ONT Re: Fuzzy Stuff
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Stan Salthe wrote (SS):
Jon Awbrey wrote (JA):
SS: Well, I am just (as one interested in probing the internalist predicament) roughly
classifying what you are saying into the exo/endo dichotomy. Internalism is very
broad, with many previous threads leading into it, so there can be more than one
position concerning it. Basically, it is the attempt to model systems as if the
modeler were inside them, and so is prohibited many of the usual scientific tricks,
like measuements from several instances or locales, or global models (as in classical
thermodynamics).
JA: I guess that I just don't get it. We commonly assume a cosmos that all of us are "inside",
but in practice we very often have to work with isolated systems that are "outside" of us,
but inside the universe, the same universe that we are inside. The in-teresting question
for me is how do we come to construe these ex-ternal systems from out of our ex-perience.
SS: Yes, that is the standard logical and scientific standpoint.
Internalism has a different aim. So, I was wrong then that
you seemed to be interested in internalist constructions.
JA: I remember reading some stuff on "internal realism" in Hilary Putnam's papers,
but it was not one the things that stuck in my mind. Is that what you mean?
I am sure that I still have those books somewhere. But I am afraid that
I tend to go by that old adage that: "An ism never did much for science,
except for prism". It may be that I spent too much time in a couple
of settings where folks did almost nothing but sit around and gossip
about what ism had been "discredited" that week. You may have noted
that I avoid even the terms "pragmatism" and "pragmatist" in favor
of "pragmatic thinking" and "pragmatician". It may seem like such
a trivial punctilio but I am convinced that keeping "pragmatic" in
its place as an adjective will prevent it from getting the big head
of most other substantive doctrines, and "pragmatician", analogous
to "mathematician" and "mortician", is calculated to remind us that
our salvation depends on good works and not faith alone --- plus it
serves as a beneficial memento mori to remind us of our fallibility.
JA: Side question: Are you using "generativity" in the sense of Chomsky?
SS: You decide -- I mean by a generative system or situation
one from which new, unpredictable situations may arise.
JA: I call that "reality".
SS: Well, if you stick with externalist constructions, then internalism
sounds just like (I would say) actuality -- the territory instead
of a map. But internalism is trying to construct new kinds of maps.
SS: A truly generative system generates new rules along with
new permutations on the old ones.
JA: Well, there is always this distinction to be made between
the rules that reality really follows, that may have been
fixed from the beginning, for all we know, and the rules
that we know that explain some portion of our ration of
reality, that are generally forever de-&-re-generating.
SS: Well, it seems to some of us possibly worth while to think about
making a model that could itself be truly generative. Of course,
it could not be based upon the usual scientific (two-valued) logic.
^^^
JA: ---------|||-------------------------------------------------------
JA: So then it's the same as what it's not?
Then how will I ever choose between it?
The two-valor bit comes not from logic
but from a need to make dicisive picks,
unless you really believe that you can
jump on your horse and ride off in all
directions at once. I'm afraid that's
a horse of a whole utter wave-function.
SS: It is not, I think, clear that in [internalist] discourse the kind of
choice you refer to can be represented. Different choices would not,
I think, be available to the system AS choices. "Hints of forms", OK,
"confusion", OK, "conception" and "birth", yes, "hints" perhaps. So,
"distinction" -- definitely not. No distinctions would be available
internally in my view.
JA: Perhaps I just do not understand this way of talking.
We are born into experience and borne into experience.
There are so many distinctions that arise in experience,
pain and pleasure, and so on, and so on, ..., and sooner
or later some of us will construe or derive these other
distinctions, like external and internal, and who knows
what all, for who knows what purpose within experience.
SS: We can make these distinctions because we are entrained by languages
and (two-valued) logic. We are looking for a more general logic,
from which two-valued could be derived for/by mechanistic systems.
JA: No, I have to go with Herr Doctor Sigismund Freud on this:
We are capable of being entranced by our mutter tongue and
our vatter brine because we enjoy and unjoy so intimately.
SS: Distinctions are pre-eminently externalist things. They are too crisp
for vague internality. Vague groping guided by tendencies, OK. Fuzzy
distinctions might be more believable.
