on another ambiguity in the word 'probable.' It may be used in
the sense of 'less than absolutely certain'; and such doubtless is the
condition of all human knowledge, in comparison with the comprehensive
intuition of arch-angels: or it may mean 'less than certain according
to _our_ standard of certainty,' that is, in comparison with the law of
causation and its derivatives.

We may suppose some one to object that "by this relative standard even
empirical laws cannot be called 'only probable' as long as we 'know no
exception to them'; for that is all that can be said for the boasted law
of causation; and that, accordingly, we can frame no fraction to
represent their probability. That 'all swans are white' was at one time,
from this point of view, not probable but certain; though we now know it
to be false. It would have been an indecorum to call it only probable as
long as no other-coloured swan had been discovered; not merely because
the quantity of belief amounted to certainty, but because the number of
events (seeing a swan) and the number of their happenings in a certain
way (being white) were equal, and therefore the evidence amounted to 1
or certainty." But, in fact, such an empirical law is only probable; and
the estimate of its probability must be based on the number of times
that similar laws have been found liable to exceptions. Albinism is of
frequent occurrence; and it is common to find closely allied varieties
of animals differing in colour. Had the evidence been duly weighed, it
could never have seemed more than probable that 'all swans are white.'
But what law, approaching the comprehensiveness of the law of causation,
presents any exceptions?

Supposing evidence to be ultimately nothing but accumulated experience,
the amount of it in favour of causation is incomparably greater than the
most that has ever been advanced to show the probability of any other
kind of event; and every relation of events which is shown to have the
marks of causation obtains the support of that incomparably greater body
of evidence. Hence the only way in which causation can be called
probable, for us, is by considering it as the upward limit (1) to which
the series of probabilities tends; as impossibility is the downward
limit (0). Induction, 'humanly speaking,' does not rest on probability;
but the probability of concrete events (not of mere mathematical
abstractions like the falling of absolutely true dice) rests on
induction