Time to stop trying to provide an account of time
Dummett and I agree that the absurdity of ‘the classical model’ of time  lies most crucially in the notion of a quantity possessing a certain magnitude such that it is logically independent of the magnitude at any other instant. We agree that this conception of the logical independence of the ‘basic quantities’ in terms of which ‘time-slices’ are to be characterized is no less absurd vis-a-vis position, mass etc. than it is vis-a-vis (e.g.) velocity. We agree that taking time simply to be characterized by continuity is in general much to be preferred to taking time to be composed of dimensionless instants.
The primary difference between us might best be described as methodological. I continue to think that Dummett does not have a fully-thought-through reason for preferring a ‘continuist’ appreciation of time to an ‘atomistic’ version of it. Dummett’s main arguments against classicalism still buy into the absurdity, the nonsenses of that model. Thus, those arguments self-refute. They unwittingly retain key elements of the very Realism which Dummett is attempting to challenge.
My criticism of Dummett has at its heart the worry that he appears to conceptualise states of affairs that he then goes on to characterize, crucially for his argument, as “conceptually impossible”. On [p.2]  of his reply to me, Dummett writes that “Latent nonsense contains enough sense for it to be possible to derive consequences from it.” He hopes therefore to have intimated a way in which one can deduce from some of one’s conceptualisations that they are conceptually impossible. I reject his suggestion. Latent nonsense only appears to do what Dummett says it does. The notion of its having a ‘senseless sense’ -- or enough sense for us to know what it would say if it actually made sense -- is itself senseless/nonsensical. (See Phil. Invs. para.500. Wittgenstein’s entire career is in significant measure devoted to rejecting the thought that latent nonsense can genuinely have consequences derived from it.)
Latent nonsense is simply nonsense -- in disguise.
Dummett speaks of finding “enough” sense that one can work out from some sentence(s) that it is nonsense. The image of a half-full bottle perhaps comes to mind; but sense isn’t like that. A half-full bottle still contains something; its contents are still usable. A sentence ‘containing’ half a sense, by contrast, is no use at all. One just doesn’t find / hasn’t found a (satisfying) use, a use of the kind one wanted to find, for the sentence(s) in question.
If Dummett really agrees that latent nonsense is nonsense (and the only conceivable alternative would appear to be the uncomfortable -- not to say bizarre -- view that the word “latent” in the expression “latent nonsense” functions in much the manner that the word “decoy” functions in the expression “decoy duck”), then he must give up the claim to be able to “operate” [p.2] with it (unless that means only: to go through certain operations/manouvres that ape what can be done with sensical utterances etc. ). E.g.: if classical mathematics is really at base unintelligible [p.2], then it is unintelligible, and that’s that. We can perhaps understand the utterer of it in psychological terms; but not what is said (for nothing is).
Dummett thinks he sort-of understands the classical model of time. It has enough sense, he thinks, for him to understand why it is ‘ultimately’ nonsense, what it is ‘trying to say’. I think that that ‘thought’ of Dummett’s is nonsense.
Dummett goes on to explain what it is in the classical model that he (thinks he) does understand: namely, the ‘continuum of real numbers’. [P.3]: “[A]ny segment of the real line...has a length.” Yes; but not a length in numbers!! In any given representation, it has a length in centimetres or whatever. It has a length incomparable with the (infinitude of the) real numbers.
So: I do not accept that the real number continuum could possibly give us any model at all of anything in the real world in the way that would be necessary for classical maths to allegedly underpin an understanding of (say) time. It (the continuum) is strictly speaking best described as incomparable with real things. One can of course measure things in the world by means of a ruler, or by means of any device that in effect uses (rational) numbers as its gradations. But I do not see that or how it could mean anything to speak of a collectivity of dimensionless points accumulating into anything with a length.
The reals get you precisely nowhere, in this connection.
