SPACE AND TIME

only a draft! 

THE SPATIO-TEMPORAL BACKGROUND

 

 

 

There is something essential about the Now that is just outside the realm of science.

Einstein

 

My intention here is to try to introduce and analyze the concepts of space and time having as points of departure our commonsense perspective. It is true that in modern physics such concepts gain different, unexpected senses. However, physicists’ concepts of space and time developed from common-sense views; and the transformations these concepts have undergone in modern physics should be seen as extensions of the primitive common-sense concepts to domains far beyond the ones to which they were originally applied. A complete rupture is impossible, since it would mean the creation of independent new concepts that would have nothing to do with what we usually understand when using words like ‘space’ and ‘time’.

 

Absolute and relational views of space and time

There are traditionally two competitive conceptions of space, which can easily be extended to time. The first view is called absolutism, or substantivalism, or platonism. It was the view advocated by thinkers such as Plato, Descartes, Isaac Newton and, from a peculiar perspective, by Kant. According to this view, space is absolute in the sense that it does not need anything else to exist. Space is like an infinitely large container occupied by physical objects: an infinitely large, borderless medium in which all things are contained. As Newton wrote in his Principia:

 

absolute space, in its own nature, unrelated to anything external, always remains identical and unalterable.[1]

 

In fact, at least at first view it seems natural that space will not change or depend on the objects contained therein. And there seems to be no sense in talking about space as being finite, at least to the extent that it seems impossible to think of a spatial frontier without admitting the existence of what is “on the other side of it”, that is, space beyond its own limits. Moreover, at least Newtonian absolute space is viewed as totally abstract; it does not interact with the bodies contained within it. And this seems to create difficulties when we consider that according to general relativity, space must be curved when it is near massive bodies, for in this case physical bodies would interact with abstract absolute space, which seems impossible.

   One consequence of the absolute conception of space is that it would continue to exist, even if it could be completely emptied; following this point of view, Kant suggested that because we can imagine there being no object in space, space should be interpreted as absolute.[2] Such an argument, however, could easily be reversed to its opposite. If we imagine that everything contained in space gradually disappeared until nothing was left, it would seem that when nothing occupied it, space itself should also disappear. What Kant suggests makes sense when considered within a particular region of space: I can imagine that all the objects in this room might disappear; as the room would remain, my idea of the nature of the space contained in it seems to be confirmed. However, it does not seem possible to conceive space without any objects to occupy or delimit it, nor the idea of never-ending empty space.

   Considerations like this lead us to the second conception of the nature of space, the relationist or reductionist view proposed by Leibniz. According to that philosopher, space is an “order of coexistence” of things among themselves (while time could be his “order of succession”).[3] We can translate this by saying that space consists of relational properties of material things which have the property of being spatial. When we talk about space, we use relational predicates such as ‘next to’, ‘above’, ‘under’, ‘in front of’, ‘within’... Thus, to communicate the location of the city of Buenos Aires, we use relational predicates, saying that it is situated 900 km south of Porto Alegre, at sea level, bordering the Rio de la Plata. According to the relationist conception, objects are not really located in space, since they themselves are what somehow constitute it, and if there were nothing in the world, there could be no space (and likewise the world itself could not exist).

   There are well-known objections against the relational conception of space. One is that if an object occupies space, then it would seem that the space it occupies could be explained in terms of relationships between spatial subdivisions constituted by the object. However, these spatial subdivisions can also occupy space, requiring that the spaces occupied by them be explicable in terms of relations among their subdivisions, and so on infinitely. The conception of space in relational terms seems to lead, therefore, to an infinite regression. However, this is not a decisive objection. A regression can be vicious or virtuous, and there is no evidence that this is a case of vicious regression.

   Another kind of objection is one that posits topological difficulties. We know, for example, that any asymmetric object has a spatial orientation, given its more extensive axis, and it is possible to object that the orientation transcends the relationships among the parts of the object.

