Gary R., Gary F., lists,
A little more on what happened to the abstract and singular symbols.
The singular symbol / the subindex designates, names, or says 'this' or
'that', etc. Earlier Peirce had accounted those functions as indexical.
In 1885 he said that demonstrative and relative pronouns and some other
things that he later called subindexes are nearly pure indices:
The index asserts nothing; it only says "There!" It takes hold of
our eyes, as it were, and forcibly directs them to a particular
object, and there it stops. Demonstrative and relative pronouns are
nearly pure indices, because they denote things without describing
them; so are the letters on a geometrical diagram, and the subscript
numbers which in algebra distinguish one value from another without
saying what those values are.
('On the Algebra of Logic: A Contribution to the Philosophy of
Notation', W 5:162-3, 1885
https://web.archive.org/web/20130301083318/http://www.helsinki.fi/science/commens/dictionary.html
(Commens's new site is temporarily down for maintenance)
In "Sundry Logical Conceptions" (1903) in EP 2, he introduces ideas of
the singular symbol and the subindex, which seem to be the same thing.
According to that text, the symbol is always a general, the index is
always an individual. In "Nomenclature" (1903) in EP 2, he introduces
the idea of the indexical legisign, which will let us use the type-token
(legisign-sinsign) division with indices like 'this'.
In the Dec. 24 1908 draft letter to Lady Welby on the ten trichotomies,
Peirce has a trichotomy consisting of (1) the descriptive sign, (2) the
designative/denominative sign, and (3) the copulant/distributive sign.
To keep a long story short, that alone tells you that the classification
will result either in iconic and indexical designatives, or in indexical
and symbolic designatives. According to Peirce's tentative
co-classifications in that letter, the result is iconic and indexical
designatives, and no symbolic designatives. Of course, Peirce did not
complete the ten trichotomies to his own satisfaction, so far as we now.
Here's an image http://lyris.ttu.edu/read/attachment/2204107/2/10ad5.GIF
of some of Peirce's co-classifications in the Dec. 24, 1908 letter,
consisting of, first, an illustration of his famous co-classifications
of the members of the three sign-trichotomies in "Nomenclature" (1903);
second, an illustration of his expanded co-classification including the
old three now numbered 1st, 4th, and 9th, by Peirce, along two new
trichotomies numbered 2nd & 3rd by Peirce, in which I stick to the
numbering of the trichotomies; and, finally, an illustration of those
same co-classifications by Peirce but with the trichotomies re-ordered
(3, 2, 1, 4, ...9) so that the lines indicating Peirce's
co-classifications follow the pattern of the standard three trichotomies.
As to what happened to the abstract symbol: In a previous post, I
mentioned that Peirce got into the abstract/concrete issue in the ten
trichotomies. The sign trichotomy abstractive-concretive-collective
consists in signs classified by the mode of being (phenomenological
category) of their object. (The abstractive sign is a sign of a quality
or possibility, the concretive sign is the sign of an individual, a
fact, etc., and so on.). According to Peirce's tentative
co-classifications in the Dec. 24, 1908 letter, an abstractive sign is
always a descriptive qualisign icon. So, there's no getting an abstract
symbol by that route. Yet obviously a word like 'redness' is a symbol
and refers to an abstraction of a quality. I guess the real question in
terms of "Sundry Logical Conceptions" (in "Syllabus", 1903), is, if the
singular and abstract symbols were both degenerate symbols, what about
afterward, when the idea of the singular symbol seems to have absorbed
back into the idea of the index via the idea of the indexical legisign?
Well, I don't know.
Best, Ben
On 10/1/2014 6:48 PM, Benjamin Udell wrote:
Gary R., Gary F., lists,
Yes, I think that the subindex is the singular symbol. Well, I can't
say, for example, that Peirce didn't have in mind more than one kind
of singular symbol, but I found no textual evidence for that. Anyway
the singular symbol is a sign for an individual thing, and is singular
in the same sense as a name like 'Socrates' is said in standard logic
to be a singular term - not because the symbol or term itself is a
singular object, but instead because it refers to a singular object.
It really seems like the subindex, which, Peirce said, is not an
individual. The simplest explanation is that the subindex is the
singular symbol. I remember years ago looking very hard for a passage
where comes out and says so, but I didn't find one.
Personal names, demonstratives, designations, etc., things that Peirce
had customarily classified as indices but then classified instead as
subindices in MS 478 (third section of "syllabus" - "Sundry Logical
Conceptions"), are once again classified as indices in his writings
after MS 478. So he quite seems to have dropped the non-index subindex.
I said that I wasn't sure that he stuck with the idea of the singular
symbol. If he flatly identified it as the subindex, then I'd say that
he dropped it. I don't know what he did with the abstract symbol,
which I take to include abstract terms like 'redness'. Peirce was very
likely aware of a traditional division of terms in logic into singular
and general and into concrete and abstract, and he gets into the
concrete/abstract thing in his ten sign-trichotomies.
Best, Ben
On 10/1/2014 5:41 PM, Gary Richmond wrote:
Ben, Gary F, lists,
So, putting your posts together, Ben, I think that you're saying that
the *Singular Symbol* is better understood as the "Subindex" (you
earlier remarked that Peirce didn't stick with the Singular Symbol
notion)? Or are they equivalent terms?
