Reality and Time

Like most of the contributors to this issue, I am a realist. It is largely a matter of instinct, though I shall also adduce arguments against some of the forms of anti-realism that have been fashionable in my lifetime. Although we ask the questions, both explicitly in scientific experiment and unconsciously in the way our sense organs operate, the answers are given us by something other than ourselves, and our statements about the world are not just projections of our opinions but claims about the way the world is, and capable of being wrong.

Fallibility is a mark of objectivity. But contrary to the arguments of the sceptics, it shows not only that we may be wrong, but that we can be right and often are. And when we are right, it is not just for you and me that our claims hold good, but for everyone. Truth is omnipersonal. It holds for the other chap too, and if he thinks otherwise, there is a contradiction between his account of the matter and ours. He may be wrong, but so also may we. We cannot, with Plato,1 dismiss out of hand how things seem to others, but are led from realism to a modified empiricism. Appearances can deceive, but only if they also can be veridical, and usually are. We should follow Aristotle rather than Plato, and in giving an account of the world, try to save appearances, and reject them only for good reason.

But appearances are not our only guide to reality. Reason also can be a source of knowledge. The Logical Positivists were wrong in holding pure reason to be purely tautological, incapable of yielding any non-analytical truth. As Roger Penrose shows with great clarity, our mathematical understanding is not just a simple matter of following specified rules of inference, but can go beyond them and recognise truths not validated by the rules hitherto accepted as canonical. That has important implications for our understanding of mathematics in particular and for any adequate account of the nature of argument in general. It supports a chastened Logicism. We can claim that we acquire mathematical knowledge through pure deductive reason without thereby suggesting that it is purely analytic, and that mathematics is simply a set of tautologies. Mathematics cannot be reduced to logic: the theorems of mathematics are not just theorems of first-order logic (the logic that computers can be programmed to do). But as we develop logic we form concepts, such as numerical quantifiers,2 and extrapolate arguments, which together lead us to indubitably mathematical propositions. We are led to a version of Platonism as an account of what there is. We need to avail ourselves of second-order logic in order to characterize the natural numbers completely, as well as to formulate other definitions and arguments, and hence to quantify over properties and relations, which therefore, according to Quine, must be supposed to exist. There is a pervasive sense of hard rationality about mathematical truth which is deeply persuasive: it is objective, and not just a matter of the way we set up definitions or play pencil-and-paper games, nor just the mental experience mathematicians want to share with one another. The combination of epistemological Logicism and ontological Platonism can be argued for on other grounds, but is strongly supported by the Understanding of Understanding that Gödel's theorem reveals.

Penrose offers a useful ABCD classification of possible positions as regards the nature of mind, and supposes that my sympathies lie in the direction of D. That is correct, but could be misleading, because my exegesis of the terms `physical' and `scientific' differs from his. It is not only that I want to allow many other forms of scientific explanation than purely physical ones, but crucially that I distinguish scientific explanations from rational ones generally. Rational explanations have to be, in the terminology of the moral philosophers, universalisable, but I distinguish two versions of the principle of universalisability, and allowing that in many cases a judgement can be reasonable, and applicable in all sufficiently similar cases, without there being an antecedently formulated rule, or moral major premise, under which all such judgements should be subsumed.3 Scientific explanations are universalisable in the strong sense: although we may need to amend and refine them many times before we have formulated them quite correctly, they are not revisable indefinitely often, but must at some stage be open to final falsification. But accepting this Popperian demarcation of science, we are led by Penrose's own exposition to recognise that human reasoning cannot be confined to any antecedently specified canon of rationality, but will always on occasion go beyond the rules in some way that is none the less rational. Explanations in the humanities are in this way open-ended. They are rational, and as such subject to the requirement of universalisability, that sufficiently similar cases should be treated in the same way, but without there being some specified canon of rationality they have to conform to. In moral argument and historical explanation we always have to allow that circumstances may alter cases, and rely on some sort of empathy, projecting ourselves into the cases under consideration, to decide how in such circumstances we should, would, or at least might, act. Understanding in the humanities is thus different from the more rigidly constrained explanation we acknowledge as scientific; we may be able to understand the behaviour of a human being, and give a rational, though not a scientific, explanation of the output of a human brain. Thus far, then, Penrose is right to place me towards his D position: only, in saying awareness cannot be explained in scientific terms, I do not say that it cannot be explained, but merely that scientific explanation is not the whole of explanation, and that there is much that is rational, though not scientific.