     It is also not too hard to find a plausible answer to this objection. In the case of the orientation of an asymmetric object, we can argue that it only exists if the object is considered in its relationship to other objects. What establishes the direction is obviously the existence of other objects related spatially to the asymmetric object. We usually give a direction to an object, because of our habit of imagining objects always related to something, even if that something is ourselves, unduly anticipating the fact that the world is occupied by other objects. By doing so, the object in question would immediately gain direction, because through it we would then be able to construct a spatially related line to other objects.

   Another objection of the same genre (originally suggested by Kant) is this: my right hand and its reflection in a mirror have identical relational properties with respect to themselves (the reflection corresponds to the left hand). But they are spatially different, which is evidenced by the fact that I cannot put my right hand glove on a hand that is its inverted symmetrical copy – as is the case with my own left hand. Now, my right hand would still be my right hand, even if it were the only object in the world. Therefore, it seems that the notion of space transcends what can be explained in relational terms.

   Something similar can be suggested with respect to my right hand: if it were the only object in the world, it would make no sense to ask if it is a right or left hand, because what we see as my right hand only makes sense to the extent that it is related to what we see as my left hand. I can only say that my right hand glove could not be put on an inverted symmetrical hand, like my left one, because in my mind I relate the glove to both hands, considering for this the relational spatial properties that I see between them. Even if I considered only my right hand and an imaginary left hand glove, I am considering the relationship in space between both objects, one real and the other imaginary. The upshot seems to be that there are relational spatial properties that make my right hand something inevitably different from my left hand. Instead of speaking for absolutism, the answers to this objection, like the above one, seem to speak for relationism.

   The main objection suggested by Newton is the famous example of the rotating bucket.[4] If a bucket filled with water rotates, the water within the bucket will rotate with it, forming a concave surface through centripetal forces. According to Newton, this is so relative to absolute space. There are, however, problems with this example. If the water remains in the bucket, it is because of the earth’s gravitational pull, which means that the phenomenon is in some way relative to the earth and the space occupied by it. A better way to exemplify the point is to imagine a dancing girl turning around herself as the only object existing within absolute space. As she rotates, her arms stretch due to centripetal forces. But how can we know that she is rotating if there is no other object in the space? Maybe precisely when we think she is spinning, it is because she is standing still and the centripetal force in this strange world acts precisely when she stops rotating. We can then imagine that there were rockets attached to her waist that make her rotate rapidly, so that her arms stretch with her movement. Maybe then the thought experiment would work. In this case, absolute space must be at work creating the centripetal forces, since they are relative to its immobility; however, Newton’s absolute space is defined as abstract and unable to interact with any physical body. It thus seems that we can reach no clear conclusion based on this example.

   In a disinterested analysis of our ordinary concept of space, it seems that the relational view has some advantages compared to the notion of absolute space. However, the issue turns out to be much more debatable when we ask whether this conclusion extends to the concept of space accepted by contemporary physics. If we turn to Einstein’s general relativity theory, we can interpret space in different ways. We can think that massive bodies curve spacetime near to them; I would guess that a relationist will suggest that spacetime creates a curved relation between physical bodies; some even exclude physical bodies from their ontology, considering them as “holes” in spacetime, a view that unfortunately (or not) conflicts with the physics of elementary particles.

 

2. The ineffable enigma of time

Time is to some extent like space: just as an object can be located between points in three-dimensional space, an event can be located among other events on the one-dimensional timeline.

   But the dissimilarities are much greater. One is that while objects occupy parts of space, changing their place in it, with time it is different: objects cannot fill time or get stuck in it, as happens in space. Differently from the way things are in space, each co-present object entirely occupies the period of time in which it exists. Moreover, unlike the case of spatial relationships, a temporal process is incongruous with its specular image: a melody played in reverse, for example, ceases to be a melody. And while we can move back and forth in space, time seems to move in only one direction, from the past to the future. If we could travel into the past, then by reversing this direction, it seems that effects could precede their causes, which would generate paradoxes: an adult could, for example, buy a gun and then, traveling into the past, meet himself at the time when he was a child and kill himself; but then, how could he have bought the gun if he was killed when he was a child? Also linked to the direction of time is the fact that we do not have the freedom to move around in time in the same way that we are free to move around in space. Time is different from a videotape. We can’t roll time back, we can’t speed it up, we cannot replay it, and we can’t slow it down. We cannot undo what has happened, and we cannot go back in time and correct our past mistakes, which can never be changed, deleted or reversed. We are driven forward by time regardless of our will and more often against it. Furthermore, although we in some way perceive the passage of time, we have no control over its passage. Also interesting is the way we measure time by means of periodical processes. The human race has counted time by the daily repetitions of sunrise and sunset, the phases of the moon, the seasons of the year, and only much later did we invent clocks, sun dials, water clocks, and hour glasses. It was always a passive way of measurement, different from the active ways we can measure space.

