THE STUDY OF MATHEMATICS 67 



him, to travel easily over the steps of the more important 

 deductions. In this way a good tone of mind is cultivated, 

 and selective attention is taught to dwell by preference 

 upon what is weighty and essential. 



When the separate studies into which mathematics is 

 divided have each been viewed as a logical whole, as a 

 natural growth from the propositions which constitute 

 their principles, the learner will be able to understand 

 the fundamental science which unifies and systematises 

 the whole of deductive reasoning. This is symbolic logic 

 ^a study which, though it owes its inception to Aristotle, 

 is yet, in its wider developments, a product, almost 

 wholly, of the nineteenth century, and is indeed, in the 

 present day, still growing with great rapidity. The true 

 method of discovery in symbolic logic, and probably also 

 the best method for introducing the study to a learner 

 acquainted with other parts of mathematics, is the 

 analysis of actual examples of deductive reasoning, \vdth 

 a view to the discovery of the principles employed. These 

 principles, for the most part, are so embedded in our 

 ratiocinative instincts, that they are employed quite un- 

 consciously, and can be dragged to light only by much 

 patient effort. But when at last they have been found, 

 they are seen to be few in number, and to be the sole 

 source of everything in pure mathematics. The dis- 

 covery that all mathematics follows inevitably from a 

 small collection of fundamental laws is one which im- 

 measurably enhances the intellectual beauty of the whole ; 

 to those who have been oppressed by the fragmentary and 

 incomplete nature of most existing chains of deduction 

 this discovery comes with all the overwhelming force of a 

 revelation ; like a palace emerging from the autumn 

 mist as the traveller ascends an Italian hill-side, the 

 stately storeys of the mathematical edifice appear in their 



