4 Mr. ELLIS, ON THE FOUNDATIONS OF THE THEORY OF PROBABILITIES. 



Nevertlieless it has been applied to a great variety of inductive results; with what success 

 and in what manner, I shall now attempt to enquire. 



(12.) Our confidence in any inductive result varies with a variety of circumstances; one of 

 these is the number of particular cases from which it is deduced. Now the measure of this confi- 

 dence which the theory professes to give, depends on this number exclusively. Yet no one can 

 deny, that the force of the induction may vary, while this number remains unchanged. This 

 consideration appears almost to amount to a reductio ad absurdum. 



(13.) If, on m occasions, a certain event has "been observed, there is a presumption that 

 it will recur on the next occasion. This presumption the theory of probabilities estimates at 



. But here two questions arise; What shall constitute a "next occasion .''" What degree 



»j + 2 



of similarity in the new event to those which have preceded it, entitles it to be considered a 



recurrence of the same event .'' 



Let me take an example given by a late writer : — 



«Ten vessels sail up a river. All have flags. The presumption that the next vessel will 



have a flag is — . Let us suppose the ten vessels to be Indiamcn. Is the passing up of 



any vessel whatever, from a wherry to a man of war, to be considered as constituting a " next 

 occasion .'" or will an Indiaman only satisfy the conditions of the question .'' 



It is clear that in the latter case, the presumption that the next Indiaman would have 

 a flag is much stronger, than that, as in the former case, the next vessel of any kind would 



have one. Yet the theory gives — as the presumption in both cases. If right in one, it 



cannot be right in the other. Again, let all the flags be red. Is it — that the next 



vessel will have a red flag, or a flag at all .'' If the same value be given to the pre- 

 sumption in both cases, a flag of any other colour must be an impossibility. 



It is to be noticed, that I only refer to the visible differences among different kinds 

 of vessels, and not to any knowledge we may have about them from previous acquaintance. 



(14.) I turn to a more celebrated application of the theory. 



All the movements of the planetary system, known as yet, are from west to east. This 

 undoubtedly affords a strong presumption in favour of some common cause producing mo- 

 tion in that direction. But this presumption depends not merely upon the number of observed 

 movements, but also on the natural affinity which in a greater or less degree appears to 

 exist among them. 



This is so natural a reflection, that Lacroix, in calculating the mathematical value of 

 the presumption, omits the rotatory movements, and, I believe, those of the secondary planets, 

 in order, as he expressly says, to include none but similar movements. But in the admis- 

 sion thus by implication made, that regard must be had to the similarity of the move- 

 ments, too much is conceded for the interests of the theory. For are the retained move- 

 ments absolutely similar ? The planets move in orbits of unequal eccentricity and in different 

 planes : they are themselves bodies of very various sizes ; some have many satellites and 

 others none. If these points of difference were diminished or removed, the presumption in 

 favour of a common cause determining the direction of their movements would be strength- 

 ened ; its calculated value would not increase, and rice versa. 



Again, up to the close of 1811, it appears (Laplace) that 100 comets had been observed, 

 .53 having a direct and 47 a retrograde movement. If these comets were gradually to lose 

 the peculiarities which distinguish them from planets — we should have 64 planets with direct 

 movement, 47 with retrograde. The presumption we are considering would, in such a case, 