More generally, I find in Gödel's theorem good reason for rejecting the reductionist tendency of our age. Although economy is a virtue, it should not be achieved at the cost of cutting things down to predetermined size. I am ready to multiply entities provided the reasons are good enough, and am prepared to declare myself a ``more-than-ist'' against the current tide of ``nothing-buttery''.

It is important in arguing with Logical Positivists and their Empiricist successors to be able to show that even in mathematics we accept as true many propositions which can be denied without simple inconsistency. But it is not only in mathematics that rationalist considerations can guide us into truth.4 I had begun to sense this as an undergraduate insisting, against strong tutorial disapproval, that some commitment to the uniformity of nature was implicit in any use of inductive inference, which I later refined in various fundamental principles of sameness. Equally fundamental in natural philosophy but distinct from these, was some concept of togetherness, which Hume witnessed to in his requirement of contiguity, or ``contiuity'' as I re-spelled it.5 I have never been able to give an entirely satisfactory elucidation of the concept. Whitehead tried, in order to provide a foundation for geometry and topology in the fourth volume of Principia Mathematica, but ran into difficulties in producing a purely mereological account of a neighbourhood, and where Whitehead failed, I have failed too.6

The interplay between continuity and discreteness is fundamental to quantum mechanics, and in a related field justifies the traditional axioms of the probability calculus, which do not need to be just posited, but can be seen as the natural way of marrying the arithmetical algebra of the real numbers with the Boolean algebra of propositions.7 The programme of generalising our two discrete truth-values, True and False, into a continuous range of probability values yields all we need in order to justify both the syntax of probability statements and the ways we ascribe probabilities in actual cases. Our ordinary ways of speaking support my view, but they are not conclusive, and there are arguments for both the frequency and the subjective account. Positivists who espouse the Verification Principle are naturally led to the frequency account, since very often the grounds on which we affirm a probability judgement are statistical. More fundamental is the fact that probability judgements are judgements, and therefore covertly universal. It is only the distinction, drawn above,8 between being reasonable and being in accordance with a rule, that enables us to distinguish a weak universalisability implicit in all exercises of reason from the strong universalisability which requires that there be some specifiable class of cases to which the judgement applies the same in every case. If we reject verificationism and allow the distinction between the weak and the strong principles of universalisability, we are not obliged to adopt a frequency interpretation, and to grapple with the many difficulties in a von Mises Kollectiv.9

But, still, probabilities are queer, and metaphysically suspect. It is tempting to follow Hume and Mackie and purge the universe of queer entities by locating all muddled and metaphysically suspect operations in our own minds, and construe our ordinary discourse as being subject to a fundamental error by reason of which we project our own mental attitudes onto the world around us.10 We talk as if probabilities exist in the outside world, when really they reflect only our internal degrees of confidence.11 James Logue deals with some objections that have been made to the subjective account, pointing out the flawed nature of the experiments on which they are based, and rightly observing that an objectivist, as well as a subjectivist, should welcome his conclusions. Certainly I do: I have never been keen on searching through the non-black things in the universe to see if there was a raven among them; and most of the other complaints against the ordinary man's assessments of probability have been based on similarly unreasonable suppositions. Much else that he says is likewise acceptable to the objectivist. There is a significant congruity in what probability theorists affirm despite their widely differing metaphysical standpoints. I attribute this to their all needing to attach numerical magnitudes to Boolean entities, be they propositions, beliefs, measurable sets, or those classes that come up to von Mises' requirements. If this can be done in essentially only one way, then, whatever the foundations, the architecture of the edifice is largely fixed.12 Other desiderata, such as independence or exchangeability, will appear under different guises, and we can debate on which approach they can be best justified. Logue argues for stability and robustness on grounds of comfort and their utility for further decision-making as against my ``hard-core realist preference for `truer' approximations to a unique unknown correct probability value''. He is right to deny the implicit precision of the unique unknown correct probability value: often probabilities are inherently imprecise, and a realist must accept that reality may in some respects be indeterminate. Where I take issue with his quasi-realism is in his locating rationality exclusively in human minds, and in accounting in terms of that alone for the rational constraints on the way we talk about things generally and make probabilistic judgments about them in particular; whereas I, by contrast, am not only a realist, but a rational realist, believing that reality itself is rational, and that it is for this reason we apprehend reality better by being rational.

