ONT Re: Information = Comprehension x Extension -- Discussion
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
ICE. Discussion Note 51
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
HT = Hugh Trenchard
JA = Jon Awbrey
Re: ICE Discussion 50. http://suo.ieee.org/ontology/msg05369.html
Copied here:
JA: There's a reason why the issues that Antti Karttunen raised about
particulars and properties and the issues that Jack Park raised
about subjects and topics came together in my mind to remind
me of the issues that Charles Sanders Peirce raised about
the interrelations of information, logic, and signs.
JA: At least, I think there is.
JA: The connection seems to be that they all have to do with this question:
| If we know something K_1 about a bunch of things X_1
| and we know something K_2 about a bunch of things X_2,
| will we know something K_3 about a bunch of things X_3?
JA: I have deliberately left some wiggle-room in the question
for who exactly gets to specify the items of knowledge and
the bunches of things in question, but that is basically it.
JA: I will make a determined effort to focus on this question from here on out.
JA: In fact, come to think of it, let me dub this the "question of determination" (QUOD).
QV. Determination. http://suo.ieee.org/ontology/thrd59.html#02377
HT responds:
HT: Although I realize the QUOD is going to prove vastly
more complicated than it sounds, springing to my mind
are the following situations in which knowledge of two
disparate systems results in knowledge of a third,
seemingly independent system (if this is even a
accurate summation of your statements, which
I recognize may not be the case).
HT: 1. If X_1 and and X_2 contain any common elements
which may also be common to X_3.
HT: 2. If some or all the elements of X_1 and X_2 interact in any way
which gives rise to novel properties (emergent phenomena) which
be describable as X_3; even if X_3 is chaotic and the precise
nature of X_3 is not predictable from the independent elements
in X_1 and X_2 in isolation, there may be some features of the
emergent properties that we can know.
HT: 3. If X_1 and/or X_2 contain implied information about X_3.
HT: 4. If X_1 and/or X_2 are in a quantum entangled state with X_3.
Hugh,
It has proved unusually difficult for me to maintain my concentration
on the main issues here. That is not unlike one of the problems that
many people have reading Peirce -- you read some bit that sounds like
'une idée très bonne' and suddenly it's thirty years later and you're
still trying to work out little more than the first few practical and
theoretical upshots of the whole big idea.
So I tried the harrowing classical strategy of staking out an overwide
horizon in 20-mule team and bone-headed ploughman-like manner, but the
thing to do next, having laid out the land in this hubristling fashion,
is to get back to the truck farm and start growing some trucks for the
next trip on the road to you know where.
For all sorts of reasons I can't say what's generally true of everything
that's suggestible by my deliberately vague statement of the main theme,
but I can give moderately concrete examples of many relatively familiar
things that I intended to fall under its tent.
Example 1. The thing about transitivity.
In particular, the intransitive relation
of set-theoretic membership "in" and the
transitive relation of inclusion "c".
What's up with that?
My last best attempt at seeing what is
really going on with that bit was here:
ICE Dis 39. http://suo.ieee.org/ontology/msg05329.html
Copied here:
JA: One of the ways of trying to make sense of such outlandish notions as
"currently noted property of x" and "discourse relative property of x"
is to augment suitably basic 2-adic relations with an extra parameter --
let us say, "instance of" and "implier of" on the logical side of the
ledger, and "element of" and "subset of" on the set-theoretic account --
thus ending up with 3-adic relations that we might symbolize this way:
Relative instantiation. j : x is y
Relative implication. j : x => y
Relative membership. j : x in y
Relative inclusion. j : x =c y
JA: In each case, we can leave the interpretation of
the "interpretive parameter" j relatively loose
for the moment, tying it to its own context of
interpretation, not to be recursive about it,
but just to be flexible in pragmatic terms.
JA: For example, j might be taken as an agent, a community, or a context,
and the context might be cultural, discursive, environmental, or any
other factor affecting the interpretation of signs that anyone might
think to conceive.
JA: Under the "agent interpretation", one might then read these expressions,
just by way of giving some possible illustrations, in any of these ways:
Relative instantiation. j : x is y. "j says x is y"
Relative implication. j : x => y. "j knows x implies y"
Relative membership. j : x in y. "j thinks x is a member of y"
Relative inclusion. j : x =c y. "j believes x is a subset of y"
JA: At the outset our task would be to identify the formal, generic, or structural
principles that are common to the whole variety of specialized interpretations,
only after that project was well under way trying to enumerate their diversity.
With that review, let me try to explain, next time,
how this question looks from the perspective of my
hyper-magnetically encompassing theme.
Jon Awbrey
P.S. I didn't think I should copy the whole Global Brain list
on those essays in "Differential Logic", but I am putting the
re-writes of the current series here:
DLOG A. http://suo.ieee.org/ontology/thrd1.html#05359
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o
http://www.cs.bsu.edu/homepages/mighty/history.html
o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o~~~~~~~~~o