10

CONTAINER SPACE AND RELATIONAL SPACE

Leibniz's attack on Newton's conception of space and Einstein's special theory of relativity are the two important starting points for modern philosophical discussions of space. The theories of Leibniz and Einstein contradict Newton's ideas but in different ways. Newtonian space is a complex notion, it is possible to criticize it in some respects and defend it in others. In order to capture the category of space its different constituent aspects must be carefully distinguished. In post-Newtonian discussions they have all too often been run together in an unfortunate manner. Leibniz's criticism is mainly that Newtonian space is not relational. The specifically Einsteinian criticism has been that space has a relativistic metric. There is also a third kind of criticism, associated with Ernst Mach, which should be kept clearly apart from the other two. It claims that what is wrong with Newtonian space is that it is not relative. Newtonian space is neither relational, nor relative, nor relativistic. It is absolute, but 'absolute' means one thing when contrasted with 'relational', something else when contrasted with 'relative' and something else again when contrasted with 'relativistic'. I shall therefore avoid this ambiguous term as far as possible and instead use 'container space', 'non-relative space', and 'non-relativistic space' respectively. I shall argue that these distinctions are related as in Figure 10.1.1 The important thing about this figure is that it shows that the category 'container space' subsumes the different concepts of space which are or have been, proposed within physical science. I shall not take into account what might be called post-Einsteinian conceptions of space, but the arguments put forward below can, I

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non-relativistic (Newton)

non-relative

relativistic

non-relativistic (Mach)

relative space

relativistic (Einstein)

relational (Leibniz)

Figure 10.1 think, be developed to take into account such conceptions.2 My aim is only to stress the inevitability of a container conception of space. If the table has something to say to the physicist, it might be that a non-relative relativistic conception of space is a consistent one; Figure 10.1 also shows the real relationship between the theories of Einstein and Mach. I shall explicate the table from left to right.

10.1 CONTAINER SPACE The container view of space claims that actual space is in one sense literally a container. Space contains things in exactly the same sense in which an ordinary container can contain things. But space cannot have ordinary limits and so in this sense it is not a container. The similarity justifies the concept 'container space', the difference indicates that a container space is categorially different from a state of affairs. States of affairs exist in container space, but space does not exist in anything else. The difference between these categories becomes obvious when one realizes how they behave with regard to aggregation. Things (= states of affairs) can be aggregated into larger things; i.e. things of second order (cf. section 6.1). An aggregate does not exist in and through itself, but only in and through its parts. The parts (the things) are primary and the totality (the aggregate) secondary. With a container space matters

146 CONTAINER SPACE AND RELATIONAL SPACE are quite different. The subvolumes or regions of space exist only as parts of space.3 Here, the totality is primary and the parts secondary. It makes no sense to speak of aggregation of the subvolumes. By 'aggregation' I refer not only to a thought operation in the sense in which one considers a number of things as if they were a single thing, but to real aggregation as when things are actually placed in space in such a way that they take on the character of a single entity. Things may in principle be moved around in space without losing their identity, but the parts of space can not be so moved. That is why container space cannot be an aggregate. That space is a container space means also that it, as a category, might be instantiated without it being the case that the category of state of affairs is instantiated. In other words, there is nothing in the category itself which implies that space could not be empty. The category of state of affairs, however, presupposes the category of space. States of affairs can only exist in a space. At this point a reminder of the rarefied level of abstraction of an ontological system is in order. Nothing we have said so far is in conflict with a theory of physics implying that the container space which we live in is, as a matter of fact or physical theory, not empty. Relational space, on the other hand, cannot even in principle be empty. Container space is a particular, even if it is a special kind of particular. Particulars like instances of states of affairs and quality- instances are characterized by the fact that they only can be at one place at a time. Of course, the same cannot be said of space. Places only exist in space and so space cannot be in a place. Nevertheless, container space has to be a particular. Otherwise it could not contain other particulars. A mere universality cannot contain what is particular. If one takes a nominalist position, the opposition between particulars and universale is clearcut; universals do not exist and so what is particular cannot be universal. From a nominalist point of view a container space does not bring in universality at all. But on the view adopted in the present work, immanent realism, everything that exists has to have both a particularity aspect and a universality aspect. 'Universals are nothing without particulars. Particulars are nothing without universale', to quote Armstrong again (cf. page 11). This means that container space, too, has to have a kind of universality.

