On the other hand, as Aristotle over-emphasized deduction so Bacon
over-emphasized induction by contending that it is the only process of
discovering universals (_axiomata_), which deduction only applies to
particulars. J. S. Mill in his _Logic_ pointed out this defect, and
without departing from Baconian principles remedied it by quoting
scientific examples, in which deduction, starting from inductive
principles, applies more general to less general universals, e.g. when
the more general law of gravitation is shown to include the less
general laws of planetary gravitation. Mill's logic has the great
merit of copiously exemplifying the principles of the variety of
method according to subject-matter. It teaches us that scientific
method is sometimes induction, sometimes deduction, and sometimes the
consilience of both, either by the inductive verification of previous
deductions, or by the deductive explanation of previous inductions.
It is also most interesting to notice that Aristotle saw further than
Bacon in this direction. The founder of logic anticipated the latest
logic of science, when he recognized, not only the deduction of
mathematics, but also the experience of facts followed by deductive
explanations of their causes in physics.
The consilience of empirical and deductive processes was an Aristotelian
discovery, elaborated by Mill against Bacon. On the whole, however,
Aristotle, Bacon and Mill, purged from their errors, form one empirical
school, gradually growing by adapting itself to the advance of science;
a school in which Aristotle was most influenced by Greek deductive
Mathematics, Bacon by the rise of empirical physics at the Renaissance,
and Mill by the Newtonian combination of empirical facts and
mathematical principles in the _Principia_. From studying this
succession of empirical logicians, we cannot doubt that sense, memory
and experience are the real origin of inference, analogical, inductive
and deductive. The deepest problem of logic is the relation of sense and
inference. But we must first consider the mental analysis of inference,
and this brings us to conceptual and formal logic.
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