FUNCTIONS AND VALUE OF THE SYLLOGISM. 255 



performing wonderful things they know not how, are 

 examples of the less civilized and most spontaneous 

 form of the operations of superior minds. It is a 

 defect in them, and often a source of errors, not to 

 have generalized as they went on ; but generalization 

 is a help, the most important indeed of all helps, yet 

 not an essential. 



Even philosophers, who possess, in the form of 

 general propositions, a systematic record of the results 

 of the experience of mankind, need not always revert 

 to those general propositions in order to apply that 

 experience to a new case. It is justly remarked hy 

 Dugald Stewart, that though our reasonings in mathe- 

 matics depend entirely upon the axioms, it is by no 

 means necessary to our seeing the conclusiveness of 

 the proof, that the axioms should be expressly adverted 

 to. When it is inferred that A B is equal to C D 

 because each of them is equal to E F, the most uncul- 

 tivated understanding, as soon as the propositions 

 were understood, would assent to the inference, with- 

 out having ever heard of the general truth that 

 " things which are equal to the same thing are equal 

 to one another." This remark of Stewart, consistently 

 followed out, goes to the root, as I conceive, of the 

 philosophy of ratiocination ; and it is to be regretted 

 that he himself stopt short at a much more limited 

 application of it. He saw that the general proposi- 

 tions on which a reasoning is said to depend, may, in 

 certain cases, be altogether omitted, without impairing 

 its probative force. But he imagined this to be a 

 peculiarity belonging to axioms ; and argued from it, 

 that axioms are not the foundations or first principles 

 of geometry, from which all the other truths of the 

 science are synthetically deduced (as the laws of 

 motion and of the composition of forces in mechanics, 



