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Substantivalism and Realism About Space, Time and Spacetime

Updated on February 9, 2015
Actually, space and time cannot be visualized!
Actually, space and time cannot be visualized!
Isaac Newton
Isaac Newton

Substantivalism and Problems

Substantivalism or Substantivism about x is the view that the item denoted by "x" is an object in the common understanding of this word. We could include abstract objects in our terminology but the historical debate that is famous, about Space and Time Substantivalism, has queried whether space and time are like concrete objects. To avoid confusion, we exclude abstract objects and we understand Substantivalism to refer to a concrete "substance" or object. The word "substance" smacks of medieval obfuscation as it is but the position that the referent of the term "space" is a concrete object is associate with Newtonian physics. This association, and the fierce philosophic debate it triggered, come to mind when the student of philosophy encounters the term "Substantivalism." Looking back into the mists of history, the Latin from which "substance" is derived render Aristotle's term "hypostasis" while "essence" - another Latin-based word - corresponds to the Aristotelian "essence." The substance is literally, in Aristotle's Greek, what stand-underneath-to-sustain: it is something like a foundation, and a concrete one too. A pair of philosophic questions that Lewis Carroll liked to bring up used to be: can there be any attributes or properties without an underlying substance to adhere to? can there be any substance without any attributes or properties adhering to it? In the specific context of the debate about Newtonian space and time, one may think of concreteness and object-hood as being critical: the claim is that space and time are substances in this sense. Newton assumed this view but not to argue it philosophically: he was compelled to make substantivalist assumptions (although he might have also been philosophically committed to them) because this was required by the construction, and the math, of his system of physics. The reason is technical, and usually passed in silence, but Newton's physics requires, to work, the availability of absolute coordinate in space and in time. By absolute coordinates we mean the coordinates relative to the substantival backgrounds of space and time respectively. We need to talk about all this in some detail.

If you try to specify spatial and temporal coordinates, indexically or relative to the spatial and temporal points you occupy (where you are at any given time moment), you notice that you can only do this relatively to some concrete items which are not space itself; and, for temporal coordinates, by following the established conventions (pertaining to GMT and to the stipulated time-zones and official time-keeping mechanisms that are available.) You could never figure out your coordinates relative to absolute space - the background substantival space of Newtonian theory - or relative to absolute time - the background "ticking" clock, not really a mechanism-clock but presumably something like a moving index, which moves with the same uniform speed, over some concrete or substantival timeflow. Indeed, you should notice that we have to use metaphors to talk about those background substances that are accounted as Newtonian space and time. When you reach for determination of coordinates you might say things like "4 feet from object w" where the object named "w" is an ephemeral and conventionally chosen item itself; or you might say, "2 hours after event z" in which case, again, the event denoted as "z" is just some happening that has local significance. Giving absolute coordinates would rather sound like "x units of space are between me and object w" and, for time, "event z2 occurs tj units of time after event z1 had occurred." No one can ever know such coordinates even if they are available (which means, even if the background space and time entities are in existence as things.) A school of thought questions altogether whether anything that is in principle unverifiable is meaningful. The broader philosophic position known as Verificationism has been discredited - because it seeks an exception for its own credibility, which cannot itself be verified! - but the point is well taken that there is something seriously problematic about the meaning of claims which are, we are told, even in principle unverifiable. Surely, this does not sound like good science but the catch is that insofar as a system like Newton's works - with its formulas themselves getting it right - we keep the system and we swallow its metaphysical assumptions. Practicing scientists assume that the success of a physical theory proves somehow that its metaphysical assumptions are themselves true. But this is not as obvious. Insofar as post-Newtonian theories in physics make different metaphysical assumptions from Newton's theory, we have a stunning example of a theory - Newton's - that was once considered the theory to end all theories and which, alas, was wiped out. We could say, of course, that this simply shows that Newton's metaphysical assumptions have themselves been discredited and replaced by whatever metaphysical assumptions are needed or warranted by subsequent theories. Nevertheless, it is not to be missed that as long as Newtonian physics was held in esteem, its metaphysical commitments were ERRONEOUSLY considered unshakable. Moreover, one could argue that the "game" in constructing and implementing theories in physics is not at all related to figuring out exactly what kinds of things exist within the universal totality. Or, more strongly, the case has been made - by the Analytical School of philosophy - that any inquiry into the broader metaphysical questions about existing things is nonsensical. All we can and have to do, according to this view, is operate within defensible and successful theories: within these theories, internally, we are committed to the metaphysics which the theories themselves pose. To try to pose the same question not internally within theories but across the board is a grave error that commits us ultimately to nonsense. This important view was initially postulated with clarity by the German philosopher Rudolf Carnap.

