122 
JOURNAL OF THE PLYMOUTH INSTITUTION. 
THE INDUCTIVE PEOCESS. 
ABSTEACT OF ME. EOBEET SMITH'S PAPEE. 
(Read February 1st, 1877.) 
This paper had for its object the discussion of some points in the 
philosophy of induction as enunciated by Mr. John Stuart Mill, 
who appears to claim as its result apodictic certainty, and can see 
no difference between the infallibility of a mathematical proposition 
and one which, being the result of a well-grounded induction, is 
termed a law of nature. 
The importance of the subject was enforced as being the basis of 
all scientific thought. 
The method of induction, which aims at the establishment of 
universal propositions from the examination of a number of in- 
dividual cases, was illustrated by a supposed bag-full of unknown 
articles, and the gradual withdrawal and examination of the 
contents, one by one ; and it was shown that any proposition 
concerning the nature of the whole contents would possess a degree 
of probability increasing with the number drawn, but only becoming 
certain on the drawing of the very last article ; and if the bag 
contain an infinite number, no such certainty could ever be 
attained, although the probability would increase with every fresh 
corroboration. 
Thus, supposing one article be drawn, and be found with 
certainty to be an apple, then we may affirm all the rest of the 
unknown articles to be apples also. Eut this proposition will 
possess only a low degree of probability, which however will 
increase with every fresh corroborative draw, and will ultimately 
become certain when the last one has been examined ; until then, we 
can never be quite sure that the next draw may not be an orange, 
or a peach. If therefore the contents be unlimited, we never 
attain certainty at all, although we constantly approximate it. 
This point was illustrated by diagrams explanatory of the mathe- 
matical notions of a curve and its asymptote, and the doctrine of 
