Space, Time and Deity
2. The Categories

Chapter 2: Identity, Diversity and Existence

Samuel Alexander

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Numerical identity and diversity

THERE are more senses than one of identity. There is, in the first place, bare or numerical identity, which is the identity of a thing with itself. Next, there is identity of kind, which is universality or generic identity. A dog is as dog generically identical with another dog. Thirdly, there is individual identity, which implies the blending of numerical and generic identity ; an individual is a particular of a certain sort. Lastly, there is substantial identity, which, besides individuality as just described, contains the element of substance. Such substantial identity is what is commonly understood by a numerically identical individual. But it is really more complex as we shall see than merely being an individual. One of its instances is personal identity.

We are concerned at present with bare numerical identity, or self-identity. Any point-instant or group of them is as such self-identical, and the self-identity of anything is its occupation of a space-time. Diversity is the occupation of another space - time, that is another place with its time. One thing is diverse from another in so far as it occupies a different point-instant from another thing or more generally a different portion of space-time. The occupation of any space-time, that is self-identity, in distinction from any other space-time is existence or determinate being. Owing to the empirical continuity of Space-Time, any piece of Space-Time and consequently any self-identity is distinct from some other self-identity, that is, it possesses an other, and is thus an existent or has existence. Existence or determinate

(195) being is therefore identity in its relation to the other. It is, as Plato taught in the Timaeus through the mouth of his Pythagorean speaker, the union of the same and the other. Identity, diversity, and existence arise out of the intrinsic nature of Space-Time as a continuum of its parts which are space-times, or rather it arises out of the nature of any space-time, as being a part of Space-Time and therefore connected with other space-times.

Such union calls for no explanation ; it is given with Space-Time itself. For Time makes Space distinct and Space makes Time distinct. We have in fact noted already that either of the two, Space and Time, may be regarded as supplying the element of diversity to the element of identity supplied by the other.[1] Any point-instant, or group of them, is therefore intrinsically itself, and other than some other, and indeed than every other, point-instant or group of them. It follows that existence is distinct from identity only in this reference or relation to the other. It therefore, to use another Platonic conception, " communicates " with the category of relation.

Defence against objections.

There is much in this if not brief yet abstract statement which calls for comment. Being is the occupation of space-time which also excludes other occupancy of space-time. This seems at first sight to be a flagrant piece of circular reasoning. When it is said that a point-instant is identical with itself and different from another, same or identical and other or different appear to be prior denominations of which point-instants are particular instances. Is not the point-instant declared to be the same as itself and other than a different point-instant ? Though I have entered a warning against such a misapprehension in the preceding chapter, I must, at the risk of repetition, renew the warning here and perhaps later again. It is not because there is sameness and there is difference, and still less because we have the notion of sameness and difference, that a point-instant is the same (as itself) and different (from another), but because there are point-instants or

(196) groups of them which are the parts of Space-Time that there is sameness and difference in existents. I am not starting from the world in which man exists with his clear-cut and reflective thoughts which he thinks to apply to particular things, but from the bare elements of the world, its primary stuff out of which things are made ; and am accounting for the notions we possess, or rather verifying them, by reference to this stuff. In the skeleton universe of Space-Time we are attempting to detect what are the primitive features of pieces of that skeleton which appear in our experience clothed in the flesh and blood of what we call empirical things, with all their richness and complexity of qualities. It is not our human conceptions of things which metaphysics seeks to exhibit but the constitution of the world itself.

Even if we avoid the mistake of supposing that such categories as same and different are supplied by the mind, and urge the old objection in the form that same and different though not conceptions made by us are yet objective universals, are the highest forms of things, and point-instants or groups of them do but participate in these ; the answer is that same and different (that is numerical sameness and difference) are indeed not only categorial characters intrinsic to any space-time but also universal, but that this consideration is at present irrelevant. The reason why same and different are categories is not that they are universals, but that they are characters which belong to any space-time and therefore to the existent which occupies it. We are concerned here with the specific nature of same and different, not with their universality. It is true that they are like all categories universal. Just as same and different communicate with relation, so also they communicate with the category of universality. There is a good sense in which a particular point-instant may be called a case of identity, that is of generic identity. An existent or being is a particular case of existence as a generic universal. The " this " in Mr. Bradley's language is a case of " thisness." We have yet to see what constitutes universality or generic identity, and we shall find that it too is founded in the

