Cf:http://inquiryintoinquiry.com/2015/06/28/relations-their-relatives-10/
Re:http://inquiryintoinquiry.com/2015/05/01/peirces-1880-algebra-of-logic-chapter-3-%E2%80%A2-comment-7-5/
Jeff, List,
I think I've refreshed enough of the little gray cells
to recall what I was trying to say back in May, and so
I'll make some attempt to answer your questions now.
First let me quote the full paragraph in question:
> Looking back from the ascent we see that the two-point universe
> {I, J} manifests a type of formal degeneracy (loss of generality)
> compared with the three-point universe {I, J, K}. This is due to
> the circumstance that the number of “diagonal” pairs, those of the
> form A:A, equals the number of “off-diagonal” pairs, those of the
> form A:B, so the two-point case exhibits symmetries that will be
> broken as soon as one adds another element to the universe.
There are two types of symmetry that we might be talking about
in the present setting and it behooves us not to confuse them:
1. There is the symmetry of the pairs of the form A:A
versus the asymmetry of the pairs of the form A:B.
2. There is the number of pairs of the form A:A
versus the number of pairs of the form A:B
and whether those numbers are equal or not.
The type of symmetry (“sameness in measure”) motivating
the above observation is the second type, the fact that
the numbers of pairs on and off the diagonal are equal.
That is the symmetry that will be broken when we pass
from the 2-point universe to the 3-point universe.
Enough for now ... Back later ...
Jon
On 6/27/2015 12:16 PM, Jon Awbrey wrote:
Jeff, List,
There appears to be a problem with the Gmane archive that I ordinarily use
in search of lost times and thoughts out of mind … and this is the time of
year when my brain runs out of steam anyway … and it may be a while before
I can get completely up to speed on this subject again … so I'll just post
a few thoughts off the top of my head …
What prompted me to my series of comments on Selection 7
(chapt. 3 sec. 4) was a very important remark that Peirce
made in passing, so smoothly so that it was all too easy
to miss its significance, namely, this:
<quote>
The forms of general relatives are of infinite variety,
but the following may be particularly noticed.
Relatives may be divided into those all whose individual aggregants
are of the form A : A and those which contain individuals of the form
A : B. The former may be called concurrents, the latter opponents.
</quote>
As I commented before, this tells us that Peirce understands the distinction
between general dual relatives and individual dual relatives, the individuals
being “aggregated” or logically summed to form the generals, and that singling
out special cases of general relatives in the way he does next is but a first
rough cut toward a complete classification. This needs to be born in mind as
we proceed toward the enumeration of triadic relations and beyond, especially
as it affects the classification of triadic sign relations.
Alright, that should recall some of the context.
To be continued ...
Jon
On 6/24/2015 6:42 PM, Jeffrey Brian Downard wrote:
Jon, Lists,
It appears that I somehow missed your May post on Chapter 3,
so thank you for re-sending the link to comment 7.5. You make
quite a number of interesting points, one of which is future
looking. You say: "Looking back from the> ascent we see that
the two-point universe ... manifests a type of formal degeneracy
(loss of generality) compared with the three-point universe....
This is due to the circumstance that the number of “diagonal”
pairs (in the two-point case) exhibits symmetries that will be
broken as soon as one adds another element to the universe."
The diagram you offer at the end nicely illustrates how those
symmetries are broken. I'm wondering if you might be able to
say a bit more about what kinds of symmetries are being broken --
and why those kinds of symmetries are lost and not others.
I feel that this should be obvious to me -- and that I should
be able to answer the question myself -- by I'm finding it to
be a bit of a challenge.
--Jeff
Jeff Downard
Associate Professor
Department of Philosophy
NAU
(o) 523-8354
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