84 Sir WilUnni Hamilton's Fi-agments of ridlosophy. 



both of whom had cultivated this science. It will probably excite sur- 

 prise to see the authority of Descartes himself likewise turned against 

 mathematics^ a science Avhich he had cultivated with so much success ; 

 this is shewn by a fragment of his life by Balllctj quoted in this volume, 

 and in which the French philosoiiher acknowledges that his own experi- 

 ence had convinced him of the small utility of mathematics, especiallj-when 

 cultivated on their own account, and without applying the means which 

 they afford us to the acquisition of other kinds of knowledge. Sir Wil- 

 liam Hamilton then compares philosophy with mathematics, and ex- 

 amines the aids which tlicy respectively afl'ord to the intellect. Claiming 

 the whole preference for philosoph}-, he affirms that a too exclusive study 

 of mathematics renders the mind incapable of observation, whether in- 

 ternal or external, of abstraction and of reasoning ; to these disadvantages 

 lie adds that of precipitating the mind either into a state of blind credu- 

 lity, or of irrational scepticism. 



But, again, if the study of the mathematical sciences cannot, like logic, 

 fortify the reason against the errors of thought, may it not at least 

 strengthen the reason itself.^ Sir William Hamilton does not think that 

 it can. According to him, the principles of mathematics being self evi- 

 dent, every step which the mind takes in the process has the same degree 

 of evidence ; every step in a mathematical demonstration can be easily 

 made, and requires only an easy application of thought ; and as a faculty 

 is always developed in proportion to its degree of exercise, it thence fol- 

 lows, according to him, that the mathematics, by submitting the intellec- 

 tual powers to a very feeble degree of activitj-, develope them in a very 

 limited manner. Further, relying on the oi~>inions of different writers of 

 distinguished character, he undertakes to shew that the study of mathe- 

 matics is accessible to all, and requires no special adaptation. The tes- 

 timonies cited are those of Berkelej-, S'Gravesande, D'Alembert, Gibbon, 

 Mmc. de Stael, and others, who, althougli less celebrated.nevertheless lend 

 their authority to countenanccthis conclusion. He exposes the double ten- 

 dency to credulity and scepticism, Vifhich often leads the individual astray 

 who gives himself up exclusively to sciences of calculation. We cannot 

 help thinking that there is somewhat of exaggeration in this assertion, 

 which is very like a paradox skilfully defended ; but it is pleasant to fol- 

 low the animated pen of a writer fully master of his subject, while he 

 draws deductions always well connected, and supported by an accurate 

 acquaintance with the history' and minute anal^'sis of human intelligence. 



Sir William Hanulton concludes by blaming the University of Cam- 

 bridge for giving too mrch encouragement to the study of mathematics 

 in preference to the other sciences. Resting his views on the principles 

 already explained, he points out the impropriety of directing the minds 

 of youth to this in preference to every other kind of instruction, seeing 

 that it is of importance to fortify the intellect with resources adapted to 

 be useful in every circumstance of life, and not in some one in particular. 



Such is the volume of Fragments we owe to the Scottish Professor. 