   Now, if time passes, what is its velocity? It is usual to answer that time passes at the rate of one second per second, which seems like a joke. But it is not, at least since Einstein’s relativity theory postulated time dilation. The passage of time can change according to the frame of reference in which it is measured. Time can  slow down for the stationary observer’s clock, either when the observed clock is moving at a relatively much higher speed, or when the observed clock is in a stronger gravitational field. Thus, if someone were moving at half the speed of light, her time would pass approximately 1/10 slower than the stationary observer’s time.

   That we are aware of the passage of time may have been one of the reasons why philosophers reflected much more on the problem of time than on that of space. After all, every human being is subject to the merciless yoke of time, which he can only evade in fantasy. As Baudelaire wrote:

 

In order not to feel the horrible burden of Time that breaks your shoulders and bends you towards the earth, you have to get drunk without pause. But on what? On wine, on poetry, or on virtue, as you wish.[5]

 

And also, as we will soon see, on philosophies of time that deny its very existence.

   Another peculiarity of the investigation into the nature of time is the disparity between the attitude of common sense and the metaphysical attitude towards it. As Augustine wrote, “What is time? If no one asks me, I know. If I want to explain it to someone who asks me, I don’t know”[6]. Time, therefore, seems to us something that is both obvious and yet an incomprehensible mystery. For philosophers such as Wittgenstein, this contrast suggests a therapeutic response: it must be a false enigma[7]. Indeed, it is quite possible that the deeper reason why some philosophers were so easily misled in trying to explain the nature of time is that they considered our statements and intuitions about time under the unconscious pressure of prejudices and psychological motivations. Consequently, that tried to explain the fact of temporality in terms that were not appropriate to understanding it. The healthy attitude could than consist in considering time simply as an irreducible fact of the physical world, as much as space, and not as a deep mystery in search of a metaphysical solution. If we adopt this view, what remains to be done is to analyze our common-sense conceptualizations of this fact, trying to find the best way to reconcile them with our scientific knowledge, always distrustful when we begin to ask ourselves questions for which it no longer seems possible to find any answer.

 

Absolute and relational conceptions of time

To understand time, we also begin with common-sense. After all, we began by searching for ways of counting time. The alternatives correspond to those concerning space: time can also be conceived as either absolute or relational. The absolute conception of time was also proposed by Newton, who wrote in his Principia that:

 

absolute, true and mathematical time, in itself and by its very nature, flows invariably unrelated to anything external.[8]

 

Time is, in the absolute conception, like a kind of “infinite one-dimensional container”, which underlies the events that occur in it. According to the relational conception, defended by Leibniz, time is an “order of succession” of things. For him time is a sequence of moments, and each moment is a set of coexisting events in a network of relations of earlier-than and later-than. Hence, time can be reduced to relationships of time between events and states of affairs. For example, we situate Kennedy’s assassination in time, to the extent that we know that this happened after he was elected president, shortly after the Cuban missile crisis, during the Cold War, before the first man landed on the moon, and well before the fall of the Soviet Empire...