(197)nature of Space-Time. But though existence is universal, a point-instant is not a mere case of the universal existence' ; but it exists because it is a point-instant, and its existence is identical generically with the existence of other point-instants for a different reason. In other words, existents exist or are subject to the category of existence because they occupy space-times, and on our hypothesis are in their simplest determination spatiotemporal complexes ; the occupation of their own space-time is a non-empirical or a priori determination of the very Space-Time of which things are made ; their existence is another name for this occupancy, that is to say for being a piece of Space-Time. That existence may be resolved into its two elements of identity and difference, because a point-instant or group of them is in the first place what it is, and in the next place is not a mere isolated point of space or instant of time, but is saturated with Time or Space respectively, and driven thereby out of its isolation into relation with point-instants other than itself. The point-instants are so far from being merely instances of identity, difference, or existence, that these categories are but the conceptual shapes of real concrete determinations of things in their spatio-temporal character. We shall find this to be true of all the categories. They are not as it were adjectives or predicates of things ; they stand for the simplest and most fundamental features (in the sense in which red is a feature of this rose) of things, and have the concreteness of Space-Time. Existence and numerical sameness and difference are the most elementary of these determinations. Consider the spatio-temporal structure which underlies any thing whatever, even if that thing be no more than a point-instant itself ; and going to the direct experience of it, as clarified by reflection, you realise that the self-identity of the thing is nothing more nor less than the experienced fact that it is the bit of space-time which it is.

Being as union of identity and difference

Existence, or determinate being, or being itself (for we shall see there is no being but determinate being), is the union of identity and difference. But this desig-

(198) nation of union must be received with caution. It is not properly a blending or mixture of identity and difference ; nor on the other hand are identity and difference to be regarded as in reality one. The splendid image of the Timaeus in which the Demiurge is represented as pouring the Same and the Other into a bowl and creating Being (Ousia) from their mixture is not by us to be understood literally, if it was so understood by Timaeus. Being is an occupation of a space-time. It does not contain within itself the exclusion of other space-times. It contains of course within itself, when it is more than a point-instant, internal difference. But the exclusion of the other which makes identity into being is its relation not within itself but within Space-Time to other space-times. As in this relation identity is being. Being is not something new made up of the two, but is the same taken along with its relation of otherness. Neither is its otherness to be conceived as one with its identity. Its otherness is its relation to the other, and that relation is what we shall call later an intrinsic relation, without which the same would not be the same. But its sameness is one character and its otherness another. It would not be different without the other, and the other is external to it, and something new ; not extrinsic to it (because of the nature of Space-Time) but yet not identical with it. Its identity is so far from being identical or one with its otherness that it would have no otherness except there were an other, and it is other than the other, not the same as the other. But the completer understanding of this, if it needs further elucidation, belongs to the inquiry into the category of relation.

Being or not-being

Being it was said is the same as determinate being or existence. This means there is no such category as bare or neutral being to which some further determination must be added to make existence. When such neutral being is examined it will be found to stand for something different from real or categorial being, either for the relation of things to thought, or as a compendious name for the relations between terms in a proposition.


We might indeed distinguish bare being from determinate being by substituting in our exposition being for identity, and not-being for difference, and describing determinate being or existence as the union of being and not-being, that is as being in relation to other being. Bare being is then simple occupancy of a space-time. But over and above the loss of the phrase numerical identity, we gain nothing for clearness. For occupancy of a space-time is ipso facto exclusion of other space-times. There are no beings (occupants of space-times) which are not existents.

But the idea of bare being leads on conveniently to the subject of not-being, which is not the bare absence of being, not in the language of the logicians a privative conception, but is equivalent to other - being, that is occupation of a different space-time. It may be the occupation of any different portion in the whole remainder of Space-Time, as when we distinguish red from what is not-red and include under not-red anything whatever whether coloured or not which is not red. Or it may be and generally is the occupation of a different portion of Space-Time within the same universe of discourse,' as when not-red means any colour which excludes red. The subject more properly comes under the head of identity and difference of sort or kind (generic). But not-being whether numerical or generic is always different being, and remains being. If we try to think of not-being as if it were something wholly disparate from being, we are surreptitiously imagining or thinking some world which has being, that is, is within Space-Time, but of a different kind. A mere blank negation is nothing at all. The nothing we can think of and experience is not nothing-at-all but is an object of some kind and is a department of being. These are ancient considerations, derived from Plato's Sophisms. They have been revived in our day to much purpose by Mr. Bergson in an admirable passage of the Creative Evolution,[2] where he interprets disorder as a different order from what we call order, and repudiates the notion of nothing

(200) except as something different from the something which constitutes the circle of our experience.

