GROUNDS OF DISBELIEF. 



407 



their abstract and hypothetical char- 

 acter, and approach nearer to the de- 

 ^ee of complication actually exist- 

 ing in nature ; insomuch that beyond 

 the limits of astronomical phenomena, 

 and of those most nearly analogous 

 to them, mathematical accuracy is 

 generally obtained "at the expense 

 of the reality of the inquiry ; " while 

 even in astronomical questions, " not- 

 withstanding the admirable simplicity 

 of their mathematical elements, our 

 feeble intelligence becomes incapable 

 of following out eflfectually the logical 

 combinations of the laws on which 

 the phenomena are dependent, as 

 soon as we attempt to take into 

 simultaneous consideration more than 

 two or three essential influences." * 

 Of this, the problem of the Three 

 Bodies has already been cited, more 

 than once, as a remarkable instance ; 

 the complete solution of so compara- 

 tively simple a question having vainly 

 tried the skill of the most profound 

 mathematicians. We may conceive, 

 then, how chimerical would be the 

 hope that mathematical principles 

 could be advantageously applied to 

 phenomena dependent on the mutual 

 action of the innumerable minute par- 

 ticles of bodies, as those of chemistry, 

 and still more of physiology ; and 

 for similar reasons those principles 

 remain inapplicable to the still more 

 complex inquiries, the subjects of 

 which are phenomena of society and 

 government. 



The value of mathematical instruc- 

 tion as a preparation for those more 

 difficult investigations consists in the 

 applicability not of its doctrines, but 

 of its method. Mathematics will 

 ever remain the most perfect type 

 of the Deductive Method in general ; 

 and the applications of mathematics 

 to the deductive branches of physics, 

 furnish the only school in which phi- 

 losophers can effectually learn the 

 most difficult and important portion 

 of their art, the employment of the 

 laws of simpler phenomena for ex- 

 plaining and predicting those of the 

 * PhUotcphie Positive yiii. 4x4-416. I 



more complex. These grounds ax« 

 quite sufficient for deeming mathe- 

 matical training an indispensable 

 basis of real scientific education, and 

 regarding (according to the dictum 

 which an old but unauthentic tradi- 

 tion ascribes to Plato) one who is 

 dyeojfidTprjTOi, as wanting in one of 

 the most essential qualifications for 

 the successful cultivation of the higher 

 branches of philosophy. 



CHAPTER XXV. 



OF THE GROUNDS OF DISBELIEF. 



§ I. The method of arriving at 

 general truths, or general propositions 

 fit to be believed, and the nature 

 of the evidence on which they are 

 grounded, have been di.scussed, as far 

 as space and the writer's faculties 

 permitted, in the twenty-four preced- 

 ing chapters. But the result of the 

 examination of evidence is not always 

 belief, nor even suspension of judg- 

 ment ; it is sometimes disbelief. The 

 philosophy, therefore, of induction 

 and experimental inquiry is incom- 

 plete, unless the grounds not only of 

 belief, but of disbelief, are treated of ; 

 and to this topic we shall devote one, 

 and the final, chapter. 



By disbelief is not here to be under- 

 stood the mere absence of belief The 

 ground for abstaining from belief is 

 simply the absence or insufficiency of 

 proof ; and in considering what i« 

 sufficient evidence to support any 

 given conclusion, we have already, by 

 implication, considered what evidence 

 is not sufficient for the same purpose. 

 By disbelief is here meant, not the 

 state of mind in which we form no 

 opinion concerning a subject, but that 

 in which we are fully persuaded that 

 !-ome opinion is not true ; insomuch 

 that if evidence, even of great appa- 

 rent strength, (whether grounded on 

 the testimony of others or on our own 

 supposed perceptions,) were produced 

 in favour of the opinion, we should 

 believe that the witne.^ses spoke falsely, 