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One might think that the universal aspect of space is nothing more than a possibility (or even actuality!) that there may be several numerically distinct container spaces. But this is wrong. There can be one and only one container space. My argument for this claim goes as follows. The concept of 'container space' entails a distinction between 'no-thing' (= 'void') and 'nothing'. If there is a container space there may be a void, but a void is a something not a nothing. Assume there are two container spaces. Then, either there is void between them or nothing between them. If there is a void, this void connects them into one single container space, and if there is nothing they are already connected and make up one space. We have a reductio ad absurdum argument to the effect that there can only exist one container space. This, it must be noted, does not at all imply that space cannot have many different qualities (e.g. geometrical qualities), even qualities which may vary over space and time. But how, it may be objected, can something which necessarily has only one instance have a universal aspect? This brings us back to the last chapter and the relations of existential dependence. One relation defined there was that of just existential dependence (D9.1 and D9.1') and another that of existential exclusion (D9.5). The relation of plural self-dependence was defined (D9.1.1) as a special kind of existential dependence. Ά is plurally self-dependent if and only if for every instance of A it is logically impossible for A to exist if another instance of A does not also exist.' Examples given were 'competitor' and 'sibling'. In the same way as D9.1.1 was obtained from D9.1 we can now create a new definition out of D9.5. We thereby obtain:

D10.1: Л is plurally self-excluding if and only if for every instance of Л it is logically impossible for A to exist if another A also exists. A universal conforming to this definition is a 'singularity-universal' (cf. 'plurality-universal', page 139). The argument above shows that container space has a universal aspect, because that is what the argument is about. And the upshot of it may now be expressed by saying that container space is a singularity-universal. Like everything else really existing, container space is both particular and universal, albeit a very special kind of universal. But that is what should be expected.

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The concept of 'container space' implies both containment and necessary singularity, but also a third thing: independence. Container space may exist without anything else at all existing. 'Independence' is here meant exactly in the sense defined in D9.2 of the last chapter. Moreover, container space is in this theory of categories the only absolutely independent category. It is independent not only with regard to one of several kinds of universal, it is existentially independent of all universals. This fact together with the fact that it is a singularity-universal gives container space the unique role it has.4

10.2 RELATIONAL SPACE Relational space may be defined by denying that the attributes of containment, necessary singularity, and independence apply to space. Relational spaces are dependent upon other entities, either ordinary things or Leibnizian monads, and are some kind of relation between these entities. They are grounded in some universal aspect of the entities, and are therefore themselves ordinary universals (i.e. not 'singularity-universals'). Being grounded universals, these spaces cannot possibly be empty and cannot contain states of affairs in the sense that container space does this. In order to clarify the view that space is merely a system of relations between things, more has to be said than was needed to introduce the container view of space. To begin with, I shall quote Rom Harre: The totality of possible pointings to possible contemporaneously existing things makes up space. Space is the totality of places where things can be at the same time. And if we think of the minimal thing as a simple point, then space is the totality of points. With one further small step in thought, we shall have space as a system of relations. If we ask how the system of places where things can be is to be organized, we can start with a relation of great simplicity, namely that of'betweenness'. If there are three things, then they can be arranged in space so that С is between A and B. This is a different configuration from that in which A is between В and C. The three things can be triply simultaneously

