238 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



our senses, connected with the crude lumps or surfaces, and 

 their rough relations, which we actually do sense?' . . . 

 What we want to do is to analyse finite figures and their 

 fearfully complicated perceptible relations into sets of terms 

 with simpler and more manageable relations. If we can 

 do this successfully we shall have killed two birds with 

 one stone. We shall have done full justice to the spatial 

 properties of what we can perceive; for our analysis is sup- 

 posed to be exhaustive. And, on the other hand, we shall 

 be able to grasp these properties and to reason about them 

 in a way that was impossible while they remained in the 

 crude unanalysed state in which we meet them in sense- 

 awareness." * Though the three problems are not specifically 

 distinguished in this quotation, the threefold character of 

 the pursuit is clearly evident. One is obliged, first, to de- 

 scribe the rough surfaces and volumes of immediate ex- 

 perience; secondly, one must define the refined points and 

 lines of mathematics; thirdly, one should show how the 

 latter are derived from or reducible to the former. 



An essentially equivalent formulation of the problem is 

 to be found in Russell. ' The first thing that appears when 

 we begin to analyse our common knowledge is that some 

 of it is derivative, while some is primitive; that is to say, 

 there is some that we only believe because of something 

 else from which it has been inferred in some sense, though 

 not necessarily in a strict logical sense, while other parts 

 are believed on their own account, without the support of any 

 outside evidence. It is obvious that the senses give knowl- 

 edge of the latter kind: the immediate facts perceived by 

 sight or touch or hearing do not need to be proved by argu- 

 ment, but are completely self-evident." 2 Data of this kind 

 may be called "hard," or psychologically primitive, and 

 are to be contrasted with "soft" data, which are psycholog- 

 ically derived. 'Psychologically, a belief may be called 

 derivative whenever it is caused by one or more other 

 beliefs, or by some fact of sense which is not simply what 



1 Scientific Thought, pp. 35-36. 2 Our Knowledge of the External World, p. 68. 



