a note on a paradox of analysis

A NOTE ON A PARADOX OF ANALYSIS 37

what is called for in each case is a decision, and the decisions may or may not reflect beliefs about matters of fact. If our purpose is to construct a semanti- cal system which is isomorphic with a natural language in specifiable ways, then appropriate meaning postulates will be introduced when it is believed that certain meaning relations obtain in that language, and appropriate exemplification postulates will be introduced when it is believed that cor- responding properties are exemplified in the world. On the other hand, i f for any reason we wish to construct a system which differs from natural languages in interesting ways, we may choose any meaning or exemplification postulates that suit our purposes.

Received September 9, 1966

NOTES 1 "Discussion: Meaning and Necessity," Philosophy, 24:69-76 (1949). -" It should be noted that in Camap's idiom, properties and relations are concepts

rather than mater/al properties and relations. Presumably, a property-concept may be exemplified by a material-property, and a relation-concept may be exemplified by ama terial-relation. The term 'material . . .' is my own. Camap says only that properties and relations may be exemplified, but assigns no special name to that which exemplifies them.

For reasons of simplicity, I shall henceforth say 'is a meaning postulate' rather than the awkward 'is either itself a meaning postulate or is entailed by other meaning postulates.'

See, for example, Logical Foundations of Probability (Chicago: University of Chicago Press, 1950), pp. 72-74; 'The Problem of Relations in Inductive Logic," Philosophical Studies, 2:75-80 (1951 ); and Meaning and Necessity (2nd ed.; Chicago: University of Chicago Press, 1956), p. 227.

A Note on a Paradox of Analysis

by K E N N E T H BARBER

STATE UNIVERSITY OF NEW YORK AT BUFFALO

Tnr. purpose of this note is to call attention to a distinction which has been frequently overlooked in the tradition and recently overlooked by Berg- mann? The distinction is between what I shall call the ontological analysis of a complex and the ontological representation of a complex. As I will show, the importance of the distinction is that overlooking it leads either to the Bradleyan regress or, as in Bergmann's case,, to a quixotic defense against it.

AUTHOR'S NOTE,: I have benefited from discussion with Edwin B. Allaire.

38 PHILOSOPHICAL STUDIES

Consider the following situation, $I, consisting of two spots: one, red and round; the other, green and square. Bergrnann's analysis of $1 is as follows: "As I assay $1, it yields six simples, four characters and two individuals, as well as four occurrences of an asymmetrical nexus I call exemplification. Nonrelational exemplification connects a character and one individual. ''2 The peculiarity of Bergmann's analysis is that each occurrence of exemplification is listed while a character, for example, is listed only once irrespective of how many occurrences of it the situation may contain. ("Even if both spots were red, red would be listed only once. ''~) This oddity leads to a paradox and results, I suggest, from (a) overlooking the distinction between an ontological analysis and an ontological representation, and (b) trying to resist the Bradleyan regress.

Let us first examine the distinction between an ontological analysis and an ontological representation. Consider a visual field containing two spots having all their simple nonrelational properties in common. The spots are complex since each contains, at least, a shape and a color. The ontologist must account for the sameness and difference of the two complexes. They are the same in that they share the same nonrelational properties; they are different in that they are two and not one. The sameness and difference of the two complexes are accounted for by their constituents. That is, each complex contains entities of certain kinds or, equivalently, entities which belong to certain ontological categories. By listing the kinds of entities contained in the complexes one can, by appealing to the relevant categorial features, account for the sameness and difference of the two complexes. Such a list is an ontological analysis of the two complexes.

Notice that in the analysis only the kinds of entities are listed. One does not also give a "rule of composition" by means of which the complexes can be reconstructed from the list. One begins with the two complexes. The analysis consists simply and solely in listing the kinds of entities contained in the complexes. But one can give, after the analysis, the ontological representation of the complexes, which representation is explicated in terms of a language designed to represent perspicuously the entities given and to reflect the categorial differences among the entities. Here one does need a rule of composition which shows how the symbols representing the constituents are combined into sentences, which sentences are, as one says, pictures of the complexes.

Although the representation incorporates the results of the analysis, the analysis must precede the representation. Failure to observe this may, among other things, result in placing the rule of composition in the analysis rather than in the representation. Such a move is surely illegitimate, for the composition rule is a metalinguistic rule for combining certain symbols into


sentences. To place the rule in the analysis, then, is to mix levels of language. Or, if not this, then presenting such a rule in the list of the kinds of things would mean that the complexes implicitly reappear in the analysis. But since the complexes are to be analyzed in the first place, it would be absurd for them to reappear in the analysis.

Having distinguished between an ontological analysis and an ontological representation, let us turn to Bergmann's analysis. Note that Bergmann lists four characters and two individuals to account, respectively, for the sameness and difference of the two complexes presented in $1. Since the spots are complex, he also lists a further entity, a tie, which serves to con- nect the entities into the complex. This tie, which Berg-mann calls 'exemplification,' is peculiar in that it is like a descriptive relation (e.g., to-the-left- of), for it is a connection between other entities; but it is unlike a descriptive relation in that (a) it needs no further tie to tie it to what it ties, and (b), it ties entities of different kinds. Hence, it belongs to a different category than do descriptive relations. We shall see that Bergmann's desire to emphasize this peculiarity is a crucial motive behind his particular analysis.