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pointed to, making three points, related by the relation of betweenness. Continuing in this and similar ways we can organize all possible places for pointing into a system of points, which can be considered and studied in abstraction from any particular things occupying the places in it. This system of points, related by such relations as betweenness, is space. To say that an individual thing is in space implies that it can be pointed to, and that means that it must be at one of the points of space.5

The emphases in the quotation are mine. I want immediately to stress that relational spaces are defined by means of the concept 'possibility'. As is well known, Leibniz already said that 'space is an order of possible coexistents'. Let us take a closer look at this type of construction. Assume that we have a number of things, all having a specific colour. Colours, we also assume, can be ordered along three dimensions: hue, intensity, and saturation. To rank, in this case, means to order into an ordinal scale. Assume further, that we can think of other things with other hues, intensities, and degrees of saturation than the things that actually exist, i.e. possible things. If the colours of all actual and possible things can be placed in three ordinal scales according to hue, intensity, and degree of saturation, then we may construct a colour space with three dimensions. To the paint dealer, by the way, this is a well-known space, but what is its ontological status? Let us think of two things having different positions in the colour space; we assume that there is a certain difference of intensity between them. This relation ('being of different intensity') is a grounded relation. It cannot be changed or cease to exist without a change in at least one of the things in question. The intensity dimension is constructed by means of grounded relations. Of course, the same is true for the two other dimensions, hue and saturation. The colour space we have described is a relational space. Such a space is merely a system of (grounded) relations between things. If there are no things (actually or potentially) then there is no space. Relational space cannot be empty. It is always secondary in relation to things, and things cannot in any literal sense be said to exist in space. Two existing things which have different hues, intensities, and degrees of saturation, have qualitatively different instances of the property colour. These property-instances exist as

150 CONTAINER SPACE AND RELATIONAL SPACE much as the things do. However, there also exist instances of three different kinds of grounded relations: difference of hue, difference of intensity, and difference in degree of saturation. These relations cannot be reduced to the corresponding properties. They are something in themselves, but in spite of this, do not exist in the same immediate way as the corresponding properties. The latter are presuppositions for the former, but the relations are not presuppositions for the properties. We might say that grounded relations can have an actual but second-order existence. Normally, a colour space is a construction based on both actual and potential things. However, let us think of a situation where, as a matter of fact, all possible colour hues, intensities, and degrees of saturation are instantiated. In such a case the relational colour space would really exist as a whole, but it would still have only a second-order existence because it is still merely a system of grounded relations. The fact that the notion of a colour space normally refers only to potential things means that it normally does not even enjoy this second-order existence. It is a mere conceptual construction, not an instantiated universal. Colour space is not the only space we can construct. A sound space can be constructed from the different tones. This space will have two dimensions, intensity and pitch, because the individual tones have the corresponding two dimensions as determinable properties. Each dimension in a relational space is a scale, and so each and every scale can be regarded as a one-dimensional relational space. If one takes things which have only the properties volume and mass, one can construct another two-dimensional relational space. It is interesting to note that a relational space can also be constructed out of things which, in some well-defined way, have length, breadth, and height. In this space all three dimensions would be of the same kind, i.e. extension. The relations in the relational spaces above are grounded relations. But it is not possible to construct one-dimensional spaces with arbitrary grounded relations. The genuine relational spaces referred to above are based on determinables like extension and colour hue, which have determinates capable of being ordered, at the very least along an ordinal scale. This is a minimum requirement which cannot be met by all properties. It seems, for instance, to be impossible to construct a relational shape-space in which every shape would have its place. The determinable 'shape'

