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is regulated by law? Anda more difficult question is: How 
do we prove certainly which laws regulate given classes of 
sequences in nature? No apparent regularity in any given 
number of sequences is enough to prove a certain law, as 
Lord Bacon has shown; for this would be merely what he 
calls inductio per simplicem enwmerationem, which he has 
proved never to be demonstrative of itself. But the logic of 
inductive demonstration is necessary to prove that such 
enumeration of agreeing cases of sequence does, or does not, 
express a real law. Thus, it appears that demonstrative in- 
duction must be pre-requisite, on this theory, to ground our 
belief in the uniformity of nature. And yet the theory makes 
that belief the @ priori ground of all our inductions. This 
view, then, resolves itself into the absurdity of assuming, as 
first premise of our argument, that which we only learn in its 
conclusion. 
How, then, can an argument from a part of the class to all 
the class become valid, against the fundamental rule of logic ? 
Not a few logicians, among whom is Sir William Hamilton 
(Lectures on Logic, 32, end), have conceded that induction 
can never give more than probable evidence of a law. He 
asserts that it is impossible for it to teach, like the deductive 
syllogism, any necessary laws of thought, or of nature. Must 
we concede this? Is the problem hopeless, the gravity of 
which these introductory paragraphs indicate? Must we 
admit that all the sciences of induction, and all the practical 
rules of life, which are virtually mductive, are for ever un- 
certain; presenting us only probabilities, of which wider 
investigations may bring us a refutation? ‘This we are loth 
to admit, even as true friends of physical science. We claim 
that inductive argument may have demonstrative force, when 
properly constructed. Such a view must be substantiated, or 
the proud name of Science should be candidly surrendered as 
to all the supposed laws of natural phenomena. Real demon- 
stration cannot be grounded in uncertainties, however much 
these may be multiplied. Moreover, the common sense of 
mankind rejects the statement that the best inductions are 
only probable. On sundry of them we unhesitatingly stake 
our welfare and lives; and experience never fails to confirm 
their truth. The question then recurs, the great question of 
the inductive logic: How does the inference seemingly made 
ae the some, or the many, to the all, become valid for the 
all ? 
As Mr. Mill has pointed out (very inconsistently for his own 
philosophy), demonstrated truths can only be proved from 
premises containing necessary principles.. To construct a 
