Franklin, Jon, Cathy, Frederik, lists,
You're welcome, Franklin.
Generally, before we get too stuck on the issue of infinite or zero
breadth or depth, let's remember what Peirce is doing, actually using
those extremes to show the implications of the ideas. How many people do
that? Another way in which we don't have to get bogged down in exact
finite-numerical determination of breadth and depth is to consider
simply increases and decreases of breadth and depth and what, among
logical acts, those changes in parts or total amount of information
correspond to. An example of what Peirce _/does/_ with breadth and depth
is in a paragraph in "Upon Logical Comprehension and Extension" (1867)
http://www.iupui.edu/~peirce/writings/v2/w2/w2_06/v2_06.htm
<http://www.iupui.edu/%7Epeirce/writings/v2/w2/w2_06/v2_06.htm> . I have
broken the paragraph up to help the pattern become even clearer.
(Remember that Breadth a.k.a. Extension times Depth a.k.a. Comprehension
equals Area a.k.a. Information.)
It is only by confusing a movement which is accompanied with a
change of information with one which is not so, that people can
confound generalization, induction, and abstraction.
/Generalization/ is an increase of breadth and a decrease of depth,
without change of information. /Induction/ is a certain increase of
breadth without a change of depth, by an increase of believed
information.
[Well, that's a neat distinction; it clarifies why Peirce speaks of
verisimilar induction rather than inductive generalization, and
implies that induction is not attenuative but instead has its
premisses entailed by its conclusions, despite how Peirce's forms
for induction look. - BU]
/Abstraction/ is a decrease of depth without any change of breadth,
by a decrease of conceived information.
/Specification/ is commonly used (I should say unfortunately) for an
increase of depth without any change of breadth, by an increase of
asserted information.
/Supposition/ is used for the same process when there is only a
conceived increase of information.
/Determination,/ for any increase of depth.
/Restriction,/ for any decrease of breadth; but more particularly
without change of depth, by a supposed decrease of information.
/Descent,/ for a decrease of breadth and increase of depth, without
change of information.
[End quote]
When I first saw that years ago, I promptly made it into a table with
fields, and was only a little disappointed to find that Peirce had not
classified all possible combinations of increase / decrease of
comprehension and of extension. He was using the ideas of comprehension
and extension to classify logical acts already named in logical
tradition, and I thought, I'll figure out what logic acts correspond to
the remaining combinations, but I didn't soon figure it out and I
drifted to other subjects. My point is that Peirce was remarkably
productive at a philosophical-logic level with the ideas of breadth and
depth. Okay, I don't know that nobody before him had attempted that sort
of thing. But it's like walking into a room full of candy bars.
I'm not sure whether he stuck with that definition of determination.
Best, Ben
On 4/20/2015 8:38 PM, Franklin Ransom wrote:
And thanks to you too, Ben!
On Mon, Apr 20, 2015 at 8:31 PM, Benjamin Udell <[email protected]
<mailto:[email protected]> > wrote:
Franklin, Jon, lists,
Yep, that was me with Peirce's ∞'s and 0's of breadth and depth,
March 8, 2015, at the link:
https://www.mail-archive.com/[email protected]/msg03282.html
- Best, Ben
On 4/20/2015 7:42 PM, Jon Awbrey wrote:
Franklin, List,
I think that was Ben Udell.
Regards,
Jon
http://inquiryintoinquiry.com
On Apr 20, 2015, at 7:30 PM, Franklin Ransom wrote:
Cathy, Frederik, lists,
Yes, Frederik, that makes sense to me. As I mentioned in my
previous post, counting qualities or characters doesn't seem to
be helpful. Although it should be possible to enumerate them, to
a point, for the purpose of some inquiry.
As I recall, Jon Awbrey in the last month or two referenced a
text from Peirce about the multiplication of breadth and depth
using symbols like 1, 0, and the infinity loop, to distinguish
cases such as essential depth and breadth, substantial depth and
breadth, the idea of nothing, the idea of being, etc. If
infinity was indeed used then, Peirce had certainly contemplated
infinite depth and infinite breadth, although perhaps not simply
in the sense of counting with no end, but in the direct sense of
being that which is without limit, so depth without limit or
breadth without limit.
-- Franklin
On Mon, Apr 20, 2015 at 11:45 AM, Frederik Stjernfelt wrote:
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