Concepts of randomness

Conclusion

I have discussed a concept of random distribution of properties in classes and defined a concept of random conjunction of properties; I have also discussed measures of various kinds of randomness. In concluding, I shall only mention some further problems which await treatment. Both the concept of random conjunction and the measures of randomness rest upon the notion of probability, which was not explicitly dealt with in this paper. Since, however, assumptions of randomness are frequently brought forward as justifications for working with probabilities, the relationship of randomness and probability should be examined in detail. Another task is to show which concepts of randomness are relevant in the sciences. It seems that the concept of random distribution of properties in classes, though interesting in itself and of relevance to statistics, has no use in theories of the empirical sciences. However, the assumption of randomness in the sense of stochastic independence, very often combined with the notion of randomness in the sense of equiprobability, or maximum primitive randomness, undoubtedly plays a role in various fields of science. I do not know of any case where the measures of randomness are directly employed; the idea of stochastic dependence and that of probabilities other than equiprobabilities are, of course, widley used. Finally, some of the assumptions of random conjunction of properties made in the sciences seem to be justifiable in terms of an actual independence of the properties. This raises the question as to whether, and to what extent, the notion of an actual independence is fundamental to concepts of randomness.