|
Jon,
A key term in the passage
below is "discourse" or "a particular point of view". The notion of
a formal context from Formal Concept Analysis may adequately
represent this idea. To review, a formal context is a triple
- (FormalObjects, FormalAttributes,
incidence)
where FormalObjects is a set of "formal
objects" (they can be anything, and in particular can be logical molecules
capable of further division or resolution in yet another formal context),
FormalAttributes is a set of "formal attributes" (they also can be
anything, and in particular may include only a few of the possible
properties of the formal objects), and a binary relation incidence
between formal objects and formal attributes.
Robert E. Kent
----- Original Message -----
Sent: Monday, November 27, 2000 7:14
PM
Subject: SUO: Doctrine Of
Individuals
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'A
Simple Desultory Philippic'
| 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 of 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.
|
| [ Note. Previously in this text, Peirce writes (CP
3.65):
| |
| | | 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 just the
number of individuals that it denotes.
| ]
|
| 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'
('to atomon')
| and 'singular' ('to kath ekaston'); 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).
|
| 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', Vol. 9, pp.
317-378, 26 January 1870;
| 'Collected Papers' (CP 3.45-149);
'Chronological Edition' (CE 2, 359-429).
Incidental
Musements:
http://www.songfta.com/songs/songindex.html
http://www.songfta.com/songs/pssb-asdp.html
http://imv.aau.dk/~jfogde/lyrics/parsley.html
http://members.nbci.com/elstongunn/simple.html
http://www.songfta.com/songs/X0008_asimpledesultory.html
http://www.stockmail.ru/~simon/acc/acc.asp?title=a-simple-a
http://www.stockmail.ru/~simon/acc/acc.asp?title=a-simple-b
More,
Later,
Jon
Awbrey
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