JA: Again, I am not sure what all is being suggested here -- I was hoping to give up
the discussion of fuzzy concepts to a more disentangled thread, as I threaded to
do with that old post on "Fuzzy Stuff" -- but I think that these issues are what
drives me to use various families and sundry samples of triadic sign relations
as my conceptual framework of choice. Here, the "object domain" contains any
old thing that we purport to make an object of "discussion and thought" (DAT),
the domains of signs and interpretant signs contain the signs and mental ideas
that we use to talk about and to think about the objects of the object domain.
JA: One of the pursuits on which I wasted a good deal of my all too wasted youth
was a desperate search for almost any alternative to "establishment" versions
of logic and set theory, and so I "experimented" with just about every brand
of what was in those lazy hazy days called "deviant logic" that came off the
wagon from our Ol' Academus's Farm to hit the dim streets of our Alley Agora,
from the milder mixes of quantum logic to the uncrispy fritters of fuzzy sets.
But that was yesterday, and yesterday's gone, and now I have settled back to
classical logic and classical music, and cannot remember what all the fuzz
was about. So I have not thought about these fuzzy general quantum vague
issues for quite some time, and mostly I am left with the impression that
if I had understood information and uncertainty better then I never would
have felt the need to wander down these interminable and meandering roads.
JA: But if Peirce really thought that generality and vaguity were worth spending
a spell of his thinking time on, then I guess that I would be duty bound to
expend a second or a third thought on them. So here are a couple of pieces
that he wrote on these subjects, which I thought that I might pass your way,
to see what you think.
| Accurate writers have apparently made a distinction
| between the 'definite' and the 'determinate'. A subject
| is 'determinate' in respect to any character which inheres
| in it or is (universally and affirmatively) predicated of
| it, as well as in respect to the negative of such character,
| these being the very same respect. In all other respects it
| is 'indeterminate'. The 'definite' shall be defined presently.
|
| A sign (under which designation I place every kind of thought,
| and not alone external signs), that is in any respect objectively
| indeterminate (i.e., whose object is undetermined by the sign itself)
| is objectively 'general' in so far as it extends to the interpreter
| the privilege of carrying its determination further. 'Example':
| "Man is mortal." To the question, What man? the reply is that the
| proposition explicitly leaves it to you to apply its assertion to
| what man or men you will.
|
| A sign that is objectively indeterminate in any respect
| is objectively 'vague' in so far as it reserves further
| determination to be made in some other conceivable sign,
| or at least does not appoint the interpreter as its deputy
| in this office. 'Example': "A man whom I could mention seems
| to be a little conceited." The 'suggestion' here is that the
| man in view is the person addressed; but the utterer does not
| authorize such an interpretation or 'any' other application of
| what she says. She can still say, if she likes, that she does
| 'not' mean the person addressed. Every utterance naturally
| leaves the right of further exposition in the utterer; and
| therefore, in so far as a sign is indeterminate, it is vague,
| unless it is expressly or by a well-understood convention
| rendered general.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.447
| http://suo.ieee.org/ontology/msg02384.html
| Perhaps a more scientific pair of definitions would be
| that anything is 'general' in so far as the principle of
| the excluded middle does not apply to it and is 'vague'
| in so far as the principle of contradiction does not
| apply to it.
|
| Thus, although it is true that "Any proposition
| you please, 'once you have determined its identity',
| is either true or false"; yet 'so long as it remains
| indeterminate and so without identity', it need neither
| be true that any proposition you please is true, nor that
| any proposition you please is false.
|
| So likewise, while it is false that "A proposition 'whose
| identity I have determined' is both true and false", yet
| until it is determinate, it may be true that a proposition
| is true and that a proposition is false.
|
| Charles Sanders Peirce, 'Collected Papers', CP 5.448
| http://suo.ieee.org/ontology/msg02387.html
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SS: As we are having brownouts, I will just make quick reply to one from Jon.
It looks as if Jon has given up thinking about fuzziness et al because they
are not practical. That is fair enough for someone trying to get his degree
and make his way. No problem. BUT, the big philosophical problem of the
mismatch between the vague actual world and the crispness of our maps
still remains.