151 ONTO LOGICAL INVESTIGATIONS seems to have determinates (= the specific shapes) which simply cannot be ordered along an ordinal scale. A defining characteristic of a relational space is that all things in it are point-formed with regard to space, another is that many things can be at or in the same place in such a space. Consider again the length-breadth-height-space just mentioned, i.e. the relational space which can be constructed with the help of things that have the three properties length, breadth, and height. Each particular thing is extended in three different dimensions but, in spite of this, has no extension in this relational space. Here a thing 'exists' in the single point (*i, Z\) which represents its length, breadth, and height; two things with the same length, breadth, and height have to be placed in or at the same place in relational space. The differences between a container space and a relational three- dimensional 'extension space' are considerable. Since every point in a relational space may contain several things, relational spaces can be regarded as ordered sets of sets of things with specific properties. With regard to such a space each thing merely is or is not an element in a certain set. An element cannot have extension within a set. In container space, however, a thing not only can but must have extension. Container space can never be identified with the set of its parts.6 My presentation of the difference between container space and relational spaces is intended to give rise to the reaction: 'How could a philosopher ever have claimed that actual space is a relational space?'. My answer is an answer in two parts. First, it has to be borne in mind that all the relations I have been concerned with in this chapter are grounded relations, but that most serious attempts (at least in this century) to construe actual space as a system of relations have in fact been based on external relations. In the quotation from Harre the relation mentioned is 'betweenness'. Mario Bunge uses the same relation in his construction in Treatise on Basic Philosophy,7 and Bertrand Russell's attempts were based on the relation of 'overlapping', which also conforms to the definition of external relation.8 Second, most philosophers lump together grounded and external relations into one single category of relations. Because of this they associate features of one subcategory with those of the other so that the claim that actual space is a relational space does not look as incredible as it did above. Assume that we have four things (a, b, c, and d) of exactly the

152 CONTAINER SPACE AND RELATIONAL SPACE same length, breadth, and height, and that these are situated along a line in container space. In the relational 'extension space' discussed above, all these four things are situated at one and the same place. However, in a space constructed with the external relation 'between', the four things cannot possibly have the same position. Thing b is between a and с, с is between b and d, and b- and-c is between a and d. This is sufficient in order for a, b, c, and d to have different places. If actual space is a system of relations, it has to be a system of external relations. Now, if actual space is a system of external relations between things, but also a space permitting empty space, then this system of relations has to make some references to potential things. An actual thing has to have the relation 'between' to potential things, too, namely those now regrded as having the places which make up the empty spaces. From an ontological point of view, we have here two possibilities. Either the empty spaces with their spatial relations exist, which means that we have a container space. In that case space makes the external relations possible, and not the other way round. Or the empty spaces do not really exist, which means that they have to be ascribed the same form of potential existence as a potential thing. In this case, things will make space possible. Space will become a construction like the relational spaces based upon grounded relations. If one believes that actual space may be empty one is forced to the conclusion that it is a container space. Relational spaces, whether based upon grounded or external relations, cannot make empty space an actuality. But in the empiricist tradition it was argued already by Berkeley that empty space is not in principle observable, and what is not in principle observable cannot in principle exist. Thus, there can be no empty space. My argument against actual space being relational vanishes. I do not believe in the empiricist inference from non-observability to non-existence, but this need not concern us here because empty space is observable. Empiricists have always been bad phenomen- ologists. Obviously, we do perceive spaces between things as empty, at least normally, i.e. when it is not misty. Empty space is in this sense very much a perceivable category. Perceivability implies possibility, which means that empty space is a possibility. And that is the premise needed for my argument in favour of container space. In order to understand why such an obvious phenomenological

153 ONTOLOGICAL INVESTIGATIONS fact has been overlooked so often, the distinction between classificatory, comparative, and quantitative concepts should be kept in mind. I am only claiming that we can directly perceive what the classificatory concept 'empty space' may refer to. The same is true, I think, for the comparative concept 'more empty space than'. But, be that as it may, it is not true for the corresponding quantitative concept. Suppose we are measuring length in the old-fashioned way by using a measuring stick. Empty spaces and things have a quality in common, extension. This peculiarity makes it possible to measure the extension of a specific empty space, as being delimited by two things, by putting the measuring stick between these two things. The extensions of empty spaces can be measured with the help of things, but they cannot be measured with the help of parts of the empty space itself. The latter cannot be moved, like a measuring stick. This means that quantitative extension is not like classificatory extension directly observable. Probably, a conflation of classificatory and quantitative extension has contributed to the tendency to regard a system of external relations both as constituting actual space and as a relational space.

