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8

EXTERNAL, INTERNAL, AND GROUNDED RELATIONS

Around the turn of the century, a lively discussion about atomistic and holistic world views was carried on in England. Among the holists were philosophers like Bradley and Bernard Bosanquet, and among the atomists and George Edward Moore. The former were British Hegelians, adherents of a sui generis variety of absolute ; the latter were among the founders of analytic . In this debate about atomism and holism, interest came to be focused on a distinction between external and internal relations. This distinction is of fundamental importance, even though, as I maintain, there can be no question of a dichotomy here. One must rather distinguish three completely different types of relations: external, internal, and grounded relations. External and grounded relations will turn out to be fundamental of my category system, whereas internal relations are merely a subcategory of the category of existential dependence. Different kinds of such dependence will be introduced in the next chapter. What I shall here, following tradition, call 'internal relations', will later be called 'mutual existential dependence'. I do not regard the three kinds of relations mentioned as subcategories of a single category of relations. But there are such great similarities between the categories that they ought to be named by the same word. If determinates of the three categories are to be represented in language, they must be represented by many-place predicates. Properties, to make a contrast, will always be represented by one-place predicates. I hope it will be clear when I speak about the categories and their determinates and when I speak about in language. However, one should remember that in idealist philosophy the two levels are fused together.

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8.1 EXTERNAL AND INTERNAL RELATIONS Hegelianism can be said to have fastened on to a peculiarity displayed by many concepts: they apparently contain a reference to other concepts. This state of affairs can also be expressed as follows: the of one leads the to another concept, and the thought of that concept can in its turn lead one to think of a third concept, and so on. If one thinks through what lies in the concept 'pupil', one quickly discovers that it contains an implicit reference to the concept 'teacher'. There can be no students if there are no teachers. The relation is the same as in the case of so-called correlative concept-constructions like 'left-right', 'husband-wife', 'mountain—valley'. If something is to the left, something must also exist which is to the right. The concept 'teacher' refers in the same way back to the concept 'pupil', but it refers also to the concept 'school'. We have a chain of concepts which refer to one another. And so we have found examples of at least conceptual internal relations. A quite common definition of an internal relation is that one term is internally related to another, if in that relation's absence the term would not be the one it is. A pupil cannot be a pupil without an internal relation to a teacher. It is easy to see how the question of internal relations is related to the question of holism. If one maintains that all relations are internal, one immediately arrives at the conclusion that everything hangs intimately together, and that (the) is the whole. To consider something in isolation is to distort it. For many philosophers it seems to have been self-evident that internal relations cannot hold between material objects, but only between concepts. The thesis that all relations are internal is thus mainly a thesis within idealist philosophy. Russell and Moore maintained against this that there exist external relations, and that the of these relations constitutes a refutation of both holism and idealism. These are, however, not the only possible positions. Ewing, in his excellent overview of this debate, Idealism: A Critical Survey, maintains that the view that all relations are internal cer- tainly implies a holistic world view, but not necessarily idealism.1 Let us look at the proposition 'The bag stands between the two chairs'. Here it is claimed that there is a relation between the bag and the two chairs, but it is impossible to say that the thought of the bag carries over to a thought of the chairs. And this is at

111 ONTOLOGICAL INVESTIGATIONS bottom not a fact about language or our power of imagination. It tells us something about the bag and the chairs in the world. We have here an external relation, a relation which is such that that which the relation connects is what it is whether the relation exists or not. The chairs are the same chairs even if the bag disappears. Bertrand Russell has proposed the following characterization of external relations: To return to relations: I maintain that there are such as that χ has the relation R toy, and that such facts are not in general reducible to, or inferable from, a fact about χ only and a fact about j only: they do not imply that * andj have any complexity, or any intrinsic distinguishing them from a Ζ and a w which do not have the relation R. This is what I mean when I say that relations are external.2

