On the simplicity of ideas
- 1 December 1943
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 8 (4) , 107-121
- https://doi.org/10.2307/2271052
Abstract
The motives for seeking economy in the basis of a system are much the same as the motives for constructing the system itself. A given idea A need be left as primitive in a system only so long as we have discovered between A and the other primitives no relationship intimate enough to permit defining A in terms of them; hence the more the set of primitives can be reduced without becoming inadequate, the more comprehensively will the system exhibit the network of interrelationships that comprise its subject-matter. Of course we are often concerned less with an explicit effort to reduce our basis than with particular problems as to how to define certain ideas from others. But such special problems of derivation, such problems of rendering certain ideas eliminable in favor of others, are merely instances of the general problem of economy. Thus it is quite wrong to think of the search for economy as a sort of game, inspired by an abnormal love of superficial neatness. Some economies may be relatively unimportant, but the inevitable result of regarding all economy as trivial would be a willingness to accept all ideas as primitive at the outset, making a system both unnecessary and impossible.Keywords
This publication has 1 reference indexed in Scilit:
- Sur la notion de l'ordre dans la Théorie des EnsemblesFundamenta Mathematicae, 1921