Abstraction and the Multiple Dimensions of Reality

Claudio Gutierrez

It is the essence of the positivist dogma that reality is, at least in principle, exhaustible, i.e., unambiguously amenable to be fitted into a (single) "filing system," (FRIEDMAN 53, p. 7) presumably a logical system similar to that of Principia Mathematica (WHITEHEAD 10). The dogma operates on the assumption of a basic dichotomy between "meaning" and "truth" which (as we tried to show in the first part of this study) is very difficult to maintain consistently. A separable tautological frame of reference is conceivable only at a given moment of time, at a given point in the history of knowledge. No advance of knowledge is feasible by "filling-out" the framework, because the framework itself must be affected by every application to new material. The reaction against positivism, on the other hand, is found, generally speaking, among authors who stress the multidimensional nature of our understanding of reality, done by the analytical operation of abstraction. Within this "abstractionist" field, however, elements of positivism are still traceable, so that several groups of thinkers must be distinguished according to the degree of remaining positivist outlook. NOTE 1 In the first place, we have writers like Lionel Robbins (ROBBINS 32) NOTE 2 and L. Von Mises and other intuitionists, undoubtedly indebted to Kant and to that extent heavily "unidimensional" in outlook. Secondly, there are authors like Max Weber and Talcott Parsons whose position is very close to a fully multidimensional conception of reality. Finally, there is Marxism, whose position in the history of political upheaval makes it very difficult to disentangle its doctrines to make them a starting point for a corrected epistemology (SWEEZY 42, pp. 6-22 ). NOTE 3 So, let us now concentrate on examining Weber-Parsons position, and in trying to improve their "analytical realism" NOTE 4 as a way of building up our own epistemological view.

I take the following texts of Parsons as some of the most revealing of his theory of knowledge:

It is in the nature of the case that theoretical systems should attempt to become "logically closed." . . . The system becomes logically closed when each of the logical implications which can be derived from any one proposition within the system finds its statement in another proposition in the same system.
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Though all theory tends to develop logically closed systems in this sense it is dangerous to confuse this with the "empirical" closure of a system. . . . (PARSONS 37, pp. 9-10)

Every system. . . may be visualized as an illuminated spot enveloped by darkness. The logical name for the darkness is, in general, "residual categories." Their role may be deduced from the inherent necessity of a system to become logically closed. . . . (PARSONS 37, p. 17)

The obviously unattainable, but asymptotically approached goal of the development of scientific theory is. . . the elimination of all residual categories from science. . . . For any one system there will, to be sure, always be residual categories of one or more other systems. For the empirical application of any one system these residual elements will be found to be involved in the necessary data. (PARSONS 37, pp. 18-19)

As can be seen from the above quotations, there is a fundamental ambivalence in the author's formulation of what we should understand as "analytical realism." In particular, when he says that for every system there must always be some residual categories, it is not clear whether he means that the other system, in which the positions of residual and positive categories would be reversed, is simply complementary of the former or rather inconsistent with it. In other words, it is not clear whether his contention has, so to speak, Gödelian overtones to it or is just another way of expressing the optimistic view of a universal science, with several compartments, of course, that would be both consistent and complete. I am inclined to think that what he means is the optimistic view. I am convinced that the other connotation would make the position closer to the truth. It is along the latter line that I plan to attempt something that we could call a reformulation of non positivist epistemology. In that vein, I want to take "residual categories" not as a token for the province of another science, but rather as a token of the very inexhaustible character of reality itself. NOTE 5 It is under this light that we should try to evaluate the contention, implicit in the literature of the defenders of economic a priori methodology, that their type of abstraction is essentially different from the type of abstraction of their Marxian counterparts: theirs is "formal," the others' "material." Does "material abstraction" make sense? The truth is that the aspect which Robbins considers important in economics–the "scarcity aspect"– and the aspect that Sweezy considers important –the "exploitation aspect"– are both equally abstract, neither being more formal or material than the other. NOTE 6 But the two kinds of abstraction are different, among other things, in that each has its own paradigm or frame of reference, the one economical, the other political. Each paradigm is sufficiently "imperialistic" so as to exclude the other; hence both cannot be maintained at the same time.

By this time the reader should be sufficiently uneasy about the plausibility of economics and politics being inconsistent with each other. For his comfort I must say that general paradigms do become reconciled, but this reconciliation comes about in the level of praxis, of concrete existence, not at the abstract level of theory where they can know nothing of each other, being as they are mutually incommensurable. Also, that their "inconsistency" is not such that each of them could say exactly the contrary of what the other is saying on a particular subject. Each one is speaking its own language, so that there is no danger of contradicting each other in the ordinary sense. In that part of their languages that is reciprocally translatable they may be saying the same thing. At the limit, however, there is always something that only one of the conflicting paradigms could possibly express and in an eminently clear way, precisely at the point where the other has become exhausted.

