Matt, Ulysses, Mara, Ben, List,
Peirce comments in several places on Mill's understanding of the phrase
"the uniformity of nature" as the basis for induction. Here's one lucid
passage, broken up into shorter paragraphs for readability and to allow for
some brief comments on the material I've placed in italics (Mill's
position) and boldface (Peirce's counter to it). However, I'm pressed for
time the next few days, so I'm sending it out sans comments because I think
the passage itself gets at the heart of question and, in truth, doesn't
really need much comment as I see it.
CP 1.92 §16. REASONING FROM SAMPLES
Many persons seem to suppose that the state of things asserted in the
premisses of an induction renders the state of things asserted in the
conclusion probable. . . Even John Stuart Mill holds that the uniformity
of nature makes the one state of things follow from the other. *He
overlooks the circumstance that if so it ought to follow necessarily, while
in truth no definite probability can be assigned to it without absurd
consequences. He also overlooks the fact that inductive reasoning does not
invariably infer a uniformity; it may infer a diversity*. . .
Mill never made up his mind in what sense he took the phrase "uniformity of
nature" when he spoke of it as the basis of induction. *In some passages he
clearly means any special uniformity by which a given character is likely
to belong to the whole of a species, a genus, a family, or a class if it
belongs to any members of that group. *I*n this sense, as well as in
others, overlooked by Mill, there is no doubt the knowledge of a uniformity
strengthens an inductive conclusion; but it is equally free from doubt that
such knowledge is not essential to induction. *
*But in other passages Mill holds that it is not the knowledge of the
uniformity, but the uniformity itself that supports induction, and
furthermore that it is no special uniformity but a general uniformity in
nature. *Mill's mind was certainly acute and vigorous, but it was not
mathematically accurate; and it is by that trait that I am forced to
explain his not seeing that* this general uniformity could not be so
defined as not on the one hand to appear manifestly false or on the other
hand to render no support to induction, or both. *
He says it means that under similar circumstances similar events will
occur. But this is vague. *Does he mean that objects alike in all respects
but one are alike in that one?* *But plainly no two different real objects
are alike in all respects but one.* *Does he mean that objects sufficiently
alike in other respects are alike in any given respect?* *But that would be
but another way of saying that no two different objects are alike in all
respects but one. It is obviously true; but it has no bearing on induction,
where we deal with objects which we well know are, like all existing
things, alike in numberless respects and unlike in numberless other
respects.*
1.93. *The truth is that induction is reasoning from a sample taken
at random to the whole lot sampled. A sample is a random one, provided it
is drawn by such machinery, artificial or physiological, that in the long
run any one individual of the whole lot would get taken as often as any
other. Therefore, judging of the statistical composition of a whole lot
from a sample is judging by a method which will be right on the average in
the long run, and, by the reasoning of the doctrine of chances, will be
nearly right oftener than it will be far from right.*
1.94. That this does justify induction is a mathematical proposition beyond
dispute. It has been objected that the sampling cannot be random in this
sense. But this is an idea which flies far away from the plain facts.
Thirty throws of a die constitute an approximately random sample of all the
throws of that die; and *that the randomness should be approximate is all
that is required.*
Ben and I recently wrote a paper touching on aspects of this issue from
Peirce's perspective for Torkild Thellefsen's book, so I know he'll have a
great deal of interest to say about it.
Best,
Gary
*Gary Richmond*
*Philosophy and Critical Thinking*
*Communication Studies*
*LaGuardia College of the City University of New York*
On Tue, May 6, 2014 at 12:30 PM, Matt Faunce <mattfau...@gmail.com> wrote:
> 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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