Gary R,
My responses interleaved.
} All particulars become meaningless if we lose sight of the pattern which they
jointly constitute. [M. Polanyi] {
<http://gnusystems.ca/wp/> http://gnusystems.ca/wp/ }{ Turning Signs gateway
From: Gary Richmond [mailto:gary.richm...@gmail.com]
Sent: 30-Dec-15 17:27
Gary F. list,
As we discussed off-list, I'll try to answer the questions you posed in your
post of 12/24, give you "the last word" in response if you'd like it, then move
this facet of the discussion off-list and, hopefully, to the 'mirror' thread,
hardly begun.
I'm away from my NYC apartment until 1/4, so I'll just give brief answers with
no textual support for now. As I noted earlier, trying to incorporate the
connection to the longish Peirce quotes you provided has, perhaps, slowed down
my response. However, since as you off-list suggested, those quotes may have
more to do with your interests than with mine, I won't much refer to them.
Also, this discussion seems to have moved on, and some of the comments by
myself and others in this and associated threads may have already offered at
least part of the answer to one of them. You wrote:
GF: In the case of the three trichotomies which you refer to as “this
particular trichotomy of trichotomies,” I’m not sure whether you meant “this
triad of trichotomies,” or are claiming that the three ‘parametric’
trichotomies represent a division of something else into three. (Or maybe
you’re just rhetorically elevating the status of this triad, as in the
expression “King of Kings”?) If you do regard them as a trichotomy (in the way
that icon/index/symbol is a trichotomy of the possible relations of the sign to
its object), then I’d like to know what it is that this meta-trichotomy divides
into three.
GR: As I've remarked in several posts this year and, really, over the years, I
use the term "trichotomy" exclusively in the sense of such tricategorial
divisions that Peirce describes in 'Trichotomic', 'A Guess at the Riddle', and
many other places. So, I do not mean simply "this triad of trichotomies," but,
indeed, "this trichotomy of tirchotomies."
GF: OK, so this trichotomy of trichotomies divides something into three, in the
sense that Peirce divides signs according to their mode of being to give three
types (qualisign/sinsign/legisign). But I still don’t see what you are dividing
into three to give the three trichotomies of signs in NDTR, or what the
parameter is according to which this thing is divided. (I am of course using
the word “thing” in the broadest possible sense, not limited to existing
things.)
GR: Still, it's possible that we are discussing, or perhaps emphasizing,
different things, you centered on the text of NDTR (which I was not in any of
my earlier posts in this thread), I on what I've been referring to as the nine
parameters of the three trichotomies.
GF: But the three trichotomies we’re talking about are the three which Peirce
defines in the text of NDTR, are they not? If not, then we shouldn’t be using
the same names for their members that Peirce gave for the three trichotomies of
signs in NDTR.
GR: So, employing the kind of diagram I typically do to show trichotomic
relations around a symbol I call the 'trikon', an equilateral triangle on its
side pointing to the right, where the three categories of a genuine trichotomic
(tricategorial) division are always in the same places, so:
1ns (firstness)
|> 3ns (thirdness)
2ns (secondness)
Although some do not agree, many Peircean semioticians consider a fundamental
semiotic trichotomy to be:
1ns (Sign = Representamen)
|> 3ns (Interpretant)
2ns (Object)
GF: Is this equivalent to Peirce’s statement that “A Representamen is the First
Correlate of a triadic relation, the Second Correlate being termed its Object,
and the possible Third Correlate being termed its Interpretant” (CP 2.242)? If
so, can we assume that “1ns” is inherent in the first correlate of any triadic
relation, “2ns” in the second correlate, and “3ns” in the third correlate? And
are these the same “Firstness, Secondness and Thirdness” which Peirce calls the
“elements of the phaneron”? I think we need answers to those questions in order
to consistently interpret these diagrams around the trikon, because it is not
at all obvious that the three categories as elements of the phenomenon are
exactly equivalent to the three correlates of a triadic relation.
