PREFACE 7 



But these difficulties, arising from various causes, are on the whole 

 more advantageous than otherwise to the general progress of know- 

 ledge. By means of a rigorous hostihty to the admission of new 

 ideas as truths, a multitude of more or less specious but unfounded 

 ideas which appear, soon after fall into oblivion. Sometimes, on 

 the other hand, excellent opinions and sohd thoughts are for the same 

 reasons discarded or neglected; but it is better that a truth once 

 perceived should have a long struggle before obtaining the attention 

 it deserves, than that all that is produced by the ardent imagination 

 of man should be too readily received. 



The more I meditate on this subject, and particularly on the numerous 

 causes which may bring about a change in our opinions, the more am 

 I convinced, that except for the physical and moral facts ^ that no 

 one can question, all else is but opinion or argument; and we well 

 know that arguments can always be met by others. Thus, although 

 it is obvious that there are great differences in the probability and 

 even the value of the opinions of different men, it seems to me that 

 we should be wrong to blame those who refuse to adopt our own. 



Should we recognise as well founded only those opinions that are 

 most widely accepted ? Experience shows clearly enough thaTl 

 persons with the most developed intellect and the highest wisdomj 

 constitute at all times an extremely small minority. The fact can 

 scarcely be questioned. Authorities in the sphere of knowledge 

 should weigh one another's worth and not count one another's numbers, 

 although indeed a true estimation is very difficult. 



Seeing how numerous and rigorous are the conditions required 

 for forming a sound judgment, it is still uncertain whether the judg- 

 ment of individuals who have been set up as authorities by pubUc 

 opinion is perfectly soimd on the topics on which they pronounce. 



There are then few positive truths on which mankind can firmly 

 Tely. They include the facts which he can observe, and not the in- 

 ferences that he draws from them ; they include the existence of nature, 

 which presents him with these facts, as also the laws which regulate 

 the movements and changes of its parts. Beyond that all is un- 

 certain, although some conclusions, theories, opinions, etc., have much 

 greater probabiUty than others. 



We cannot rely on any argument, inference or theory, since the 

 authors of these intellectual acts can never be certain that they have 

 taken into account the true data, nor that they have admitted these 



^By moral facts I mean mathematical truths; that is to say, the results of 

 calculations whether of quantities or forces, and the results of measurements ; since 

 it ia through intelligence and not through the senses that these facts become known 

 to us. Now these moral facts are just as much positive truths as are those relating 

 to the existenoB of bodies that we can observe. 



