ONT Re: Tone, Token, Type

[Jon Awbrey <jawbrey@oakland.edu>]

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Our texts for today:

1870.  http://suo.ieee.org/ontology/msg04332.html
1883.  http://suo.ieee.org/ontology/msg03204.html

For ease of reference, I repeat here once again Peirce's remark
on the "doctrine of individuals", breaking it into smaller parts:

| 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).

Nota Bene.  On the square bracket notation used above:
Peirce explains this notation at CP 3.65 or 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.

Let me emphasize the following statements:

1.  The logical atom, or term not capable of logical division, must be
    one of which every predicate may be universally affirmed or denied.
    Such a term can be realized neither in thought nor in sense.

2.  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.

3.  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.

4.  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.

5.  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 [that the number
    of stipulated individuals that 'I' denotes is exactly one].

6.  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.

Jon Awbrey

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