ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 35
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Of course it is always possible that the whole collection of statements
that Peirce makes in the present context with regard to such things as
information, comprehension, extension, along with their relations to
one another, the lot of which we give the name of "theory" without
promising anything more than a nominal title, will turn out to be
inconsistent with each other, and thus our trials to find simple
intuitive models of this "theory" will have their difficulties
explained on account there being no models of any kind, simple,
intuitive, or otherwise. But I've learned to give Peirce the
benefit of the doubt in trials like these, so I will proceed
in a constructive vein, but keep a weather eye toward the
possibility of contrary evidence.
In that light, I need to examine another set of suggestive statements
that Peirce makes, again concerned with a principle of relativity, but
this time claiming that the distinction between individual and general
is relative to a context of discourse, which I take to be no different
from saying that it's relative to a particular form of interpretation.
There are hints of this idea in the Harvard and Lowell Lectures of 1865-66,
but a very clear discussion of it appears in the 1870 "Logic of Relatives":
| 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, 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, 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.
Additional excerpts and discussion with
respect to this topic can be found here:
DOI. Doctrine of Individuals
01. http://suo.ieee.org/ontology/msg04754.html
02. http://suo.ieee.org/ontology/msg04756.html
03. http://suo.ieee.org/ontology/msg04757.html
04. http://suo.ieee.org/ontology/msg04758.html
DOI. Doctrine of Individuals -- Commentary Notes
01. http://suo.ieee.org/ontology/msg04755.html
02. http://suo.ieee.org/ontology/msg04759.html
03. http://suo.ieee.org/ontology/msg04760.html
04. http://suo.ieee.org/ontology/msg04761.html
Jon Awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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