If we, then, speak of Newtonian metaphysics, we can leave it at that this particular school of physics requires absolute coordinates to work. Of course, to quibble, even absolute coordinates are relative - to absolute space and time. This, however, is not at all impressive. What we do mean by "absolute" in "absolute coordinates" is precisely, by definition, coordinates that are relative to absolute space and absolute time. We can consider these coordinates to be relational, like all coordinates are: we don't have any contradiction between relational and absolute (as might have between relative and absolute.) The crucial claim is that absolute space and absolute time exist and - per Substantivalism - they are concrete objects of some sort. Carnap's view is a recent sophisticated claim - not without its critics - but the traditional view has been that the Newtonian metaphysical commitment to absolute space and time appeals to the intuitions of intelligent humans like us. At the same time, and fascinatingly, space and time have always been known, as concepts, to trigger a whole slew of problems, puzzles and perhaps genuine paradoxes. We know that this happens with such fundamental concepts as "true" and "false" - but it also happens with attempts to ponder over the meanings and implications from stipulating that space and time are substances - or that there are, there exist, such substances as space and time are taken to be.

The ancient philosopher Plato spoke of "chora" - something like the modern concept of "space." There is an impression, when one reads the Timaeus - the Platonic dialogue where this is brought up - that "chora" is some special type of concrete object. Plato, of course, has a far-reaching metaphysics that includes as real the abstract objects that are concepts (including all the concepts of mathematics and also the linguistic predicates we use, which are supposed to be attributable correctly or not to items depending on whether those items "reflect" or "partake of" the substantival attributes or concepts which Plato calls "eide" or Forms.) "Chora" poses problems and Plato seems aware of that. This kind of problem, incidentally, never goes away when the philosophic topics of space and time are to be discussed. If an object denoted by "a" is in space, then the logical predicate being-in-space is predicated of the object. Thus, "being-in-space" would require a Form. Is this Form to be the "chora?" We are doomed whether we answer yes or no. If we answer "yes," then "chora" itself must be in space: the Platonic Forms are self-predicable (Beauty is perfectly beautiful, etc.) But, if "chora" is in space, then it is not an abstract object; yet, the Forms are supposed to be abstract and cannot be in space, or in time for that matter. So, we should not have a Form that is something like the space we are talking about. If, on the other hand, we accept that we don't have a form like this, then what are the standards of correctness that we look up to when we claim truth for the statement "x is in space?" In Plato's philosophy, the question of what makes claims true or false is ultimately decidable only by looking up to an abstract standard.

The above problem - regarding the status of "chora" which cannot be a concrete object but cannot be an abstract object either - is peculiarly Platonic. Yet, it anticipates a problem of the modern or Newtonian concept of space: is space itself in space? If we take as a principle that every concrete substance has to be in space, then space must be in space. This, however, triggers an infinite regress: the space within which space is located - call it space 2 - as concrete substance itself must also be in space - space 3 - and this space must be in space - space 5 - and so on, ad infinitum. It is not an analytic truth (it is not a truth trivially given, and inescapable on the basis of the meanings of its words) that concrete objects have to be in space. In other words, the statement "a concrete object is in space" is not trivially true like "a triangle has three angles." It does not have to be true. The problem, however, is that within a theory like Newton's this principle seems postulated: every concrete object, the laws of whose mechanics are specified, is presumed to be in space. And then an exception must be made for ... space itself even though space too is to be considered as a concrete object. We see here clearly a first peculiarity of substantivalist space.

