xxxi.J LIMITS OF SCIENTIFIC METHOD. 765 



must have been arbitrary determinations which led to the 

 production of things as they are. 



Possibility of Divine Interference. 



I will now draw the reader's attention to pages 149 to 152. 

 I there pointed out that all inductive inference involves 

 the assumption that our knowledge of what exists is com- 

 plete, and that the conditions of things remain unaltered 

 between the time of our experience and the time to which 

 our inferences refer. Eecurring to the illustration of a 

 ballot-box, employed in the chapter on the inverse method 

 of probabilities, we assume when predicting the probable 

 nature of the next drawing, firstly, that our previous 

 drawings have been sufficiently numerous to give us 

 knowledge of the contents of the box ; and, secondly, that 

 no interference with the ballot-box takes place between 

 the previous and the next drawings. The results yielded 

 by the theory of probability are quite plain. No finite 

 number of casual drawings can give us sure knowledge of 

 the contents of the box, so that, even in the absence of all 

 disturbance, our inferences are merely the best which can 

 be made, and do not approach to infallibility. If, however, 

 interference be possible, even the theory of probability 

 ceases to be applicable, for, the amount and nature of that 

 interference being arbitrary and unknown, there ceases to 

 be any connection between premises and conclusion. Many 

 years of reflection have not enabled me to see the way of 

 avoiding this hiatus in scientific certainty. The conclusions 

 of scientific inference appear to be always of a hypothetical 

 and provisional nature. Given certain experience, the 

 theory of probability yields us the true interpretation of 

 that experience and is the surest guide open to us. But 

 the best calculated results which it can give are never 

 absolute probabilities; they are purely relative to the extent 

 of our information. It seems to be impossible for us to 

 judge how far our experience gives us adequate information 

 of the universe as a whole, and of all the forces and pheno- 

 mena which can have place therein. 



I feel that I cannot in the space remaining at my com- 

 mand in the present volume, sufficiently follow out the 

 lines of thought suggested, or define with precision my 