Beginning from the starting-point of the number line, which starting-point Dummett shares with his philosophical ‘opponents’, Dummett is inclined to represent time as though his representation were a picture of a (some-)thing rather than (roughly) a picture of a conception. I.e. Dummett does not take seriously enough the ineluctable sense in which time is conceptual, and not simply something which we find in (the fabric of) the universe. Here, I find Dummett’s position insufficiently ‘anti-Realist’.
picture of time as a picture of a thing might be dissolved by thinking of time
as at base involving comparative
statements. Thus our regular time-telling might be therapeutically paraphrased
roughly thus: as she walked 
Isn’t wondering what time is made up of rather like wondering what the orbit of a planetary or stellar body is ‘made up’ of? And the latter seems just not a very good wonder, just not a reasonable question.
This is why I do not think that I misunderstand Dummett’s argumentative strategy (as he claims I do). What Dummett does, so he says, is “...to take a mathematical function that can readily be described in classical maths, and then try to describe a change in physical magnitude that would be represented by such a function, in accordance with the classical representation of time and change on the model of the classical continuum; when the result proves to be nonsense, I take that as a good ground for saying that the classical model is not an intelligible conception of physical time.” ([p.4] emphasis added) As noted above, I believe that Dummett unhelpfully (or even incoherently) represents the classical continuum. The key question, though, is what we can intelligibly hear Dummett as meaning by words like “intelligible”.
What are we to make of Dummett’s terms of praise and criticism? For he wobbles on the question of whether or not the views he wants to criticise are nonsense. One might say that he wants the Realist views on time that he criticises to make (patent) sense and yet at the very same time to be (latent) nonsense. But that is a pretty patent case of wanting to eat and not eat one’s cake at the same time.
Dummett tries to suggest that he is not trying to accomplish as grand a project as I claim he is. He writes: “To say that time is a continuum of instants, or that [time] is not [a continuum of instants], is not to attempt to say what time is.” ([p.6] emphasis added). This seems a somewhat bizarre claim. Surely to say that time is a continuum of instants is trivially, obviously to say something pretty major and definite about what time is. And, contra Dummett, it surely doesn’t help to substitute the expression “the structure of time” [p.7] for “time” here. To say “what structure time has” is just a fancy way of saying something about the nature of time, about ‘what time is’. (Unless, as considered below, it is rather just a fancy way of talking about the grammar of time. In other words, talk of the ‘structure’ of time might be successfully deflated into talk of ways of doing and talking (of) time.) Questions such as whether there is a time between each two times, however close they are to each other, are not answerable through mathematical nor even physical or metaphysical enquiry. They are, rather, either questions that are responsible to the way in which some genuine enquiry is conducted, or they are not questions at all. They are matters of what in some particular genuine domain of enquiry one is prepared to treat as separate times or as the same time (Cf. ‘Did they cross the line at the same time, or not?’, in Athletics).
As Dummett notes [p.10], I think that the questioning of whether it makes sense to claim that time is a continuum of instants does not entail “giving an alternative theoretical account”. (To give any such account appears to me to necessitate ‘standing outside time’, viewing it ‘from sideways on’, as McDowell puts it. I do not think that this is something which cannot be done (Anti-Realism), but that no sense has yet been given to the thought that there is something here that we can or cannot do. That is why I question both Realism and Anti-Realism. To suppose that the notion of viewing time as if from outside has something like a senseless sense is simply to deepen one’s embeddedness in confusion.)
scepticism about the project of saying what time is does not mean that I am
“indifferent to philosophy” [p.9] ... unless Wittgenstein, Austin, Hertz etc.
were similarly “indifferent”. Dummett says of ‘the
question of time’ that “it is a problem that has perplexed me for a great many
years. It perplexed
Dummett asks, “Is someone who believes that there are no non-denumerable sets bound to deny that there are any denumerable sets, either, on the ground that the term “denumerable” only makes sense if there is a genuine contrast class?” [p.12] No; but they will probably find the term ‘denumerable set’ then systematically misleading.
We should ask what is really being said by someone who denies that there are non-denumerable sets. If what they are claiming is most perspicuously put via the suggestion that no sense has yet been successfully given to the notion of ‘non-denumerable set’, then it would surely be better to speak simply of sets, and their being ‘denumerable’ will then be only a matter of their being sets. If someone were to go on to say, “Yes; and they are as a matter of fact all denumerable!”, we should have a right to ask why they thought they were actually succeeding in saying anything sensical at all by adding this. For they are ruling out nothing whatsoever by their words. Their words have no evident function; so we should want to know what they took themselves to be doing with those words.
