Of course, in the study of such complicated phenomena as occur in biology and sociology, the mathematical method cannot play the same role as, let us say, in physics. In all cases, but especially where the phenomena are most complicated, we must bear in mind, if we are not to lose our way in meaningless play with formulas, that the application of mathematics is significant only if the concrete phenomena have already been made the subject of a profound theory.
A. D. Aleksandrov, A General View of Mathematics. In: A. D. Aleksandrov, A. N. Kolmogorov, M. A. Lavrent’ev, Mathematics: Its Content, Methods and Meaning. Moscow 1956 (trans. 1964)

Post filed under epistemolgy, mathematics, method, statistics.

3 Comments

  1. a quite interesting quote. Loosing the eloquence of your open quote, I suggest that some mathematical games of computational sociologists indeed seems meaningless, however the root of this problem might fall back on the classic sociologist. The question I am meet with is exactly a confused one: ‘Where are the profound theories in the complicated fields of sociology?’

    • It’s indeed a big problem. The parts of sociology that do not only apply statistics – for Aleksandrov this would not be “mathematics” as understood in his paper – but indeed do model behavior are generally based on very, very reduced theories of human beings and their relationships, e.g. in sociometrics, social exchange theory, and much of economics. This kind of modelling can certainly be interesting as an intellectual exercise and useful in a context where behavior is limited and well understood, e.g. in flight situations. But I think that computational approaches applied to the really difficult social and cultural questions (domination, ideology, etc.) are much more useful when they are aiming at description of data rather than coming up with law-like models.

  2. Indeed visualizations, descriptives and data-mining techniques are useful, when investigating empirical problems. What I am getting at is an old discussion about theory, or the lack of formal theories that attempts to transcend simple reductions in sociology, biology and economy. But this is a different agenda concerned with prediction and control, as opposed to the empirical problem of revelation and exposure.

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