I may add that negation as a category is equivalent to not-being. Negation is not merely a subjective attitude of mind. That is only an instance of negation, in the region of mental acts. Negation or negativity is a real character of things, which means exclusion or rejection. Not-white is the character which excludes or is different from white. In this sense it is true that all determination is negation. For all definite occupation of space-time is other than other such occupation and excludes it.

Neutral being

There is no category then of being other than that of determinate being or the existent. Since existence is occupancy of a space-time in exclusion of other occupancy, and since such occupation is always temporal, existence must not be limited to present existence but includes past and future. But various attempts might be or have-been made to find a being which is wider or more comprehensive than existence. Such being may be called neutral being, but in no case is such neutral being a category, of which determinate being is a species, or closer determination.

Thus it may be said that there is neutral being which corresponds to the copula in judgment, and is what is meant whenever we say is.' But, in fact, the linguistic copula is ' is appropriate only to certain propositions, those, namely, in which the terms are in the relation of subject and attribute. In some propositions, as Mr. Bradley has pointed out, it does not occur at all (interjectional ones) ; in others the relation of the terms as Mr. Russell insists is not expressed by the copula at all, but may be, for example, a relation of quantity, as in ' A exceeds B in intellect,' or of causality, as in Brutus killed Caesar.' A special importance has come to be attached to is' because with more or less ingenuity any proposition may be tortured artificially into the subject- attribute form. There is indeed in every proposition something implied which happens to be expressed by the copula in ordinary categorical propositions ; but that something is not 'being' but the reality of whatever relation the proposition

(201) expresses between its terms. For a proposition is the explicit analysis of a complex, and asserts the reality of the relation thus exhibited, whether it is the relation of substance and attribute, or causality, or the like.[3] What corresponds to the copula is thus not being but reality, and reality is at least existence or determinate being ; it may be and is much more, but at any rate it is not less and wider than existence. It is not something simpler of which existence is a specialisation. The attempt to look for a category more pervasive than other categories is in truth vain, for categories as such are all alike pervasive, and belong to all things. There is much however to be said before the statement can be accepted that all propositions deal with existents ; in particular, we have yet to consider how propositions which involve universals can be so described.

Being, i.e. neutral being, may be understood in a different sense as the object of thought. Whatever the mind thinks of has being or is formally objective.' A recent writer [4] proposes to say, accordingly, that there is a world or summum genus of subsistence, of which what exists in space and time is a part. Determinate being would, according to this, be a special determination of subsistence' or being in the widest sense. The reason for introducing this notion is that besides true propositions there are errors and mere imaginations and

(202) there are also what are now known, since Prof. Meinong's work on the subject,[5] as supposals, where there is neither truth nor error, since no belief is entertained ; for example, that the Earth is flat is still maintained by certain persons ' ; it is reported that a victory has been gained,' in neither of which cases is the included proposition a belief, but a supposal. The consideration of this notion must be delayed till we have reached that special kind of empirical existent, the mind, and inquire into the relation of the subject of knowledge to the object. My contention against any being other than spatio-temporal is in fact that we begin at the wrong end if we start with the fact of errors or supposals which appear undoubtedly to be and yet not to be existent, so that we are led to conceive a being which is less, and wider, than existence. Whereas if we begin not with ourselves and what we think, but with what the world is in its simplest terms, of which world we are a part, we arrive at a different and less perplexing result. We shall find reason if we pursue this method to reject the notion that existence in Space and Time is something added to some more formal reality, call it being, call it subsistence, call it what corresponds to the is ' of propositions ; and to conclude on the contrary that such being is real or determinate being with something left out, that it implies the interference of the subject or the empirical mind with the real world in Space and Time ; that it is not prior in analysis to reality but, rather, subsequent to it ; and that error does not give us a new and more shadowy being than the spatiotemporal reality, but is the world of determinate being misread. Here for the present it is enough to note that being as the mere formal object of thought is a conception derived from the relation of the world to an empirical part of itself, the mind.