GR: If one accepts that categorial division, then one can diagram the
trichotomy of trichotomies, yielding what I've termed the 9 parameters, as
follows:
As to the Sign itself:
1ns (Qualisign)
|> 3ns (Legisign)
2ns (Sinsign)
. . . . . . . . . . . .As to the Interpretant:
. . . . . . . . . . . .1ns (Rheme)
. . . . . . . . . . . . |> 3ns (Argument)
. . . . . . . . . . . .2ns (Dicent)
GF: Is this equivalent, in your view, to Peirce’s trichotomy “according as its
Interpretant represents it as a sign of possibility or as a sign of fact or a
sign of reason”? I don’t think so, and if I’m right, then it’s problematic for
you to use the same terms for the members of the trichotomy that Peirce uses.
But I’ll wait for your answer before explaining the difference I see.
As to the Object:
1ns (Icon)
|> 3ns (Symbol)
2ns (Index)
GF: Is this equivalent, in your view, to Peirce’s trichotomy “according as the
relation of the sign to its object consists in the sign's having some character
in itself, or in some existential relation to that object, or in its relation
to an interpretant”? I don’t think so, because your division is “as to the
Object” while Peirce’s is as to the relation of the sign to its object.
Divisions of sign types as to their objects are certainly possible — Peirce
gives two of them in his 1908 ten-trichotomy analysis — but that’s different
from what Peirce is doing to come up with this particular trichotomy. But maybe
you’re just using a kind of shorthand here, and it is the representamen’s
relation to the object that you are trichotomizing?
GR: There seems to be growing consensus on this list (and more generally) that,
whether you call these nine 'parameters', as I do, or 'TERMS', as does Jon,
they are most certainly not 'monadic signs' as Sung seemed to be arguing (I
discussed the ambiguousness, as I see it, of the term 'sign' in Peirce's usage
in another post).
As to your question regarding 'Involution' you wrote:
GF: Another term you’ll need to define is “involution.” Where Peirce uses this
term — notably in “The Logic of Mathematics” (c.1896) — it is implicitly
defined by being paired with “evolution,”
and you quoted several passages from that paper. For now I'll just say that my
understanding of what Peirce is getting at in these passages is that
'evolution'--and, as he's uses it in "The Logic of Mathematics," he is not at
all referring to his own agapastic theory of evolution (which follows a
different vectorial path), but, rather, of Hegel's dialectical one, which we
sometimes over-simplify as (and here I'll use 1st, 2nd, and 3rd (as distinct
from 1ns, 2ns, and 3ns which are abbreviations for the categories themselves),
to point to what in trikonic I refer to as a particular order of the paths, the
six possible 'vectors' through which one might 'pass' in a genuine
tricategorial relation):
GF: I think it’s clear that in the “Logic of Mathematics” (and in other papers
from around that time) Peirce is referring to logical (not biological or
cosmological) evolution and involution, which he explicitly equates with
logical synthesis and analysis respectively.
GR: Hegelian 'Evolution' (dialectical order):
1st, 1ns (Thesis)
|> 3rd, 3ns (Synthesis)
2nd, 2ns (Antithesis)
Although he does not give it in "The Logic of Mathematics," Peirce makes clear
elsewhere that his own version of this dialectical order is:
1st, 1ns (Something)
|> 3rd, 3ns (Medium)
2nd, 2ns (Other)
As I see it, in "The Logic of Mathematics" Peirce immediately offers the mirror
path to this order as 'Involution', and he strongly suggests that it is by
'involution' that one 'derives' the three categories, that is, by commencing at
thirdness (3ns):
Involution:
3rd, 1ns (Monad)
|> 1st, 3ns (Triad, involves Dyad and Monad)
2nd, 2ns (Dyad, involves Monad)
GF: Yes, and this confirms the equivalence of involution and analysis (as
opposed to synthesis). Thirdness involves secondness and secondness involves
firstness, thus we can by prescission abstract both secondness and firstness
from the thirdness of the phenomenon by analyzing the universal phenomenon.
Yes, of course there's a seeming contradiction, he remarks, because in
vectorial progression one 1st, commences at 3ns (and this, he suggests, is what
makes categorial thinking so difficult for even--and especially, he says--the
best and strongest minds). So, as I see it, for him this vector represents a
way of representing how the categories are derived. (This can be nothing more
than a brief sketch here, so I am hoping that we'll be able to discuss it
further in the 'mirror' thread, along with other mirrored paths.)
GF: OK, and I hope my questions can help to fill out the sketch.
Gary f.
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to peirce-L@list.iupui.edu . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to l...@list.iupui.edu with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
