ONT Re: Information = Comprehension x Extension -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ICE. Discussion Note 3
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
AK = Antti Karttunen
JA = Jon Awbrey
i forgot to attach my script for
the "lord of the relatives",
so i will do it now.
interspersals and continuation below.
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.
JA: 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.
JA: 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".
JA: 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.
JA: 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.
JA: take your pick, gimli ...
another way to see the practical necessity of categorical coding --
by the way, "code" <- cauda = trucated tree trunk used as a slate,
compute <- putare = to prune and to graft, tally <- talea = twig --
is to view it as a relation between the world of infinite sources
and the creature of finite re*sources. by pigeonhole principle,
the creature is forced to make infinite re*use of finite means.
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.)
i think that if existential graphs were done right, it would equip us
with a medium for doing logical analysis and declarative programmming
all in one, but we have yet to see that.
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".
JA: 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.
one of the reasons that moderns and even some post*moderns have
trouble understanding folks like leibniz and even descartes is
due to the attempt of their immmediate followers to hack apart
the descriptive and normative facets of their work, due partly
to the lack of comprehension that these epigones had for the
normative aspect, which they could only disparage as being
"teleological". indeed, a lot of the normative thinking
of both leibniz and descartes is coded up in "theology",
which the normatively-challenged find it near impossible
to decode. descartes presents the most extreme case
of a thinker who hacked up his own work out of fear
of what happened to galileo.
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.
yes, some insight into this can be gained from
his "note on a limited universe of marks":
LMU. http://stderr.org/pipermail/inquiry/2003-April/thread.html#396
JA: 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.
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?)
back when oops started, it was just a heuristic strategy
that was dual to pops (procedure oriented programming).
before there got to be language regimes dedicated to
enforcing it rigidly, to the perverse exclusion of
every other strategy, it was a healthy alternative,
often used in a mixed bag of methods that could be
adapted to the problem of the moment. at any rate,
it seems like yet another one of those wave-particle
things that shouldn't be forced one way of the other.
and then, functional programming style was always the
more inclusive strategy that got ignored in the process.
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,
one way to think of this "superfluous comprehension" is in terms of quotients.
when we have a syntactic domain L, say, all the wffs in some formal language,
and then we take the quotient L/E of L by some equivalence relation E, say,
logical equivalence of expressions in L, then the extent to which we have
many different ways of expressing the same logical proposition gives us
a certain redundancy factor.
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?
this has to do with peirce's criticism of the "doctrine of individuals".
he is really saying that it would take in general an infinite amount of
information to pin down a logical atom, a genuine individual, but that
in practice we never have that much information, so we always work with
conventional atoms or nominal individials, those that we agree to split
no further hairs about, relative to a particular context of discussion.
DOI. http://stderr.org/pipermail/inquiry/2003-April/thread.html#401
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
http://www.cs.bsu.edu/homepages/mighty/history.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o