ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 7
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| The fog comes
| on little cat feet.
|
| It sits looking
| over harbor and city
| on silent haunches
| and then moves on.
|
| Carl Sandburg, "Fog", 1916
AK = Antti Karttunen
CSP = C.S. Peirce
JA = Jon Awbrey
AK: But this puzzles me:
CSP: | In the same way, when he learns that 'D' is red,
| the term 'D-like red' becomes equivalent to 'red'.
AK: Because here D belongs to the realm of
Sphere, Extension, and Breadth, so how
can you compare it with "red"? (What is
"D-like" red, or "Antti Karttunen-like red"?)
JA: my guess is that "x-like" means "having all of the discourse-relative
or currently noted properties of x". but we have in this discourse
currently noted only the property Red of D, or properties that are
immediate implications of that. in effect, D serves merely as
yet another exemplar of the quality Red, as that is all the
information that we have of it.
JA: more generally, peirce's use of "particulars" and "properties" is more
like particles and waves than the usual hard lines that the descent of
mind that de-evolved from atomic logicism imagines it can draw between
absolute individuals and absolute predicates.
it's a thing i've been looking for an excuse to get back to,
and the occasion of your remark provides as good a catalyst
as any i've seen lately for getting around, back, down tuit.
and let me invent a not-so-subtle subtitle for it that i'll
design to startle if not to shock, and that is a little bit
that i'd like to call "peirce-heisenberg uncertainty" (phu),
and by this phu to say that c.s. peirce in 1865 had already
discovered by sheer logical detection and lectured publicly
on all of the principal principles of the later-to-be-great
uncertainty principle. in effect, it says that information
is the only "symmetry invariant meaning" (sim) that we have,
that it can be cast to moderate and relative extents, never
to absolute degrees, as information about individuals or as
information about qualities, but only in a trade-off within
the quantity of information that avails itself at any given
moment, though the quantity and quality of information will
of course be free to vary from moment to moment in due time.
i will copy this to the global brain list, because it bears
on some discussion there about the "limits of localization".
one more alias: the "folly of particles and waves" (fopaw).
let us begin by returning to the text and the context of your puzzlement:
ICE. http://stderr.org/pipermail/inquiry/2003-March/thread.html#194
ICE 19. http://stderr.org/pipermail/inquiry/2003-March/000212.html
| To explain this, we must remember that the process of induction is a
| process of adding to our knowledge; it differs therein from deduction --
| which merely explicates what we know -- and is on this very account called
| scientific inference. Now deduction rests as we have seen upon the inverse
| proportionality of the extension and comprehension of every term; and this
| principle makes it impossible apparently to proceed in the direction of
| ascent to universals. But a little reflection will show that when our
| knowledge receives an addition this principle does not hold.
|
| Thus suppose a blind man to be told that no red things are
| blue. He has previously known only that red is a color;
| and that certain things 'A', 'B', and 'C' are red.
|
| The comprehension of red then has been for him 'color'.
| Its extension has been 'A', 'B', 'C'.
|
| But when he learns that no red thing is blue, 'non-blue'
| is added to the comprehension of red, without the least
| diminution of its extension.
|
| Its comprehension becomes 'non-blue color'.
| Its extension remains 'A', 'B', 'C'.
|
| Suppose afterwards he learns that a fourth thing 'D' is red.
| Then, the comprehension of 'red' remains unchanged, 'non-blue color';
| while its extension becomes 'A', 'B', 'C', and 'D'. Thus, the rule
| that the greater the extension of a term the less its comprehension
| and 'vice versa', holds good only so long as our knowledge is not
| added to; but as soon as our knowledge is increased, either the
| comprehension or extension of that term which the new information
| concerns is increased without a corresponding decrease of the other
| quantity.
|
| The reason why this takes place is worthy of notice. Every addition to
| the information which is incased in a term, results in making some term
| equivalent to that term. Thus when the blind man learns that 'red' is
| not-blue, 'red not-blue' becomes for him equivalent to 'red'. Before
| that, he might have thought that 'red not-blue' was a little more
| restricted term than 'red', and therefore it was so to him, but
| the new information makes it the exact equivalent of red.
| In the same way, when he learns that 'D' is red, the
| term 'D-like red' becomes equivalent to 'red'.
|
| Thus, every addition to our information about a term is an addition
| to the number of equivalents which that term has. Now, in whatever
| way a term gets to have a new equivalent, whether by an increase in
| our knowledge, or by a change in the things it denotes, this always
| results in an increase either of extension or comprehension without
| a corresponding decrease in the other quantity.
|
| For example we have here a number of circles
| dotted and undotted, crossed and uncrossed:
|
| (·X·) (···) (·X·) (···) ( X ) ( ) ( X ) ( )
|
| Here it is evident that the greater the extension the
| less the comprehension:
|
| o-------------------o-------------------o
| | | |
| | dotted | 4 circles |
| | | |
| o-------------------o-------------------o
| | | |
| | dotted & crossed | 2 circles |
| | | |
| o-------------------o-------------------o
|
| Now suppose we make these two terms 'dotted circle'
| and 'crossed and dotted circle' equivalent. This we can
| do by crossing our uncrossed dotted circles. In that way,
| we increase the comprehension of 'dotted circle' and at the
| same time increase the extension of 'crossed and dotted circle'
| since we now make it denote 'all dotted circles'.
|
| CSP, CE 1, pages 463-464.
|
| Charles Sanders Peirce,
|"The Logic of Science, or, Induction and Hypothesis",
| Lowell Institute Lectures of 1866, pages 357-504 in:
|
|'Writings of Charles S. Peirce: A Chronological Edition',
|'Volume 1, 1857-1866', Peirce Edition Project,
| Indiana University Press, Bloomington, IN, 1982.
that's the set-up, the spike may take some time to accumulate.
jon awbrey
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http://www.cs.bsu.edu/homepages/mighty/history.html
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