Dummett claims that “it is very far from absurd to suspect a language of embodying an incorrect metaphysical idea” [p.16]. On the contrary, we ‘New Wittgensteinians’ strongly suspect it is absurd, and that Dummett is unclear about what he actually wants to do with these words. For one believes that a culture or language can embody a metaphysics only at the cost of Relativism.
Still less is the human form of life as a whole constrained by language. It is not at all clear that the project of giving an intelligible account of how humans could so much as be constrained or limited or distorted by language  has ever gotten anywhere at all, despite much effort having been expended on it. All that can embody incorrect ideas are things which people say, moves they attempt to make in some ‘language-game’.
Actually -- and this is crucial -- I am doubtful that anyone can get so far as actually saying something metaphysical, or purveying a metaphysical idea. I think that people can only actually say things that appear to be metaphysical, things that they themselves would withdraw if they saw them more clearly. I think ‘metaphysical idea’ is ultimately an empty category, possibly like ‘non-denumerable set’. Once we were clear that roughly this is the least misleading thing to say (if it is), then eventually we should have no need of speaking of ‘non-metaphysical ideas’.
However, I do not claim to know that the question as to the nature of time is senseless. That is the kind of thing that Carnap might have claimed to know; he or his followers might have said that any such question can be shown by rigorous logico-philosophical methods to be meaningless; but Wittgensteinians are far from such
(post-)positivism. My attitude to philosophical questions is resolutely ‘therapeutic’ -- but it may be that sometimes the best therapy is to admit that the question one is looking at is genuine (or at least can ‘contain’ deep and perhaps-perfectly-sensible questions). For instance, one may conclude that it is on a borderline with physical science, and therefore cannot untendentiously be ‘ruled out’ as ‘metaphysical’.
This attitude -- rather than being “quietist”, let alone “philistine” (Dummett’s words) -- is one of exploring what it is that people wish to do (including, sometimes, me) when they try to answer philosophical questions. I am not trying to silence anybody or nihilate any real topic. Rather, I want to understand what it is that such people are doing, and to engage in conversation with them. I have a reasonably open mind about where I might go, or end up, in that conversation. To dogmatically take up a ‘nihilist’ or ‘quietist’ view, would not be to hold to Wittgenstein’s methodological injunctions to give up all explanation, to give up all opinions -- to state as theses only what everyone will agree to and withdraw anything else.
My recommendation is, as Dummett says, to get on with our “normal social
life”  -- but that recommendation is NOT to be taken as ‘quietistic’ or ‘nihlistic’. Philosophy leaves everything that is not nothing (i.e. everything that is not agreed to be nonsense) as it is. That means that whatever interest or concern some person or community has with time and exactitude (or otherwise) is just fine, providing they can in the end (i.e. after thinking things through, perhaps with a philosopher as interlocutor) satisfy themselves that their interest hangs together / makes sense. I am urging that certain would-be-interests -- in particular, those of some philosophers -- can be shown to the philosophers themselves not to make sense. My efforts fail as long as the philosophers in question do not agree. But the various actually non-nonsensical interests in time of physicists, of people trying to determine who won a race, of prisoners etc. are of course absolutely fine. I do not yet understand what interest one can have in the real nature of time above and beyond the totality of natural-scientific and human-scientific and practical interests. On [pp.14-15], Dummett writes, “So there is a question to be answered about what form a maximally accurate specification of the time of occurence would take: a question not to be brushed aside by saying, “We all know perfectly well how to say when something happened.”” But I mean that we all know this perfectly well most of the time and for all practical purposes  in ways specific to the domain in which we are operating at any given time. Crucially, for instance, don’t scientists already have ways of sorting this out? I am unclear what Dummett takes himself to be contributing to those debates or proceedures. Will Dummett’s paper (or alternatively his opponents’ papers) be of use to physical (or other) scientists? If he could show me how it might, that would considerably deflate the power of my criticisms. But I don’t see that a role for THE maximally accurate specification of the time of occurence of an event has been laid down or clearly-defined, and I don’t see scientists needing Dummett to help them in their thinking about the explicit and ‘implicit’ margins for error  which they actually have.
