Mathematics, Science of Possibility†

† Reproduced by permission of Schools Council Publications. Note: The views expressed in this article are not necessarily those of the Schools Council.

Summary

The question ‘What is mathematics about?’ can be answered in two different ways: with an account of the character of mathematical activity as seen from the inside, and with an account of the relation of mathematical activity to other kinds of activity. The well‐known logistic, formalist and intuitionist accounts of mathematics are of the first kind. They shed virtually no light on the question how mathematics relates to other activities, and as a consequence of this they provide little illumination for laymen, philosophers and students approaching mathematics from the outside. In this paper an account of the second kind is offered, suggesting that mathematics is centrally concerned with the investigation of the possibilitiesof the real world: that the relevance of mathematics is to hypothetical, rather than to actual, situations. A naturalistic account of mathematics on these lines treats the symbolism of mathematics as a form of ‘apparatus’ which we use to construct models of situations. Manipulation of the mathematical model is broadly equivalent to exploring the possibilities of the situation represented by the model. A special feature of mathematics as ‘apparatus’ is that the intrinsic physical properties of the apparatus vanish, leaving only the symbols needed to preserve a record of the manipulation.

† Reproduced by permission of Schools Council Publications. Note: The views expressed in this article are not necessarily those of the Schools Council.

Notes

† Reproduced by permission of Schools Council Publications. Note: The views expressed in this article are not necessarily those of the Schools Council.