MATHEMATICS VERSUS PSYCHOLOGY 13 



ternal world, the belief in God, nay even the belief in the existence 

 of our own minds as distinct from the hosts of ideas which flit 

 through them is matter, not of knowledge, but of blind instinct, 

 which science can in a measure account for, but which it must in 

 vain attempt to justify. If substances are thus to be subjectively 

 interpreted, so also are relations. These are but various ways 

 of comparing ideas; or, more precisely, they are complex ideas 

 formed from simpler ideas by the inexplicable process of com- 

 parison. Certain classes of relations for example, the equality 

 or inequality of quantities or numbers are found to be com- 

 pletely determined by the ideas compared ; that is to say, while 

 these ideas are unchanged the relation remains the same. Such 

 relations give rise to no peculiar problem. They are expressed 

 by universal propositions, from which valid deductions may be 

 made; and in the cases above mentioned the deductions are so 

 extensive as to constitute special sciences. The other class of 

 relations (those of space and time, identity, and causality) are 

 more remarkable. 1 The utmost analysis of any acknowledged 

 cause and effect (for example) will reveal no quality or combina- 

 tion of qualities in either or both that determines why the one 

 should be thought to produce the other. And the most exact 

 attention to two bell-tones will disclose no shade of difference 

 between them that could account for the one's being heard as 

 preceding or following the other. In every such case, therefore, 

 the relation must be supposed to be determined by other ac- 

 companying sensations, feelings, or ideas. Thus the second of 

 two bell-tones may be accompanied by a memory-image of the 

 first. In the case of^causality, the relation depends upon a feeling 

 of 'necessary connection,' which accompanies the habitual move- 

 ment of the imagination from one event to another, when they 

 have frequently been observed to occur in close succession and 

 uniform order. Causal necessity is therefore by no means equiva- 

 lent to logical implication. Nor is it a property of the operations 



x The inclusion of identity in the list is at first sight surprising. But it is 

 meant that at most a complete resemblance can be actually determined by the com- 

 parison of two ideas. The interpretation of this as identity is another thing. 



