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 Bertrand Russell and George Edward Moore. The former were British Hegelians, adherents of a sui generis variety of absolute idealism; the latter were among the founders of analytic philosophy. 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 categories 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 concepts in language. However, one should remember that in idealist philosophy the two levels are fused together. 110 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS 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 thought of one concept leads the mind 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) truth 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 existence 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 being 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 fact 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 facts 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 property 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.3 112 EXTERNAL, INTERNAL, AND GROUNDED RELATIONS 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 meaning 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 time 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 truths 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.