The fact that the two stones χ and у lie at a particular distance from each other, i.e. Rxy, is completely in keeping with there existing stones ζ and w such that ζ is exactly like x, and w is exactly like у with respect both to substance (they are the same sorts of stones) and properties. The relation of 'lying at a certain distance from one another' is thus an external relation according to the definition. Consider now the case where one stone χ is twice as large as another stone y. The relation 'twice as large as' does not meet the requirement for external relations set by Russell. There cannot exist stones ζ and w exactly like * and у if the relation 'twice as large as' does not also hold between ζ and w. If ζ is just as large as χ and w just as large as y, and χ is twice as large as y, ζ must be twice as large as w. The relation 'twice as large as' is not an external relation. (It is not an internal relation either - as will be shown in 8.3 - but a grounded relation.) Russell's characterization of external relations presupposes, as one can easily see, that one can in advance delimit what are facts about χ and what are facts about у. In my example of an external relation, 'lies a certain distance from', it is presupposed that the positions (places in space) of* and ζ are not facts about χ andy. If we deny this assumption and say that the positions of χ and у are facts about them, then the relation 'lies a certain distance from' would not be an external relation. Because then it would not be possible to find stones ζ and w, exactly like χ and JI, which lack that relation. I shall come back to this case later.3

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8.2 INTERNAL RELATIONS AND FORMAL LOGIC Ewing distinguishes, in the book mentioned above, ten different senses of 'internal relation' which have appeared in the debate. The tenth is the one he considers, as do I, to be the one which best captures the concept: A is internally related to В by the relation r when it is logically impossible for A to exist unless В existed and was related to it by r.+ I shall not discuss precisely what Ewing might have meant, but only take this as a starting point. A good candidate for the term 'internal relation' is the relation between the properties (determinables) length and breadth. It seems to be logically impossible for a thing to have a certain length A without at the same having a breadth B. It seems as if the same can be said of the introductory example teacher (A) - pupil (B). It is impossible for someone to be a teacher if he is not in some way related to some pupils. A teacher without pupils is not a real teacher, only a potential teacher. Ewing's definition of internal relations was: Ά is internally related to В by the relation r when it is logically impossible for A to exist unless В existed and was related to it by r.' Here a logical relation between non-linguistic phenomena (A and B) is introduced. This calls for a small digression into logic and logical relations. Analytic philosophy has given the concept 'logic' a meaning which makes it difficult to imagine logical relations as anything other than linguistic relations expressing analytical or falsities. The distinction between analytic and synthetic truths will be taken up in chapter 16. Here I shall isolate the question what logic is from the question of logic's possible analyticity. In analytic philosophy logic has been identified with formal logic. And formal logic is, fundamentally, theories of inferences whose validity or invalidity is determined exclusively by properties of the so-called logical constants. In sentential logic 'and', 'or', 'if-then', and 'not' are dealt with; predicate logic deals, in addition, with 'all' and 'some'. What is typical of logical constants is that with their help one can conjoin simpler propositions to form complex ones. Today there are at least two different interpretations or

113 ONTOLOGICAL INVESTIGATIONS explications of the logical constants. The classical interpretation is based on the concept of truth. The logical constants are thought to give truth conditions for complex sentences, given the truth values of the simpler sentences. The sentence Ά and B' is true when Ά' is true and 'B' is true; otherwise it is false - to take a simple example. A logical truth is, on this intepretation, a truth which essentially only includes logical constants. Ά or not-A' is a logical truth because it is true independently of the truth of Ά'; the sentence includes essentially only the logical constants 'or' and 'not'. 'Logical truth' and 'logical constant' become correlative concepts; they presuppose one another. A slightly different way of viewing logic is due to the so-called constructive interpretations. These start from a concept of provability rather than from the classical concept of truth. The logical constant 'if-then' is interpreted so that the sentence 'if A then B' is provable if there exists a method for deriving a proof of В from a proof of A, and only then. On this interpretation the concepts 'logical constant' and 'provability' become correlative concepts. They presuppose or can be defined in terms of one another. Formal logic, then, independently of different interpretations, is at bottom concerned with logical constants. The question which Ewing's definition of internal relations raises is the question whether logic really can be limited to theories concerned with logical constants. It is not so important in this context to know where the boundary around the logical constants runs. Whether one considers the concept 'belongs to the set' as a logical constant or not is of little importance. But it is important to see that the relation between length and breadth, or between the concepts 'length' and 'breadth', between teacher-pupil or between the concepts 'teacher-pupil', has nothing to do with the logical constants according to any reasonable delimitation of 'logical constant' (cf. pages 115-17, below). In order to meet the requirement that logic always primarily concerns language, one can easily reformulate Ewing's definition so that internal relations become relations between concepts. One then obtains the following:

the concept Ά' is internally related to the concept 'B' via the relation r, when it is logically impossible correctly to apply Ά' if 'B' cannot be applied correctly (and simultaneously).

114 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS

The example of internal relations given earlier may now be reformulated in the following way. The concept 'length' cannot be applied correctly if the concept 'breadth' cannot simultaneously be applied correctly; and the concept 'teacher' cannot be applied correctly if the concept 'pupil' cannot be applied correctly. From this definition of internal relation it becomes easier to see its relationship to formal logic. Propositions are true or false, concepts are correctly applied or not. Between propositions relations can hold such as that if certain propositions are true, then it is logically impossible for certain other propositions to be false; and between concepts such relations can hold as that if a certain concept is correctly applicable, then it is logically impossible for certain other concepts not to be correcdy applicable. The type of logical necessity which is connected with internal relations might be called material logic as distinct from formal logic. Material logic is then a theory about certain 'material' concepts, while formal logic is about logical constants. I do not claim to present here a complete account of such a material logic, but I maintain that the existence of internal relations shows that such a logic exists. The question whether it includes more than internal relations will be left open. There is a comprehensive discussion concerning the relation between such a logic and formal logic.5 As I see it, the discussion has not been fruitful, but of course the view presented here makes it clear that I consider those who have advocated a logic besides formal logic as not being completely mistaken. Whether a logical truth is to be derived from logical constants or internal relations is not something which is always immediately apparent. It can seem self-evident that the concept 'yellow' is internally related to the concept 'colour'. It is logically impossible to correctly apply 'yellow' if it is not simultaneously possible correctly to apply 'colour'. But if one holds that 'colour' is by definition the same as the disjunction of 'yellow' and all the other colours, then of course the logical impossibility is derived from the logical constant of disjunction. Something like this holds for modal logic. Here it can seem as though one has an internal relation between 'necessity' and 'possibility'. It is logically impossible correctly to apply the concept 'necessary' to a particular state of affairs if it is not simultaneously possible correcdy to apply the concept 'possible' to the same state of affairs. That which is

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necessary must be possible. 'Np —» Pp' is logically true, and this fact is not dependent on the logical constant involved, 'if. . . then • • ·' (—but on the internal relation between \ΛΡ and 'P'. It is, however, not only propositions which can be built up from simple to complex ones with the help of the logical constants. The same holds, to a certain extent, for concepts. This follows from what has already been said about the concept 'colour'. From the concept 'possible' or the operator 'it is possible that' one can construct new complex concepts or operators with the help of the logical constant of negation, for example, 'it is impossible that' and 'it is possible that it is not the case that'. These two concepts can in their turn be united in the concept 'it is impossible that it not be the case that', which is the same concept as 'it is necessary that'. The concepts 'possibility' and 'necessity' can be defined in terms of one another with the help of negation. The apparently internal relation between 'necessity' and 'possibility' turns out to be a logically necessary connection between 'it is impossible that it is not the case that' and 'it is possible that', and this connection seems to have its basis in a logical constant. Modal logic appears to belong to formal logic. This type of reasoning about modal logic can also be applied to deontic logic and preference logic. But no such application enables us to define the concepts 'teacher' and 'pupil' in terms of one another with the help of logical constants. Some, but not all, relations which seem to be internal can be reduced to relations based on logical constants. And what is important in this context is not that certain relations can be reduced, but that certain cannot be reduced. Formal logic is, to repeat, at bottom concerned with logical constants. Material logic may be defined as a theory about a special kind of necessary interrelationship between substantive concepts. In both cases it makes sense to speak of 'logical impossibility'. Whether formal logic is 'existence-free', I shall not discuss. But obviously material logic has existential implications. If it is logically impossible to correctly apply the concept Ά' if 'В' cannot be correctly applied simultaneously, then there must also exist some kind of necessary connection between the non-linguistic phenomena A and B. If Ά' is correctly applied then of course A must exist. All this shows that it is not as odd as analytic philosophy has made it seem to speak of logical impossibilities and