The classical or Newtonian space is supposed to be everywhere (although notice the awkwardness of the expression "space is everywhere" since we are not assuming that there is an underlying space for ... space to be at.) It seems that this space, although ubiquitous, has no empirically verifiable attributes. It has no color, odor, texture... Newton could do no better than to offer thought experiments for showing that substantival space exists. Such thought experiments (which are not experiments, as the word is used, but rather philosophical arguments) posit hypotheticals that cannot be empirically reproduced: the objective is always to show that space cannot be eliminated: that, even in the space of any objects, space would still be present. For instance, this strategy for proving that space exists aims at showing that some hypothetical object, if it suddenly appeared, would be able to move and, crucially, it would be able to detect motion because of inertia if it were to accelerate. It is assumed that "x moves", for any x, implies "x moves through space." In other words, "motion" and "motion in space" are treated as interchangeable. A more complicated thought experiment due to Newton is the celebrated bucket experiment: once again, it is stipulated that there is nothing besides the items in the hypothetical. The stipulations are about items as needed - and also for concentration of the mass of the item in a single point, as required by Newtonian mechanics. The criticism that was made by the Positivist school was that such experiments are not empirically reproducible. And, even if carried out, one might well assume that some other object, no matter how far away, is responsible for the observed intertial effects - and not necessarily that space exists and makes motion and acceleration and (in the case of the bucket experiment) persisting concavity of the water's surface after the motion of the bucket has ceased. We are pressed, then, to turn to a fundamental subject: space substantivalism stakes its case by taking it that we cannot make sense of motion (or of distance) and of concomitant inertial effects without stipulating a substantical space. But is this true? Is it impossible to account for what we mean by such notions as "distance" or "motion" without having a substantival notion of space?

This brings us to the other key term we need to introduce. Suppose that we agree that we need a concept of space in order to make sense of certain phenomena to which we are empirically committed: inertial effects in accelerated motion, persisting concavity of the water's surface in a bucket after the bucket has ceased to gyrate and without any other objects around it. and characteristic counterpart relationships (like between left hand and right hand or between a mirror image and its original, which we attribute to orientation in space.) Agreeing that we need a substantival notion of space, the question arises if this has to be a notion of really existing space. Do we have to take space as a concrete substance to really exist or can we remain agnostic about what kinds of things exist and still cling to a substantival space for some other reason? Such reasons may be: our theory requires it, the human mind works this way or any mind that is like the human mind works this way... This view of space is still Substantivalist, since we entertain a notion of space as concrete substance that supports or contains (speaking, again, metaphorically) all other objects; but this new view is Anti-Realist: we no longer take it that this substantival space we are talking about really exists - and by "really exists" we have to agree to mean "exists independently of whether any mind thinks about it." The surprise is that we can combine Substantivalism about space with Anti-Realism about space. This seems to be a counterintuitive position. Newton himself was both a Substantivalist and a Realist about space - and about time too. Scientists to this day continue to be committed to both Substantivalism and Realism with respect to the objects to which they are committed by their theoretical model's metaphysics. To appreciate that the other combination we saw - Substantivalism with Anti-Realism - is counterintuitive, realize what that view implies: if there are intelligent beings, and no space or time are to be intuited as notions, things (whatever they are) are not really in space or in time. The most famous defender of space Substantivalism who is also an Anti-Realist is the German philosopher Immanuel Kant.