10.3 RELATIVE SPACE I shall now introduce the concepts of 'relative space' and 'absolute' (in the sense of 'non-relative') space, and show that neither kind of space is in conflict with a container conception. Moreover, I shall claim that whether space is relative or not, space has an explanatory function. First, however, we have to talk about relative and absolute motion. In one sense all motion is necessarily relative. When a thing moves, it moves with regard to something, i.e. with regard to some instantiated universal, be it other things, quality-instances, or space. Motion is, as I have argued earlier, a pure Gestalt in time and with regard to time it may be taken as absolute. But with regard to space it necessarily involves a relation.9 What I shall mean and what is usually meant by 'relative motion' is, however, a motion where it is not in principle possible to decide whether the one relatum moves with regard to the other or vice versa. Uniform motion in Newtonian mechanics is a relative motion. Whether a moves with regard to b or b with regard to a is

154 CONTAINER SPACE AND RELATIONAL SPACE impossible to decide. It does not matter whether a and b are two things or whether α is a thing and b is space. The same is not, however, true for all kinds of motion. At least not according to Newton himself and his closest disciples. Acceleration with regard to space was supposed to have, in contradistinction to uniform motion, observable consequences. Whether a thing accelerates in relation to space is in Newtonian mechanics a significant issue. In order to grasp what is involved here one can think of a man travelling over the sea in a ship on a cloudy coal-black night. Whether the ship is at rest or moves with uniform velocity is impossible to decide. However, the man can feel acceleration, provided it is not too weak, when he feels that he is being pushed backwards. The famous discussion between Leibniz and Newton's disciple Clarke, concerned among other things the question whether acceleration should be regarded as absolute or relative. Of course, this discussion is the really interesting one from a physical point of view, but it is not obviously interesting from a categorial point of view. A theory of categories is situated on another level of abstraction than physical theory, and what is interesting at one level need not be interesting elsewhere, even though there sometimes exist tangible connections between the two. Assume that we have a binding argument, given the Newtonian framework, either for the view that acceleration is absolute or for the view that it is relative. What would the philosophical implications have been in each case? If it is proved that there is absolute motion, then of course it follows that there is a container space of such a character that it allows absolute motion. We have got a non-relative container space. From my point of view, problems can only occur if it is proved that accleration is relative. If this is the case we can construct an argument to the effect that space is not a container space. For the argument we need the principle that what has no explanatory function does not exist. We take this principle and relative motion as incontestable premises. Assume, then, that actual space is a container space. This means that where there is motion between two bodies a and b, there are always three possibilities open:

(1) only a is moving in relation to space;

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(2) only b is moving; (3) both a and b are moving.

As space cannot distinguish between the possibilities it has no explanatory function, and so it does not exist. In such an argument, however, there is a hidden premise to the effect that explanation of motion is all that matters for space. This premise is false. Space can have, and does have, other explanatory functions. Everyone who accepts the possibility that two simul- taneously existing things may have exactly the same qualities, has to face one of the classical philosophical problems: what individ- uates things? How is it possible for qualitatively identical things to be numerically different? Container space is the explanation; this kind of space functions as a principle of individuation. Two things can be numerically different but qualitatively identical because they can be at different places in space. In such a way container space has a philosophically explanatory function. However, I shall not go into the discussion about principles of individuation. Instead, I shall discuss some explanatory functions that are closer to physics. Container space is needed in order to explain some real properties of things which do not have a direct connection with motion. This idea is due to Nerlich, who, in turn, is indebted to Kant. Kant tried to prove the existence of container space; true, not an objectively (i.e. independently, cf. note 4) existing space, but space as a subjective form of intuition of the transcendental ego, but this makes no difference here. One of his arguments was to point out that the difference between a right hand and a left hand can be explained only by taking account of their different relations to space. The usual counter-argument is given a nice formulation by Wittgenstein at sentence 6.36111 of the Tractatus:

Kant's problem about the right hand and the left hand, which cannot be made to coincide, exists even in two dimensions. Indeed, it exists in one-dimensional space

о χ — χ о a b

in which the two congruent figures, a and b, cannot be made to coincide unless they are moved out of this space. The right hand and the left hand are in fact completely congruent. It is quite irrelevant that they cannot be made to coincide.

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A right-hand glove could be put on the left hand, if it could be turned round in four-dimensional space.10 Wittgenstein has a relational conception of space, and it is this presupposition which makes the argument run so smoothly. A container space has a definite number of dimensions. If it is three- dimensional actual things cannot be turned around in a fourth dimension; if it is four-dimensional then the actual things cannot be turned in the fifth dimension. Relational spaces, on the other hand are merely constructions, and so in a sense it is arbitrary whether you speak of three or four or more dimensions. If, really, the number of dimensions of space was arbitrary, there would not be any right-hand or left-hand properties. Things which, like right and left hands, lack inner differences but in spite of this cannot be made to coincide, Nerlich calls 'enantiomorphic things'. Things which can be made to coincide (e.g. two spheres) he calls 'homomorphic'. A thing is not enantiomorphic in itself but only in relation to a space. Some things are homomorphic independently of the qualities of container space; certain things are homomorphic in some but enantiomorphic in other spaces. If a two-dimensional container space were to exist, then two L-shaped things with the 'foot' to the the right and left, respectively, would be enantiomorphic if the space were like an euclidean plane but homomorphic if space were like a Moebious strip. Whether something is enantiomorphic or not depends on which kinds of movements the structure of space permits. A right hand and a left hand are 'put into' space in different ways. Only a container space can explain the existence of enantiomorphic properties." Container space has an explanatory function even if it is a relative space, a space of such a character that all motion in it is relative.

10.4 RELATIVISTIC SPACE Container space is extended, which means that even empty space has spatial distances. If there is container space there should be a space metric. The problem here is, as I remarked earlier (see page 154), that a space metric can only be physically established by means of things, i.e. indirectly. This is the reason why Newtonian mechanics and special relativity give rise to different space metrics. If Newton's mechanics, including the existence of absolute

157 ONTOLOGICAL INVESTIGATIONS acceleration, were true, a space metric would be univocally definable. We could then in principle find out both the numerical value of the spatial distances of space and when something is moving with regard to space. Such a space metric is a non-relative space metric. If Newtonian mechanics were true, but implied relative motion, we would still in principle be able to establish a space metric giving correct distances between all points in space. However, we should never know whether our coordinate system was in motion in relation to space or not. We should have a relative space metric. That space has a relative metric does not imply that it has a relativistic metric. In Newtonian mechanics, the length of a body not affected by any forces is uniquely determined. The length is, to talk the language of the physicist, invariant with regard to both time and all frames of reference. And it is so independently of whether all motion is relative or not. Let us now have a look at the theory of special relativity. According to this theory, the extension of a thing co-varies with the inertial system to which it belongs, and the thing can at one and the same time belong to several such systems. An inertial system is a co-ordinate system in which a thing not affected by any forces is at rest or in uniform motion with regard to the co-ordinate system. If a certain co-ordinate system is an inertial system, then all co-ordinate systems moving uniformly with regard to the first system are inertial systems, too. Within each inertial system, the lengths of the things are uniquely determined, but they are not uniquely determined for all inertial systems. The latter fact means that if we try to ascribe numerical values to distances between points in space, we get different values depending on which inertial system our measurements are based on. The space metric becomes relative to the inertial system. Now we must watch our words here. 'Relative metric' means here something quite different from what it meant above. It is better to say that we have got a relativistic space metric, i.e. a space metric which is different in different inertial systems. This is not necessarily the case in the spaces I have called relative. We have two distinctions which can be combined:

Table 10.1 Non-relativistic space Relatwistic space Non-relative space Newton Relative space Mach Einstein

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The 'Newton square' says that spatial distances can be uniquely determined (space is non-relativistic) and that motions with regard to space can be detected (space is non-relative). Einstein denied both claims, but Mach only the latter. Mach opposed Newton but did not anticipate Einstein. His position is as self-sufficient as those of Newton and Einstein. The empty space in Table 10.1 represents a position that has not, as far as I know, been discussed among physicists and philosophers. But it is a possible position. It amounts to saying that there is one inertial system which is at rest in relation to space. This system gives us the true spatial distances of container space. We have got a non-relative space. It is still however relativistic in the sense that these distances can never be measured in any other inertial system. They can of course be calculated by means of ordinary Lorentz transformations. A moving inertial system functions, metaphorically speaking, in the same way as a distorting mirror does. Which system is the privileged basic one must be established by means of hypotheses external to the co-ordinate transformations of special relativity, but that is no objection to the possibility of the position of the empty square in Table 10.1.12 If one takes this position there is an obvious harmony between the concepts of 'relativistic space' and 'container space'. The theory of special relativity does not without further ado imply a rejection of the container conception of space. So, let us return to the space which is both relativistic and relative. If space is both relativistic and relative each inertial system has its own spatial metric and we have no means of deciding between them. Space as a 'singularity-universal' has consequently no explanatory function with regard to the different metrics. When I discussed the concept of 'relative motion', I argued that container space is necessary in order to explain the existence of enantio- morphic properties. Let us now see whether we need this explanatory function also with regard to relativistic spaces. That space is relativistic means not only that lengths and spatial distances vary with the inertial system; some other properties like mass and shape also vary, but, it is also important to note, not all properties do. Electric charge, for example, is invariant. Therefore the question we should answer is the question whether the property of enantiomorphism is also an invariant property. And the answer is: 'Yes'. A left hand which has a certain shape in one inertial

159 ONTOLOGICAL INVESTIGATIONS system has another shape in another inertial system, since it is contracted in the direction of the movement of the inertial system but not in the other directions. But the left hand is still a left hand in every inertial system. 'Left-handedness' is invariant. Contraction is one thing, turning a thing inside out like making a right-hand glove of a left-hand glove is quite another. In this way it can be maintained that container space is needed by Einstein's special theory of relativity. But let us also look at the traditional solution to the problem of variant space metrics: Minkowski's proposal to regard time as a fourth dimension of container space itself. In the space he constructed, a movement is an entity with a four-dimensional extension (a 'world line') which is uniquely determined, i.e. invariant for all inertial systems. In consequence, the spatial metric (which is now four-dimensional) becomes uniquely determined too. Three-dimensional space with its relative and relativistic metric is interpreted as a three- dimensional projection of the true four-dimensional space. Minkowski's space-time has peculiarities of its own, but it satisfies all requirements for something being a container space. It is a particular, it is one, it is independent and it may in principle be empty, but everything that actually exists exists in it. I am defending the category container space, and with regard to that, Minkowski's conception of relativistic space as four-dimensional is immediate support rather than a problem. I have not suggested that space is three-dimensional, nor that all dimensions of space have the same character, nor that space is non-relative, nor that space is non-relativistic. Neither have I tried to say the opposite. The claims I have made are five in number:

(1) For our world, each possible ontology has to rely on a container space. (2) No development within physics is in conflict with the category of container space. (3) Container space is a necessary condition for external spatial relations; consequently, external spatial relations function as criteria of container space. (4) Container space functions as a principle of individuation. (5) Some 'properties' of things (enantiomorphic properties) are necessarily relations between the things and container space.

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