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

[Jon Awbrey]

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QUIPS.  Discussion Note 5

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BU = Ben Udell

Re: QUIPS-DIS 3.  http://stderr.org/pipermail/inquiry/2005-May/002604.html
In: QUIPS-DIS.    http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

Ben,

I continue from where I left off ...

BU: On the other hand, what sort of first-order information
    does a logical operator like "and" carry?  It seem more
    an operator on information than like information itself.
    Likewise words like "or" and "not".  This is related to
    the question of how one gets information-theoretically
    at the "psychological novelty" or "novel aspect" of a
    deductive conclusion.  There's no information in that
    conclusion except in a second-order sense, i.e., in
    the relatively novel combination of signs.  But this
    is the very viewpoint from which we seem confronted
    with second-order indexicality and second-order
    iconicity, though one might argue that this is
    just the level of qualisigns, not of the truly
    general legisign, which (according to Joe as
    versus Tom Short) is essentially the sign's
    acceptation, not merely the repeatedly
    instantiable form of a sign.

A sign bears information by virtue of reducing
our uncertainty about some object or objective.
That is how signs arise in the life of inquiry.
A sign like "and" is useful for indicating the
presence of a specific form of constraint that
affects the qualitative properties of a system.
By abstracting the form of constraint from its
particular contents, we arrive at the relation
among truth values that captures the basics of
logical conjunction.  We can tell that there's
information in the relation among truth values,
specifically, {t:t:t, f:t:f, f:f:t, f:f:f}, in
the usual way, because not everything that can
happen actually does, in other words, of the 8
possible 3-tuples only 4 occur in the relation.

BU: On the other hand, if the *bearing* or *carrying* of first-order information
    by a sign like "and" or "not" is questionable, then, still, what about a sign
    like "+"?  It does seem to tell us info, for instance in "5+7", that none of
    the 5 are among the 7.  Perhaps the "of" in "sum of" doesn't carry information
    but only operates on information?  Whatever the case there, still, more generally,
    mathematics does involve uncertainties, and does not seem to reduce to deductive
    logic.  But then to top it off, Jon sounds like he's hinting that he thinks that
    maybe symbols could denote or connote somewhat arbitrary things -- qualities or
    concrete things -- without indexical or iconic aid -- as if the "orbits" or
    "formal constraints" may reach much farther into the everyday idiosyncratic
    than is usually imagined.  Or instead perhaps Jon has only logical operators
    in mind?  Or only logical and mathematical objects?  But, in the case of
    mathematical objects, how will mathematical information be conveyed without
    the aid of mathematical diagrams (icons)?  Then again, Jon may mean mainly
    that the most general definitions of signs do not themselves compel symbols
    to be involved with icons and indices and that he is unsure and curious
    just where that leads, even if he grants that the natural way of symbols,
    in Peirce's view and in truth, is involvement with icons and indices.

The "of" that is used to paraphrase functional or relational
application or composition does indeed operate on information,
namely, the information that constrains or defines the values,
functions, or relations being combined, but it also embodies
information in its own right, since it combines these things
in accordance with constrained principles, or specific laws.
This is part of what is meant by the "laws of the symbol".

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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