There are more surprises. We have been going along with the claim that we cannot make sense of distances or durations of events unless we allow for space and time as concrete entities. We may choose between Realism and Anti-Realism about such entities but we have no option about considering them to be concrete substances. Nevertheless, even this is not necessarily the case. The meaning of the sentence "the distance between a and b is s units" is not logically equivalent with the meaning of the sentence "the length of underlying space spanning the distance between a and b is s units." To go from the first to the second we need the assumption that ... there is underlying space. We are not proving this way that there is underlying space but we are presupposing it. Can we still make sense of "the distance between a and b is s units" without speaking about space at all? The answer is affirmative but the way this is done is rather counterintuitive; it also commits us to abstract objects - not space or time as concrete objects but to relations. We will simply say that the distance between two items is not a matter of substantival occupation (taking up space by applying the yardstick) but it is a matter of a brute given: there is a relation in which the things named by "a" and "b" happen to be involved and this relation is the distance. This is a two-place relation (which we can symbolize by D(a, b) for distance between "a" and "b."). Of course, this is not yet satisfactory because we want to serve the view that we commonly have - the view that distances do change over time. This does not faze us. We step up to a three-place relation as follows: D(a, b, t) - the distance between the things named "a" and "b" at a conventionally assigned value to a point on the time-flow that we designate by "t". Interestingly, we need make no metaphysical commitments about space or time. It seems that we have to commit to some metaphysical theory of relations.

G.F.W. Leibniz
G.F.W. Leibniz
Sydney Shoemaker
Sydney Shoemaker

The Relational Theory of Space and Time

We can make sense of the sentence "the distance between a and b is s measurable units at time t." This can be represented as a four-place relation, D(a, b, s, t). There is no substantival space or time to talk about. So, where are "s" and "t" considered to be included in? We can define a set of spatial point and a set of temporal points, S and T. If it is Newtonian physics we are dealing with, then we have that the overlap of S and T is the empty set - no common items between the two. Take the T set, for instance. It is infinite (with the non-denumerable infinity size of real numbers.) T= {..., t, ...} This represents the time flow. We buy into whatever metaphysical commitments are to be incurred by set theory of course. Is this time flow we are talking about a substantival entity? We need no such assumption. Leibniz, the great critic of Newtonian substantivalism, took persons to be "monads" and spatial and temporal relations to be variable or dynamic attributes of those monads. But this does not mean that the monads are in space or in time because there are no such substances. It is as if you were to think about a videogame in which the characters have properties of spatial and temporal coordinates and have such characteristics as distances from each other - but they are not to be thought of as being in space or in time. You might take them to be in space and time but if you think about this carefully you realize that this cannot be the case. This metaphor shows that what seems intuitive is one thing and what we need to commit ourselves to for a theory to work is a different matter. The design and development of the videogame situations are intuitively interpreted by us as committing us to space and time since we talk about video characters being in such and such places and moving and so on; but the language that is used for designing and implementing all this has nothing to do, and has no need, for some objects like background space and background time.

Take the set T. A relation is imposed on its elements. This is the relation we call strict ordering in mathematics, symbolized by "<". For any ti and tj, members of T, they are related as follows: either ti<tj, or tj<ti, or ti=tj. This means that the "<" relation is, as we say, strongly connected. This relation has other properties: it is irreflexive (for any t, it is not the case that t<t); it is antisymmetric (if ti<tj and tj<ti, then it must be that ti=tj); and it is transitive (if ti<tj and tj<tk, then it must be that ti<tk.) If different theories of time are to be developed, this can be done by imposing additional properties on the relationship "<".

Of course, we could take the setup we used above to be a way of representing the substantival time flow. But the point is that we need no such stipulation. Leibniz, the great critic of Newtonian Substantivalism, had specific objections to taking space and time as things. We might think that we would run into problems, puzzles, even paradoxes by rejecting Substantivalism about space and time. Let us consider some examples.

