28 
agreement expresses the universal law, because the cases 
actually tested bear a so much larger ratio to the cases not 
tested. But it must be remembered, if the intuitive and 
original character of our judgment of cause be denied, we 
have no means, except the empirical, to know whether the 
cases of sequence still untested, and therefore unknown, will 
conform to our supposed law or not. And the belief arising 
out of this supposed calculus of probabilities is utterly decep- 
tive. For the number of cases tested, however large, is still, 
in the mind of the most learned. physicist, infinitesimally 
small, compared with the number of the unknown cases 
occurring in nature, not to speak of the more multitudinous 
cases In past ages. When the physicist has observed for 
years, the number of instances empirically tested does bear a 
larger ratio to the number with which he began. ‘True, and 
this is precisely the delusion which cheated Mr. Mill’s mind. 
But it is the increased ratio of the empirically known to the 
unknown which is necessary, for the purpose of even grounding 
a probability. But this still remains infinitesimally small. 
Again, the postulate of the uniformity of nature would not 
be, on Mr. Mill’s theory, even one that might be provisionally 
assumed, because it is obnoxious at its first suggestion, and 
throughout our provisional course of inquiry, to apparent con- 
tradictions. To the merely empirical eye nature appears 
variable and capricious almost as often as she does constant. 
So that, had our inductions only an empirical basis, instances 
of apparent testimony against this general premise might 
multiply as fast as instances of seeming concurrence in its 
favour. ‘The real reason that the results of induction are not 
thus embarrassed is that true induction is not merely empirical, 
as Mr. Mill supposes. Once more, if the general premise 
underlying each case of induction is only an assumption, then 
it is @ priori possible it may involve an error. If it does, 
why may not that element of error be multiplied and spread 
itself through the body of connected processes in a geometrical 
degree? ‘Then the body of supposed science is always liable 
to turn out, after all, ike the Ptolemaic hypothesis of the 
heavens, an inverted pyramid, an ingenious complication of 
propositions forced into a seeming harmony by their common 
trait of involving the radical error. Science has often shown 
that a hypothetic structure may be widely built out, and may 
stand long in apparent strength, and yet be overthrown. 
We close this refutation with this testimony from Esser, 
adopted by Hamilton (Logic, Lec. 32, end): “It is possible 
only in one way to raise induction and analogy from mere 
probability to complete certainty, viz., to demonstrate that the 