It is difficult to debate the issue and to get a grip on quasi-realism, just because it is so quasi. One consideration, in addition to those cited by Peter Hodgson, which reassures me that my instinctive realism is not just instinctive is the way our understanding of quantum mechanics has developed. If, as it seems, no sensible hidden-variable theory can be true, and we cannot construe the probabilities of quantum mechanics as merely statistical or as due to some necessary ignorance, then we must posit objective probabilities in giving an adequate account of quantum mechanical reality. The objective theory is not just natural and rationally defensible, but is the only one that accommodates the most fundamental physical theory we have.

I began to look for other a priori justifications for our fundamental assumptions and accepted ways of arguing. Euclidean geometry seemed to me to be not just one among many possible axiomatic options, but pre-eminent---in later years I have given my lecture audiences a Which? Guide to Geometries, ending with a commendation of Euclid as the Best Buy. I argued the case in Euclides ab Omni Naevo Vindicatus,13 pointing out, among other things, that in differential geometry we assume that, in the small, every respectable space is almost Euclidean. Harvey Brown takes this line of argument a stage further; he makes it the fundamental constraint on the General Theory that it should approximate to the Special Theory in the small, that is, that sufficiently small regions of spacetime should be Lorentzian; and argues that that should be the key constraint, and not that it should tend towards the Special Theory as space becomes emptier and emptier of matter. This is in line with the other constraints on the General Theory, that its spacetime should be continuous, indeed, differentiable; it also avoids difficulties with the concept of a matter-free spacetime and with the problem of obtaining a conceptual grip on an absolutely universal force, such as gravitation.

To require that a spacetime be locally Lorentzian acknowledges a certain primacy of flat over curved spacetime, and we may wonder why Lorentzian-ness should be thus privileged. Harvey Brown refers to the many derivations of the Lorentz transformation mentioned in Peter Hodgson's and my Spacetime and Electromagnetism, and rightly points out a lacuna in the assumptions stated there to be needed for Einstein's 1905 derivation. The isotropy of space is required as well as homogeneity. But the mistake is illuminating, and shows the way a priori considerations often work in physics. We start with deep intimations of uniformity, which constitute the unarticulated background against which differences are noted. Sometimes we are forced to recognise that some difference is important, and that it is only relative to a certain feature that phenomena can be properly characterized or laws of nature properly formulated. We are aware of the differences, but overlook the various similarities still assumed to hold. So it was in the development of the two great theories of relativity in this century. So, too, in a smaller way, I failed to distinguish the symmetry under change of direction from the symmetry under change of position or of magnification, which are part of our general understanding of space.

The concept of symmetry arises in Natural Philosophy from that of sameness, and is best treated by means of the theory of groups. Euclidean geometry, too, can be vindicated in group-theoretical terms: although the groups that leave invariant the features of other geometries are not bad, the Euclidean group is particularly good, possessing reflection, the simplest non-trivial discrete operator, rotation, the simplest cyclic continuous operator, and translation, the simplest serial continuous operator. Symmetry is a fundamental key to understanding the physical world around us. But what is often missed is that the concept of symmetry involves difference as well as sameness. The hexagonal ice crystal is symmetrical because if it were rotated through 60o, it would make no difference.14 There is an interplay between some undeniable difference---it has been rotated---and some evident similarity---it still looks the same. The concept of similarity confuses many philosophers, because they think it is a simple dyadic relation, whereas it is really triadic: one thing is similar to another in a certain respect. Much of physics has been concerned with refining the samenesses we had assumed to underlie phenomena, sometimes finding that not every change left physical features invariant as had been expected (parity, for example), at other times seeking deeper symmetries that still were preserved even when more superficial ones were not: but often the issue has been clouded by too sharp a distinction between `relative' and `absolute', which obscures the fact that though distances and durations are relative to a frame of reference, spacetime separation and the magnitude of the four-vector are not. Harvey Brown points out the way that many physicists have been misled by the term `relative' in their understanding of the real import of the General Theory. Relative it is---in some respects, but not in all. Its spacetime has topological properties---continuity, dimensionality, differentiability---that characterize it absolutely, and can be properly thought of as features of Spacetime with a capital S, as Graham Nerlich, in his Shape of Space, convincingly argues.

Arguments from sameness are always attractive, but cannot always be adequate. It is difficult not to be attracted by Einstein's vision of all the laws of nature being subject to deep symmetries, that of covariance under the Lorentz transformations being the most important. Parmenides and Spinoza beckon us into acknowledging the wholly integrated, perfectly symmetrical One as the Ultimate Reality. But perfect symmetries are often broken in reality. Parity, contrary to all our intimations of symmetry, is not conserved. Time is not isotropic. Heraclitus insists: our experience of time's irrevocable passing cannot be ignored,15 and is itself an ultimately decisive argument against claims for the wide application of the Equivalence Principle.

