ONT Doctrine of Individuals
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Any genuine appreciation of what Peirce has to say about identity,
indices, names, proper or otherwise, and the putative distinctions
between individual, particular, and general terms will have to deal
with what he wrote in 1870 about the "doctrine of individuals".
Notice that this statement, together with the maxims
that "Whatever has comprehension must be general"
and "Whatever has extension must be composite",
pull the ruga -- and all of the elephants --
out from underneath the nominal thinker's
wishful thinking to find ontological
security in individual names, which
said nominal thinker has confused
with the names of individuals,
to turn a phrase back on same.
Jon Awbrey
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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.
|
| 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', Volume 9, pages 317-378, 26 January 1870,
|'Collected Papers' (CP 3.45-149), 'Chronological Edition' (CE 2, 359-429).
Note on the square bracket notation that was used above:
Peirce explains this notation at CP 3.65, cf. CE 2, 366.
| 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 that it denotes.
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