   As the relational conception of time is based on the relations of change of things or events, one conclusion supported by this conception is that there can be no time without change, since time is measured through regular changes, without which nothing could count as objective evidence of the passage of time. Of course, it is entirely possible that nothing ever happens in a certain region of the universe; but this is only imaginable to the extent that things happen in other regions, allowing us to detect and measure the time that has passed between events. We ourselves, the observers, are constantly changing. The assumption that there may be time without change also leads to paradoxical results. If we admit it, then we can assume that the whole world, including ourselves, could “freeze” in time for a period of a year without undergoing any change, after that returning everything to its normal course, as if nothing had happened. Now, assuming that this freeze encompassed the entire universe, we would never know it happened.

   The difficulty with this hypothesis is that it violates a reasonable principle of verifiability, according to which experiences incapable of demonstrating that statements about time are true or false are meaningless. Since the idea of our whole world existing without any change is completely unverifiable, it seems that we can quietly conclude that it makes no sense. It is as absurd as the statement, also completely unverifiable, that the entire universe, along with everything in it, doubled in size while you were reading this paragraph.

   There is an ingenious thought-experiment conceived by Sidney Shoemaker to show that it is not true that the existence of time without change is completely unverifiable.[9] Suppose that the world consists of three regions: A, B and C. The inhabitants of region A of the world observed that region B froze in time for a period of one year every five years; after that B continued its normal course, without the people of region B noticing. The inhabitants of A also found that region C freezes for one year every four years. The inhabitants of regions B and C, in turn, realized that region A freezes for the same period every three years. In a year without freezing, the inhabitants of the three regions meet to discuss the issue, concluding that these freezes not only occur in the regions of others, but also in their own, since the reports of freezing presented by the inhabitants of the other regions correspond to the periodic freezes of events observed by others in them. However, considering this, they will soon discover that after a certain number of years the three regions must freeze simultaneously! In this case, a whole year will pass without the whole world undergoing any change, and this fact will be indirectly verified. Doesn’t it seem that there might be time without change? Or should this year be crossed out of the calendar?

   Against Shoemaker’s proposal, we can conceive the following problem: Imagine that freezing occurs in reverse proportion: in region A there would be one year without freezing every three years, in region B one year without freezing every five years, and in region C a year without freezing every four years. In this case the same number of years should go by without change, with all regions frozen. It seems that now we begin to resist counting time in this manner; we would then prefer to discount the years of total freezing, establishing a variable periodicity for the freezing of each region and discounting the time when all regions are frozen as a timeless time. We can extend this reasoning as we like, supposing, for instance, that for a thousand years the three parts of the world remained in a state of hibernation until one or two or three of them woke up from the frozen period of time… Would they have any reason to believe that time had passed? Similar relativizations suggest that there is no time without change. Finally, one can argue that even in Shoemaker’s thought experiment what supports the hypothesis of a common time without change (the totally frozen period of time) are the changes that regularly occur in the other parts of the world. 

 

The thesis of non-reality of time

The idea that we are prisoners of the merciless yoke of time had strong effects for metaphysical thinkers with a certain propensity to invent intellectual placebos for human suffering. Hence some philosophers have ended by denying the reality of time. The most ingenious attempt in this sense was that of the English idealist philosopher J.M.E. McTaggart.[10]

   He begins by considering two distinct ways of conceiving time. The first one appeals to what he calls the A-series (in fact, a sequence). The A-series is dynamic, basically appealing to the properties of being future, being present, and being past. The second way to conceive time appeals to the static B-series. A B-series is basically characterized by the properties of being earlier and being later.

   According to McTaggart, the B-series doesn’t really explain time, because the concept of time essentially involves change. Such a concept, however, cannot be captured by the consideration of B-series, since it is static; events are dated relative to each other, and this once and for all. Thus, knowing that Kennedy’s death preceded the election of Richard Nixon does not clarify the change, since the relationship of temporal anteriority established between the first and second events is immutable.

