Do we (seem to) perceive passage? Philosophical Explorations, 17, 188–202.

Kutach, D. (2011). The Asymmetry of Influence. In Craig Callender (ed.), Oxford Handbook of Philosophy of Time. Oxford University Press.

Latham, A. J. Holcombe. A. and K Miller (ms). “Temporal Phenomenology: Phenomenological Illusion vs Cognitive Error.”

McTaggart, J. M. E. (1908). The Unreality of Time. Mind, 17(68), 457–474.

McTaggart, J. M. E. (1921). The Nature of Existence Vol 1. Cambridge, CUP.

McTaggart, J. M. E. (1927). The Nature of Existence Vol 2. Cambridge, CUP.

Parsons, J.  (2007). “Theories of Location”, Oxford Studies in Metaphysics, vol. 3., pp. 201–232.

Paul, L. A. (2010). Temporal experience. Journal of Philosophy, 107, 333–359.

Price, H. (1996). Time’s Arrow and Archimedes’ Point: New Directions for the Physics of Time, Oxford: Oxford University Press.

Prosser, S. (2012). Why does time seem to pass? Philosophy and Phenomenological Research, 85, 92–116.

Torrengo, G. (forthcoming). “Feeling the passing of time”. The Journal of Philosophy.

[1] See Baron et al (2015) for an articulation of such arguments.

[2] See for instance Braddon-Mitchell (2013); Hoerl (2014); Torrengo (forthcoming) and Latham et al (ms).

[3] See for instance Latham et al (ms).

[4] See for instance Paul (2010); Prosser (2012).

[5] See for instance Price (1996) as an example of a C-theorist.

[6] See Barbour (1999); for philosophical discussion see Baron and Miller (2014 and 2015).

[7] See for instance Kutach (2011).

[8] See Barbour (1999).

[9] Ingthorsson uses the term ‘A-view’ to pick out presentism exclusively, and uses A/B hybrid to pick out other views that include an A-series, such as the growing block and moving spotlight view which hold that some non-present objects exist.

[10]See Parsons (2007); Gimore (2014) and Eagle (2010).

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