372 Dr. Dorothy Wrinch and Dr. H. Jeffreys on Certain 



the principles of pure logic alone. Accordingly, the funda- 

 mental data in any branch of science must consist of a finite 

 number of observational results and some a priori postulates. 

 One consequence of this is that we can never prove the 

 existence of a limit to which a series of entities known 

 by experience may tend, for in order to establish the- 

 existence of such a limit we should need to have knowledge 

 that an infinite number of such entities are within a definite 

 distance of that limit. This by itself would not be a fatal 

 objection to any such theory, for there seems to be no 

 hope of constructing a theory of knowledge without some 

 assumptions, and it may be considered that in the case 

 in question certain conditions are satisfied under which 

 the existence of the limit is known a priori. But what 

 is more serious is that in a physical problem we do not 

 merely w^ant to know that the limit exists; we also want 

 to know its value according to some system of measurement, 

 and that value can never be known a priori ; indeed, if 

 it w^ere, there would be no need to make measurements at 

 all. Thus, if a limit is ever used in a physical theory, its 

 value and all propositions about it are neither a priori 

 nor known by experience, and therefore are not primitive- 

 propositions that can be used as the data of a theory of 

 knowledge. 



A defect arising from the use of infinite classes is present 

 in Mr. Bertrand Russell's treatment* of physical objects as 

 classes of sensibilia. In order to obtain a deductive theory 

 he defines a physical object as the class of all its aspects,, 

 including those which are not perceived. Now an un- 

 perceived aspect, or sensibile, obviously is not known, and 

 therefore, on Mr. Russell's theory, we could never assert 

 any proposition about the physical object. We could never, 

 for instance, say whether it satisfied any physical law or 

 not ; however often the law was verified for perceived aspects, 

 it w^ould always be possible that it was violated by the 

 unperceived ones. The qualities of the latter can at the 

 most be inferred from the perceived ones, and this cannot 

 be done unless difficult assumptions as to the resemblances 

 between perceived and unperceived sense data are intro- 

 duced. 



Prof. Whitehead's theory f appears to be unworkable 

 for similar reasons. Events, instead of sensibilia, are for 

 him the fundamental entities, but he also requires the use of 



* < Mysticism and Logic,' pp. 145-167 (1917). 



f ' An Enquiry into the Principles of Natural Knowledge ' (1919). 