   For McTaggart, the only sequence that might be able to explain time is the A-series, which is dynamic. That is what we mean when we talk about the passage of time. It is thanks to the A-series that we can make sense of certain metaphors, such as that humanity steadily marches towards the future, or that time is like a river passing by, or that future events are approaching us, passing by us as they become present and then leaving us behind to be lost in the anonymous obscurity of the past... All of this obviously includes the concept of change. The difficulty arises when we consider that any event in sequence A (say, Kennedy’s death) is forever in the future, is forever present and forever becoming past. This means, according to McTaggart, that three incompatible predicates are applied to A-series events: future, present, and past. Since it is not possible without contradiction to apply incompatible predicates to the same thing – for example, I cannot say that I am sitting and at the same time standing – he concludes that time cannot be real.

     The obvious answer to this argument is that an event can be past, present, and future, but not at the same time. I can perfectly well be seated and standing at different times: I was sitting before; now I’m standing. Similarly, without contradiction the same event can be future at one time and then present and past at two other subsequent times. McTaggart anticipated this objection, though he presented an obscure argument to answer it.[11] I think the best way to make this argument intelligible is by ignoring unimportant details, paraphrasing it as follows:

 

 Even if an event X is only present, past or future at different times, it is alternatively considered present, past or future with respect to a given moment M. But this given moment M can also be considered present, past and future in relation to other moments M1, M2, and M3, which are simultaneous, future or past in relation to it. In this case, it seems that we have again fallen into a contradiction, and if we want to avoid it, we will have to consider that each of these new moments is also past, present or future in relation to other moments M11, M12, M13... and so on infinitely. Hence, either we fall into a contradiction or into an infinite regress.

 

Admitting this paraphrase, a return to infinity can indeed be produced. The problem is that nothing proves it is illegitimate. To highlight this, consider the following analogous reasoning about the incompatible relationships of being equal, smaller, or greater, in the sequence of integers. Suppose we are examining a number that follows another in a sequence. When we get to number 6, we see that it is equal to itself, smaller than 7 and greater than 5. But this is not contradictory, since the concepts of equal, smaller, and greater, are applied here to different numbers. However, here too one can take a step further, analogous to the argument above, suggesting that although 7 is greater than 6, 7 is also equal to itself and smaller than 8, which in turn is greater, equal, and smaller than other numbers, and so on. Should we therefore conclude that this regression to infinity is illegitimate, making the series of integers incoherent? Of course not, since the relationships of being greater, smaller, and equal, although incompatible, are between numbers that are either random or arranged in reverse order. The same can be said about the multiplication of relations between moments alluded to by McTaggart. The fact that it is possible to multiply time relations limitlessly does not make them contradictory, because when incompatible they occur between things that are always random or inversely arranged.

   The thesis that a B-series does not explain change is questionable. According to the B-series form of explanation, we have change when a spatial cross section at a later time is different from the same cross section at an earlier time. The only difference between these sequences is that in the B-series change isn’t subjectively felt, because it is not centered in the observer.

   The real importance of McTaggart’s argument lies the multiplicity of reactions it was able to stimulate. An interesting idea arising from the discussion of this argument is that sequence B is fundamental. Sequence A concerns the course of time from the perspective of a present observer, while sequence B concerns time in abstraction from any particular perspective. We can, by replacing indexical terms such as ‘now’, translate statements relating to sequence A into statements relating to sequence B. For example, instead of saying “Yesterday I went to the dentist”, I can say “On 23/3/2001 C.F.C. says he went to the dentist the previous day”.

   The A-series has an analogue in space: I can say that object A is in front of me, that B is at my side, and that C is behind me. But I can also say that objects A, B, and C are aligned one after the other. In the first case I am talking about space like an A theorist, while in the second case I am talking about space like a B theorist. What clearly distinguishes the A series is that it is subject-centered. And all we can say against sequence B is that it is not its business to provide our subjective feeling of time’s flow.  

 

Presentism, eternalism, growing block theory…

Considering the A-series from an ontological perspective, we find four possible positions: presentism, eternalism, growing block theory, and decreasing block theory.

