[Inquiry] Re: Attribute, Impute, Represent -- Discussion

[Jon Awbrey]

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AIR.  Discussion Note 18

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JA = Jon Awbrey
KM = Kirsti Määttänen

Re: AIR-DIS 15.  http://stderr.org/pipermail/inquiry/2005-April/002571.html
In: AIR-DIS.     http://stderr.org/pipermail/inquiry/2005-April/thread.html#2566

In part:

JA: Here I have graver doubts.  It still seems to me, on the
    strength of other definitions of the sign relation, that
    a sign can bear information about an object without the
    involvement of adjunctive icons or indices of any sort.

KM remarks:

KM: An additional question to Jon:

KM: How does "of" (Peirce's example of a pure symbol)
    bear information about an object?  What kind of
    an object would it be?

Kirsti,

A good question!

>From the context in which he mentions it, that is, in the same breath
with the symbols for several other fundamental logical operators, one
may guess with some certainty that Peirce is referring to the English
paraphrase of what he more generally calls "relative multiplication".
This is the operation that we employ when we say "L of M", where the
slots of "L" and "M" are filled in either with the appropriate sorts
of relative and/or non-relative terms or with the types of relations
that naturally fit.  The operation of relative multiplication is
all at once a generalization of functional application, as when
we read "f(x)" as "f of x", functional composition, as when we
read "f o g" as "f of g", and ordinary multiplication, as we
see in phrases like "the double of x", "the triple of x",
and so on.

That will do for the first instalment,
as I have to take a break for a while.

Jon Awbrey

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