82 



triangle cannot be framed without the simultaneous destruc- 

 tion of a concept in which these magnitudes are represented as 

 equal. That is to say, the subject and predicate cannot be 

 united in the same intuition the proposition is unthinkable." 1 



The above is a rather interesting statement, after having 

 been told that the "space intuitions which we recognize as 

 necessary * * * are the fixed functions of fixed structures that 

 have become moulded into correspondence with fixed outer 

 relations." Now Spencer has told us that "the inner relations 

 must correspond with the outer ones; and therefore that the 

 order of states of consciousness must be in some way expres- 

 sible in terms of the external order." Yet here he states that 

 an unbelievable proposition is one which admits of being 

 framed in thought, although the thing predicated has never 

 happened, and we should reach the position that propositions, 

 and therefore relations, occur in thought which have no coun- 

 terpart in outer relations: as to how such proposition came 

 into consciousness at all is inexplicable. 



In regard to the inconceivable proposition, Spencer states 

 that "the concept of a triangle cannot be framed without 

 simultaneous destruction of a concept" in which one side 

 of such triangle is represented as being equal to the other two. 

 But this is simply the logical proposition that 'A cannot be 

 both A, and not-A, at the same time'. Since Spencer under- 

 stands by a triangle, that in which two sides must be together 

 greater than the third side, it is of course, as he says, "un- 

 thinkable" that it should be anything else. But the unthink- 

 ableness of the contrary is merely a result of definition, not 

 of any "absolute relation in the environment". 



It might be contended, however, that "perpetually-re- 

 peated experiences" account for our attribution of necessity 

 to logical and mathematical relations. But will this furnish 

 the required necessity, either in connection with the so-called 

 external absolute relations or for inner fixed intuitions? 



For example, that one has always experienced the arc of 

 the segment of a circle as longer than the chord, is no guar- 

 antee in the least that such a proposition will hold for the next 

 case in which the arc and the chord are experienced together 

 that is, there is no empirical reason for postulating the re- 

 lation as 'universal and unchanging'. Or again, that two 

 sides of a triangle have always been experienced as greater 

 than the remaining side does not imply, from the mere enu- 

 meration of particulars, any 'objective impossibility' in con- 



1 " Principles of Psychology" 427. 