Partly for these reasons, I don’t entirely accept what Dummett says in the final paragraph of his paper, above. I would accept the final sentence (urging that I should try to go ahead and clarify the grammar of time ‘positively’) as in many ways a fair challenge; but I think Dummett may have an idea in mind of what I think ‘logical grammar’ can do that is not my idea. Not only do I not believe that the clarification of logical grammar can be carried out once and for all, I do not believe it can be carried out ‘positively’, at all.I take some inspiration here from Tractatus 6.53, which I think intimates an aspect of Wittgenstein’s later methods that is too often ignored: namely, that they are resolutely negative, and dialectical/dialogical, and not participative in the sub-Fregean, post-Carnapian, Rylian projects of ‘logical geography’. I think there is no positive task to be undertaken of saying in general what it is that “we mean...when we ask at what time an event took place.” [p.16]  I think the only task to be undertaken is to ‘return’ us to the actual ‘language-games’ in which people ask, specifically, questions like that.
The ‘clarification of logical grammar’ in respect of such contexts is just to make clear to (particular) people that their language etc. is clear, so long as they do not look askance at it through the spectacles of an inappropriate ‘paradigm’ (e.g. ‘Realism’, or ‘Constructivism’). And what I tried to do in my paper was to ask what it could be that is meant by Realism and Anti-Realism hereabouts, and to urge in particular that the latter is (in important respects) best seen as a deviant form of the former. So, I can undertake ‘logical grammar’ only by working within and at the borders of concrete contexts where people are actually putting words like ‘time’ to use, and by questioning those who would say (as Dummett says) that there is something more to be done by way of making clear what they (‘can’ or ‘should’) mean.
But I can help present the grammar of time perspicuously also by making clear just how much of it is already clear even in Dummett’s own modelling -- and, sometimes even more so, in that of his opponents. For: just as Dummett sometimes reminds us of features of our  lives in and with time (such as the endless possibility, usually, of further narrowing of the ‘margin of error’ in a measurement of time), so, albeit through a glass darkly, the classical model can be seen as a large fragment of our grammar(s) of time. What Dummett says is just fine, so long as it can be cashed out as itself constituting the clarification of logical grammar that he challenges me [p.16] to provide). The problem with the classical model would then be that it presents itself as model of a thing, not as a grammar of something not well characterised as a thing (though not as a nothing either). But, rather than as a theoretic tool, it can be read as an accurate reflection of (most of) what we say about time. For, while it risks occluding the ‘flowingness’ of time; and its application may be restricted by innovations (e.g. Einstein’s) in physics; it captures pretty well the concept of the ‘time-line’ that in so very many contexts we must take for granted. For instance: the relation of times at points along such a line is of course (like the relation of numbers along the number line) transitive.
Dummett emphasizes that the classical model is a model; but in arguing for its inevitable incoherence he misses its possible harmlessness if it is taken not as a general truth, nor even as gesturing at a truth at all, but rather, as a (latent) piece of grammar. Thus Dummett’s revisionism is on balance unhelpful: it would arguably be better if anything to stick with Realism, which is by and large closer to our grammar. (Dummett is insufficiently anti-Realist in his latent Realism; and he is overly anti-realist in arguing against the grammar of time. Compare Phil. Invs. para. 402 -- Dummett attacks the normal form of expression as if he were attacking a statement.)
If the advocate of ‘classicalism’ insists that they are not to be understood as noting our grammar, but rather as stating facts, then, like Dummett, I cannot agree with them. Dummett claims that the absurdity of the classical model then lies in basic quantities (e.g. position, mass) being allowed to have values that are utterly independent of one another from one instant to the next. That this is indeed absurd can be determined with relative facility by an inspection of ordinary ways of talking and being in time and space. But Dummett does not allow himself the resource of any appeal to the ordinary. His main argumentative resource is rather the (nonsensical) argument addressed earlier about the alleged incoherence of the descriptions (of imagined discontinuities within physical processes) that he himself gives. But if one is prepared to allow the whole machinery of dimensionless instants to get off the ground at all (as Dummett is), then there would surely be nothing to stop such descriptions from being perhaps correct. As I say, they are evidently not at present everyday descriptions; but maybe they might find some use (e.g.) in quantum theory. What is Dummett’s argumentative resource against such a possibility (the possibility that a physical scientist might find it useful or even necessary to speak of particles as existing only for dimensionless instants)? He appears to have none whatsoever; yet he thinks he is entitled to proclaim that such a possibility is “incoherent”.