The Parsonian approach, we have seen, lends primary importance to the "positive" rather than to the "residual" categories, The approach of "transcendental realism," on the contrary, considers residual categories as vital. They represent the radically unformalizable assumptions or powers of non formal thought on which the whole edifice of science is founded. Let us, in this connection, look into the distinction, which may prove important, that Parsons makes between logical and empirical "closure" of a system:

Any given concrete phenomenon is. . . a meeting ground. . . of a number of different laws. So the complete scientific explanation of the concrete phenomena can only be achieved by the application of all the theories involved. . . Science is always concerned with successive approximations.

Thus the element of "necessity" in scientific law inheres only in its logic . . . But this logical necessity. . . must. . . not be carried over to concrete phenomena. The logically closed system of scientific theory must not arbitrarily be made an empirically closed system. . . . (PARSONS 37, pp. 184-5)

I interpret this distinction as saying that a paradigm can be mistakenly viewed as an unidimensional representation of reality, as a full rendering of its (empirical) content. This, I think, is what Parsons considers wrong in positivism, namely that it easily leads us to expect empirical closure of the scientific system. Now, I think that the non positivist attempt to present a multidimensional representation of reality might result in frustration if it is understood as a conjunction of complementary paradigms. The "dimensions" will then be also conjoint, so that we will have a new single –although conjunctive– dimension. No advance into authentic multidimensionality will have been made at all. We will still have an empirical closure of the system. In order to maintain the distinction between logical and empirical closure we will have to take residual categories as tokens for our ignorance as such, not as tokens of our ignorance relative to another paradigm, complementary of the first in a conjunctive sense. We could probably say that the paradigms are complementary rather in the sense of the disjunction: one of them at least, in every case, must be true. In this conception, theory, i.e., heuristically advanced hypotheses, will be what is expressed in the residual categories. The positive ones are rather an expression of analyticity or direct empirical confirmation. The "prophetic" empirical content, our anchorage in reality as it were, will be implicit in the fundamental commitment that we make when we adopt a particular theoretical point of view or paradigm. "Logical closure" will then coexist with "empirical openness" in the sense that the corpus of a science will be treated as a system only with the help of theoretical notions, not reducible to what we directly know by means of our senses and operations of logical inference. NOTE 7 The system will be logically closed to the same extent that its degree of empirical openness may be dealt with as a datum, which is the same as saying that the synthetical character of a theory is not necessarily correlated to its not being analytical. All theory, even the empirically meaningful, must be self-validating –analytical in some sense– in order to be theory at all. That is why the intervention of residual categories or theoretical notions is absolutely necessary. But we could also say, in what would amount to a philosophical generalization of Gödel's theorem, that no theory can be consistent except the one which leaves room for continual heuristic achievement and the operation of alternative paradigms.

This resource of taking man's ignorance as a means for advancing knowledge –as has been shown is the case in the employment of "residual categories"– is not a new trick in the historical process of science. It has proved itself a very powerful device in several famous crucial instances. The discovery of the infinitesimal calculus can be counted as one (motion is not easily conceived as subject to number –to wit, Zeno's renown paradoxes; so, let us take the unintelligible notion of a numbered motion as our starting point!). The discovery of the theory of relativity is another (the concept of simultaneity at a distance is a scandal to physics; so, let us take its defined postulation as our starting point!). The underlying principle of this trick seems to be that if we place the ineradicable darkness at the center, as a result all the rest will come under full light. What is implied here, as in any case of really "multidimensional" paradigms, is a sort of interplay between knowledge and ignorance, the one growing at one point while the other dwindles at some other point. The phenomenon is also visible in the analysis of language; for example, in the inseparability between meaning and assertion, emphasized in our discussion of the naturalistic conception of value. That interplay may be compared to the ironing of surfaces topologically inadequate. You can make sure that some part of the surface will be smooth, but only under the condition that wrinkles will appear somewhere else on the surface. This topological NOTE 8 ambiguity seems to be essential to all knowledge bearing on reality. If one tries to get rid of it entirely one would end up destroying all knowledge. One draws precisely and rigorously only the arguments one wants to refute. That is why one would better read the opponents of a particular theory to find the perfect summary of it! Why is it, one may also ask, that the only really effective argument in philosophical controversy is the indirect proof, i.e., reductio ad absurdum? It is not because every reasonably sound theory is coherent and consistent up to a point, and because no theory can be consistent and complete as well?

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