The dynamic account of time can be argued against. Michael Lockwood goes through the difficulties raised by our ordinary ways of speaking, and answers, more carefully than I did, McTaggart's famous objection to the coherence of traditional expressions of the dynamic concept, and rightly maintains that we should talk not only of past, present and future events, but more fundamentally of past, present and future times. He also considers Smart's objection, that if time flows, it must flow with respect to hyper-time or some other implausible entity, and argues that no vicious regress is inevitable in talking of time going by. I myself should be more brusque. We not only have an intuitive sense of passage, but can raise and answer the question `How fast does time flow?' because our own sense varies from occasion to occasion and from person to person. We contrast the metric given by public clocks with our subjective assessment; time flies when dancing with the beloved and dawdles during the second period of compulsory French or on Friday afternoon before a Bank Holiday weekend.

In the Special Theory, as Lockwood observes, we naturally speak of clocks slowing down. Further occasions for talking of the speed of time might arise if two different time-scales---say t-time and tau-time were to emerge in the development of physics, with one being fundamental to the speed of light and the Special and General Theories, and the other to quantum mechanics. We might then be led to speak of time itself slowing down, or speeding up, as time passed by. More generally, we could adapt Shoemaker's argument for the intelligibility of a temporal vacuum: although we always can, since time is one-dimensional, recalibrate our measure of time to ensure that the temporal parameter of transformations in phase-space is simply additive,16 the price may be horrendous, and we may find that we can express the laws of nature very much more simply if we allow that the flow of time is, pace Newton, itself unequable.17 These are mere speculations, but enough to show that the metaphors we naturally use to express our intuitive sense of the passage of time are not metaphors only, but could, in certain circumstances be used to express empirical possibilities.

Lockwood uses the possibility of time flowing at a different rate to argue positively for the intelligibility of the dynamic account of time. He argues that a proponent of this dynamic view should think of the word `now' as being able to function not only as a rigid, but also as a non-rigid designator, which could, had time passed at a different rate, refer to a date different from the one it actually does refer to. Like all such arguments, it turns on subtle differences between the various modalities involved in outlining the different possibilities. At one level we find it easy to envisage time having run differently: ``If I had my life over again, I should have lived it very differently''; ``If it were already tomorrow, I should no longer be wondering what class I was going to get''. We find it very easy to project ourselves imaginatively into other temporal standpoints---Reichenbachian reference points can be adopted at will---but at that level of possibility we find it equally easy to put ourselves in another's shoes: ``If I were you, I should . . . ''. Lockwood seeks a more stringent modality in which `I' cannot refer to anyone but me, but `now' might refer to some other time than that which is actually present. The possibility of time going at different rates meets this requirement---it could not affect the me-ness of me, but would alter the now-ness of now. The other possibility he considers arises from the tree-like semantics of the dynamic account of time, which gives us a canonical test for the present moment on each tree, namely the first node at which branching occurs, but also allows a non-modal comparison between different worlds in terms of similar characteristics. Nick Lockwood could then reasonably envisage a cyborg coming across from a parallel world which was modally co-present though closely similar to some world accessible in our future.

In these and other ways Lockwood argues for the intelligibility of the dynamic view of time, but in the end he denies its actual truth, because it runs counter to Einstein's Equivalence Principle. Though not in the end accepting arguments from symmetry as conclusive, I acknowledge the force of his contention. Experience, too, is not conclusive, and may have to be massaged to fit rational requirements. For me it was Laplace rather than Einstein who seemed to be denying the openness of the future presupposed by free will, of which I was firmly convinced, both as an immediate intuition and as a precondition of moral deliberation and responsibility. Being myself highly counter-suggestible, I was imaginatively prepared to refute Laplace by finding out what his prediction for me was, and then doing the opposite. But, of course, the finding out would be a new input, which would make the old prediction inapplicable. In order to overcome this objection, I was led into problems of self-reference, and thus to the application of Gödel's theorem to self-conscious rational agents, as a conclusive proof of their not being determined in any Laplacian way, thereby not only making room for the freedom of the will, but requiring some dynamic account of time.

