Individuality, Identity, Teridentity

[Jon Awbrey]

Ontology, Systems, Structure Lists —

Some problems can't be solved in the paradigms where they first appear,
which is why we keep recurring to them without quite freeing ourselves
from the loops in which they ensnare us. Questions about the supposed
uniqueness of supposed individuals and the dyadic relation of identity
are as old as the ship of Theseus and the morning and evening star(s)
we steer by.

Peirce, of course, took another course ...

As fortune has it, I find myself waylaid between bouts of travel, with
promises to keep when it comes to Peirce's information formula, so let
me leave this for now with a link to one of the most critical passages
in all of Peirce's explorations:

C.S. Peirce • Doctrine Of Individuals
http://intersci.ss.uci.edu/wiki/index.php/C.S._Peirce_%E2%80%A2_Doctrine_Of_Individuals

<QUOTE>

In reference to the doctrine of individuals, two distinctions should be borne in mind.
The logical atom, or term not capable of logical division, must be one of which every
predicate may be universally affirmed or denied. For, let A be such a term. Then,
if it is neither true that all A is X nor that no A is X, it must be true that some
A is X and some A is not X; and therefore A may be divided into A that is X and
A that is not X, which is contrary to its nature as a logical atom.

Such a term can be realized neither in thought nor in sense.

Not in sense, because our organs of sense are special — the eye, for example, not
immediately informing us of taste, so that an image on the retina is indeterminate
in respect to sweetness and non-sweetness. When I see a thing, I do not see that it
is not sweet, nor do I see that it is sweet; and therefore what I see is capable of
logical division into the sweet and the not sweet. It is customary to assume that
visual images are absolutely determinate in respect to color, but even this may be
doubted. I know no facts which prove that there is never the least vagueness in
the immediate sensation.

In thought, an absolutely determinate term cannot be realized, because, not being
given by sense, such a concept would have to be formed by synthesis, and there would
be no end to the synthesis because there is no limit to the number of possible predicates.

A logical atom, then, like a point in space, would involve for its precise determination
an endless process. We can only say, in a general way, that a term, however determinate,
may be made more determinate still, but not that it can be made absolutely determinate.
Such a term as “the second Philip of Macedon” is still capable of logical division — into
Philip drunk and Philip sober, for example; but we call it individual because that which
is denoted by it is in only one place at one time. It is a term not absolutely indivisible,
but indivisible as long as we neglect differences of time and the differences which accompany
them. Such differences we habitually disregard in the logical division of substances. In the
division of relations, etc., we do not, of course, disregard these differences, but we disregard
some others. There is nothing to prevent almost any sort of difference from being conventionally
neglected in some discourse, and if _I_ be a term which in consequence of such neglect becomes
indivisible in that discourse, we have in that discourse,

[I] = 1.

This distinction between the absolutely indivisible and that which is one in number from
a particular point of view is shadowed forth in the two words individual (τὸ ἄτομον) and
singular (τὸ καθ᾿ ἕκαστον); but as those who have used the word individual have not been
aware that absolute individuality is merely ideal, it has come to be used in a more general
sense.

(CP 3.93, CE 2, 389–390).

</QUOTE>

Charles Sanders Peirce, “Description of a Notation for the Logic of Relatives,
Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”,
Memoirs of the American Academy, Volume 9, pp. 317–378, 26 January 1870,
Collected Papers (CP 3.45–149), Chronological Edition (CE 2, 359–429).

Note. On the square bracket notation used above: Peirce explains this notation at CP 3.65.

<QUOTE>

I propose to denote the number of a logical term by enclosing the term in square brackets, thus, [t].

The number of an absolute term, as in the case of I, is defined as the number of individuals it denotes.

</QUOTE>

The document history on that page contains links to a number of earlier discussions
on the predecessors of our current ontology list, various collateral lists, and the
lists where I kept copies of my own posts. Here's just the first few:

===2000 • Conceptual Graphs List===

* http://web.archive.org/web/20020322102614/http://www.virtual-earth.de/CG/cg-list/msg03592.html

===2002 • Ontology List • Selections & Comments===

* http://web.archive.org/web/20070629181450/http://suo.ieee.org/ontology/thrd23.html#04332
# http://web.archive.org/web/20070226082502/http://suo.ieee.org/ontology/msg04332.html
# http://web.archive.org/web/20070226082513/http://suo.ieee.org/ontology/msg04348.html
# http://web.archive.org/web/20070226082523/http://suo.ieee.org/ontology/msg04352.html
# http://web.archive.org/web/20070226082537/http://suo.ieee.org/ontology/msg04353.html
# http://web.archive.org/web/20070226082547/http://suo.ieee.org/ontology/msg04354.html
# http://web.archive.org/web/20070226082625/http://suo.ieee.org/ontology/msg04363.html

Later ...

Jon

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