viii CONCEPTUAL RECONSTRUCTION 129 



Now we may deal with our concepts, combining and 

 re-combining them in numberless ways, without thought 

 of any reference to reality or to anything whatever beyond 

 themselves. This is the work of pure fancy. We may 

 also deal with them with the purpose of gaining further 

 knowledge of reality by means of our operations. This is 

 conceptual thinking. But in so doing we may or may not 

 act with clear consciousness of their ultimate reference. 

 Without this consciousness we may go a long way in 

 certain directions without error, while in other directions 

 we are landed in serious fallacies. 



For though, for the purposes of knowledge, the concept 

 has value only through its reference to the real order, 



on the data and processes by which they are formed and the results 

 to which they lead. If these conform to experience they are valid 

 though the existential judgment founded on them is not true. Their 

 validity is therefore dependent on other concepts to which they stand 

 related, it is relative or extrinsic. 



Validity is a wider conception than truth. It is the character of a 

 datum or a process which yields truth, or, more generally, it is the cause 

 or ground of truth. With false premisses a valid process yields false 

 results, but they are results which would truly follow from those 

 premisses. As applied to a perfected system of knowledge the two terms 

 would coincide, as in such a system all the data and processes would be 

 explicitly asserted in the form of propositions which would be true. In 

 anything short of such a system valid processes yield truth only on 

 the condition that they are free from dependence on any data or 

 processes which are invalid. Conversely, true results may be derived from 

 invalid processes. 



The consideration of a perfect system of knowledge indicates that 

 a valid process may be converted into a true proposition. Thus a 

 concept which is intrinsically or unconditionally valid is one which 

 may always be expressed as a true existential judgment. But an 

 imaginary expression cannot as such be so converted. The process of 

 calculation, however, in which it forms a part and by which we prove, 

 say, that equation A involves equation B, may be expressed in the 

 true proposition ' where A is true B is true.' The imaginary expression 

 then has validity in this and in similar combinations with other 

 concepts, but not otherwise. That is, it has a dependent or conditional 

 validity. 



It may, of course, prove possible to find some ' real ' meaning for all 

 imaginary expressions, i.e. at bottom to find a sense in which they 

 are applicable to the world of experience. If so, cadit quaestio, but in 

 the meanwhile it is, I think, impossible (a) to deny all validity to such 

 expressions, () to allow them any independent validity. They have 

 validity only as links in a train or combination of thought. 



I 



