194 Professor Whewell on the Mathematical Exposition 



the assumed principles lead, whatever be the complexity of tlieir 

 combination. And such a mode of proceeding will be of very 

 great advantage to truth ; inasmuch as it will make it inevitably 

 necessary to separate the moral axioms and assumptions on which 

 the theories rest, from all other matter which may tend to ob- 

 scure or confound them. It will also separate entirely the two 

 parts of the subject which it is of immense imjjortance to keep 

 separated; — the business of proving these assumptions, and that 

 of deducing their conclusions. Much ingenuity has been shewn 

 in reasoning downwards from assumed principles. These prin- 

 ciples are however so few and general, (we do not now speak of 

 their truth or applicability) that the task of deducing their results 

 is almost entirely a business of the mathematical faculty; and 

 might have been done in a few pages by clothing them in mathe- 

 matical formulae. 



4. It would seem indeed as if the present state of the science 

 of Political Economy were that which peculiarly called for this 

 rigorous and scientific form to be given to its mathematical por- 

 tions. It is by some reduced to a set of principles hardly more 

 numerous or less general than the laws of motion : and the cases 

 to which the economical principles are applied, are certainly not 

 less complicated than the cases to which mechanical principles 

 are applicable. Now we can easily imagine what would have 

 been the result if men had, without the aid of consistent mathe- 

 matical calculation, attempted to make a system of mechanical 

 philosophy. There would have been three errors difficult to avoid. 

 They might have assumed their principles wrongly ; they might 

 have reasoned falsely from them in consequence of the complexity 

 of the problem ; or they might have neglected the disturbing 

 causes which interfered with the effect of the principal forces. 

 And the making mechanics into a Mathematical science supplied 

 a remedy for all these defects. It made it necessary to state 



