[Inquiry] Re: Pure Symbols -- Discussion

Mon Mar 28 13:00:03 CST 2005

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PS.  Discussion Note 10

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JP = Jim Piat
JR = Joe Ransdell

JP: So it seems to me as well, but how then do we account for
    what Peirce said at the end of the quote provided by Gary.
    Do you think that perhaps the Peirce comment is misleading
    out of context?

JR: I believe Gary was overlooking the importance of what
    is happening in that context, Jim.  First, though,
    let me reproduce the quotation from Peirce:

CSP: | Every word is a symbol.  Every sentence is a symbol.
     | Every book is a symbol.  Every representamen depending
     | upon conventions is a symbol.  Just as a photograph is an
     | index having an icon incorporated into it, that is, excited
     | in the mind by its force, so a symbol may have an icon or an
     | index incorporated into it, that is, the active law that it is
     | may require its interpretation to involve the calling up of
     | an image, or a composite photograph of many images of past
     | experiences, as ordinary common nouns and verbs do;  or
     | it may require its interpretation to refer to the actual
     | surrounding circumstances of the occasion of its embodiment,
     | like such words as 'that', 'this', 'I', 'you', 'which', 'here',
     | 'now', 'yonder', etc.  Or it may be pure symbol, neither 'iconic'
     | nor 'indicative', like the words 'and', 'or', 'of', etc.
     |
     | C.S. Peirce, CP 4.447
     |
     |"Logical Tracts, No. 2" (c. 1903), in 'Collected Papers', CP 4.418-509.
     | http://www.existentialgraphs.com/peirceoneg/existentialgraphs4.418-529.htm

JR: The context is precisely a discussion of the various semiotical properties
    of one of the elements of his graphical logical system, namely, the line of
    identity, the larger context being his explanation of that system generally.
    The editors date it c. 1903.  Now there might be more than one way of construing
    logical connective terms like "and", "or", and "of", but to understand Peirce we
    have to bear in mind that he was very well acquainted with the terminist logic of
    the late medieval period and with the scholastic logican's practice of distinguishing
    between syncategorematic words such as those just mentioned, and categorematic words
    such as the common nouns and verbs, the proper names, the demonstrative pronouns and
    other referentially functioning words with which they -- the syncategorematic words --
    always appear in a complete sentence.  Calling them "syncategorematic" apparently
    conveyed the idea that they only perform their logical function (i.e. have symbolic
    meaning) as auxiliary somehow WITH the categorematic words.  I don't know how exactly
    they described the auxiliary function, but the point would be that the sign value --
    symbolic value -- depends essentially on their use with signs whose sign-value would
    be of the sort which is directly given by association with iconic and indexical
    functions, as described in that paragraph above.  Thus their "purity" as symbols
    would be owing to their distinctive functions in relating first of all to the
    words which are symbolic in a more fundamental way -- less pure -- in the sense
    that they directly involve iconic and indexical functions.  Thus he was not
    talking about absolute detachment of these "pure" symbols from the indexical
    and iconic but rather noting that they are of the peculiar class of symbols
    whose relation to the lattter is indirect, via the other class of symbols
    which they are in the service of somehow.  But they are as dependent on
    the iconic and indexical as are the signs upon which they depend.

Joe,

Familiar with the distinction I'm sure Peirce was -- adopt it as
his main account of logical operators I'm just as sure he did not.
Indeed, the principal employment of the "syncategorematic" dodge in
contemporary times has been as the last resort of the dyad-in-the-wool
syntacticists in denying an independent semantics to logical operators,
which they feel compelled to deny precisely on account of the fact that
the operational meaning -- the first approximation to a pragmatic meaning --
of these symbols affords the clearest and simplest examples of irreducibly
3-adic relations.

Incidentally, the invocation of higher intentional terms is precisely
'one of the ways' that Peirce extracted the concept of a "truth value".
"Considering the effects" of logical operators on these truth values
is 'one of the ways' of re-presenting them as having an independent
operational meaning, that being in terms of k-adic relations over
the truth-value domain B = {false, true}, constructions that are
these days known as "truth tables".  The binary connectives get
their operational meaning in terms of 3-adic relations over B,
and many of these are ireducibly 3-adic in a strong sense of
irreducibility.  That is one the main reasons for referring
to them as "pure symbols".

I will explain my emphasis on "one of the ways" another time.
Suffice it say that we ought to be wary of genetic fallacies.

Jon Awbrey

JR: I don't know how they typically thought of syncategorematic terms as doing this --
    there might be other ways of doing this -- but it seems to me the most natural
    way would have been to make use of the idea of them as being second intentional
    terms, which take first intentional (categorematic) terms as such as their object,
    which latter, in their turn, take non-signs (i.e. things not regarded as signs)
    for their objects.  And the crucially important thing in this case would be that
    second intentions refer to first intentions AS intentions, i.e. AS referential:
    the object of second intention thus can be said indifferently to be the first
    intention OR the nonintentional object which it is about, it really makes no
    difference how you construe it; i.e. the second intention's object is both
    the first intention AND its object AS so related to one another, in any case.
    If you were to pile a third intention on top of that -- and I have seen Peirce
    speak of "third intentions" -- it would be about the relation between the second
    intention and its referent, which is about the relation between a first intention
    and its referent,  and thus would have as its its referents the second intention,
    the first intention, and the nonintentional object of the latter.   Add a fourth
    intentional level and it would have four referents, never losing contact with the
    bottom level, and so forth.  Always, there is at the basis the first intention
    and its object, i.e. the categorematic symbol with its basic indexical and
    iconic functions.

