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
On 11/1/2015 11:43 PM, Franklin Ransom wrote:
Ben, list,
With respect to the logic of relatives, I don't have much to say.
Perhaps as I work through Vol. 3 and 4, I'll have something to say.
As for deduction and the state of information, what I recall is that
since information applies to natural classes, and not artificial
classes, an actual change must occur through synthetic inference. I
had something of a disagreement with Frederik Stjernfelt during the
seminar on this point, i.e. about whether artificial kinds can have
information or not; in his early work, Peirce is clear that only
natural kinds can have information (Frederik believes this untenable).
Yet it is clear that we can apply deduction to artificial kinds. The
idea with deduction is that it can make ideas clearer or more distinct
with respect to one another, but it can never change the state of
information. So when a term's meaning is restricted (as you say,
deductive conclusions have less information than their premisses),
this doesn't change the state of information itself; nothing is lost
or gained in the overall state. Notice that information and logical
quantity are not co-extensive--we can think of logical breadth and
depth analytically, without reference to synthetic propositions, as we
do in the case of artificial classification.
From Peirce, "Upon Logical Comprehension and Extension", the sixth
section or 'paragraph':
In the case of deductive reasoning it would be easy to show, were it
necessary, that there is only an increase of the extensive
distinctness of the major, and of the comprehensive distinctness of
the minor, without any change in information. Of course, when the
conclusion is negative or particular, even this may not be effected.
Meaning, of course, that not even increases in distinctness may occur
when the conclusion is negative or particular. In any case, change in
distinctness is not change in information. Perhaps, if we wanted to
contemplate possible changes, or as Peirce puts it, 'conceived'
changes, we could do that, but they would still not be actual changes
in information. It's also not clear that such conceived changes would
be deductions anyway.
Ben, you said:
I don't think Peirce was restricting scientific method's use of
induction to qualitative induction, he was just saying that it was
the most usual kind of induction, and elsewhere he says that, among
kinds of induction, it has the most general utility.
Yes, I get that (I guess I didn't get that across in my last post). I
don't think I'd realized before that qualitative induction has the
most general utility, and don't recall reading that before. But it is
clear that is what he means in this passage, and it is somewhat
enlightening for me.
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?
Franklin
On Sun, Nov 1, 2015 at 6:39 PM, Benjamin Udell wrote
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