Einstein's Equivalence Principle cannot prevail. Lockwood stigmatizes my interpretation of the Equivalence Principle as purely negative, and claims that the equivalence of all inertial frames is the positive manifestation of a far-reaching symmetry. But symmetry principles presuppose differences as well as similarities: there must be some differences between different frames of reference, and those differences must be capable of being relevant to some of our concerns. The best reason, if it were available, for picking out some frame of reference as pre-eminent would be one grounded in physical theory, and in the passages Lockwood cites, I instanced the rest frame of the aether, had there been one, as the best sort of reason. But the reason does not have to be as good as that: Newton was prepared to do without it. In either case the significance of Galilean covariance in mechanics is recognised, and the fact that mechanics is not a Theory of Everything does not seriously undermine its great importance and explanatory power. To take a different example, both Newtonian mechanics and Electromagnetism are date-indifferent: their laws apply irrespective of when an interaction takes place. But it is perfectly compatible with this for Newton to believe on theological, or us on cosmological, grounds that the universe was created at a particular date, and that the absolute date, though irrelevant for mechanics and electromagnetism, is relevant for geology and biology. So too in the present case, even in claiming that inertial frames are equivalent so far as the Special Theory is concerned, we concede that they are in some respects different. Though it would be nice, from my point of view, if there were some deep reason inherent in physical theory for picking out one frame of reference above all others, the reason does not have to be a fundamental one, and the Friedmann models, even if not theoretically fundamental, none the less give us a natural frame of reference. Admittedly, it is only an approximation, and we cannot pick out an absolutely exact frame of reference, or define cosmic time to an absolute degree of precision, but those are unreasonable demands. What has been shown is that within physics itself, we do not subscribe to the Equivalence Principle so unreservedly as to eschew all use of Friedmann models and all mention of cosmic time; in which case it is unreasonable to call in aid the Equivalence Principle to discountenance our ordinary way of talking about time, and the dynamic account it encapsulates.

Quantum mechanics, with its continual collapse into eigen-states, argues for a dynamic view of time. Admittedly, the interpretation of quantum mechanics is a hazardous enterprise. I plead an obstinate but economical realism, which I share with Peter Hodgson, though I am not so optimistic as he is that the objections to the realist option can be easily overcome, and my realism is a more qualified one than his. Quantum mechanics precludes our making measurements in all the respects we would naturally want to, although we can, as he points out,18 ascribe precise values to the position and momentum of an electron after the event. Many physicists explain our inability to make precise predictions or assign precise values to non-commuting "observables" (a most unfortunate nomenclature) in terms of some sort of necessary ignorance, as Heisenberg's original gamma-ray microscope account of the uncertainty relations suggested, rather than an ontological indeterminacy grounded in the very structure of quantum mechanics. It is here that different accounts of probability lead to different understandings of quantum mechanics and vice versa. If probability is inherently statistical, then it follows at once that quantum mechanics gives only a partial account of what is going on in each individual case, as Einstein maintained. Similarly if probability is subjective, we construe quantum mechanics as setting limits to what we can know, but imposing few ontological constraints on what actually exists. But if, as I maintain, probability statements are particular, not statistical, and ascribe objective values rather than express the degree of confidence we feel, then quantum reality is bound to be very different from the reality we are familiar with in our interaction with medium-sized material objects. We are not so much trying to look at a particle, and disturbing it in the process, as trying to tune an old AM wireless, where the more precisely we select the frequency for the radio station we want to hear, the less faithfully will high musical notes be represented; the trouble lies not in our apparatus but in our attempts to characterize the underlying electromagnetic wave in certain specific, not wholly compatible, ways. It is not that our measuring methods are inadequate, but that what is being measured cannot be characterized in the way traditional macroscopic objects can.

It is an unpalatable conclusion, and many physicists, Einstein among them, have sought to evade it. But the very argument Einstein adduced to show that quantum mechanics was incomplete has, by a twist of fortune, made it extremely implausible that it could be completed by the addition of any determinate hidden variables. For if we could assign hidden variables to two separated quantum-mechanical systems that would determine the probabilities of their yielding certain results on being measured, we should have to ascribe to them probabilities that are not borne out by experiment. This argues very strongly indeed against any plausible hidden-variable theory together with a statistical or subjective interpretation of probabilities, and in favour of an account that ascribes objective probabilities for the state function's collapsing into each available eigen-state. My realism, therefore, is importantly different from Hodgson's. His is a more determinate realism, and accommodates the apparent indeterminacies of quantum mechanics as corollaries of its incompleteness and our ignorance of what is really the case: mine invokes no ignorance or incompleteness, and requires that quantum reality really is as quantum mechanics portrays it, however puzzling and counter-intuitive that may be.

