422 CONSTITUTION OF THE INTELLECT. [CHAP. XXII. 



the present day to the spirit of emulation or cupidity, does not 

 tend to weaken the influence of those more enduring motives 

 which seem to have been implanted in our nature for the imme- 

 diate end in view. Upon these, and upon many other questions, 

 the just limits of authority, the reconciliation of freedom of 

 thought with discipline of feelings, habits, manners, and upon 

 the whole moral aspect of the question, what unfixedness of 

 opinion, what diversity of practice, do we meet with ! Yet, in 

 the sober view of reason, there is no object within the compass 

 of human endeavours which is of more weight and moment than 

 this, considered, as I have said, in its largest meaning. Now, 

 whatsoever tends to make more exact and definite our view of 

 human nature, in any of its real aspects, tends, in the same pro- 

 portion, to reduce these questions into narrower compass, and 

 restrict the limits of their possible solution. Thus may even 

 speculative inquiries prove fruitful of the most important prin- 

 ciples of action. 



1 1 . Perhaps the most obviously legitimate bearing of such 

 speculations would be upon the question of the place of Mathe- 

 matics in the system of human knowledge, and the nature 

 and office of mathematical studies, as a means of intellectual 

 discipline. No one who has attended to the course of recent 

 discussions can think this question an unimportant one. Those 

 who have maintained that the position of Mathematics is in 

 both respects a fundamental one, have drawn one of their strongest 

 arguments from the actual constitution of things. The mate- 

 rial frame is subject in all its parts to tlie relations of number. 

 All dynamical, chemical, electrical, thermal, actions, seem not 

 only to be measurable in themselves, but to be connected with 

 each other, even to the extent of mutual convertibility, by nu- 

 merical relations of a perfectly definite kind. But the opinion 

 in question seems to me to rest upon a deeper basis than this. 

 The laws of thought, in all its processes of conception and of 

 reasoning, in all those operations of which language is the ex- 

 pression or the instrument, are of the same kind as are the laws 

 of the acknowledged processes of Mathematics. It is not con- 

 tended that it is necessary for us to acquaint ourselves with those 

 laws in order to think coherently, or, in the ordinary sense of 



