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

[Jon Awbrey]

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QUIPS.  Discussion Note 10

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JA = Jon Awbrey
JR = Joe Ransdell
JW = Jim Willgoose

I will replicate in this context some remarks that
I made in a related connection, correcting a few
typos and adding some additional explanation.

I am using the term "pure symbol" in one of the particular senses and
usages that Peirce made of it, namely, to denote a symbol that does not
have an icon or an index "incorporated" into it, meaning that the active
law that the symbol is does not require its interpretation to "involve"
the calling up of an icon or an index, in other words, "a pure symbol",
neither iconic nor indicative, like the words 'and', 'or', 'of', etc."
The verbose equivalent, "symbols that involve no icons or indices",
is too cumbersome to use all the time, and the more handy acronym
for the same thing, STINIOI, has met with stylistic objections.
The fact that the same term is apparently used, even by Peirce,
in several different senses, does present problems in reading,
but if we let persistent misinterpretation deter us from the
useful senses of words, we will quickly lose all our senses.

Re: "Passage on Diagrammatic Reasoning From MS 293" (see below).

As a person who has taken a special interest in graphical syntaxes for logic,
including most especially Peirce's, for almost 40 years now, I am gratified
to see them geting some general attention.  Some of the most characteristic,
distinctive, insightful, farsighted features of Peirce's whole approach to
logic can be found with especial saliency in these graph-theoretic forms.

In its bearing on the existence of pure symbols, the conclusion is the same.
There are such things as symbols that do not incorporate icons and indices
in their basic function as symbols, indeed, some of the most genuine types
of signs, in the sense that that their interpretation is wholly independent
of anything but the fact that they do get interpreted to mean what they do,
are most evident in Peirce's graphical syntaxes for logic.

The fact that composite and hybrid symbols exist
does not imply that pure symbols do not exist.
The fact that compostite and hybrid symbols are
important and interesting does not imply that
pure symbols are not important or interesting.

The fact that pure symbols combine with all types of signs
to form complex types of expressions with their own types
of informative meaning does not mean that the pure symbols
which are thus combined do not have their own connotations
and denotations.

Jon Awbrey

Previously:

JW: I have been following the discussion of pure symbols for awhile
    and thought I may have detected some sources of potential confusion.
    First, a token is sometimes understood as a symbol (especially early on).
    But if a token is thought of as a part of the 1st trichotomy of signs,
    then one could be led to think of the analysis of a symbol in terms
    of that trichotomy only.  Second, Peirce discusses 2nd intentional
    logic in NLC . But there, the indices of a term taken in 2nd intention
    are quite different from the 1st intentions of that term.  If they were
    not different, there would be no point to the distinction. In effect,
    terms taken in 2nd intention do not have 1st intentional objects as
    their object. For instance, I can specify a rule for the use of the
    term "Man" and compose an index made up of instances of the term.
    Yet there is no evidence until I turn to the 1st intention of the
    term. But the 1st intention of the term "Man" is not the same sort
    of index as a mere list of symbol-tokens of a type.  Furthermore,
    there is nothing in the shape or color of any of the tokens to
    indicate the 1st intention of the term "Man."    Pure symbols
    fail to furnish evidence (of the right sort).

JW, quoting CSP:

| No Symbol can do more than apply a "rule of thumb" resting as it does entirely
| on Habit (including under this term natural disposition);  and a Habit is no
| evidence.  I suppose it would be the general opinion of logicians, as it
| certainly was long mine, that the Syllogism is a Symbol, because of its
| Generality. But there is an inaccurate analysis and confusion of thought
| at the bottom of that view;  for so understood it would fail to furnish
| Evidence.  (MS 293)

JW: In CP 4.447, Peirce uses more obviously pure symbols such as "or" and "and."
    But the previous analysis by way of 2nd intentions makes the same point.
    An index composed of pairs of instances (or "blanks" in the algebra of
    logic) without the evidence afforded by a diagram assigning truth values
    or otherwise exhibiting the transformation (1st intentions) fails to
    provide evidence. I think that formation rules for syntax and the
    practical necessity of considering a type of symbol, however,
    may count towards examples of  pure symbols.

JR: The long paragraph which follows below is from a Peirce manuscript,
    MS 293, dated by Robin as c. 1906.  It is also referred to as "PAP"
    from an acronym used by Peirce himself for "Prolegomena to an Apology
    for Pragmaticism".  This paragraph is quoted by Frederik Stjernfelt
    in his paper "Diagrams as Centerpiece of a Peircean Epistemology",
    'Transactions of the C.S. Peirce Society', XXXVI No. 3, Summer 2000,
    357-392.

JR: Stjernfelt's paper is basically a careful and highly sophisticated
    critical commentary on this paragraph, in which Peirce provides an
    account of how the interpretation of a diagram works, using the
    technical terms he began to develop extensively in his late work.
    I cite it here in part because of its obvious theoretical interest,
    but also to help explain why I think it so important to understand
    how symbolism works in co-operative relationship to iconism and
    indexicality.  I would not myself attempt to unpack it analytically
    here, apart from consideration of how Stjernfelt does this in his
    paper; but I think something can be learned about Peirce's semeiotic
    just by reading carefully through this illustration of it.  Stjernfelt
    is, I believe, at the University of Copenhagen.