A second moral follows from anti-correlation, experimentally borne out by Aspect, and seems to require some violation of locality. Most physicists have concluded, ruefully,19 that the only way to preserve realism would be to allow some instantaneous, or at least superluminal, transmission of causal influence, so that the act of measuring one quantum mechanical system would immediately affect the other, and hence the result of making a subsequent measurement on it, no matter how great a distance separated them. IF we treat the two separated quantum mechanical systems as really separate, then it seems we must abandon either realism or else locality. But, perhaps it is a mistake to assume that when a quantum mechanical system breaks up into two and they become physically separated, they thereby become quantum-mechanically separated too. Rom Harr‚ raises the question of how fundamental our space-time variables are. It is a profound question, and brings into issue the different conceptual ties that anchor time and space in our conceptual structure. But while I concede that there is a question here, I doubt if it should lead us to a Leibnizian as opposed to a Newtonian construal of time and space.

Harr‚ distinguishes a ``nether world'' from a ``manifest world''. It is the modern version of Plato's Cave. The world made manifest to our senses is one we do not fully understand until we are liberated from the bounds of sense and can intellectually grasp things as they really are. Only, whereas for Plato liberation came through a mystical apprehension of the Form of the Good, for us it is achieved by the patient search, usually by the methods of natural science, for the best explanation. And consequently, since economy is a characteristic of scientific explanation, the nether world of the modern scientist is a greyer world than the manifest world, involving fewer qualities, and hoping to explain the manifold richness of the manifest world within an austere conceptual scheme, in contrast to Plato's assumption that it was within the Cave that everything was grey unlike the polychromatic splendour of the world outside. The nether world of the modern scientist has no room for secondary qualities. Colours, sounds, smells and tastes are to be accounted for in terms of vibrations in the electromagnetic field and the atmosphere, and the chemical structure of the substances in contact with our noses and tongues. But primary qualities are allowed in his nether world, and so they are generally supposed not to be explained away. The manifest squareness of the table is due to a corresponding squareness in the nether world. Hence the dualism of space-time variables, which occur both as part our description of the manifest world and as part of the necessary conceptual structure of the nether world intended to explain the workings of the manifest world.

The questions then arise: Which qualities are, or should be, primary? and Why? Different answers have been given, and once it no longer seems absolutely obvious that certain qualities are necessarily primary, we begin to wonder whether perhaps they, too, might be explained in terms of some more basic theory still. We no longer accept the corpuscularianism of the Seventeenth Century as self-evidently fundamental, and look to sub-atomic entities to explain the behaviour of atoms, and fields to explain the transmission of causal influence. Matter is being transmuted into massergy, the separate time and space of Newtonian physics has been replaced in the Special and General Theories by an integrated, and indeed, curved, spacetime, so why should not that evaporate similarly into something altogether more tenuous? So far as the natural sciences go, there is no warrant for supposing that time and space should be immune to conceptual revision. But scientific pressures to revise our concepts of space and time, though important, are not the only ones, and other considerations may lead us to resist revision, or to accommodate it in a different way from what, on the scientific view, would be most natural. Electric charge and spin may be entirely up for grabs, and if a better theory operates with them in altered guise, there is little more to be said. But time is tied up with the passage from future to past, with agency and change, and space with the individuation of things; and these cannot be entirely dispensed with, or modified in any way we happen to think desirable.

The distinction between primary and secondary qualities is not solely that primary qualities are those that enter into our fundamental scheme of explanation in terms of which secondary qualities are to be explained---and explained away. Although explanatory power is a leading mark of objectivity, interpersonal invariance is also important. De gustibus non disputandum, and rather than argue about the real tastes of things, we ascribe tastes to the gustatory reactions of the taster, not to any real property of what is being tasted. With colours and shapes, however, the conceptual pressures do not all act in the same direction. Sight is a distance sense: we typically talk about the colours and shapes of distant objects we do not have to bring close to our bodies to savour, and hence we are concerned with their properties as manifested to us from where they are. But, again typically, when we talk about them, we are talking about them at the same time while occupying different spatial positions. The fact that we have bodies, and that two bodies cannot be in the same place at the same time, imposes its own structure on interpersonal objectivity. Apparent shapes, the shapes things appear to have to each of us seeing them from our differing standpoints, are almost always going to be different: if the reader will look at the four corners of the ceiling in his room, he will see each of them having an apparent angle of more than a right angle. If we are to talk about them it will be no good my ascribing to one corner an angle of 120o and you 130o; the only angle we can both agree on is not the varying apparent angle but the invariant objective right angle which will be the same whatever point of view we happen to adopt. We learn, from an early age, to describe elliptical-seeming pennies as circular, bent sticks in water as straight, and distant objects as large. Psychologists have discovered that even when instructed to match the apparent elliptical shape of round objects, we tend to choose less elliptical ellipses than the ellipses on the retina really are, the more so if there are visible clues, as on a coin, to the object's real shape.20 Perhaps we would have learned differently had we been brought up in the Amazonian jungle; and, more pertinently to our present concern, perhaps we are learning differently with respect to colour with the advent of artificial illumination and coloured spectacles. For most of man's intellectual history light has varied with time but not position. Although at sunrise or sunset the sky might be golden or red and at other times blue or grey, it would, when we talked about it, be the same for you as for me. We did not have to learn to distinguish the real colour of an object from the hue that it appeared to have as seen by each of us; and, not having been forced to make that distinction, we could seriously ask ourselves whether porphyry was coloured in the dark. Now it is different. It is quite difficult to represent the world of appearances as they ought to appear, just because we are impelled to experience them as they really (or so we think) are. Artists have to learn how to share with others the impressions they themselves receive. Our ordinary world is not a world of appearances only but of appearances construed in accordance with canons of reality.