   According to presentism, only present states of affairs exist. The past once existed, but it no longer does, and the future will exist, but it does not yet exist. This is our common-sense view: we do not care about future and past things in the same way we care about what is around us right now. We feel the present, even if it is only through things happening in the present. Everyone who once felt great pain or was in a situation of great danger knows that the present counts much more than the past, when the pain or the danger is over; and they also know that if the future counts, it is because it can become the present. If we accept the A-sequence view that time can only be present, past, and future, then we can argue that since the past has existed and the future still does not yet exist, then only the present exists. According to eternalism, not only the present, but also the future and the past exist. According to increasing block theory, only the present and the past exist, so that the number of things existing in the universe is constantly increasing. And according to the decreasing block theory, only the present and the future exist, with the result that the number of things existing in the universe is constantly decreasing. Few philosophers would defend the latter view, since we all tend to agree that the future exists only as a possibility, while the past has already existed as a present and therefore has existed (or exists) necessarily and immutably.

   I am a presentist. One problem philosophers have found with presentism, which makes them favor views such as increasing block theory, is that if we accept that only the present exists, we cannot find truth-makers for events that occurred in the past (or will occur in the future). I can find a truth-maker for the statement “I am hungry now”, since I have my present feeling of hunger as its truth-maker; but I cannot find a truth-maker for “I was hungry yesterday”. Or, to give a more compelling example: I can find a truth-maker for the statement “Dogs exist”, since I have a pet dog at home, and its present existence makes the statement true. But consider the statement: “Dinosaurs once existed”. There is no present dinosaur able to make my statement true. How could we relate ourselves to things that no longer exist?

   There are a number of fancy attempts to solve this problem from the presentist viewpoint. However, one way to deal with arguments against presentism is simply to explain them away as metaphysical pseudo-problems. To make this clear, let us first distinguish original truth-makers like my present hunger or my pet dog from secondary truth-makers like my memory of being hungry yesterday or the existence of dinosaur fossils. We have a thousand reasons to believe that these secondary evidences are trustworthy. They are present. The same can be said regarding statements about the future. We know that the following statement about the future is true: “In five billion years our sun will transition to a red giant phase”. Of course, we cannot have access to what will occur in five billion years. Yet a comparison between our sun and the fate of other similar stars that have already passed the present stage of our sun already serves as a secondary truth-maker. The conclusion is that the truth-maker argument against presentism fails miserably.

   There are other difficulties. Consider the statement: “I admire Plato”. It expresses a relation between me and Plato. How can something that exists be related to something that does not? Furthermore, consider the statement “Alexander the Great was born before Napoleon”. How can a relation between two non-existing things be formulated? Finally, the present is very thin, maybe something so thin that it is in danger of disappearing. How can existence or reality be accommodated with such disappearing thinness?

   Consider the statement “I admire Plato”. This is puzzling only if we imagine that this statement implies that I admire someone who never existed. But since Plato existed, and there is plenty of secondary evidence that he did exist, it makes sense to say that I have a relationship of admiration to someone who existed in the past. The same concerning the relation between two things that existed at different times in the past, like Napoleon and Alexander. There is no mystery in the relation between an existing thing and a thing that once existed, or between things that once existed. They do not both need to exist right now to be related. In the same way, there is no mystery in the relation between an existing thing and a fictional one or even between two or more fictional things. All we need is to relate them in our imagination.

   However, the main argument against presentism and for eternalism comes from relativity theory. What is present from the perspective of one observer within a frame of reference can be past or future from the perspective of other observers within other frames of reference moving away from or approaching the observer, and there can be innumerable different frames of reference. This seems to speak for eternalism: since the present might be past or future for different observers, existence must also be past, present, and future.

