Abstract
In this historical introduction Capecchi analyses in what manner the relation between mathematics and sociology has changed. Three phases are presented: (a) Paul F. Lazarsfeld’s choices concerning theory, methodology and mathematics as applied to sociological research; (b) the relations between mathematics and sociology from statistical methods to artificial society and social simulation models; and (c) the new possibilities offered to sociology though by artificial neural networks. Then the changes in the methodological problems linked to the relation between mathematics and sociology are analysed together with the changes in the most important paradigm utilized in sociological research namely the paradigm of objectivity; the paradigm of action research/co-research and the paradigm of feminist methodology. At the end of the introduction, some new possible synergies are presented.
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Notes
- 1.
The proceedings of the seminar were published in Sternberg et al. (1965).
- 2.
Lazarsfeld (1967).
- 3.
Lazarsfeld (1954), pp. 3–5, 8, 10, 16. The quotations from PFL (1954) have been organized in a different way.
- 4.
- 5.
In this paper the term paradigm, in the sense attributed to it by Kuhn, has been used for the following: (a) standpoint methodology; (b) methodology; (c) research methods. The definitions are by Sandra Harding (2004, p. 44; 1987, p. 2): standpoint epistemology “sets the relationship between knowledge and politics”; methodology is “a theory and analysis of how research does or should proceed”; research method “is a technique for (or way of proceeding in) gathering evidence. (…) In this sense there are only three methods of social inquiry: listening to (or) interrogating informants, observing behaviour or examining historical trace and records”.
- 6.
Warren S. Torgerson (1958) gives the following definitions for the four types of scales: (i) nominal scale: when between the two elements A and B of the same variable, it is possible to indicate only the relation A = B, A ≠B; (ii) ordinal scale: when between two elements of the same variable, it is possible to indicate the relations A < B, A = B, A > B; (iii) interval scale: when the scale has no natural origin and operations such as A: B, A × B are possible, but the origin and units of measure are arbitrary (as in test scores); (iv) ratio scale when the scale has natural origin (as in the age variable) and operations such as A: B, A × B are possible.
- 7.
See the article by PFL (1969).
- 8.
PFL and Thielens (1958, p. 121) explain their choice as follows: “We have used the term permissive when often the reader, quite correctly, might prefer that we speak of liberal or progressive teachers. We have avoided these two words because they have changed their meaning too often in the great debate of the last decades.”
- 9.
The essay Ideal Types and Explanation in Social Sciences is in Hempel (1965, p. 155–171).
- 10.
- 11.
On this subject, see Filippo Barbera and Nicola Negri (2005).
- 12.
The two applications of linear casual models I am referring to here are (a) an application to classify the differences between active members of the Communist Party and Christian Democrats, which appeared in English in Capecchi (1973) and (b) an application on the behaviour of voters in Italy, which appeared in English in Capecchi and Galli (1969).
- 13.
The models presented by Capecchi and Moeller in a wider social entropy theory is in Kenneth D. Bailey (1990).
- 14.
For a more complete analysis, see Coleman et al. (1966).
- 15.
Axelrod’s quotations in this article by John Barrie are from Axelrod (1981, pp. 315–316).
- 16.
About “synchronicity” linked to the discussion between Jung and Wolfgang Pauli, the book edited by Lance Storm (2008) is suggested.
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Capecchi, V. (2010). Mathematics and Sociology. In: Capecchi, V., Buscema, M., Contucci, P., D'Amore, B. (eds) Applications of Mathematics in Models, Artificial Neural Networks and Arts. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-8581-8_1
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