However, not only is exemplification listed in the analysis, but each occurrence of exemplification is listed. To understand Bergmann's reason for listing each occurrence, consider a second situation, $2, consisting of two spots: one, red and square; the other, green and round. $1 and $2 are different. Hence, it is argued, their respective analyses must reflect this difference. This is accomplished by assaying $1 and $2 so that in the analyses it is shown that red is tied to round in $1 and that red is tied to square in $2. To list an occurrence of exemplification, then, is to list exemplification along with the entities which it ties. If exemplification were merely listed four times, but not with the entities which it ties, then there would still be no difference between the assays of $1 and $2. That is, both would contain the four universals, two particulars, and four occurrences of exemplification. There being no difference in the assays, the assays would not reflect the difference between $1 and S~.

This shows why each occurrence of exemplification must be listed but does not as yet sufficiently explain what an occurrence of exemplification is. For Bergrnann then says: "Even if both spots were red, red would be listed only once." a But if 'red' occurs only once in the analysis, how are we to understand the claim that exemplification is listed along with the entities it ties? For this would seem to imply that the analysis of the one spot in $1 is red, round, a (the individual), and a-exemplification-red, a-exemplification-round. This cannot be the correct representation of an occurrence of exemplification, for red is now listed twice, contradicting Bergmann's as- sertion that under no circumstance is red to be listed more than once.


Furthermore, such a representation leads immediately to the following paradox: We are given a situation, $1, to analyze. The situation consists of four facts: This spot is red; This spot is round; That spot is green; That spot is square. Now in the analysis occur a-exemplification-red, a-exemplification- round, b-exemplification-green, b-exemplification-square. The difficulty is that a-exemplification-red is simply the fact that this spot is red. If so, then the analysis of $1 in effect lists $1 again. If this is the case, then, since we could originally ask for the analysis of $1, we can again ask for the analysis of $1 when $1 appears in the analysis of $1. Thus, in order to give the analysis of $1 we have to give an infinite number of analyses since each analysis of $1 contains S~ again.

At this point one might attempt to avoid the objection by representing an occurrence of exemplification without at the same time relisting the individual and the character tied by exemplification. For example, relegate both 'a' and 'red' to subscripts, writing ~exemplificationrea, and then stipulate that such subscript representation is not to be understood as a relisting of red. The analysis of the one spot in S~ now reads: a, red, round, ,exemplifi- cationre~, ,exemplification~ou~d. But this attempt, I suggest, is untenable for reasons Bergmann himself would accept. 5 Upon this interpretation the sign for exemplification becomes complex, containing an indexical and an ad- jectival feature. The latter indicates what is common to all occurrences of exemplification, the former indicates what is different in each occurrence of exemplification. The occurrence, then, must be complex. Furthermore, the complexity can only serve to introduce the fact into the analysis, for what is different in each occurrence of exemplification is that exemplification is a constituent of a different fact in each case. And since the indexical feature introduces the fact into the analysis, we are again faced with the paradox of an infinite regress.

One can agree with Bergmann that there is a difference between $1 and S:. But the difference in this case has nothing to do with the problem of individuation, for the appearance of different particulars in S~ and $2 solves this problem. Rather, the difference Bergmann is concerned with is between the facts themselves and not between the constituents of the facts. Hence, he in effect introduces the category of fact into the analysis, which introduc- tion immediately leads to the regress. Bergmann accomplishes the intro- duction by placing the composition rule in the tie, since the symbol for exemplification also indicates which entities it ties. That is, in the anah,sis Bergrnann does not merely want to account for the fact that the entities in S~ and $2 are combined, for the listing of exemplification alone would ontologically ground their combination adequately, but he also wishes to represent how they are combined. The categorial features of the entities


in $1 and $2 allow for several possible combinations but there is no categorial feature of these entities which allows one to conclude that they are combined i~a a particular way. 6

Nor need there be such a categorial feature. The fact that the entities may be combined in several ways allows one to represent several possible combinations. Which combinations are to be represented depends solely on which combinations the world in fact contains. Bergmann's desire to represent which combinations obtain leads him to include the representation in the analysis. This confusion in turn leads to the placing of the composition rule in the analysis which in turn yields the infinite regress.

Nor is the infinite regress the only unfortunate result o~ this confusion. For Bergmann then argues [rom the representation to obtain an ontological difference between exemplification and things (characters and particulars). Since exemplification must be represented in a certain way, i.e., along with the entities which it ties, whereas things are listed alone in the analysis, it is claimed that exemplification is dependent on things in a sense in which things are independent of exemplification. 7 But if one clearly separates the analysis from the representation, it is seen that neither the analysis, i.e., the mere list of entities, nor the representation yields such a difference; for if one assumes that the Principle of Exemplification holds, then characters and particulars only exist in conjunction with exemplification. Hence, characters, particulars, and exemplification, however they are represented, are always represented together. Since neither the analysis nor the representation yields this sense of dependence, Bergrnann only obtains it by fusing the analysis and the representation. When explicating the sense in which particulars and characters are independent he appeals to the analysis, i.e., the list of entities; when explicating the sense in which exemplification is dependent he appeals to the representation, and in particular, to how the fact is represented.