Philosophers have given much less attention to sounds, but our ears, like our eyes, learn to discern the underlying message in the babble of incident noise. As we tune the wireless, it makes a great difference whether or not the language is one we know, and if it is we can make it out in spite of much interference, and if it is not we can hardly hear it at all. Equally with music, we can pick out a snatch of Beethoven without being able to identify the key or the instruments. Few people have perfect pitch, but many can recognise tunes. Our ears, even before the advent of wireless learned to focus not on the particular frequencies that stimulated our eardrums, but the unvarying relations between them that turned up again and again. Even within one auditory occasion, as when the gramophone runs down or a Doppler effect alters the notes we hear of the postbus's horn in an Alpine valley, we instinctively compensate for the adventitious alteration in the apparent sound in order to hear the real signal, which is accounted real by reason of some significant invariance, not explanatory power.

Harr‚'s manifest world is not just a world of unexplained appearances, and so, too, the nether world is not just a contrasting world of explanatory realities. The rationale of the descriptive distinction between primary and secondary qualities stemmed from our having bodies which could not both be in the same place at the same time, and the dominant reason why Harr‚ thinks our nether-world concepts of space and time need to be revised is that quantum-mechanical entities are not things, subject to the condition that a thing cannot be in two places at once. Unfashionably, I dissent from the current orthodoxy that holds that bodies are essential for securing personal identity;21 I regard my body as desirable, but not necessary to my being me: it is my ideas, my communications, my habits of mind, my jokes that make me the person that I am, and above all my ability to make up my mind for myself; and although I should be sorry to be disembodied, I could still, provided I were telekinetically linked up to the World-Wide Web, be myself and make a contribution to the tide of intellectual ideas. But I should still be a temporal being, and I should quite like to have some position, even if not an exclusive one, in some sort of space in which I could have commerce not only with persons, as in cyber-space, but with impersonal entities too. Once I start on the spatial path, I shall be wanting space not only to be continuous but to have more than one dimension and preferably three, to have objects invariant under the Euclidean group of operations, and to have a ``conical'' structure for the continuous propagation of causal influence, and hence a spacetime with Lorentz signature and with communication from one spatiotemporal position to another being subject to the Lorentz transformations. These are desiderata different from the two standard thing-like requirements of a thing's not being in two places at the same time and two things not being in the same place at the same time. If the nethermost world is a non-corpuscularian one, we need not repine. Waves, extending over the whole of space but not exclusively so, are intellectually acceptable. But waves alone will not dissolve all our difficulties, and in particular the EPR ones that Aspect has verified experimentally. In order not to abandon the requirement of causal influence being propagated continuously in spacetime, we may be led to accept a nether space that manifests itself to us as multiply connected. None of the desiderata I have indented for would rule that out, and if we are faced with the alternatives of our manifest space being simply connected space with multiple identities and causal anomalies, or being multiply connected space with simple identities and local causality, we may well prefer the latter.