And what do you make of the "Abstract Symbol" in the same sentence in
which the "Singular Symbol" occurs?
Here are the Subindices quote followed by the Singular/Abstract
Symbol quote again for ready reference for whomever may be interested
in this analysis.
Subindices or Hyposemes are signs which are rendered such
principally by an actual connection with their objects. Thus a
proper name, personal demonstrative, or relative pronoun or the
letter attached to a diagram, denotes what it does owing to a
real connection with its object but none of these is an Index,
since it is not an individual. CP 2.284
There are two kinds of degenerate symbols, the Singular Symbol
whose Object is an existent individual, and which signifies only
such characters as that individual may realize; and the Abstract
Symbol, whose only Object is a character. CP 2.293
Best,
Gary
*Gary Richmond
Philosophy and Critical Thinking
Communication Studies
LaGuardia College of the City University of New York
C 745
718 482-5690*
On Wed, Oct 1, 2014 at 2:00 PM, Benjamin Udell wrote:
Gary R., Gary F., lists,
I'm not sure that Peirce stuck with his idea of a Singular Symbol.
CP 2.293-4 is from the "Syllabus" (circa 1902, according to the CP
editors). In a "Syllabus" passage - the one on subindices a.k.a.
hyposemes, dated 1903, he said that indices are individuals - he had
not embraced the idea of the indexical legisign yet.
[Quote]
_/Subindices/_ or _/hyposemes/_ are signs which are rendered
such principally by an actual connection with their objects.
Thus a proper name, [a] personal demonstrative, or relative
pronoun or the letter attached to a diagram, denotes what it
does owing to a real connection with its object but none of
these is an Index, since it is not an individual.
[1903 | Syllabus: Syllabus of a course of Lectures at the Lowell
Institute beginning 1903, Nov. 23. On Some Topics of Logic | EP
2:274]
I dimly remember another passage touching on this issue in
"Syllabus" but it's been years and years.
Best, Ben
On 10/1/2014 1:04 PM, Gary Richmond wrote:
Gary F, lists,
Gary wrote that in rereading the Speculative Grammar part of the
Syllabus that this struck him:
GF: that the interpretant of a dicisign or proposition
represents the sign itself as well as its object, and
represents it as an /index/ — which, strictly speaking, lacks
the /generality/ which makes the argument a symbol and thus
more genuine.
I think that your rewording /is/ helpful (but then see the CP
2.293-4 quoted below which tends to complicate the matter for me);
and, further, that your notion that the reason that Peirce did so
much self-rewording was "to get through to the real, general,
genuine Thought that was . . . a piece of the Truth" and not a more
(mere) personal expression of it, makes good sense. I'm not sure
that his re-wordings /always/ made his thinking more transparent,
but often enough they did.
You also asked why I thought that Peirce's comment that "A proof or
genuine argument is a mental process which is open to logical
criticism"
GR: . . . is in any way incompatible with the notion that the
dicisign might be described as 'degenerate' relative to the
argument.
First, would you say that a 'proof' is but a species of genuine
argument? While it makes a kind of sense to me to say that the
dicisign is degenerate relative to the argument, I wonder if this
isn't straining Peirce's terminology a bit. Perhaps I was thinking
that Peirce speaks in places of degenerate symbols /per se/. For
example:
. . . while the complete object of a symbol, that is to say,
its meaning, is of the nature of a law, it must denote an
individual, and must signify a character. A genuine symbol is a
symbol that has a general meaning. There are two kinds of
degenerate symbols, the Singular Symbol whose Object is an
existent individual, and which signifies only such characters
as that individual may realize; and the Abstract Symbol, whose
only Object is a character. CP 2.293
I think the meaning here is fairly clear, that there is one kind of
genuine symbol (one having a "general meaning"--but that would seem
to apply to symbols other than the 'proof' would it not?) and two
kinds of degenerate symbols, the Singular (its object being an
individual) and the Abstract (its object being a character). But in
speaking of" the immediate interpretant of an index," Peirce goes
on to say:
Although the immediate Interpretant of an Index must be an
Index, yet since its Object may be the Object of an Individual
[Singular] Symbol, the Index may have such a Symbol for its
indirect Interpretant. Even a genuine Symbol may be an
imperfect Interpretant of it. So an icon may have a degenerate
Index, or an Abstract Symbol, for an indirect Interpretant, and
a genuine Index or Symbol for an imperfect Interpretant. CP 2.294
I'm having considerable difficulty parsing this second paragraph,
especially as to how he's using the terms 'imperfect' and
'indirect' (as opposed to 'intended'?) But it seems to me that it
might be important--especially in getting at the concept of
"genuine"--to try to grasp Peirce's meaning here.
Best,
Gary R
*Gary Richmond
Philosophy and Critical Thinking
Communication Studies
LaGuardia College of the City University of New York
C 745
718 482-5690*
On Wed, Oct 1, 2014 at 11:31 AM, Gary Fuhrman wrote:
-----------------------------
PEIRCE-L subscribers: Click on "Reply List" or "Reply All" to REPLY ON PEIRCE-L
to this message. PEIRCE-L posts should go to [email protected] . To
UNSUBSCRIBE, send a message not to PEIRCE-L but to [email protected] with the
line "UNSubscribe PEIRCE-L" in the BODY of the message. More at
http://www.cspeirce.com/peirce-l/peirce-l.htm .