Dummett has done a sparkling job of setting out powerful reasons for believing there remains a philosophically-consequential difference between Realism and Anti-Realism. He and I agree that our dispute is in the end more about the nature of philosophy (in particular, about what terms of philosophical criticism are coherent and workable) than it is specifically about the nature of time. Its ramifications thus go far beyond the terrain on which we have conducted much of the discussion. Realism seeks to provide an account of time as if from outside (the language and practice of) time. Anti-Realism seeks to provide an account of time as if the viewpoint ‘outside time’ is (more or less regrettably) unavailable to us. The deeply-different conception of philosophy that I urge would rather we give up the attempt to conceptualise (‘the’ structure of) time, whether from a fantasized ‘unlimited outside’ or from the allegedly ‘limited inside’ of our life. (Unless the latter just means no more (and no less) than contributing, if and where necessary, to the perspicuous presentation of time-talk.)
The fantasy of limits, ‘limits’ that constrain us or that we can notionally escape, is -- as McDowell has powerfully argued -- still exercising a nefarious influence on Anglo-American philosophy. I urge that the fantasy be overcome, and then the debate -- between Dummett and his Realist ‘opponents’ -- will no longer exist.
 At least as this term ‘time’ is normally employed, including in physics (Though see my discussions of the classical model seen as representing (part of) the ‘grammar’ of time, and of the perhaps-imaginable employment of the classical model in physics, below).
 All page references in square brackets are to Dummett’s “How should we conceive of Time?”, in this issue of this journal.
 This at least is the argument of most of the
essays in The New Wittgenstein (Alice Crary
& R. Read eds), (
 See ibid., and also C.Travis’s recent work, for the central importance of a serious contextualism (minimally, at the level of the sentence, which cannot unmisleadingly be taken to be composed of units of meaning), without which one can seem to understand nonsenses.
 Sometimes it seems to us that we are deriving consequences from something, but our realization that what we have engaged in is (e.g.) a reductio ad absurdum should lead us to reassess how things at first seemed.
 Thus, as Dummett says [p.16], we can achieve “illumination about ourselves” through coming to understand our incoherent desires in relation to our words.
 Is Dummett covertly thinking of a line as being actually made up of / constituted by (a succession of) points? A line, as I point out in my “Against time-slices” (Philosophical Investigations 26:1 (2003), 24-43), is a continuous thing, not literally a succession of points. The idea of such a ‘thing’/figure as a succession of points is a convenience that sometimes helps us think and calculate -- that enables for us a certain analytical perspective in geometry -- but this idea should not be reified, as though we could intelligibly ask for a literal answer to the question, ‘What is a line made of?’The fishiness of that question is of a piece with the fishiness of the question as to what time is composed of.
 This is, of course, because of the property of ‘density’ [p.4].
 Similarly, even the fairly clear and helpful differentiation between (fuzzy) realist and constructivist models which Dummett offers [on p.12] retains what I have called the latent Realism(s) of Anti-Realism: both the troubling tendency to attribute/predicate vague being - ‘exact inexactness’ -- to the magnitude of temporal intervals, and the broader tendency to assume that there must be a ‘yes - or - no answer’ to the question of whether Realism or Anti-Realism is right (true? sensical?).
 Of course, temporality is still embedded in the grammar here. I do not mean to assert the reducibility of time, nor to suggest that time as part of the (wholistic) framework of our thought and life can be completely dispensed with, but only wanting (somewhat like Einstein) gradually to detach someone who is assuming that time must be a substantial thing from the felt force of that assumption.
 Cf note 7, above. Asking what time is (made up of) is like asking, absurdly, what a line is (made up of). (Cf. on this also Tractatus 6.3611 and the surrounding text.)