JR: I don't know whether the scholastics ever got into levels higher
    than second intentional but Peirce at least dabbled with that idea.
    But wouldn't this raise the spectre of a possible out-of-control
    regression of higher and higher logical levels?  No, but I will have
    to explain why in a separate post.  The immediate and most important
    point -- in response to your question -- is that, construed this way,
    the second intentional (syncategorematic or pure symbols) would depend
    on the iconic and indexical every bit as much as the first intentional
    symbols (the categorematic terms) depend on them, and thus would be
    equally true regardless of how pure or superpure or supersuperpure
    the symbols became, because they would always be dependent on the
    icons and indices at the bottom.

JR: However, the relation to the iconic and indexical could be more direct
    than that at every successive level.   Thus if Peirce was thinking along
    these lines he might say -- this is just a possibility with some moderate
    degree of plausibility -- that the pure symbols must use icons and indices
    that exhibit and indicate the impure symbols, just as the impure symbols
    must use icons and indices to exhibit and indicate the non-signs (i.e.
    the entities not regarded AS signs) at the bottom.  And indeed in the
    next paragraph Peirce actually addresses this -- as it seems to me --
    in discussing the line of identity, a basic element in his graphical
    logic.  That is, he is treating the notational device as an expression
    of a "pure symbol" which, if construed as a second intention, could be
    seen to have a higher order iconic and indexical function just as the
    categorematic terms of which these are the representation depend upon
    iconic and indexical functions.  Clearly, as an example of a pure symbol --
    which is what the context suggests it is supposed to be -- it is being
    said to involve all three functions at once.  (The unpublished MS which
    this comes from is an exposition of his logical graph system circa 1903.)
     Thus he says of this notational element in his new graphical logic that:

CSP: | The value of an icon consists in its exhibiting the features of a state
     | of things regarded as if it were purely imaginary. The value of an index
     | is that it assures us of positive fact.  The value of a symbol is that it
     | serves to make thought and conduct rational and enables us to predict the
     | future.  It is frequently desirable that a representamen should exercise
     | one of those three functions to the exclusion of the other two, or two
     | of them to the exclusion of the third;  but the most perfect of signs
     | are those in which the iconic, indicative, and symbolic characters
     | are blended as equally as possible.  Of this sort of signs the line
     | of identity is an interesting example.  As a conventional sign, it
     | is a symbol;  and the symbolic character, when present in a sign,
     | is of its nature predominant over the others.  The line of identity
     | is not, however, arbitrarily conventional nor purely conventional.
     | Consider any portion of it taken arbitrarily (with certain possible
     | exceptions shortly to be considered) and it is an ordinary graph for
     | which Fig. 81 might perfectly well be substituted.
     |
     |                       ----is identical with-----
     |
     |                                 Figure 81
     |
     | But when we consider the connexion of this portion with a next
     | adjacent portion, although the two together make up the same graph,
     | yet the identification of the something, to which the hook of the one
     | refers, with the something, to which the hook of the other refers, is
     | beyond the power of any graph to effect, since a graph, as a symbol,
     | is of the nature of a law, and is therefore general, while here there
     | must be an identification of individuals.  This identification is
     | effected not by the pure symbol, but by its replica which is a thing.
     | The termination of one portion and the beginning of the next portion
     | denote the same individual by virtue of a factual connexion, and that
     | the closest possible;  for both are points, and they are one and the
     | same point.  In this respect, therefore, the line of identity is of
     | the nature of an index.  To be sure, this does not affect the ordinary
     | parts of a line of identity, but so soon as it is even conceived, [it
     | is conceived] as composed of two portions, and it is only the factual
     | junction of the replicas of these portions that makes them refer to the
     | same individual.  The line of identity is, moreover, in the highest degree
     | iconic.  For it appears as nothing but a continuum of dots, and the fact
     | of the identity of a thing, seen under two aspects, consists merely in the
     | continuity of being in passing from one apparition to another.  Thus uniting,
     | as the line of identity does, the natures of symbol, index, and icon, it is
     | fitted for playing an extraordinary part in this system of representation.
     | CP 4.448

JR: I probably explained this poorly, Jim, but I am saying that with his
    background in scholastic logic, something like this would be natural for
    him.  The higher order logical level gives the motivation for speaking of
    symbols of a special type, and it might or might not be congenial with the
    structure of intentionality (in the scholastic sense) to treat the higher
    level symbols as using higher level icons and indices -- it might be better
    not to do that -- I don't know -- but even if so that would not eliminate
    the dependence of the "pure" symbols from the indexical and iconic functions,
    in any case, .and my intention is merely to illustrate one possibility that
    he might have exploited in dealing with that formal problem.  I am sure
    there are still other ways in which the "purity"  of certain symbols could
    be duly noted without resort to what seems to me to be a senseless notion
    that some symbols don't require icons and indices in order to perform
    their function,.   Isn't that dependency what pragmatism is all about?

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