INTRODUCTORY EXPLANATIONS. 3 



their being false. However improbable it may be, for in- 

 stance, that the barbarians did not overturn the Roman 

 empire, we do not recognise the same sort of sensible cer- 

 tainty in our moral certainty of the fact which we have in 

 our knowledge that fire burns, or that two straight lines 

 do not enclose space. And we perceive a difference in the 

 quality of our knowledge, when any alteration takes place 

 in our circumstances with respect to exterior objects. 

 That fire does burn is more certain than the account of 

 the fall of Rome : that fire yet to be lighted will burn 

 may or may not be more certain than the historical fact, 

 according to the temperament and knowledge of the in- 

 dividual. And thus we begin to recognise differences 

 even between our (so called) certainties ; and the com- 

 parative phrases of more and less certain are admissible 

 and intelligible. It is usual to begin the subject by 

 saying that our certainties are only very high degrees of 

 probability. This is not practically true at the outset ; 

 yet so far as deductions can be made numerically, 

 with respect to our impressions of assent or dissent, it 

 will be shown to be correct so to consider the subject. 

 We have a process to go through before we can arrive 

 at such a conclusion, as follows : When a child is 

 born, there is a certain degree of force, which we allow 

 to the assertion that he will die aged 50. To it we 

 answer that it may be, but that that particular age is 

 unlikely compared with all the rest, though, at first 

 sight, as likely as any other. If the assertion be made 

 of two children, that one or other will die aged 50, 

 we^ readily admit that our " it may be, but it is not 

 likely," is no longer the same assertion as it was before. 

 It is of the same sort, but not of the same strength : the 

 assertion is more probable , and wherever we have the 

 notion of more and less, we feel the possibility of an answer 

 to the question, ' f how much more or less ? " and which 

 we should produce if we knew how. First impressions 

 would induce us to suppose it twice as probable that the 

 assertion may be made of one or other of two children, 

 as of one alone ; and so on. Let this false measure (for 

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