Franklin, list,
I ran into a place where Peirce mentions eight forms of induction
besides two that he had discussed in the past. It's in the Carnegie
Application, though which I had looked the other day but somehow missed
this:
MEMOIR 19
ON ARGUMENTS
4th paragraph in "From Draft A - MS L75.35-39" (pp 35-39)
http://www.iupui.edu/~arisbe/menu/library/bycsp/l75/ver1/l75v1-06.htm#m19
[Begin quote]
Induction is the highest and most typical form of reasoning. In my
essay of 1883, I only recognized two closely allied logical forms of
pure induction, one of which in undoubtedly the highest. I have
since discovered eight other forms which include those almost
exclusively used by reasoners who are not adepts in logic. In fact,
Norman Lockyer is the only writer I have met with who in his best
work, especially his last book, habitually restricts himself to the
highest form. Some of his work, however, as for example, that on the
orientation of temples, is logically poor.
[End quote]
I'll catch up with your other questions later.
Best, Ben
On 10/31/2015 6:04 PM, Franklin Ransom wrote:
Ben, list,
Thank you for your help with my inquiry, Ben.
I appreciate your searching on my behalf for the nine forms of
induction. After thinking about it a bit, I think I must have gotten
the idea of nine forms of induction from the 10-trichotomy
classification of signs into 66 classes. Ten of those signs are
considered "inducent" (as Nathan Houser remarks in his "The Scent of
Truth"), so I suppose that would suggest ten, not nine. Besides which,
it's not clear that each sign class should come with a distinct form
of inference. So, I suppose that's where the idea came from, and is
likely mistaken as far as inferring there being so many forms of
induction. I'll go with the idea that Peirce only ever identified
three--crude, qualitative, and quantitative.
As to the other question:
I had seen 2.102, but partly had forgotten about it while reading the
sections at the end of Vol. 2, and partly it doesn't quite explain how
abduction should now be thought of, in particular it's contrast with
induction and deduction. The quote from the letter to Carus is
interesting in remarking on the point of contrast with induction,
although a bit ambiguous to my mind. After looking over the other
links you gave, I don't see much of anything I didn't already know,
with the exception of the letter to Carus that you pointed out.
In Vol. 2, the distinction between plausibility, verisimilitude, and
probability are introduced in paragraphs 662 and 663, so I was aware
of this later distinction; I note that there are paragraphs in Vol. 8
as well, easily found by looking for the search term "plausibility".
Although probability is no longer the unifying idea in addressing the
validity of abduction, there does seem (to me, at least) a likeness
between plausibility, verisimilitude, and probability, and thus his
earlier way of thinking about the three inferences with respect to
probability is perhaps not so far off the mark.
The passage from the letter to Carus causes me difficulty; I'm unsure
how to interpret it. Consider an expanded form of the passage, that
includes the intervening paragraphs, from Vol. 8 of CP:
"229. When one contemplates a surprising or otherwise perplexing state
of things (often so perplexing that he cannot definitely state what
the perplexing character is) he may formulate it into a judgment or
many apparently connected judgments; he will often finally strike out
a hypothesis, or problematical judgment, as a mere possibility, from
which he either fully perceives or more or less suspects that the
perplexing phenomenon would be a necessary or quite probable consequence.
230. That is a retroduction. Now three lines of reasoning are open to
him. First, he may proceed by mathematical or syllogistic reasoning at
once to demonstrate that consequence. That of course will be deduction.
231. Or, second, he may proceed still further to study the phenomenon
in order to find other features that the hypothesis will explain (i.e.
in the English sense of explain, to deduce the facts from the
hypothesis as its necessary or probable consequences). That will be to
continue reasoning retroductively, i.e., by hypothesis.
232. Or, what is usually the best way, he may turn to the
consideration of the hypothesis, study it thoroughly and deduce
miscellaneous observable consequences, and then return to the
phenomena to find how nearly these consequences agree with the actual
facts.
233. This is not essentially different from induction. Only it is most
usually an induction from instances which are not discrete and
numerable. I now call it Qualitative Induction. It is this which I
used to confound with the second line of procedure, or at least not to
distinguish it sharply.
234. A good account of Quantitative Induction is given in my paper in
Studies in Logic, By Members of the Johns Hopkins University,†14 and
its two rules are there well developed. But what I there call
hypothesis is so far from being that, that it is rather Quantitative
than Qualitative Induction. At any rate, it is treated mostly as
Quantitative. Hypothesis proper is in that paper only touched upon in
the last section."