   Here the answer is also easier than many believe. We neither need to reject modern physics, nor select our own frame of reference (our world here on the surface of the Earth) as the only privileged one, nor search for an absolute frame of reference. What we do need to do is simply to accept the fragmentation of time as a fact about the universe that does not greatly reduce the importance of our observer-centered concepts of future, present, and past. We might accept that there are many futures, pasts, and presents, corresponding to many different frames of reference, though still accepting that our frame of reference here on the surface of the earth is privileged, simply because it is here that we feel the passage of time and live our lives: our own time is what matters to us! At least for this thin kind of anthropocentrism we are correct. The civilized alien inhabitants of a planet similar to the earth located in a very distant galaxy would have the same right to practice their own alien-centrism. This view could be called many-presentism. It admits of many possible presents, with their own pasts and futures, being much more demanding than this mingled and blurred outsider view called ‘eternalism’, which does not deserve the name, since it borrows its meaning from the A-theory, in which eternity would be the sum of all times, without beginning or end. Finally, the fact that the now is frame relative does not mean that the now must be subjective, as some proponents of the B-theory suggest. The now is objective insofar as it can be shared by observers belonging to the same frame of reference; and even if we abstract the existence of human observers, we can consider that if there were human (or non-human) observers within the same frame of reference, they would experience the same now that people are able to presently experience. And even distant events, for instance, what is happening in a spaceship orbiting the planet Jupiter, considering that the earth is approximately 40 light-minutes distant from Jupiter, we can adjust the difference by saying that their present is ~40 minutes later than ours. Moreover, concerning events belonging to a different frame of reference in a very distant place and moving away from or approaching us, we can also adjust their past or future presents in conformity with our own present, taking into account the time dilation predicted by relativity theory (for instance, we can say that because of time dilation a rocket sent to a nearby star ten years ago will only reach our present moment after a calculable amount of time).

   The last remark allows us to give an answer to four-dimensionalism, a metaphysical view that seems to be vindicated by eternalism and contemporary physics.[12] According to four-dimensionalism, material objects cannot be completely present here and now, since they are constituted by temporal parts or stages that complement one another during the time period of their existence. Thus, if Lewis has the intrinsic property of an upright posture when standing, he will have the intrinsic property of a curved back when sitting. Since his existence is four-dimensional, there is no incompatibility between these two properties. My presentist answer is that by having an upright posture, Lewis already has the dispositional property of a curved back, and this dispositional property is obviously present. When Lewis is sitting, he has the dispositional property of standing straight. Even if these properties are intrinsic, they are not essential to Lewis.[13]

   The truth about four-dimensionalism is that it is the result of a confusion between the material object (which has “endurance”), and the process (which has “perdurance”). A process defines itself through its temporal parts (Consider a football game: it is only decided after the game is over; consider the Second World War: one could only evaluate the process after it was over, but not in its beginning; the German defeat at Stalingrad was a decisive “slice” in this process, though it could not be predicted at the beginning of the process. Consider the present invasion of Ukraine by Vladimir Putin, which only began while I was writing this: a process was initiated; the complete identification and further evaluation of this process will only be made afterwards, for instance, by historians in the future, (if humanity still has a future); an individual, for instance, a thief who in the night breaks into your home is someone defined as a thief insofar as he is recognized as such. He is not a semi-thief who broke into your home while the semi-thief who leaves or is caught by the police is another, very different one. The identity of a material object (I assume that a person is in the end nothing but a material object) is something that belongs to the present as something we can objectively identify within our specious present.[14]

 

Space, time, and tropes

Ontological entities like the universals and particulars considered in the first chapter are often located within or outside a space-time background. This was the case of realism. The one-category tropical view of the world can be placed within this background. After all, a trope was characterized by us as a spatio-temporally localizable entity, which means that we will not be able to reduce space and time to tropes, even to relational tropes, without circularity. But at second thought, is this really true?

   Maybe not, if we adopt a relationist view of space and time. Why not introduce the relational space and time relations as tropes that are spatio-temporally localizable? Consider the following example: the Southern Cross constellation. It is made up of five stars. The main axis of the cross is made up of three stars, and the distance between the first and the second is approximately two-thirds of the distance between the second, the central star, and the third one. Considering the arms, they have two stars apparently at (visually) almost the same distance from the central one. Now, the relation of distance between the first and the central star can be considered to be a space-trope of (apparent) distance. Here the objection that by definition a trope is a spatio-temporally localizable property is satisfied without circularity, since the spatial relation between the first and the central stars is located in a network of other spatio-temporally localizable tropes.