Actually, my advisor has done a bit of R&D on fuzzy engineering
and so we have made a deliberate effort to build bridges between
our various interests, the closest approach to which is the source
of that little essay to which I keep recurring. One of the reasons
that I regaled you with that long and winding bio-narrative was to let
you know that I had been looking into Zadeh's papers on fuzzy sets almost
from the very beginning, say, from 1972 or so. So my reflections on fuzzy
topics are the outgrowth of an internal critique of a onetime true believer,
even though I have been a true believer in most things at one time or another.
JA: It's buried a bit, I know, but this note still
contains the gist of my best thinking on fuzzy:
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Strangely enough, there is a funny sort of relationship between
ontological relativity (multi-perspectives? poly-ontologies?),
fuzzy sets, and triadic relations, perhaps (I am still guessing)
of the sort that John Sowa had in mind.
Consider a fuzzy set as a triadic relation of the form x E^r S
among an element x, a degree of membership r, and a set S.
You may, of course, substitute "concept" for "set" if you
prefer that way of thinking about things.
Ask yourself: Where do these assigned degrees of membership come from?
Imagine that they come from averaging the results of many judges binary
{0, 1} = {out, in} decisions.
Now consider the more fundamental triadic relation from which this
data is derived, the relation of the form x E_j S that exists among
an element x, an interpreter (judge, observer, user) j, and a set S.
If we use these sorts of relations as the basic formal structures of
our representation, then there is enough elbow room, I am guessing,
to have all of our cakes and to eat them too. In other words, if
we consider JS's questions ("World's Largest Individual Organism",
17 Aug 2000 08:56 EDT):
| Do you represent a chair as a construction of wood and metal?
| Do you represent it as an enormous buzz of interacting atoms?
| Do you represent it as an object for human beings to sit on
| without considering the details of its construction?
|
| John Sowa (JS): http://suo.ieee.org/email/msg00608.html
Then it becomes possible to give them the Joycean answer:
Yes. Yes. Yes.
The not so Joyce-ful task is to keep each view parameterized by the
community of interpretation that finds it compelling, interesting,
practical, useful, or "to their purpose" at a given moment, and
to figure out how to maintain a not-too-chaotic form and medium
of communication among these diverse communities.
Yes? No? Indifferent?
http://suo.ieee.org/ontology/msg02990.html
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There is a connection between fuzzy set theory and "topos theory", and further
with what are called "modest sets" and "partial equivalence relations" (PER's),
the sort of acronym, if there were no better reason, that the Peircean in me
could hardly resist. See the following books:
| Michael Barr & Charles Wells,
|'Category Theory for Computing Science',
| Prentice Hall, London, UK, 1990.
| J. Lambek & P.J. Scott,
| 'Introduction to Higher Order Categorical Logic',
| Cambridge University Press, Cambridge, UK, 1986.
SS: The triadic formulation could be used with less specified or more specified objects,
I agree. It is general enough for that. The interpretants generated by the system
of interpretance could get increasingly more specified as they lead from one to the
next as the system constructs its view of the object.
JA: Maybe that is one way to go about it, but the way that I am thinking about at present
is to make the interpretant the arbiter of the moment's classifications and decisions.
When it comes to attributing vagueness to the actual world,
I think that is likely to be a mistaken way to go about it,
no matter what version of fuzzy, persian, topos theory one
finds to be useful or not in the end. A similar diversion
arises in the so-called theory of "partial objects", where
most folks I know that have gone down that road come back
saying that they wish they had realized at the beginning
that it's not the object, the "Ding An Sich" (DAS), that
is partial, but only our human knowledge of it. All of
these issues are related, of course, to standard themes
in pragmatic philosophy, the upshot of which induces me
to prefer the following way of transforming yout tenet:
From:
| BUT, the big philosophical problem of the mismatch between the
| vague actual world and the crispness of our maps still remains.
To:
| The mismatch between the real world,
| which is more than the actual world,
| and the maps of our poetic conceits
| 'is' the fuzziness of that relation.
Jon Awbrey
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Determination
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