Gary, all,
Yes, that's an especially lucid quote. I'll just add that it comes from
"Lessons from the History of Science" - the CP editors' title, as far as
I can tell. It's from MS 1288 "The Principal Lessons of the History of
Science (LHS)", "published in part as 1.43-125" according to the Robin
Catalog. The CP editors say it's a manuscript of notes for a projected,
but never completed, _History of Science_ circa 1896. - Best, Ben
On 5/6/2014 2:15 PM, Gary Richmond wrote:
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. / *In 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*
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