[Arisbe] Abstraction, Analogy, Example, Icon, Metaphor, Model, Morphism, Paradigm, Prototype, Simulation
Jon Awbrey
jawbrey at att.net
Sat May 3 08:26:51 CDT 2008
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Abstraction, Analogy, Example, Icon, Metaphor,
Model, Morphism, Paradigm, Prototype, Simulation
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Archiving an extra copy of this old note from the SUO list,
that alludes to and partially quotes previous discussions
on the Peirce List, especially with Tom Gollier, I think.
http://suo.ieee.org/email/msg01293.html
Jon Awbrey
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Subj: Abstraction, Analogy, Example, Icon, Metaphor,
Model, Morphism, Paradigm, Prototype, Simulation
Date: Thu, 05 Oct 2000 14:14:05 -0400
From: Jon Awbrey <jawbrey at oakland.edu>
To: John F Sowa <sowa at bestweb.net>
CC: Stand Up Ontology <standard-upper-ontology at ieee.org>
John Sowa wrote:
| Jon,
|
| Please forgive me for deleting all the poetry from your note,
| but there are a couple of points which I believe are essential
| and which I would like to highlight.
|
| First is the quotation from John Dewey (a student at Johns Hopkins,
| who unfortunately dropped out of the second semester of Peirce's
| logic course because it was "too mathematical"):
|
| | | Many definitions of mind and thinking have been given.
| | | I know of but one that goes to the heart of the matter: --
| | | response to the doubtful as such. No inanimate thing
| | | reacts to things 'as' problematic.
| | |
| | | John Dewey, 'The Quest for Certainty'
|
| This is a good illustration of Peirce's point that the essence of mental phenomena
| lies in irreducible triadic relations. The example of "problematic" is typical:
| A is problematic to B because its presence requires a response C. There are many
| other words that could be substituted for "problematic" in Dewey's quotation:
| goal, threat, food, cause, ..., all of which are important for the SUO (or
| applications that use it) and none of which can be defined without using
| three variables (or pronouns, or other substitutable terms): A, B, C.
|
| | I cannot even promise that something similar will never occur again,
| | since metaphor is one of those straws that I commonly grasp in moments
| | of extreme anxiety and otherwise frustrated attempts to get across
| | what I think is crucially important.
|
| I am not against the use of metaphors since they are essential for
| all scientific progress (e.g., the solar system as a metaphor for
| Niels Bohr's atom). But at some point, it is necessary to state
| the punch line that relates the metaphor to the "problematic"
| thing we are dealing with.
|
| | ... a graduated series of virtual reality transitional environments,
| | is crucial to the break up, the chunking, or the factoring of a difficult
| | environment into components that one can learn to take one step at a time.
| |
| | There is, of course, a catch. It comes in the form of a trade-off between
| | the "ideality" or the "niceness" versus the "realism" or the "roughness"
| | of the constructed CE. A virtual environment that is too "virtual" may
| | be a nice place to visit or live in, but you will not learn very much
| | about the world outside from being there.
|
| This is indeed a serious concern, and I am afraid that many projects
| in ontology concentrate on what lies beneath the lamp post because
| the light is better there than the places where the "problematic"
| things really are.
|
| | And this is what I suspect that we might be doing,
| | inadvertently or not, when we try to rid ourselves,
| | by hook or by crook, of these irritating ambiguities,
| | bedevilments, confusions, duplicities, equivocations,
| | imprecisions, indistinctions, obscurities, vacillations,
| | vagaries, and the general run of what I usually just call
| | "uncertainties".
|
| I agree with that point.
|
| | Now, of course, we should not "embrace"
| | these things in the sense that we want to remain afflicted
| | with them forever or for long, but I think that for just
| | that reason we need to have a means for thinking about
| | them in a progressively clear fashion, and to realize
| | that when they do arise in the objective situation,
| | and they will, that that is just the way things
| | sometimes are, and that it is necessary at such
| | times to be able to tolerate the various senses
| | of uncertainty for long enough to face them,
| | and without flinching. We will not learn
| | how to do this if we have been taught by
| | our training that this fuzzy kinda stuff
| | is all just epiphenomenal -- and that it
| | will go away if we just ignore it.
|
| I also agree with this point, but I don't believe that we
| are going to clarify the ambiguities by using an ambiguous
| language to explain them. The following diagram, which comes
| from the "knowledge soup" chapter of my KR book, illustrates
| a distinction that I would like to emphasize:
|
| http://www.bestweb.net/~sowa/ontology/mthworld.gif
|
| On the left of the diagram is a picture of the real world, and on
| the right is a theory expressed in an unambiguous version of logic.
| In the middle is a mathematical model, which mediates the two.
| The mapping from the logical language to the model is formal,
| precise, and unambiguous. But the mapping from the model
| to the world is approximate, fuzzy, debatable, elusive,
| uncertain, .... Engineers have a good slogan, which
| I also like to quote: "All models are wrong, but
| some are useful."
|
| I use that diagram as a criticism of what I believe to be the
| fundamental weakness of the so-called "fuzzy logic" -- what
| I call "the fallacy of misplaced fuzziness". Lotfi Z. puts
| the fuzziness between the language and the model, which is
| the worst possible place to put it. I maintain that the
| fuzziness occurs between our models and the real world.
| Our models are precise, our language is precise, but
| it is the world that is fuzzy. We are not going
| to get to the heart of that fuzziness by using
| a fuzzy language.
|
| John Sowa
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John,
No sweat about exiling all the poets from this
or any other Re:Public -- I gather that they
have become quite accustomed to it by now,
and I tend to suspect that they would not
have it any other way. It gives them all
a well-deserved holiday from the likes
of us straight-latticed types.
