THOUGHTS ON BELIEF AND EVIDENCE. 243 



and unhappy results. Truth is as much a reality which man. may rea- 

 sonably hope to obtain in what are called matters of opinion, as in ques- 

 tions of physical science, and no wise man is blind to its importance ; 

 but associated feeling, prejudice, habit, interest, act so powerfully, 

 though often indirectly, and unperceived by the individual, that the 

 right decision on questions of the kind under consideration, important 

 as it is, must unavoidably be more slow of attainment than where we 

 can appeal directly to the senses. The kin(| of evidence available and 

 the proper tests of truth on questions religious, moral, metaphysical, 

 political and social are subjects of vast importance and universal inte- 

 rest, but their discussion would lead me far beyond the bounds 1 must 

 prescribe to myself. The general principle is clear. Every opinion 

 is the expression of a generalization, implying the sufficient knowledge 

 of a number of particulars. It rests on observation or acquaintance 

 with facts directly or indirectly obtained. It is vitiated by assuna- 

 ing as facts what are not so, or by insufficient or wrongly conducted 

 induction. Freedom of opinion means the right of every individual 

 to decide doubtful questions for himself by such means as to him 

 appear best, an inalienable right of human beings, and the full 

 recognition of which is the best means of securing the ultimate pre- 

 valence of truth, and of the good which attends it, but this recogni- 

 tion is not for a moment to be supposed to imply indiiference to truth 

 in the possession of which consists the highest good and highest hap- 

 piness of man, and the promotion of which is one of the noblest 

 objects of philanthropy. 



It remains for me to speak of the nature of our belief in mathe- 

 matical propositions. There is manifestly some great difference in 

 kind between this belief and that which we have in our sensations, or 

 in any generalisations respecting the changes or relations of objects or 

 ideas. Belief in a mathematical proposition is not merely confidence 

 but absolute certainty of a kind unattainable in other subjects of 

 thought and involving the absurdity of believing otherwise. This 

 peculiarity of mathematical propositions seems to depend on their 

 being concerned wtth a limited class of ideas, and with them not as 

 they may be obtained by our senses, but as pure abstractions of the 

 mindo We separate number and the forms of extension from the 

 objects, by means of which alone we could first acquire these ideas. 

 We define the fundamental ideas in terms which exclude the real and 

 physical, leaving us a pure abstraction. In this we do nothing really 



