Here's Mill's position as given by Sigwart.
Logic, Vol. II pg. 299 –301, 303:
In one respect J. S. Mill holds the same views as Hume. For him
nothing is given but particular sensations, and these sensations are
originally subjective states of feeling. But there must be some way
of proceeding from these to science in the full sense, and this way
is to be shown by inductive logic ; this will be, moreover, the only
way in which we can pass beyond immediate experience to the
knowledge of something which we do not experience immediately.
Induction, as he defines it, is that operation of the mind by which
we infer that what we know to be true in a particular case or cases
will be true in all cases which resemble the former in certain
assignable respects—the process by which we conclude that what is
true of certain individuals of a class is true of the whole class,
or that what is true at certain times will be true in similar
circumstances at all times.
But he goes on to add that this process of inference presupposes a
principle, a general assumption with regard to the course of nature
and the order of the universe, namely, that what happens once will,
under a sufficient degree of similarity of circumstances, happen
again, and not only again, but as often as the same circumstances
recur. This proposition, that the course of nature is uniform, is
the fundamental principle, or general axiom of induction.
Every particular so-called induction is therefore a syllogism, of
which the major premise is this general principle, and which can be
expressed as follows:—
Under similar circumstances, the same event will always happen.
Under circumstances a, b, c, D has been found ;
Therefore under circumstances a, b, c, D will always be found ;
It is clear, although Mill has not sufficiently noted it, that,
regarded only in this aspect, the particular case proves just as
much as a whole series of cases, and that I can draw exactly the
same conclusion from a single observation as from many similar
observations.
But now the question arises as to the origin of the universal major
premise and the consequent significance of this syllogism; and here
comes in again Mill's doctrine as to the nature of the syllogism of
which we have already spoken (I. § 55, 3, p. 359). The universal
major premise cannot explain the inductive process, for it is itself
obtained by induction; it is indeed one of the latest and highest
inductions grounded upon preceding partial inductions. The more
obvious laws of nature must have been already recognised by
induction as general truths before we could think of this highest
generalization. Hence we can only regard this highest major premise
as a guarantee for all our inductions in the sense in which all
major premises contribute something to the validity of their
syllogisms; the major premise contributes nothing to prove the truth
of the conclusion, but is a necessary condition of its being proved,
since no conclusion can be proved for which there cannot be found
from the same grounds a valid universal major premise.
In other words, we really infer only from observed cases of
uniformity to other cases ; because we have found a uniform relation
between a certain number of phenomena, we infer that it will be so
also with every other class of phenomena; but, according to Mill,
this latter conclusion—a real Aristotelian inference from example—is
only certain if we can infer from the observed uniformities to
general uniformity.
Upon what ground can we infer from a number of instances of observed
uniformity to universal uniformity? […]
[…]
pg. 303:
Taking away with one hand what he gives with the other. Mill shows
in the uncertainty of his views the helplessness of pure empiricism,
the impossibility of erecting an edifice of universal propositions
on the sand-heap of shifting and isolated facts, or, more
accurately, sensations; the endeavour to extract any necessity from
a mere sum of facts must be fruitless.
The only true point in the whole treatment is one in which Mill as a
logician gets the better of Mill as an empiricist; namely, that
every inductive inference contains a universal principle; that if it
is to be an inference and not merely an association of only
subjective validity, the transition from the empirically universal
judgment all known A's are B to the unconditionally universal all
that is A is B can only be made by means of a universal major
premise, and that only upon condition of this being true are we
justified in inferring from the particular known A’s to the still
unknown A’s. But then the universal major premise cannot be obtained
simply by means of a summation of facts, for this by itself can
yield no more than it says, that in a certain number of cases A was
B, and as pure matter of fact contains no reason for passing beyond
these A’s to other A’s ; it must have some other origin than in
previously perceived facts, and our right to make use of it must
have some other ground than the narration of cases which have been
observed so far.
On 5/5/14, 9:37 PM, U Pascal wrote:
Mara, Ben, List
I'm excited for the discussion that you have set up with your
introductory remarks. Keeping it brief, (I'm sneaking this email in
while at work) I wanted to focus one of your first questions:
Is the assumption that the universe is regular enough to afford
explanation? Or is it simply an affirmation of the power of the
combination of instinct, intuition, logic, mathematics, and
phaneroscopy to create explanatory patterns out of randomness?
Peirce's argument against Mill's notion that we can form knowledge
about the universe because it is regular has always puzzled me. It
strikes me that this argument is of fundamental importance (especially
when dealing with themes the of truth & reality), however I've always
felt something lacking in my understanding of Peirce's take down. If
somebody is willing to rehearse Mill's position and Peirce's response,
I think we could get closer to answering Mara & Ben's question.
Best,
Ulysses
--
Matt
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