'All men are mortal; Smith is a man, therefore Smith is mortal,' means
that we know, before drawing our inference, that literally all men are
mortal, we must already have discovered that Smith is mortal; if we did
not know beforehand that Smith is mortal, we were not justified in
stating that _all_ men are mortal. Nor is it an escape to interpret 'All
men are mortal' to mean that immortals are excluded from 'man' by
definition. For then the question is merely begged in the minor premiss.
That 'Smith is a man' cannot be asserted without assuming that he is
mortal. If, lastly, 'All men are mortal' be taken to state a law of
nature conjoining inseparably mortality and humanity, the logician
either already knows that Smith is rightly classed under the species
'man,' and so subject to its mortality, or else he _assumes_ this. But
how does he know Smith is not like Elijah or Tithonus, a peculiar case,
to which for some reason the law does not apply? Will he declare it to
be 'intuitively certain' that whatever is called, or looks like, a case
of a 'law' _ipso facto_ becomes one?

The logician's analysis of reasoning, then, breaks down. In whichever
way he interprets the Syllogism it is revealed as either a superfluity
or a fallacy: it is never a 'formally valid inference' that can compel
assent. But common sense is undismayed by the pragmatist's discovery
that if the Syllogism is to have any sense its premisses _must_ be taken
as disputable; for, unlike Formal Logic, it has perceived that men do
not reason about what they think they know for certain, but about
matters in dispute.

4. It is not necessary to dwell at length on the futility of the formal
notion of Induction. Formal Induction presupposes that enough particular
instances have been collected to establish a general rule; but in actual
practice inductions always repose, not on indiscriminate observation,