Franklin, list,
Thanks for pointing out those subsequent passages and unraveling them
for us. It's been a while since I read "Upon Logical Comprehension and
Extension" from beginning to end.
When Peirce previously in the same paper defined induction as increasing
the breadth without changing the depth, the idea seem to be that of
extending the character to a larger population which is asserted to
exist, i.e., induction's conclusion asserts an actual increase of
breadth without asserting a change of depth. But he comes to say of
induction:
[....] On the other hand, P is not yet found to apply to anything
but S', S'', S''', and S^iv , but only to apply to whatever else may
hereafter be found to be contained under M. The induction itself
does not make known any such thing. [....]
[End quote]
It is true that the induction does not _/make known/_ the truth of its
conclusion's claims, but in this picture the induction does not even
_/assert/_ the existence of a larger, encompassing population, but
instead leaves it conditional and hypothetical, so the breadth increase
is potential, not assertedly actual. Moreover the conclusion isn't
usually framed like "whatever else may hereafter," it just says "Any M
is P" and this doesn't even entail that there are S's found to be M & P.
This is a question of what is the fairest way to frame an inference. You
make a good point about Peirce not bringing iconicity and indexicality
much into the account in that paper. If the sample is an index, as he
later said, of the whole, what sort of actual index indicates a
hypothetical, potential whole?
You wrote,
It is a bit unclear to me why some of the changes in information
didn't seem to correspond to one of the three inferences [....]
[End quote]
I had that thought recently too. I once tried to make a table of all the
changes in information and I found that the potential size of the table
was rather larger than I expected. If all mental action has the form of
inference, then they all must be related to inferences in some way.
Best, Ben
On 11/2/2015 6:29 PM, Franklin Ransom wrote:
Ben, list,
You wrote: "But can the induction of characters and qualitative
induction be understood as increasing only the breadth, not the depth?"
My understanding is that, since characters have to do with depth, not
breadth, then it is not possible to understand the induction of
characters and qualitative induction as increasing only the breadth,
and not the depth. In fact, it is the other way around: They increase
only the depth, and not the breadth.
However, though that is my understanding, what Peirce actually says is
more complicated. The following quote from "Upon Logical Comprehension
and Extension", sixth section or paragraph, will help:
"There is, therefore, this important difference between induction and
hypothesis, that the former potentially increases the breadth of one
term, and actually increases the depth of another, while the latter
potentially increases the depth of one term, and actually increases
the breadth of another."
I tried to think this out, but it is a bit complicated to work out. If
I recall correctly, at this point in time Peirce hasn't really adopted
the icon and index point of view on propositions. Both terms are
symbols, each of the terms contributing their own breadth and depth by
necessity; which, as I understand it, has to do with the cases in
which the term-symbol appears as predicate and as subject in other
propositions. The term-symbol's appearance as a predicate will then
increase its breadth, because it is applied to a new subject, while
its appearance as a subject will increase its depth, because a new
predicate has been applied to it. If one thinks about it in this way,
the nuances of information theory and the role of inference is in
ascription of modifiers to the increase, such as actual, potential,
conceived, etc. It may be helpful to consider what he said preceding
the statement quoted above:
Induction requires more attention. Let us take the following example:--
S', S'', S''', and Siv have been taken at random from among the M's;
S', S'', S''', and Siv are P:
any M is P.
We have here, usually, an increase of information. M receives an
increase of depth, P of breadth. There is, however, a difference
between these two increases. A new predicate is actually added to M;
one which may, it is true, have been covertly predicated of it
before, but which is now actually brought to light. On the other
hand, P is not yet found to apply to anything but S', S'', S''', and
Siv, but only to apply to whatever else may hereafter be found to be
contained under M. The induction itself does not make known any such
thing. Now take the following example of hypothesis:--
M is, for instance, P', P'', P''', and Piv;
S is P', P'', P''', and Piv:
S is all that M is.
Here again there is an increase of information, if we suppose the
premises to represent the state of information before the inferences.
S receives an addition to its depth; but only a potential one, since
there is nothing to show that the M's have any common characters
besides P', P'', P''', and Piv. M, on the other hand, receives an
actual increase of breadth in S, although, perhaps, only a doubtful one.
The part that you referenced with respect to generalization is
potentially illuminating, as this may show the way to understanding
the new place of abduction or hypothesis in the theory of information.
Thank you for pointing out this material. It is a bit unclear to me
why some of the changes in information didn't seem to correspond to
one of the three inferences, and perhaps they are key to thinking more
about abduction from an informational perspective. You're certainly
giving me much to ponder over!
With respect to your recent discussions on classifying basic inference
modes, I haven't been following closely, and so couldn't comment. But
understanding that reference helps me understand what you meant when
you said that in the previous post.
Franklin
On Mon, Nov 2, 2015 at 9:35 AM, Benjamin Udell wrote:
Found an error of thought in my post. Corrected below with 'DELETE'
and 'INSERT' tags. Sorry. - Best, Ben
Franklin, list,
You wrote:
I'm somewhat curious about the last thing you said, "[f]or my part,
extension and comprehension seem more useful in exploring inference
than in defining basic modes of inference." Would you be willing to
elaborate on that a bit? I would suppose that in order to explore
inferences in that way, one would already have to know which
inferences causes changes in which quantity and how they change it.
But perhaps this is not necessarily the case; or even if it is, some
or even most of the time we don't need to know which inferences
effect which changes, so long as we can appreciate that changes in
the information of a sign occurred. Maybe you think about it in this
way?
[End quote]
I actually haven't been exploring comprehension and extension much
lately, but I notice when others do, Peirce in particular. In "Upon
Logical Comprehension and Extension" (1867), Peirce defined induction
as increasing the breadth (extension, denotation) while leaving the
depth (comprehension) unchanged, and defined generalization as
increasing the breadth while decreasing the depth such that the
information (breadth × depth) unchanged. But can the induction of
characters and qualitative induction be understood as [*DELETE*]
keeping unchanged the product of breadth × depth? [END DELETE]
[*INSERT*] increasing only the breadth, not the depth? [END INSERT]
Anyway, more on generalization: In "A Guess at the Riddle" (1877–8
draft,
http://www.iupui.edu/%7Earisbe/menu/library/bycsp/guess/guess.htm and
Essential Peirce 1:273), discussing evolution, he wrote, "The
principle of the elimination of unfavorable characters is the
principle of generalization by casting out of sporadic cases,
corresponding particularly to the principle of forgetfulness in the
action of the nervous system." In 1903 in "Syllabus", Essential
Peirce 2:287,
http://www.commens.org/dictionary/entry/quote-syllabus-syllabus-course-lectures-lowell-institute-beginning-1903-nov-23-some,
Peirce said that there is a kind of abduction that concludes in a
_/generalization/_ from a surprising observation. This resembles
induction on the surface but one can see that it differs from
induction by originating an idea rather than testing an idea by
examining a fair sample; it also differs in that it adds something
(breadth) beyond that in the premisses but also omits something (some
of the characters or depth) that was in the premisses. This stuff is
interesting but generally the conceptions of inductive and
particularly abductive inference get slippery, as Houser noted about
abduction in "The Scent of Truth"
http://www.academia.edu/611929/The_scent_of_truth. Anyway, I was
alluding to my discussing recently on peirce-l the idea of
classifying basic inference modes by entailment relations or, to the
same effect, by truth/falsity preservativeness (basically by
compounding the deductive/ampliative distinction with a
repletive/attenuative distinction), but the result is un-Peircean in
defining four modes.
Best, Ben
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