116 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS internal relations in the non-linguistic part of the world. Ewing is right to say that Ά is internally related to В by the relation r when it is logically impossible for A to exist unless В existed and was related to it by r'.

8.3 INTERNAL AND GROUNDED RELATIONS Now we come to the question what V really stands for. External relations can always be represented by expressions of the form Rxy, where R is the relation and χ and у are the relata - that which the relation relates. This is so because the definition of external relation itself means that the relata, from a logical point of view, can exist independently of one another. The relation must then also be something in itself, and be referred to by means of a special concept. In the case of internal relations on the other hand, the opposite relationship holds: the relata cannot exist independently of one another, and the relation need not be anything substantial in itself. This might be the reason why ordinary language lacks special concepts for the internal relations.6 As a consequence, it is misleading to formalize internal relations with the help of the expression Rxy. This is clear also in the example given. Let * be 'length' and у be 'breadth'; where is the concept which is to correspond to R? Let χ be 'teacher' and у be 'pupil'; where is the concept corresponding to R? On the basis of these facts I shall remove V from Ewing's definition. We then obtain our definition of internal relations: D8.1: A is internally related to В if and only if it is logically impossible for A to exist if В does not exist, and vice versa. That the definition of internal relations lacks a special relational term has seduced some philosophers into believing that there is no relation at all. Armstrong, for example, writes that: One model that does seem helpful is the way that the size of a thing stands to its shape. Size and shape are inseparable in particulars, yet they are not related. At the same time they are distinguishable, and particular size and shape vary independently.7 Size and shape I see as being internally related. It is logically impossible for the one property to exist without the other, and vice

117 ONTOLOGICAL INVESTIGATIONS versa. The distinction between size and shape refers to , so it cannot only be a question of distinguishability in thought. And if two or more entities are distinguishable in reality, yet belong together, there must be, as far as I can see, relations. Peter Strawson has, in a similar context, spoken of 'non-relational ties', but to speak of a 'tie' instead of a relation is of course to admit the existence of a very peculiar kind of relation.8 Let us now try to make the definition of internal relation clearer by specifying it for three different cases: the case where the relations are properties (1); the case where they are substances (2); and the case where the relation connects a substance and a property (3). In the definitions one can easily exchange 'property' for 'property-instance' and 'substance' for 'substance-i/utan«'.

(1) Two properties are internally related if and only if it is impossible for an instance of a state of afTairs to have one of the properties without also having the other, and vice versa. Examples: Length-breadth; colour—shape, pitch—sound-intensity. (2) Two substances are internally related if and only if it is logically impossible for the one substance to exist if the other does not exist, and vice versa. Examples: Teacher—pupil; priest-congregation; capitalist—worker. (Point (2) above can be reformulated so that one speaks of substrates rather than of substances. One then obtains the following: two substrates are internally related if and only if it is logically impossible for the one to exist до Л if the other does not exist as B, and vice versa. Examples: A person cannot exist as a teacher if there does not exist a person who exists as a pupil.)

