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

[Jon Awbrey]

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AIR.  Discussion Note 27

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JA = Jon Awbrey
KM = Kirsti Määttänen

Re: AIR-DIS 26.  http://stderr.org/pipermail/inquiry/2005-May/002637.html
In: AIR-DIS.     http://stderr.org/pipermail/inquiry/2005-May/thread.html#2637

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, 'Collected Papers', 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

KM: Having been off-line for a while, I'm now lost
    in the hundred or so unread mails.  I've read
    a couple of your subsequent mails (along with
    some of the discussion around pure symbols)
    responding to the question I posed, but
    I chose to respond to you starting from
    this one. 

KM: In response to:

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

KM: You wrote: 

JA: 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". 

KM: I was quite puzzled with your suggestion that Peirce
    is referring to relative multiplication.  As you know,
    formal logic is definitely not within my expertise, and
    the snippet from CP 4.447 cited on the list did not give
    a clue of reference to relative multiplication, with which
    you no doubt are like a fish in water.  I, for my part, am
    like a fish on dry land, unfortunately.

KM: On relative multiplication my memory of reading Peirce
    gives me nothing.  So, it cannot serve as a ground for
    mutually familiar examples.

Here is the beginning of a web-e-tude
on Peirce's 1870 "Logic Of Relatives":

LOR.  Logic Of Relatives
LOR.  http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750

LOR-COM.  Logic Of Relatives -- Commentary
LOR-COM.  http://stderr.org/pipermail/inquiry/2004-November/thread.html#1750

LOR-DIS.  Logic Of Relatives -- Discussion
LOR-DIS.  http://suo.ieee.org/ontology/thrd20.html#04460
LOR-DIS.  http://stderr.org/pipermail/inquiry/2004-November/thread.html#1768
LOR-DIS.  http://stderr.org/pipermail/inquiry/2005-January/thread.html#2301

The first mention of (relative) multiplication is here:

LOR 5.  http://stderr.org/pipermail/inquiry/2004-November/001754.html

The reason why Peirce doesn't always use the adjective "relative"
in front of the substantive "multiplication" is that he considers
this to be the more general and therefore the default case of the
concept, since the non-relative multiplications of all varieties,
including the logical conjunction denoted by "and", can all be
derived from the relative form of multiplication.

KM: To me the context of the snippet, laying down the basic conventions
    of the system of existential graphs, and within it in the context of
    describing the peculiar nature of the line of identity in Peirce's
    system of graphs, does not either give me any clue to why relative
    multiplication would be what Peirce is referring to.  Can you shed
    any light (preferably in manner a appropriate for ignorants) to
    this seeming mystery?

Although Peirce is engaged in explaining his existential graphs,
the subject matter is still just logic, and the paragraph above
is simply a capsule review of some basic facts about his theory
of signs, as it pertains to the subject of logic.  He begins by
instancing some hybrid cases, saying "a symbol may have an icon
or an index incorporated into it ..." -- he certainly missed an
opportunity to say "must" instead of "may" if he truly believed
that the catholic incorporation of icons and indices within the
fold of every symbol was a must-be rather than a may-be -- then
he gives abundantly clearly the alternative possibility, "Or it
may be pure symbol, neither 'iconic' nor 'indicative', like the
words 'and', 'or', 'of', etc."  If he had meant the word "pure"
in the sense of "original idea" instead of "deprecated replica",
then it fails to explain why he chose these examples instead of
a more random list of symbols.  Now, the identity relation does
happen to be the "identity" or "unity" operation with regard to
relative multiplcation (CP 3.68), but I wouldn't venture to say
that Peirce had this linkage in mind, at least, not consciously.

To be continued ...

Jon Awbrey

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