 It is also striking that Dummett entitles the paper to which I am replying, “How should we conceive of Time?” (underlining added). The capital-letter is perhaps a little sign of reification in Dummett. Whereas, as I allow in my “Against time-slices” (op.cit.), the classical picture of time can potentially be quite harmless, as can even the concomitant picture of the history of the universe as consisting in the succession of its states, provided one doesn’t treat time as composed of dimensionless instants, as built up out of these alleged ‘units’. And provided one doesn’t insist that instants be explanatorily prior. Dummett can’t see that these pictures can in the end be harmless, because he has to regard them as “absurd”/”incoherent”, if he is to motivate the claim that an alternative picture of what time is composed of is necessary. But the very idea of time as composed of anything is itself not motivated.
 The scare-quotes here are of course vital, for the expression within them is one I am suggesting we do not find any satisfactory use for. To stand outside time is to stand outside our concepts, our language, our practices. I.e.: it is nothing at all.
 It would rather be like saying that “That’s a tree” is of course always true (when pointing to a tree) ... even if the utterance interrupts the middle of someone else’s flow, and is a propos of nothing. Which, in turn, is rather like saying “Good Morning” half-way through a conversation. (These examples of course are from Wittgenstein’s On Certainty.) I should be more inclined to ask a person who did that, “What on earth are you talking about??” or “What are you doing?!”, than to say to them “Very true.”
 Other than in ways that are with some effort avoidable -- e.g. we start saying “she” rather than “he”, to alter the ‘genderedness’ of the English language.
 P.208 of my “Is “What is time?” a good question to ask?”, Philosophy 77 (2002), 193-209.
 Including here of course the practical purposes of scientists. I follow Wittgenstein, Cavell, Kuhn and Harold Garfinkel in taking the sciences to be thoroughgoingly practical enterprises (including normally in their theorizing), where the contrast class for ‘practice’ is the asymptotically-vanishing class of ‘metaphysics’. This is not to deny that a clarification of the grammar of time can ever improve our scientific understanding of reality [Dummett, p.16]; but if and when it does so, that IS PART OF a revolutionary change in the Kuhnian sense, not confirmation of one or another metaphysical theory of time. (See notes 20 & 21 of my ibid. .)
 On [p.10], Dummett supposes that I “...would agree that we cannot determine the duration of any temporal interval T save to within a margin of error.” Well, I agree that in many contexts this is a grammatical remark. But it is not always salient and applicable. Sometimes, there is no role for that concept (‘margin of error’). Sometimes, e.g., one measures and quite simply leaves it at that. (Cf. Phil. Invs. para. 80f.)
 On one (anti-scientistic) reading of Davidson, he showed many years ago that there is something essentially confused about any (non-everyday, ‘essentialist’) interest in the alleged question of what and when exactly events are.
 I aim here to echo some key moments near the close of Tractatus (and in Wittgenstein’s remarks to Ogden on its translation) where Wittgenstein insists that he is no ideal-language theorist, but rather aims to show how everyday language is already in order just as it is. For discussion of how Wittgenstein is never a philosophical policeman (because, e.g. his later ‘reminders’ have no substantive content, but are rather simply attempts to return one to the everyday), see my ““The first shall be last...””, forthcoming in Investigating On Certainty (eds. Brenner and Moyal-Sharrock; London: Routledge, 2003).
 Again, a fuller story, for which there is no space here, would offer differential accounts of the language of time in physics, in the prison, on holiday, etc. .
 And this, despite the fact that, in his original paper , “Is time a continuum of instants?” (Philosophy 75 (2000), 497-515), he is quite prepared to make dogmatic claims like the following (p.503): “[Consider] a pair of objects which, throughout a certain interval, were exactly 2cm apart, save at one particular instant in that interval, when they were 4cm apart. Our conception of physical quantities is plainly such that this supposition makes no sense.” My suggestion, in a nutshell, is that we have to try to find out what someone who made such a supposition was trying to say. We might reluctantly conclude that the answer was, “Nothing”, i.e. that even they themelves didn’t in the end know what they were trying to say. We might conclude this after conversing with them, or at least after comparing what they said with ordinary and possible usage of the English language (including, when relevant, of physics).