(3) A substance is internally related to a property if it is logically impossible for the substance to exist without the property in question, and vice versa. Examples: commodity—price; electron—negative electrical charge. Case (3) is the closest I come to a discussion of or essential properties. Several discussions of internal relations have taken as their starting point the concept of essence. It has been said, for example, that one thing is internally related to another if, in the absence of that relation, it could not be what it is, i.e. would lack its essence. As I see it, this is misleading and gets things the

118 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS wrong way round. We should define 'essence' and 'essential property' with the help of the concept of internal relation. (3), above, is a good definition of 'essential property'. The definition has as a consequence that one and the same substance can have a number of essential properties. An essential property is, according to the definition, essential in relation to a certain substance, not in relation to a certain thing. According to the definitions given, a thing can only have essential properties via one or some of its substances. A property, as a determinable, can be internally related to a substance or to another property without the corresponding determinate having that internal relation. It is the determinables 'colour' and 'shape' which primarily are internally related, not the determinates 'blue* and 'round'. This has certain consequences which I shall return to in chapter 12.1.9 It should also be noted that the definition of internal relation leaves room for the existence of entities which are internally related to themselves. We can put this as follows: Ά is internally related to A if it is logically impossible for A to exist if another A does not exist.' A can thus only exist as a multitude. One example is 'capitalist'; a person cannot be a capitalist if there do not exist at the same time other capitalists. (I assume that capitalism by definition implies competition.) I shall now once again take a look at the relation between external and internal relations. Russell's characteristic rendition of external relation can be reformulated in the following definition: D8.2: Rxy is an external relation if and only if it is logically possible that there exist a ζ and a w with exactly the same qualities ( = substance or property) as χ andj, respectively, but between which the relation R does not hold. If 'external relation' and 'internal relation' were contradictory opposites one ought to obtain the definition of 'internal relation' by exchanging the expression 'it is logically possible that' (in the definition of 'external relation') for the expression 'it is logically impossible that'. But this does not work, and I shall now explain why. The definition of 'external relation' has as a consequence that it is logically possible for χ and у to exist independently of any instance of the relation R. (If £ and w can be exactly like χ and ^v, but lack the relation R, it must also be logically possible that the

119 ONTOLOGICAL INVESTIGATIONS relation R fails to obtain between * and y.) If, however, one negates this consequence of the definition of 'external relation', then one obtains a synonymous formulation of the definition of 'internal relation' (see above, p. 117): D8.1': χ and у are internally related if and only if it is logically impossible for * and j to exist independently of each other. The negation of the definition of 'external relation' itself (D8.2) actually gives us the definition of the third type of relation earlier hinted at, namely 'grounded relation'. We obtain: D8.3: Rxy is a. grounded relation if and only if it is logically impossible for there to exist a ζ and a w with exactly the same qualities as χ and j, respectively, but between which the relation R does not hold.10 The difference between external and grounded relations can also be expressed in the following way: If Асу is an external relation then χ and у can both exist without R being instantiated, but if Rxy is a grounded relation then R is necessarily instantiated when both χ and у are instantiated. In this chapter I shall restrict my examples of grounded relations to examples where R is grounded in qualities of χ and y, but this restriction does not follow from the definition. Later on (section 12.2) I shall take into account grounded relations which are grounded in external relations. If we stick to cases where χ and у are qualities, then the ontological specificity of grounded relations might well be best understood via an epistemological approach, where, in a broad sense, we may speak of logical derivability. If χ and у are entities and Rxy an external relation, then R cannot be derived from the qualities of χ and y, but if Rxy is a grounded relation it can be so derived. The differences between the three kinds of relations discussed can be illustrated as in Figure 8.1. It is easy to find examples of grounded relations. If χ is twice as large as y, then it is logically impossible for there to exist a ζ exactly like χ and a w exactly like y, such that ζ is not twice as large as w. Or, in other words: if one knows the size of χ and j, then one can also derive the proposition that χ is twice as large asy. If* is heavier than_y, then it is logically impossible for there to exist a ζ exactly like * and a w exactly likely, such that ζ is not heavier than

120 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS

Relations not Relations derivable from EXTERNAL where it is the qualities of logically the relata. possible for the relata to exist Relations GROUNDED independently derivable from of each other. the qualities of Relations the relata. Relations INTERNAL where it is logically impossible for the relata to exist independently of each other.