The use of the term subsistence in the above statement to describe bare being inclusive of being in space and time, is not in itself a matter of much consequence, but it is unfortunate because subsistence' is used by

(203) Mr. Meinong (and the usage has become established through him) to describe not being as such or bare being, but that kind of being which contrasts with particular existence. Subsistence is, it is thought, timeless or eternal being, and it belongs to universals and to supposals. For instance, I may say that A exists ; but it is urged that the proposition that A exists ' does not itself exist. The battle of Waterloo was fought in 1815 ; but it is said, the fact that it was fought then is something independent of the time of the actual battle. The issue which is here raised is a different one ; are universals or supposals or facts that' out of Time and Space ? There is no doubt of the reality of these things ; but have they or not being within Space-Time, or determinate being ? We are about to show in the following chapter that universals are not timeless. But at any rate the word subsistence marks a distinction between two classes of objects of thought, two groups of reality, for which it is important to have a distinctive designation.

The Hegelian identity of being and not-being

It may throw light on the denial here made of any being which is less than determinate being, as well as upon other matters, if I stop to consider briefly the famous doctrine with which Hegel's logic opens, that being is the same as not-being, and the two are merged into the category of becoming. If being were concrete being, something which has a place in the world of reality and not in the inventions of abstract thinking, the one thing which is more obviously true about it than another is that it is not identical with not-being, but different from it, that is, that it is not identical with the other but other than it. But being is not on this doctrine concrete. It stands for the least that can be said about anything, namely, that it is, and it is quite true that such being is indistinguishable from nothing. Instead of concluding
that neither of them is anything at all, Hegel proceeds to declare their synthesis to be becoming,' which as he himself maintains is the first concrete notion. But how can bare abstract thoughts, abstractions as he allows them to be, combine or be combined to produce a concrete

(204) one ? or how could they be combined if they were identical and not different ? Or if we suppose that we treat them as a mere analysis of becoming, how could a concrete real thought be analysed into two abstractions ? Such an analysis is not comparable to our own analysis of Space-Time into the two elements of Space and Time. For each of these elements is concrete, and is only an abstraction when it is supposed to exclude the other. They are as concrete as body and life are in the organism. Had becoming, which is in fact motion or Space-Time in its simplest conceptual form, been analysed into being and non-being as different but mutually involved elements with becoming, becoming would have been equivalent to what we have called existence, for the existent is nothing but motion (that is Space-Time). But it would not be the thoughts themselves which produced their own unification, but the character of the concrete of which the concept becoming is the concept. It would indeed be a gross misreading of Hegel to suppose that he " manufactured the world out of categories." He is a perfectly concrete thinker, and to each thought corresponds a reality. But the inadequacy of his conception of the relation of thought to nature betrays itself at the outset of his triumphant procession of thoughts. Instead of conceiving the thoughts as the concepts of what is given in nature, he treats nature as a falling off from thought. But all true or concrete thought is tied down to nature ; all its balloons are captive ones. The transitions from thought to thought are not made by thought itself, for transition is only possible to thoughts which are alive. The thoughts owe their connection not to thought but to the motions of which they are the thoughts. And when once the glamour is gone from the first transition from thesis (being) through antithesis (nothing) to synthesis (becoming) the principle of the whole series of logical forms which is founded on this principle, and really uses the contrast and identity of being and not-being, becomes suspect. No wonder that to some like Mr. Bradley these logical concepts appear to be shadows. Realities they are not, for they live in a region of thought divorced from its

(205) material, which in the end is nothing but Space-Time. There is no way from logic to nature in Hegel, as his critics have often observed, except through a metaphor.[6]

The law of contradiction

The so-called Laws of Thought, regarded as metaphysical laws, follow at once from these considerations. The most important of them is the law of contradiction. Ultimately that law means that occupation of one piece of Space-Time is not occupation of a different one. A thing cannot be both A and not-A at once, for if so it would occupy two different space-times. Or more shortly the meaning is that one space-time is not another. I have not yet spoken of generic identity nor of substantial identity ; but even now it is plain why the law is true where we speak of attributes and not of numerical identity or difference. For if a thing has the attribute A, that attribute is, as in the thing, a numerically distinct individual. The red of this rose is generically identical with other reds, but it is as in this rose individual. This rose cannot be both red and not-red, for otherwise it would in respect of its red be at once in a piece of Space-Time, and in a piece of Space-Time which the first piece excludes. Considered on the other hand as a law of our thinking, the law of contradiction means that the thinking of one object and the thinking of its contradictory occupy mutually exclusive places in the mental space-time.

The law of identity means that to occupy Space-Time is to occupy it, that a thing is itself. The law of excluded middle means in its metaphysical interpretation that given a special occupation of Space-Time, every occupation of

(206) Space-Time is either that or belongs to the rest of Space-Time, and is another way of expressing the relation of any being to not-being.