   The same could be suggested concerning time. If we accept a relationist view of time, some earlier or later time trope is localizable temporally, but this does not make this characterization circular, since it is within a line of temporally localizable tropes. Thus, suppose that the two-hour time is t2. Consider now the temporal line that includes t2:

 

Ø E1_____t1______E2______t2_______E3_______t3_________E4

 

Event tropes E1, E2… E4 are temporally located, but this does not prevent us from also considering time-interval tropes as temporally localizable: t2 is temporally localizable between E2 and E3, for instance. In principle, at least, according to relationism, space and time can be reduced to tropes. And in modern physics this would not change: why could there not be a dilation of time-tropes? Why could we not have curved space-time tropes? It would be of considerable parsimonious advantage if all the world, space and time inclusive, could be explained only in terms of tropes.

 

Subjective time

It is important to distinguish physical time from psychological and so-called biological time. Psychological time is time as we perceive it. It is physical time as we subjectively measure it. For instance, time seems to pass faster as persons age, and this is a psychological phenomenon. Biological time, for its part, is time regulated by the physiology of living organisms, such as the circadian rhythms of sleeping or of menstruation or the process of aging. Biological time, however, is nothing but physical time as measured based on biological processes.

   Philosophers like Henri Bergson were tempted to put psychological time ahead of physical time, rejecting the reality of the latter. According to him,  objective time is not real, since it is spatialized and intellectualized; the only real time comes from the direct experience of the flux of time in the form of duration (durée). Duration relates to memory, since in memory the past survives in the present. It was already objected that Bergson confuses the memory of the past with the past, treating the problem in a mystifying way. This form of philosophy has served our psychological defense mechanisms by giving more importance to psychological time, since we are more able to access and control it. However, it is a question of survival that our subjective time remains sufficiently similar to objective physical time.

Some provisory conclusions

A-series and B-series are complementary, though only the A-series can be really be translated into the B-series. The A-series explains time from the observer’s point of view. It justifies our presentism. The B-series, on the other hand, explains time from a non-observer centered point of view. Present, future, and past, are observer-centered, and eternalism is a bogus concept. Four-dimensionalism is a mere confusion of objects with processes. I have a bias towards relationism, since I cannot conceive of absolute space or even time. But I confess that I have no good argument for it.

 

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[1] Isaac Newton: “Absolute Space and Time”, in J. J. C. Smart (ed.): Problems of Space and Time (New York 1964), p. 81.

[2] Immanuel Kant: Critique of Pure Reason, A 24, B 39. In Kant’s idealism, however, space is an a priori pure form of intuition, which does not belong to the world in itself.

[3] Leibniz: “The Relational Theory of Space and Time” (excerpt), in J.J.C. Smart (ed.), Problems of Space and Time, p. 89.

 

[4] Isaac Newton, The Mathematical Principles of Natural Philosophy, Book I, Scholium.

[5] “Pour ne pas sentir l’orrible fardeau du Temps qui brisé vos épaules et vous penche vers la terre, il faut vous enivrer sans trêve. Mais quoi? De vin, de poésie, ou de vertu, à votre guise.” Le Spleen de Paris, XXXIII.

[6] Confessions, XI, 14.

[7] See Ludwig Wittgenstein: Blue Book, Oxford 1958, pp. 6, 26-27 and 108.

[8] Isaac Newton: “Absolute Space and Time”, ibid., p. 81.

 

[9] S. Shoemaker: “Time Without Change”, in R. Lé Poindevin and M. McBeath (eds.): The Philosophy of Time, Oxford 1993.

 

[10] J. McT. E. McTaggart: “Excerpt from The Nature of Existence”, in P. V. Inwagen and D. W. Zimmerman (eds.): Metaphysics: the Big Questions, Oxford 1998.

 

[11] See sec. 331-332.

[12] David Lewis, On the Plurality of Worlds (Oxford: Blackwell Publishing) Ch. 4. Sec. 2.

[13] For my answer to the problem of personal identity, see chapter IV of this book.

[14] The famous Heraclitian dictum, according to which one cannot step into the same river twice is easy to answer, since a river is roughly identified by its course and origins and never by the water that flows in it.