ONT Re: Information = Comprehension x Extension -- Discussion
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ICE. Discussion Note 2
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AK = Antti Karttunen
JA = Jon Awbrey
AK: About Peirce:
JA: here is where peirce comes in, defining a concept
of "information" and a measure |...| of information,
with |information| = |comprehension| x |extension|.
JA: another slightly mysterious thing he says is:
"information is superfluous comprehension".
AK: There is something which don't quite make me satisfied with
any of these "existential graphs", types and instances,
etc. Somehow they always feel something just "set up"
over a real world, making it more or less violence.
yes, the objective world is how it is, sandy or rocky,
but logic involves drawing lines in the sand and making
decisions that we will act one way or the other, but not
both, when the time comes to act. working back from the
moment of discrete action projects binary splits over all.
several things about the time order. peirce developed his
theory of information in the 1860's and later introduced a
primitive logarithmic measure for it based on combinatorial
principles. strictly speaking, the logical graphs, first the
"entitative graphs" and then later the dual "existential graphs",
were not developed until late in the 1890's. and you cannot take
sowa's current elaborations of "conceptual graphs" as an accurate
reflection of either peirce's system or his philosophy of logic.
peirce said that a conceptualist was just a confused nominalist,
for one thing. however, it is possible to see the beginnings
of the logical graphs in the variable binding schemes that
peirce used in his 1870 "logic of relatives" and also in
his discovery of the "amphecks" in 1880, that were much
later rediscovered by sheffer and called the "strokes".
i will attach the beginning of my notes on the
1870 LOR, and here is a note on the amphecks:
JA: ZOO Discussion 13. http://stderr.org/pipermail/inquiry/2003-November/000939.html
JA: LOR. http://stderr.org/pipermail/inquiry/2003-March/thread.html#184
JA: LOR. http://stderr.org/pipermail/inquiry/2003-April/thread.html#243
AK: Maybe because there are just a few very discrete,
well delineated things in the real world, before
it all gets diluted into a chaotic continuum.
yes, you can say that we "construct" the reals
from the dedekindest cuts, or you can say that
we merely "reconstruct" them thus in our minds.
take your pick, gimli ...
AK: (Or is it just that e.g. those Sowa's conceptual graphs resemble too
much of standard object-oriented programming paradigm to me, as in:
http://www.hum.auc.dk/cg/Module_I/1050.html
that I will get an immediate gut-reaction.)
AK: E.g. the physics at particle level seems to quite discrete, e.g. quanta,
and all the symmetry groups formed by subnucleonic particles like quarks
and so on (unless it is an artifact shaped by the modern perspective), which
is the ultimate reason (I think) that the elements really can be classified
so elegantly as Mendeleyev did (so we cannot slip to a complete nominalism!)
and furthermore this well-categorizable discreteness seeps through chemistry
to biology, where the underlying genetic code (which is just molecules!)
corresponds quite well with the idea of types (or classes or genera and
species, whatever) but even that would NOT be so, if all the intermediate
animals would still be living here, as Richard Dawkins has pointed out!
(E.g. would you give human rights to Australopithecus as well? With
whom it would be proper to procreate?)
AK: Also, the phases of the most substances like water are well-lineated
(the solid, the liquid and the gaseous plus maybe the plasma, actually
corresponding well with the four elements of the ancients. See the title
picture in Leibniz's dissertation...) so we can have concepts like "lake"
or "sea" or "island".
it is important to distingusish the "descriptive sciences" like
physics, chemistry, biology, psychology, even "ontology", from
the "normative sciences" logic, ethics, aesthetics. even when
they look at the same data, as logic and psychology often do,
they have different ends in view. logic purports to have
knowledge of how we "ought" to think if we desire to
achieve the ends proper to thinking, a portion of
which ends are to guide action for the sake of
our natural human interests. this is much
more involved that simply describing
how people think, with no concern
for better or worse.
AK: So, there really seems to be such things as "classes" or "types",
which are not just artefacts of a human mind. (which is a kind of
a pattern recognition network, specialized to classify perceptions
to certain categories?) and if I interpret Peirce right, this belongs
into the realm of Content, Comprehension and Depth, while the set of
instances (e.g. the animal individuals themselves) belong to the realm
of Sphere, Extension and Breadth.
discrete classification seems to be a backward projection
of the dichotomous choice involved in action. let us put
many-worlds interpretation of quantum mechanics aside for
now, since most of us still experience the need to choose.
like now, i must be off to sleep ...
jon awbrey
AK: (And there is something fishy here when I try to reconciliate these two realms.
Or maybe my thinking is just hopelessly corrupted by the standard OOP-dogmatism,
as is anybody's who is playing too much with computers?)
AK: So, when Peirce says that:
CSP: | Let us now return to the information. The information of a term
| is the measure of its superfluous comprehension. That is to say
| that the proper office of the comprehension is to determine the
| extension of the term. For instance, you and I are men because
| we possess those attributes -- having two legs, being rational,
| &c. -- which make up the comprehension of 'man'. Every addition
| to the comprehension of a term lessens its extension up to a certain
| point, after that further additions increase the information instead.
AK: I first thought naively, that "a certain point" is the point when
we have specified, say a man, up to a single individual, and then
the additional facts just elaborate his habitus,
AK: but then later, he says:
CSP: | You never can narrow down to an individual.
| Do you say Daniel Webster is an individual?
| He is so in common parlance,
| but in logical strictness he is not.
| We think of certain images in our memory --
| a platform and a noble form uttering convincing and patriotic words --
| a statue --
| certain printed matter --
| and we say that which
| that speaker and the
| man whom that statue
| was taken for and the
| writer of this speech --
| that which these are in
| common is Daniel Webster.
| Thus, even the proper name
| of a man is a general term or
| the name of a class, for it names
| a class of sensations and thoughts.
| The true individual term the absolutely
| singular 'this' & 'that' cannot be reached.
| Whatever has comprehension must be general.
AK: which is a kind of ... don't know a word for this
branch of thinking, but maybe "perceptual pluralism"
or such?
AK: So what is that "certain point" then?
AK: Then, interpreting this:
CSP: | 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.
AK: So, before knowing the truth about read and non-blue,
the blind man had a conceptual graph something like this:
color
/ \
/ \
/ non-blue
/ /
red /
\ /
\ /
non-blue red
AK: but after it, the lattice changes to:
color
| \
| \
| non-blue
| /
| /
|/
red (= non-blue red),
AK: as an arrow is added between non-blue and red,
and thus the "non-blue red" = glb(red, non_blue)
happens to be red itself.
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 you can compare
it with "red"? (What is "D-like" red, or
"Antti Karttunen-like red"?)
AK: Up till later, as so far I have printed and read only 17 pages of that
over hundred pages Peirce-notes you sent me. Sometimes his language is
quite hard to follow, but fortunately, "the logic of science" seems to be
translated to Finnish as well. Tomorrow I'll go again to the University
library in Helsinki, and get few other translations of Leibniz and Couturat.
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http://www.cs.bsu.edu/homepages/mighty/history.html
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