In the beginning of this paper I claimed that failure to observe the distinction between an ontological analysis and an ontological representation leads to an infinite regress similar to Bradley's. Oddly enough, in Berg- mann's case, this failure in part stems from a desire to avoid the Bradleyan regress. It was noted that exemplification must be distinguished sharply from descriptive relations, for while both are connections among entities, the latter still need a tie to tie them to their relata. If exemplification were of the same nature, the following paradox would result. Bradley, in analyzing the fact referred to by 'A is B' into A, B, and a relation between them, argues: 'There is a relation C, in which A and B stand; and it appears with both of them.' But here again we have made no progress. The relation C has been admitted different from A and B, and no longer is predicated of them.


Something, however, seems to be said of this relation C, and said, again, of A and B. And this something is not to be the ascription of one to the other. If so, it would appear to be another relation, D, in which C, on the one side, and, on the other side, A and B, stand. But such a makeshift leads at once to the infinite process. The new relation D can be predicated in no way of C or of A and B; and hence we must have recourse to a fresh relation, E, which comes between D and whatever we had before. But this must lead to another, F; and so on, indefinitely. Thus the problem is not solved by taking relations as independently real. For, if so, the qualities and their relation fall entirely apart, and then we have said nothing. Or we have to make a new relation between the old relation and the terms; which, when it is made does not help us. It either itself demands a new relation, and so on without end, or it leaves us where we were, entangled in difficulties. 8

Bergmann is well aware of this pattern, as the following remarks show: A complex is an entity among whose constituents are at least two things. A thing which is not a complex is a simple. Simples, to form a complex, must be connected by fundamental ties. (A class of simples is not a complex.) A fundamental tie needs no further tie to tie it to what it ties. (Otherwise we would be faced with an infinite regress a la Bradley.) In this sense things are and fundamental ties are not independent. That is another ontological difference between things and fundamental ties?

Bergmann has indeed uncovered an ontological distinction between things and fundamental ties, which distinction must be insisted upon in order to avoid Bradley's consequences. This ontological distinction can only be explicated by talking about the categorial features of the entities involved. Bergmann, however, wishes to secure the distinction by giving it a linguistic reflection in the representation. This, I suggest, is a motive for his insisting that exemplification must be listed in the analysis along with the entities which it ties, while things are listed alone.

To see this, consider the analysis in the following way: One begins with a complex entity and then lists its constituents. Since the constituents are joined together in the complex, an entity which performs this function must be listed. With respect to the list, this merely means that one has another word or symbol. That is, the mere listing of the entities doesn't reveal the radically different nature of the tie; the list, being a string of symbols, doesn't reveal, to put it linguistically, how one of the symbols joins with the other symbols to make a sentence. Hence, it appears that we have in this conception of analysis a linguistic reflection of Bradley's paradox: How can we get a sentence out of a string of marks merely by adding another mark to the string?

Bergmann's defense at this point is, in effect, to list the sentence by listing

HEMPEL'S CRITERION OF MAXIMAL SPECIFICITY 43

exemplification along with the entities which it ties. Thus the fact reappears in the analysis of the fact. Again, if one clearly separates the analysis f rom the representation it is seen that the paradox does not arise. For although one needs a composition rule to construct a linguistic picture of the fact from the list given in the analysis, this does not mean that the linguistic picture itself occurs in the analysis. The analysis simply is the list of signs standing for entities. Hence, there is no worry about combining the signs in the list into a sentence which occurs in the list.

Thus the desire to secure the difference between exemplification and things becomes a motive for blurring the distinction between the analysis and the representation. One can agree with Bergmann that the difference must be secured and, if I am right, it can be secured without blurring the distinction.

Received November 22, 1966

NOTES 1 Gustav Bergmann, "Stenius on the Tractatus," Theoria, 29:176-204 (1963); also

reprinted in Bergmann's Logic and Reality (Madison: University. of Wisconsin Press. 1964), pp. 245-71.

-~ In Logic and Realihr, p. 245. Ibid., p. 245. Ibid., p. 245. Bergmann, "Synthetic A Priori" in Logic and Reality, pp. 272-301. See especially

pp. 281-83. Wittgenstein makes essentially the same point. See Tractatus, 2.0122 and 2.0231. In Logic and Reality, pp. 244-45.

8 F. H. Bradley, Appearance and Reality (Oxford: Oxford University Press, 1962), p. 18.

In Logic and Reality, p. 245.

Hempel's Criterion of Maximal Specificity by G E R A L D J. MASSEY

MICHIGAN STATE UNIVERSITY

IN HIS recent essay "Aspects of Scientific Explanation, ''1 Hempel claims to have resolved a problem which has much vexed orthodox analysts of statis- tical explanation, viz., the problem of epistemic ambiguity. For those readers unfamiliar with the concept of epistemic ambiguity, let me cite

a note on a paradox of analysis

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