[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 33

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AB = Auke van Breemen
JA = Jon Awbrey

Re: Pure Symbols And Pure Copulants -- Discussion
Cf: QUIPS-DIS 32.  http://stderr.org/pipermail/inquiry/2005-May/002716.html
In: QUIPS-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

Auke, Peirce Listers,

Replies inter-plied infra.

AB: My sympathy in the past discussion on pure symbols has been on both sides.

Then you have my sympathy!

AB: So, the attempt to reconcile both perspectives formed the background
    of my mail on symbols and symbolical relations.  In hard to decide
    cases like this I discovered in the past that it can be helpful
    to go to the Welby classification since Peirce relocated and
    added some semeiotic distinctions in that exchange of idea's.
    The subject of the past discussion could have been a reason
    for Peirce to add such a distinction.  I paste the first
    four triads, those that pertain to the sign in itself
    and to the relation between sign and its objects.

    1st, According to the Mode of Apprehension of the Sign itself,
    2nd, According to the Mode of Presentation of the Immediate Object,
    3rd, According to the Mode of Being of the Dynamical Object,
    4th, According to the Relation of the Sign to its Dynamical Object,

AB: The forth triad is the well known one that gives the iconical,
    indexical, and symbolical relation of the sign to the object.
    The second triad looks like an attempt to settle the issue
    of symbols vs symbolical relations.  It seems that the
    copulants possess much, if not all, of the characters
    that have been attributed (by Peirce and Jon) to pure
    symbols.  This would mean that Peirce himself used
    symbol to cover different issues at the same time
    and that, in the Welby exchange, he had an occasion
    to settle this issue in line with his triadic system.
    The quote from Jon is from the pure symbol discussion
    and serves the purpose of connecting that discussion
    to the 2nd triad.

AB, quoting JA:

JA: If I had to pick a better word than "pure" for this,
    I might have chosen "primitive", in the formal sense
    that suggests "basic", "fundamental", "irreducible".
    Thus, in geometry, the concepts of points and lines
    are primitives, undefined in absolute terms, though
    characterized in relation to each other, and further
    in terms of the particular geometry that they support,
    as specified by the particular set of axioms in force.

AB: Some ten years before the 'Tractatus' was being finished Peirce wrote:

CSP: | On the other hand [is] the distinction of 'Designatives' such as
     | concrete subjects of signs or essentially nominative signs, [and]
     | 'Descriptives' such as Predicates and Predicative Signs (such as a
     | portrait with a legend designating the person represented), [with]
     | Abstract nouns to be reckoned among Descriptives.  The copulants are
     | likewise indispensable and have the property of being 'Continuant'.
     | What I mean is that the sign "A is red" can be decomposed so as
     | to separate "is red" into a Copulative and a Descriptive, thus:
     | "A possesses the character of redness."  But if we attempt
     | to analyze "possesses the character" in like manner, we
     | get "A possesses the character of the possession of the
     | character of Redness';  and so on 'ad infinitum'.  So it
     | is, with "A implies B", "A implies its implication of B",
     | etc.  So with "It rains and hails", "It rains concurrently
     | with hailing", "It rains concurrently with the concurrence
     | of hailing", and so forth.  I call all such sign Continuants.
     | They are all Copulants and are the only 'pure' copulants.
     | These signs 'cannot be explicated':  they must convey
     | Familiar universal elementary relations of logic.
     | We do not derive these notions from observation,
     | nor by any sense of being opposed, but from our
     | own reason.  This trichotomy, then, sustains
     | criticism and must be marked ([mu]) at least.
     | I would mark it ([delta]) if I were satisfied
     | with the distinction between Descriptives and
     | Denominatives.
     |
     | C.S. Peirce, 'Collected Papers', CP 8.352

Yes, I think that these passages are very pertinent.
What Peirce calls "continuous predicates" in another
letter to Lady Welby (14 Dec 1908) have come up once
or thrice before in this connection, and these appear
to be pretty much the same things what he is calling
"continuants" here.

Jon Awbrey

Cf: Continuous Predicates and Hypostatic Abstraction
At: http://stderr.org/pipermail/arisbe/2001-April/000429.html

| When we have analyzed a proposition so as to throw into the subject everything
| that can be removed from the predicate, all that it remains for the predicate to
| represent is the form of connection between the different subjects as expressed in
| the propositional 'form'.  What I mean by "everything that can be removed from the
| predicate" is best explained by giving an example of something not so removable.
| But first take something removable.  "Cain kills Abel."  Here the predicate
| appears as "--- kills ---."  But we can remove killing from the predicate
| and make the latter "--- stands in the relation --- to ---."  Suppose we
| attempt to remove more from the predicate and put the last into the form
| "--- exercises the function of relate of the relation --- to ---" and then
| putting "the function of relate to the relation" into a another subject leave
| as predicate "--- exercises --- in respect to --- to ---."  But this "exercises"
| expresses "exercises the function".  Nay more, it expresses "exercises the function
| of relate", so that we find that though we may put this into a separate subject, it
| continues in the predicate just the same.  Stating this in another form, to say that
| "A is in the relation R to B" is to say that A is in a certain relation to R.  Let
| us separate this out thus:  "A is in the relation R^1 (where R^1 is the relation
| of a relate to the relation of which it is the relate) to R to B".  But A is
| here said to be in a certain relation to the relation R^1.  So that we can
| expresss the same fact by saying, "A is in the relation R^1 to the relation
| R^1 to the relation R to B", and so on 'ad infinitum'.  A predicate which
| can thus be analyzed into parts all homogeneous with the whole I call
| a 'continuous predicate'.  It is very important in logical analysis,
| because a continuous predicate obviously cannot be a 'compound'
| except of continuous predicates, and thus when we have carried
| analysis so far as to leave only a continuous predicate, we
| have carried it to its ultimate elements.  (SW, 396-397). 
|
| C.S. Peirce, "Letters to Lady Welby", pp. 380-432 in:
| Philip P. Wiener (ed.), 'Charles S. Peirce, Selected Writings',
| Dover Publications, New York, NY, 1966.  Originally published as:
|'Values in a Universe of Chance', Doubleday & Co., New York, NY, 1958.

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