Figure 8.1 w. The relations 'to be twice as large as' and 'be heavier than' thus manifest those attributes which characterize grounded relations. That χ (e.g. a cube) has twice as large a volume as_> (another cube) does not at all mean that it is logically impossible for χ to exist independently ofy, or vice versa. The same is the case if one lets χ and_y be quality-iaftanc«. That in the one cube there is an instance of a certain size is logically independent of the other cubes having an instance of twice this size. The relation 'to be twice as large as' is consequently not an internal relation. But if both the property-instances in question are given, then necessarily also the relation 'twice as large as' is instantiated. This means that the relation is grounded, not external. The category of grounded relations sheds light on what was said about universals in re in chapter 1. is necessarily a grounded relation but qualitative is not. Assume that we have two colour-instances, one is medium red and one is dark red. Both instances have a particularity aspect and a aspect; the latter makes up their respective qualitative identity. But another universal is instantiated also: similarity. Like every universal it has to have a particularity aspect. Its particularity aspect is the particularity of the two colour-instances. Of course, similarity has a qualitative identity of its own because it is a

121 ONTOLOGICAL INVESTIGATIONS universal too, but the point is that similarity cannot be a fundamental universal. It is a relation, and it is grounded. The same is true even for exact similarity. Qualitative identity of a colour hue exists even if there is one and only one instance of the colour hue, whereas exact similarity needs two instances of the colour hue in order to be instantiated. That two instances are qualitatively identical means that they instantiate the same universal; that two instances are exactly similar means that there is a grounded relation. It is a very tiny difference, but still a difference.

8.4 WORLD AND LANGUAGE A good deal of misunderstanding can occur with regard to the dividing up of relations into the three categories of external, internal, and grounded, if one does not carefully distinguish the linguistic level from the world itself to which the categories belong. There is no unambiguous connection between categories and different types of concepts. I have pointed out earlier (see above, page 37) that general terms do not only pick out properties, and proper names do not only name thing-instances. With regard to internal relations it may be said that if an internal relation holds between A and B, then the concept Ά' cannot be correctly applied if the concept 'B' cannot also be correctly applied. But the reverse does not follow. If there are two concepts Ά' and 'B' which are related to each other in the way just described, then this does not imply that there are also properties or substances A and В which have an internal relation. Certain oddities like 'open texture' can occur in concepts, but not in reality. Consider the sentence 'Umeä lies between Skellefteä and Örnsköldsvik': Is 'lies between' here an external relation? In the case of the sentence 'the green ball lies between the blue and the red one' there does not seem to be a problem. The relation 'lies between' presents itself immediately as external. But this is not the case in the first sentence. This depends on 'open texture'. Balls can be moved around without this being considered to affect their identity, but whether cities could be moved without losing their identities is an open question. Up to now there has been no need for a demarcation, since cities at the moment simply cannot be moved. If it became possible to move cities then one

122 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS would have to consider whether or not place is a defining property of cities. If place is considered to be such a property, the relation 'lies between' will of course be a grounded relation. A category system is a theory about the world, not a theory about concepts. The theory of internal relations has nothing to do with theories which say that a concept must be able to be contrasted with another concept in order for us to be able to understand it. Saussure maintains for example that a concept's meaning is determined partly by those concepts standing beside it in the sentence (its syntagmatic relations) and partly by contrasting concepts (its paradigmatic or associative relations).11 Paradigmatic relations to, for example, 'writes' include 'wrote' and 'has written', as well as concepts like 'speaks' and 'sings'. There is also a paradigmatic relation between 'teacher' and 'pupil' as well as between 'yellow' and 'blue'. But there is an internal relation only between teacher and pupil. In order for a colour word to be understandable it has to have contrasting concepts; but once we have understood it, we see that what it refers to can exist independently of whether that which the contrasting concepts refer to exists or not. The paradigmatic relations between colour words must not be identified with internal relations. On the other hand, in the case of internal relations, one could say that one obtains some of the paradigmatic relations for free.

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