Suppose that we have to respond to the following hypothetical. "The distance between a and b, as conventionally measured, is s units. We assume, for the sake of this hypothetical, that we can remove some of the background space between a and b. In other words, we play the Substantival game. Although the Substantivalist has no idea of how anyone could "remove" space - and this is presumed physically impossible - it is not logically impossible to run a science-fiction scenario in which we claim that some background space has been removed between a and b. Now, we are asked the question: is the distance between a and b the same or is it shorter?" In this case, most people would probably not realize that they MUST give the answer that the real answer between a and b must now be shorter. This shakes our confidence that our intuitions are indeed deeply in favor of Substantivalism. The Anti-Substantivalist cannot make sense of this scenario - since she rejects substantival background space. The result is that the Anti-Substantivalist cannot allow for any exotic tale by which distance is altered even without anything moving. The Substantivalist, however, must allow that distance can in theory be altered even without anything moving. Which one of the two is now more intuitive?

Another hypothetical, due to the philosopher Sidney Shoemaker, tests intuitions about time and it goes as follows. This one might seem to favor the view that Newtonian substantivalism about time is better placed to handle certain problems. Assume that it is possible to stop motion of all objects, as in some Twilight Zone episode. Also assume that, once frozen or rendered immobile, objects can possibly be made to move again. Is it later that the objects start moving again following the initial move? The Substantivalist has to answer affirmatively, since background time cannot be stopped ever. The Anti-Substantivalist has to answer negatively - that it is not later that the objects are moving following the freeze. It seems that the Anti-Substantivalist is in trouble here. We surely want to be abl to say that "all the objects in the universe unfroze AFTER they had been frozen" but to be able to speak of "after" commits us, it seems, to the Substantivalist assumptions of a background cosmic clock or absolute time. Yet, it is not so clear that the Anti-Substantivalist cannot speak of before and after relationally. Take an object that is frozen at t1 and unfrozen at t2. Can we make sense of "t1<t2" even without any t's in between t1 and t2? This is not the case of the set T we spoke of above but we can actually do this. Suppose we symbolize by "Lt2" the statement "t2 is later-than-t1." So, we can make sense of t2 being later than t1 simply as a matter of predicating of t2 the attribute "being-later-than-t1." We take this to be a brute given.

Shoemaker complexified his hypothetical by making different universes that can "look" into one another be capable of being frozen in certain ways. Suppose that our universe looks into universe U2. We realize that we have a gap in our observations - in U2 effects seem to have proliferated for whose causes we can account theoretically but have not recorded as observed. The best assumption is that our universe froze for a certain period of time. Yet, the obects in U2 were not frozen. Do we have to assume that background time was running or can we simply appeal to the motions of the objects of U2? Shoemaker ingeniously stipulates that in a multiverse like this there could be periodicities involved in the freezing of universes so that, at a regular interval, it so happens that all universes freeze. Moreover, our observations have established that every freezing episode lasts the same amount of time. Now, we measured this time in terms of unfrozen universes. But what about our expectations that at some point all universes are to freeze? Wouldn't it make sense in that case to continue to say that this comprehensive freezing lasts as long as each freezing lasted when not all the universes had frozen? But in this case no objects are moving anywhere. So, this hypothetical appears to be suppportive of a Substantivalist case for time. Is this true?

Substantivalism or Relationism?

Relationism can deal with any challenge that arises but its ways of giving account might seem ad hoc when contrasted to the explanations offered by Substantivalism. The difference lies in that Substantivalism offers a deeper explanation about many phenomena. For instance, let us consider incongruous counterparts: left and right hand, mirror image and its original, chemical compounds with the same composition but different properties whose constituents must then be like a mirror image of each other. As Immanuel Kant pointed out, a pair of left and right hand are distinguishable even if they share all the properties we can think of - but then there must be at least one property they don't share: this property is "orientation in space" whuch means that they are incongruous counterparts of each other. Relationism can take "orientation in space" to be a relational property and still posit this property without accepting substantival space. Or we can think of left-handedness and right- Handedness as properties that admit of no further analysis - no deeper explanation by reference to a substantival space.

This is a liability for Anti-Substantivalism but, on the other hand, Substantivalism commits us to a sort of entity that is akin more to what a religious doctrine would broach up - something undetectable but all-encompassing, something unlike any other object but presumably required as background or container for all objects.


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