But still there are difficulties with time. Time is integral to personal identity, in a way that space is, arguably, not.22 Scientific theories may make do with a one-dimensional isotropic temporal dimension, but then have to be glossed before we actually apply them: we learn to throw away advanced potentials. It is noteworthy that while the Special and General Theories have made time more space-like, in quantum mechanics---which is arguably more fundamental, more nether than either---time is treated in a markedly different fashion from space; and, more noteworthy still, that on a realist construal of quantum mechanics the difference between past, present and future, and hence also the direction of time, is reflected in the collapse of a superposition of wave-functions, representing the many different possible course of events in time to come, into one definite eigen-function, representing the single actuality of the present and the unalterableness of the past. This seems to be right. Although we may be led to modify or refine our concept of time as we attain a deeper and deeper understanding of reality, we cannot so far revise it as to lose some of its fundamental properties as manifested in our ordinary experience. If time were cyclic we should lose our concept of personal identity; if we could alter the past we should lose our concept of action and achievement; if the future were not open we should lose our concept of autonomy and agency. However deep we go, we cannot abandon these. But this, of course, is not to say that we cannot go deep. In the nethermost world we might be able to ground our concept of time in some more fundamental modal one. I tried, with only limited success, to do this in a chapter in my The Future, with an interplay between an S4 modal logic of possible futures, which are transitive and branching, and an S4.3 logic of the one and only unalterable past stretching linearly backwards.23 More might be done in that direction. But always subject to certain constraints. However nether the world we posit, its only claim on our acceptance is its explanatory and integrative power, and explanations explain only if they save at least some of the phenomena, of which our experience and understanding of time is as fundamental as any can be. J.R. Lucas E-Mail (not reliable) john.lucas@merton.OXFORD.AC.UK WWW site

1. Republic VII, 529.

2. See, especially, David Bostock's Logic and Arithmetic, I & II, Oxford, 1974 & 1979.

3. See J.R.Lucas, ``The Lesbian Rule'', Philosophy, XXX, 1955, pp.195-213, and ``The Philosophy of the Reasonable Man'', The Philosophical Quarterly, 13, no. 51, April, 1962, pp.97-106; I make use of this distinction in my argument (see below to fn.8]) against the frequency interpretation of probability.

4. My predecessor in Merton, W.H. Walsh, remarked in the 1950s, contrary to the tenor of the time, that it was the Rationalists, not the Empiricists, who would have the most to teach us about the philosophy of physics in the second half of the Twentieth Century.

5. Space, Time and Causality, Oxford, 1984. 6. Many years ago I inscribed a title page `To David Bostock and all my colleagues' in what was intended to be camera-ready copy of a book The Conceptual Roots of Mathematics: it is still collecting dust among my unpublished works.

7. ``The One Concept of ``Probability'', Philosophy and Phenomenological Research, XXXVI, no.2, December 1965, pp.180-201, and The Concept of Probability, Oxford, 1970. 8. p.2 (check). 9. See more fully, J.R.Lucas, The Concept of Probability, Oxford, 1970, ch.5, pp.95-100. 10. J.L.Mackie, Ethics: Inventing Right and Wrong, Harmondsworth: Penguin, 1977. 11. It is worth noting that Mackie did not adopt a projectivist account of probability values, though he did for moral values: see his Truth, Probability and Paradox, Oxford, 1973.

12. See J.R.Lucas, ``Truth, Probability and Set Theory'', in Mathematical Logic in South America, A.I.Aruda, R.Chuaqui, N.C.A. da Costa, eds., North Holland, 1980, pp.209-217. 13. British Journal for the Philosophy of Science, XX, 1969, pp.1-11. 14. A consideration I found very telling against the Verification Principle, which when I was an undergraduate, I was told by my tutor to try harder to believe. 15. I remember on my sixth birthday looking up at the clouds as they passed over the top of the house, and pondering, with useless regret, the fact that I should never be five again. 16. See A Treatise on Time and Space, London, 1972, $14, pp.78-84.

17. Scholium to Definition VIII.

18. p.6 of his TS.

19. Though Peres' derivation (cited by Hodgson [p.17 of his TS]) without any assumption of locality still leaves a scintilla of doubt.

20. See R.H.Thouless, British Journal of Psychology, 21 and 22, 1931; J.J.Gibson, The Perception of the Visual World, Cambridge, Mass., 1950, pp. 169-172; O.L.Zangwill, Introduction to Modern Psychology, London, 1950, pp.30-34; R.L.Gregory, Eye and Brain, London, 1966, pp.152-153.

21. J.R.Lucas, ``A Mind of One's Own'', Philosophy, 68, 1993, pp.457-471.

22. J.R.Lucas, A Treatise on Time and Space, London (Methuen), 1973, Part I, esp. SS1, 2, and 9.

23. The Future, Oxford (Basil Blackwell), 1989, ch.10.