So my difficulty is with paragraph 233. When he says "[t]his is not
essentially different from induction," I'm not sure what 'this' he
means.I would think that it refers to the subject of paragraph 232,
but paragraph 232 looks to me as though it simply describes ideal
scientific method--abduce a hypothesis, deduce its consequences, and
then induce the consequents and compare whether the consequents
induced conform to the consequents expected to follow from the
antecedents. I don't understand why the instances are not usually
discrete and numerable, and I do not understand why this is
qualitative induction. Why is this restricted to qualitative
induction, and why are the instances not usually discrete and
numerable? If you could enlighten me here about how I'm
misinterpreting the passage, I would be thankful.
In general, I find Peirce much more focused on understanding abduction
from the standpoint of methodeutic in his later work (I have read some
literature which makes just this point), and wonder how he could have
given a fuller treatment of abduction from the standpoint of critical
logic once he changed his views about how abduction and induction
differ. What is the place of abduction in the theory of information,
if not the induction of characters? I suspect that getting clearer
about this will also help in getting clearer about induction.
-- Franklin
On Fri, Oct 30, 2015 at 12:01 PM, Benjamin Udell <[email protected]
<mailto:[email protected]>> wrote:
Franklin, list,
I looked around but found nothing on the nine forms of induction.
As to abductive inference:
I guess you've already seen CP 2.102
http://www.commens.org/dictionary/entry/quote-minute-logic-chapter-i-intended-characters-treatise
Writing in 1910, Peirce says that "in almost everything I printed
before the beginning of this century I more or less mixed up
hypothesis and induction" and he traces the confusion of these two
types of reasoning to logicians' too "narrow and formalistic a
conception of inference, as necessarily having formulated
judgments from its premises." A Letter to Paul Carus circa 1910,
CP 8.227–8. See under "Hypothesis" at the Commens Dictionary of
Peirce's Terms.
http://www.commens.org/dictionary/entry/quote-letters-paul-carus-1
Also see CP 8.234 to Carus, where he says that his earlier
formulation of abduction was more quantitative induction than
qualitative induction
http://www.commens.org/dictionary/entry/quote-letters-paul-carus-0
Generally you can look through
http://www.commens.org/dictionary/term/hypothesis-%5Bas-a-form-of-reasoning%5D
http://www.commens.org/dictionary/term/abduction
http://www.commens.org/dictionary/term/retroduction
http://www.commens.org/dictionary/term/presumption-%5Bas-a-form-of-reasoning%5D
My sense of it has been that Peirce thought that he had confused
two kinds of inference in his idea of hypothetical inference, and
that one of them was right but got confused with idea of induction
in his mistaken effort to cast hypothetical reasoning as a kind of
probable or likely reasoning. In later years he distinguishes
firmly among deductive probability, inductive likelihood a.k.a.
inductive verisimilitude (the conclusion's likeness to the
premissual data), and abductive plausibility, which last he
regards as instinctual simplicity, naturalness. In his early
treatments of hypothetical inference, he pretty consistently has
it occasioned by an odd or surprising phenomenon or observation
and gives it an explanatory role.
Best, Ben
On 10/29/2015 6:07 PM, Franklin Ransom wrote:
Hello list,
I just finished Vol. 2 of the Collected Papers, and had a
couple of questions, if anyone is interested in helping out.
Going through the material on induction towards the end of the
volume, much of it seemed to be from Peirce's earlier work on
induction, where hypothesis or presumption (or abduction) is
conceived of as an inference having to do with inferring that
a character or set of characters apply to an object or set of
objects. However, the editors included a piece from 1905 that
treats of crude, qualitative, and quantitative induction. My
understanding is that Peirce came to believe in his later
years that what he had originally identified as hypothesis is
actually qualitative induction, and hypothesis or abduction is
something else. But in the selected piece from 1905, Peirce is
not clarifying that point and instead has some other remarks
about qualitative induction. I am wondering whether Peirce was
consistent about maintaining in his later work that the
earlier view of abduction really should be considered
qualitative induction, or if Peirce's views about this topic
are more complicated. It strikes me as odd that the editors
might have purposely misled readers about this point
concerning hypothesis and qualitative induction, but I have
difficulty seeing it otherwise. Perhaps this point is
clarified in later volumes of the CP?
My second question is that I recall hearing at some point that
Peirce identified nine different kinds of induction, but I
don't recall seeing anything by Peirce about this. I was
hoping I would find something in the CP, but I'm not so sure I
will find it now. Does anyone know anything about this, and
where I might look for it? I'm not sure if I've asked about
this before; please forgive me for not remembering if I have.
-- Franklin
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