THE INDUCTIVE PROCESS. 
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ultimate ratios, by which an arc is said to be ultimately equal to 
its chord ; and the very best generalizations from experience — those 
which are the unexceptional exponents of all experience on the 
subject — were compared to the curve and the arc, which ever 
tend more and more to become coincident with the asymptote and 
chord respectively, but never become quite so. 
Mr. Mill distinctly states that the operation for which he claims 
certainty is not the method which consists in the complete examina- 
tion of every included case, which, although formally certain, is 
quite abortive as an attempt to add to our stock of knowledge. 
His induction is, " Without doubt a real process of inference 
its conclusion embraces more than is contained in the 
premises." It is " more than a summing up of what has been 
specifically observed in the individual cases which have been 
examined ; it is a generalization grounded on those cases, and 
expressive of our belief that what we there found true, is true in 
an indefinite number of cases that we have not examined, and are 
never likely to examine." {Logic, vol. i. p. 187.) 
Applying the above illustration, Mr. Mill's induction is of the 
kind in which, the contents of the bag being unlimited, we predicate 
something of the unknown contents, by virtue of the knowledge 
we possess of the ones we have examined, and not of the kind in 
which, the number being limited, we examine the whole, and 
embody the result in a proposition. 
Now it is evident that we should have no warrant in drawing 
such a conclusion, except only as a probability, unless we had some 
previous reasons for knowing that the articles were all alike. If 
we knew that the fruit in the bag were all of the same kind, we 
should be justified in concluding them to be all apples after we 
had seen a few only as a sample of the whole. 
It is from this principle that the modern system of induction, as 
compared with the ancient, derives its superiority. Archbishop 
"Whately has remarked that every such induction may be thrown 
into the form of a syllogism, of which the major premise is a 
proposition affirming the uniformity of nature, which when ex- 
amined resolves itself into the generalization known as the law of 
universal causation. 
Whence then does this law derive its validity ? 
Prom another induction surely, says Mr. Mill; but from one 
which is co-extensive with all human experience. Let us grant 