These conclusions are obvious from the premisses, but they lead to another which will be unwelcome to a method of thought which has predominating influence at the present time. The criterion of reality (or truth) has been found in self-contradiction ; what is self-contradictory cannot be ultimately real but only apparent. The principle is valid, if it means that what is self-contradictory is neither ultimately nor derivately real but downright false ; it derives its validity however not from any self-evidence, but from the experiential or empirical nature of Space-Time. The reason why nothing can be real which contradicts itself is not that this is an axiom of our thought, but that reality since it occupies a space-time does not occupy a different one. Deriving its validity then from Space-Time itself, it cannot be employed to undermine the reality of Space and Time and reduce them to appearances of an ultimate reality which is neither, but accounts for both. If Space-Time is the ground on which the criterion of contradiction is based, Space and Time are not themselves contradictory. To suppose so would be like invoking the authority of law to break law, or sinning against the conscience conscientiously.

To find out what is contradictory we must therefore have reference to experience itself, of which the principle of contradiction is the statement of the simplest feature. As reflected in our thinking, the test is that of internal self-contradiction or verbal inconsistency. Accordingly, the only way in which the test of contradiction can be successfully applied in the hands of Mr. Bradley to show that the categories, or even such notions as the self, which have been put forward as real in their own right are not so, is to show that they arc inherently inconsistent. But this as has been pointed out[7] is not what has been

(207) done. And if it could be done, the pretenders would not have even possessed a secondary reality but would be false. As a matter of fact what has been done is to show that these conceptions present great difficulties and the appearance of inconsistency to the understanding. But perhaps it is their inconsistency which is apparent and not they themselves. If we are right and all the categories are derived from the nature of Space-Time in any part of it, they are all real in their own right and ultimately, because Space-Time is the stuff of which all things are made and the categories are its simplest characters.

If such an answer were intended as a short way with absolute idealism, it would seem to the defenders of that method merely cavalier, because it starts from Space-Time as a given experience. The only way which is either possible or respectful is the long way. We have first to verify in detail the assertion that categories are properties of any space-time. Even then it will, be urged that Space and Time are riddled with intolerable difficulties, although these difficulties may not amount to inherent self-contradiction. These difficulties must be examined and if possible removed. I am persuaded that the alleged inconsistencies of Space and Time arise from the separation of either of them from the other : from neglecting the temporal character of Space and the spatial character of Time ; and that consequently the Space and Time which are thought to be inconsistent are not Space and Time at all, as Space and Time enter into real experience. But as the arguments against their reality turn on the ultimate unreality of relation, any further discussion is best deferred until we reach that category.


  1. See above, Bk I. ch. i. p. 60.
  2. Evolution créatrice, ch. iv. pp. 297 ff. Eng. tr. pp. 232 ff.
  3. Even the existential proposition, e.g. King George exists, means that the subject is a part of the whole reality of existence. For further remarks on the assertion of reality in the proposition, see later, Bk. III. ch. x. B.
  4. W. P. Montague, in The New Realism (New York, 1912) ; essay on A Theory of Truth and Error,' p. 253. I have borrowed the name neutral being' from Mr. Holt (see his essay in the same book, and his Concept of Consciousness), who uses it in a different sense. His neutral being is a being which is neither mental nor physical, the simplest form of which appears to be categories such as identity and difference. Also Mr. Montague, to whom I refer here, does not use the phrase neutral being at all, and he does not call his subsistence being, and perhaps would not do so (see his account of isness ' on p. 263), Both his doctrine and Mr. Holt's seem to me, however, in the end to imply what I call neutral or bare being, the idea of something simpler than the world of Space-Time. I stand in many respects so close to them that I am the more anxious to make the real differences clear.
  5. Uber Annahmen (Leipzig, 1910, ed. 2). The notion of neutral being discussed in this paragraph is not imputed to Mr. Meinong.
  6. It will be plain from the sequel why for me Hegel's conception of an evolution in thought of logical categories is mistaken. There is only an evolution in time of empirical existences which occupy space-times. Hegel's categories are in fact not categories at all, as they are understood here, the a /owl, constituents of all existences. They are rather the concepts of the various phases of natural existence : e.g. they include 'mechanism' and chemism ' and 'life.' Or perhaps it is truer to say that the two notions of categories as a priori features, and categories as concepts of phases, of existence, are not clearly separated. Hence the apparent movement in thought is only artificial.
  7. See in particular a paper of Mr. G. F. Stout's, Proceedings of the
    Aristotelian Society
    , N.S. vol. Alleged self-contradictions in the
    concept of relation,' especially section a.

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