How difficult is calculus

On the logic of social science theories

Methodology of the Social Sciences pp 165-183 | Cite as


One problem of an empirical-theoretical social science - i.e. a social science that tries to construct and test informative and true theories - is the logical connection between the formulated statements. In this chapter we first want to use a simple example to explain how logic and mathematics can be applied in an empirical science and what advantages such an application has.

This is a preview of subscription content, log in to check access.


Unable to display preview. Download preview PDF.


  1. The following is a purely formal representation of the propositional calculus of logic, although only two rules of deduction are given. It should be emphasized that no attempt is made to present the problems encountered in the construction of artificial languages. Google Scholar
  2. Usually, in addition to the transformation rules, a number of axioms are formulated that are used in derivations. See, for example, Kutschera and Breitkopf 1971, Chapter 6, Google Scholar
  3. Cf. for example the following three publications: Rudolf Carnap, Formal and Factual Science; Morris R. Cohen, Ernest Nagel, The Nature of a Mathematical System; Carl G. Hempel, On the Nature of Mathematical Truth, all reprinted in: Feigl and Brodbeck 1953. Google Scholar
  4. On the different meanings of the concept of model see in particular Brodbeck 1959; Suppes 1960; Spinner 1969.Google Scholar
  5. The games at WFF’N PROOF are constructed in a similar way: see Allen 1962.Google Scholar
  6. There is a controversy about the distinction between analytic and non-analytic (i.e. synthetic) sentences. For a more precise characterization of “analytically true” and “analytically false” and for the discussion of the distinction “analytical-synthetic”, see Stegmüller 1969, pp. 60-62; 1970, pp. 181-182, pp. 206-211; 1968, pp. 291-319. A more easily understandable presentation can be found in Savigny 1970, 5.103-120, also in Carnap 1969, sections 27 and 28. Cf. also the two essays by the same author: “Meaning Postulates” and “Meaning and Synonymy in Natural Languages”, in Carnap 1956b, pp. 222-229 and pp. 233-247. A German version of the last-mentioned article can be found in Sinnreich 1972, pp. 145-163.Google Scholar
  7. These two hypotheses are taken from the following article in a greatly modified and simplified manner: Heyt and Opp 1968. Our example relates to our attempt, the Embezzlement theory by Donald R. Cressey from the Anomie theory Derive Google Scholar
  8. We are thinking here above all of the application in the context of cognitive balance theories. Cf. on this, in summary, Hummell 1969; Taylor 1970. Google Scholar

Copyright information

© Westdeutscher Verlag GmbH, Opladen / Wiesbaden 1999

Authors and Affiliations

There are no affiliations available