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References
Cf. G. Homans, Social Behaviour: Its Elementary Forms, New York, 1961.
Cf. A. Malewski, O zastosowaniach teorii zachowania [Applications of Behaviour Theory], Warszawa, 1965.
Cf. Thibaut and Kelley, The Social Psychology of Groups, New York, 1959.
Cf. J. Dollard and N. Miller, Psychology and Psychotherapy, New York, 1950.
Controversies over reductionism will be discussed below in greater detail.
D. S. Ranulf, Moral Indignation and Middle Class Psychology, New York, 1968.
To be read: every x which is an element of the set X has the property B.
It is assumed here for simplicity that aggressiveness and tendencies to disinterested punishment are equivalent to one another, since otherwise the schema of inference would become excessively complicated. The formula is to be read: for every x which is an element of the set X, if x is A, then x is B.
To be read: every x which is an element of the set X is in the situation A.
Cf. Adorno et al., The Authoritarian Personality, New York, 1950.
All three propositions from the paper by H. Zetterberg, On Axiomatic Theories in Sociology, in P. F. Lazarsfeld, M. Rosenberg (eds.), The Language of Social Research, New York, 1955.
To be read X 1 is included in X.
“Reduction in the sense in which the word is here employed, is the explanation of a theory or a set of experimental laws established in one area of inquiry by a theory usually though not invariably formulated for some other domain”. E. Nagel, The Structure of Science, Ch. XI, Reduction of Theories, New York, 1961, p. 338.
Cf. the logica analysis of this reduction in Nagel's book quoted in footnote 13.
See e.g. J. Olds, Physiological Mechanisms of Reward, in Nebraska Symposium on Motivation, Lincoln Nebraska, 1955.
As will be seen below, not only general laws, but more elementary laws as well may occur in the explanans.
The term correspondence rule was introduced by R. Carnap, who, however, used it to denote theorems which describe relationships between terms in “language of observation” and those in “language of theory”, so that for him they served to impart empirical meaning to theoretical terms, which lacked such a meaning. Here the meaning of the term in question is much broader, and hence the term rule of reductive correspondence strictly corresponds to that meaning in which this term was used by Carnap in some cases of reduction only, namely, in those in which the explaining law is formulated in the language of “latent properties”, and the explained law, in the observation language. Cf. R. Carnap, Methodological Character of Theoretical Concepts, in Minnesota Studies in Philosophy of Science, Vol. I.
Cf. H. Speier, The American Soldier and the Sociology of Military-Organizations, in R. K. Merton, P. Lazarsfeld (eds.), Continuities in Social Research, Glencoe, 1950.
The term intervening variable is being interpreted in different ways. Some-times it stands for any latent variable, which is introduced to explain a manifest relationship. In other cases it stands for any variable A, which is introduced to find out the intermediary link between the variables that occur in a sequence: A 1→B 1 and thus to obtain the causal chain: A 1→A→B 1. It is in the latter sense that it is used in this paper.
Cf. P. E. Meehl, On the Circularity of the Law of Effect, in “Psychological Bulletin”, 1950.
See: J. Dollard, N. R. Miller, Personality and Psychotherapy, New York, 1950.
This is probably the most frequent interpretation used in psychoanalysis, where it is usually assumed, on the strength of a definite theory of personality, that it is exactly repression which indicates whether an inner experience is, or is not, a source of anxiety.
A rule of reductive correspondence need not necessarily state that a set of elementary properties and a complex property are equivalent to one another. It could also take on the form of an implication in the form: {ie405-1} but this would result in additional complications in the reduction schema, complications which the present paper could not cover. The problem is analysed more comprehensively in the book, quoted in footnote 1, which appeared in Polish.
Cf. S. Ranulf, Moral Indignation and Middle Class Psycbology, cit.
There is one more way of reducing such a law: instead of introducing two separate rules of reductive correspondence we reduce the entire sequence. The rule of reductive correspondence then takes on the form: {ie406-2} On the strength of such a rule of reductive correspondence and making the same assumptions as to the elementary laws and their initial conditions we may explain the law {ie406-1}.
Cf. the analysis of interaction in: H. Blalock, Causal Inference in Non-Experimental Research, Chapel Hill, North Carolina, 1961. For the typology of kinds of interaction see also S. Nowak, Causal Interpretation of Statistical Relationships in Social Research, “Quality and Quantity”, I (1967).
Cf. the analysis of the various meanings of the terms whole and part and the various meanings of the formulation “a whole is more than the sum of its parts” in E. Nagel, The Structure of Science, cit., pp. 380–397.
The symbol R(x) stands here for singulary, binary and m-ary relations holding between elements x of the set E. Singulary relations may be termed properties, and so they will sometimes be called in this paper.
Cf. A. Malewski, Treść empiryczna teorii materializmu historycznego [The Empirical Content of the Theory of Historical Materialism], in “Myśl Filozoficzna”, (1958).
If the last-named condition is not satisfied, then we have to do with a variety of the “emergence” of global law, which is discussed in the last section of the present paper.
Note that interaction of elements under a single inter-elementary law is not to be confused with interaction of different non-additive regularities, which is discussed more extensively in connection with the problem of emergence.
In this case, too, both a definitional and an empirical rule of reductive correspondence may also take on the form of a one way implication (see footnote 23). Since this complicates the reduction schema by requiring additional assumptions, such cases are disregarded here.
Cf. M. Brodbeck, Methodological Individualism. Definition and Reduction, in M. Brodbeck (ed.), Readings in the Philosophy of Social Sciences, New York, 1968.
See the analysis of the problem of emergence in M. Brodbeck, op. cit., E. Nagel, op. cit., and C. Hempel, Aspects of Scientific Explanation, Glencoe Ill., 1965.
M. Brodbeck, in his article quoted above, says that an elementary law which is valid for certain elements in isolation should, for the purpose of such a reduction, be completed with certain composition rules, which will show how the schema x behaves in the system of relations R 1 (x). The present writer is inclined to suggest that such a law should be modified so that R 1 (x) should be taken into consideration in the antecedent of that law and that a new consequent should be defined for the configuration of conditions R 1 (x)∧a(x), when the original law is no longer needed.
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Nowak, S. The logic of reductive systematizations of social and behavioural theories. Qual Quant 5, 389–391 (1971). https://doi.org/10.1007/BF00218990
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DOI: https://doi.org/10.1007/BF00218990