JR, quoting CSP:

| To begin with, then, a Diagram is an Icon of a set of rationally related
| objects. By 'rationally' related, I mean that there is between them, not
| merely one of those relations which we know by experience, but know not how
| to comprehend, but one of those relations which anybody who reasons at all
| must have an inward acquaintance with. This is not a sufficient definition,
| but just now I will go no further, except that I will say that the Diagram
| not only represents the related correlates, but also, and much more
| definitely represents the relations between them, as so many objects of the
| Icon. Now necessary reasoning makes its conclusion 'evident'. What is this
| "Evidence"? It consists in the fact that the truth of the conclusion is
| 'perceived', in all its generality, and in the generality of the how and the
| why of the truth is perceived. What sort of Sign can communicate this
| Evidence? No index, surely, can it be; since it is by brute force that the
| index thrusts its Object into the Field of Interpretation, the
| consciousness, as if disdaining gentle "evidence". No Symbol can do more
| than apply a "rule of thumb" resting as it does entirely on Habit (including
| under this term natural disposition); and a Habit is no evidence. I suppose
| it would be the general opinion of logicians, as it certainly was long mine,
| that the Syllogism is a Symbol, because of its Generality. But there is an
| inaccurate analysis and confusion of thought at the bottom of that view;  for
| so understood it would fail to furnish Evidence. It is true that ordinary
| Icons -- the only class of Signs that remain for necessary inference --
| merely suggest the possibility of that which they represent, being percepts
| 'minus' the insistency and percussivity of percepts. In themselves, they are
| mere Semes, predicating of nothing, not even so much as interrogatively.  It
| is, therefore, a very extraordinary feature of Diagrams that they 'show' --
| as literally 'show' as a percept shows the Perceptual Judgment to be true --
| that a consequence does follow, and more marvelous yet, that it 'would'
| follow under all varieties of circumstances accompanying the premisses. It
| is not, however the statical Diagram-icon that directly shows this; but the
| Diagram-icon having been constructed with an intention, involving a Symbol
| of which it is the Interpretant (as Euclid, for example, first announces in
| general terms the proposition he intends to prove, and then proceeds to draw
| a diagram, usually a figure, to exhibit the antecedent condition thereof)
| which Intention, like every other, is General as to its Object, in the light
| of this Intention determines an Initial Symbolic Interpretant. Meantime, the
| Diagram remains in the field of perception and imagination; and so the
| Iconic Diagram and its Initial Symbolic Interpretant taken together
| constitute what we shall not too much wrench Kant's term in calling a
| 'Schema', which is on the one side an object capable of being observed while
| on the other side it is General. (Of course, I always use 'general' in the
| usual sense of general as to its object. If I wish to say that a sign is
| general as to its matter, I call it a Type, or Typical.) Now, let us see how
| the Diagram entrains its consequence. The Diagram sufficiently partakes of
| the percussivity of a Percept to determine, as its Dynamic, or Middle,
| Interpretant, a state [of] activity in the Interpreter, mingled with
| curiosity. As usual, this mixture leads to Experimentation. It is the normal
| Logical effect; that is to say, it not only happens in the cortex of the
| human brain, but must plainly happen in every Quasi-Mind in which Signs of
| all kinds have a vitality of their own. Now, sometimes in one way, sometimes
| in another, we need not pause to enumerate the ways, certain modes of
| transformation of Diagrams of the system of diagrammatization used have
| become recognized as permissible. Very likely the recognition descends from
| some former Induction, remarkably strong owing to the cheapness of mere
| mental experimentation. Some circumstance connected with the purpose which
| first prompted the construction of the diagram contributes to the
| determination of the permissible transformation that actually gets
| performed. The Schema 'sees', as we may say, that the transformate Diagram
| is substantially contained in the transformed Diagram, and in the
| significant features to it, regardless of the accidents -- as, for example,
| the Existential Graph that remains after a deletion from the phemic Sheet is
| contained in the Graph originally there, and would do so whatever colored
| ink were employed. The transformate Diagram is the Eventual, or Rational,
| Interpretant of the transformed Diagram, at the same time being a new
| Diagram of which the Initial Interpretant, or signification, is the Symbolic
| statement, or statement in general terms, of the Conclusion. By this
| labyrinthine path, and no other, is it possible to attain to Evidence;
| and Evidence belongs to every Necessary Conclusion. (Quotation from
| Eisele 1976, pp. 316-19)
|
| C.S. Peirce, "PAP", MS 293 (1906), NEM 4, pp. 316-319
|
| [Prolegomena for an Apology to Pragmatism], MS 293 (1904), pp. 313-330 in:
| Carolyn Eisele (ed.), 'The New Elements of Mathematics by Charles S. Peirce,
| Volume 4, Mathematical Philosophy', Mouton, The Hague, 1976.

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