[Inquiry] Doctrine of Individuals

[Jon Awbrey]

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DOI.  Note 1

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| 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 sweetUess 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.
|
| C.S. Peirce, 'Collected Papers', CP 3.93

Peirce defines the "number" ['t'] of a logical term 't' as follows:

| I propose to assign to all logical terms, numbers;  to an absolute term,
| the number of individuals it denotes;  to a relative term, the average
| number of things so related to one individual.  Thus in a universe of
| perfect men ('men'), the number of "tooth of" would be 32.  The number
| of a relative with two correlates would be the average number of things
| so related to a pair of individuals;  and so on for relatives of higher
| numbers of correlates.  I propose to denote the number of a logical term
| by enclosing the term in square brackets, thus ['t'].
|
| C.S. Peirce, 'Collected Papers', CP 3.65

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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