University Reform. 297 



ends here. It is indeed a fallacy to suppose that 

 greater certainty is attainable in geometry than 

 elsewhere. Not greater certainty, but greater 

 precision, is that which distinguishes the results 

 obtained by mathematical deduction. Dealing 

 constantly with definite or determinable magni- 

 tudes, its processes are characterized by quantita- 

 tive exactness. It is not obliged to pare off and 

 limit its conclusions, to make them tally with 

 concrete facts ; but can treat of length as if there 

 were no such thing as breadth, and of plane sur- 

 faces just as if solidity were unknown. It is thus 

 the most perfect type of deductive reasoning ; 

 and if logical training is to consist, not in re- 

 peating barbarous scholastic formulas or mechan- 

 ically tacking together empty majors and minors, 

 but in acquiring dexterity in the use of trust- 

 worthy methods of advancing from the known to 

 the unknown, then mathematical investigation 

 must ever remain one of its most indispensable 

 implements. Once inured to the habit of accu- 

 rately imagining abstract , relations, recognizing 

 the true value of symbolic conceptions, and fa- 

 miliarized with a fixed standard of proof, the 

 mind is equipped for the consideration of quite 

 other objects than lines and angles. The twin 

 treatises of Adam Smith on social science, where- 