I have changed the title of this discussion as a way
of attempting to bring out the more positive aspects
of what I see as a complex of many underlying topics.
The notion of "abstraction", of course, becomes associated
with this list of concepts for a significantly distinctive
reason than the notions that fall into the other slots, and
so I will take it up first, though by no means finish with it.
By way of establishing immediate relevance to ontologies,
I will just remind people of the important distinction
that you make between 'axiomatic' and 'prototypic'
ontologies:
<http://www.bestweb.net/~sowa/ontology/>
<http://www.bestweb.net/~sowa/ontology/gloss.htm>
I have recently been instructed, by folks who ought to know,
that a presentation of any research topic ought to begin with
a historical introduction and a review of the literature, so,
in a token gesture to that type of advice, I was planning to
go back to Aristotle and tell you how he would tell us that
this all got started, but, on second thought, I think that
I will begin with something out of a more recent exchange
that I had with one of the habitués of the Peirce Forum,
on this very topic of "abstraction".
My reasons for interjecting this particular exchange
into the present context are twofold:
1. I think that our ambivalent, nay, "amtrivalent" usage
of the term "abstraction" amply illustrates one of the
significant types of ambiguity that still prevails in
both our casual and our formal idioms, and that will
prove recalcitrant to being "managed" without losing
touch with the way that the rest of the world speaks --
perhaps not entirely a bad thing, still, it's not so
easy being an exile if you have not got used to it,
yet.
2. I think that everyone will immediately recognize the
abstract similarity that exists between the diagram
that I draw below and the one that I drew a couple
of days ago in my conversation with Chris Menzel
about assertions and propositions in sentential
calculus or "zeroth order logic" (ZOL), to wit:
f
X -----> B
\ ^
<x<1>, ..., x<n>> \ / f'
\ /
v
B^n
You may remember that this was supposed to illustrate
the "factoring" of a proposition f : X -> B = {0, 1}
into the composition f'(c(x)), where c : X -> B^n is
the "coding" of each x € X as an n-bit string € B^n,
and where f' is the mapping of codes into a co-domain
that we interpret as t-f-values, B = {0, 1} = {F, T}.
The full discussion can be found in the SUO archive at:
<http://ltsc.ieee.org/logs/suo/msg01251.html>
More, later,
Jon
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Tom Gollier wrote:
|
| Jon,
|
| You write:
|
| | Try to think for a while like a simple-minded logician
| | and not like a psychological phenomenologist.
What I meant by that was something like this:
Abstractions are just partial descriptions,
descriptions that leave out a lot of detail.
It is our bound fate as human narrators that
all of our descriptions will be abstractions,
as long as we talk about anything significant,
extractions from the wealth of possible detail
that are likely to be partial in both of these
senses, incomplete and biased, and hence they
will be samples, selections, simplifications,
specimens, symptoms, ..., and thus to make
a long story short, signs, just signs.
So the question is not really whether there is something more
to the subject after we have finished with our partial account --
if the subject was interesting, there will always be more to say.
The question is just whether certain sorts of partial description
can be useful in understanding a vastly more complex reality.
And classifying the patterns in "how we think" according to
your favorite system of logical forms can indeed be useful,
depending on your favorite system, of course.
[ Digression:
| This makes it sound like logic is a descriptive science,
| just another branch of psychology, and, of course, we all
| know that this particular idea is just not sound. Perhaps
| it always begins as a descriptive description of language,
| like noticing the tautology in "descriptive description",
| but then it becomes a prescriptive doctrine that says,
| in the same instance, "Quit saying stuff like that!",
| or a normative science that says, more contingently,
| "If you are interested in achieving a certain economy,
| effectiveness, and efficiency in your communication,
| then you will want to avoid the use of such redundant,
| repetitive, and needless to say 'pleonastic' phrasing".
| And you probably have heard about how Peirce championed
| what he called a "non-psychological" account of logic,
| with respect to which I have explained the funny way
| that mathematically trained people then and now still
| use the prefix "non" in such cases, almost an acronym
| for "not of necessity", to widen a subject beyond its
| initial domain by dropping one or more of the initial
| axioms. What this means is that we can still regard
| the descriptive study of "how we think" as providing
| data, and some of the most fascinating data, indeed,
| considering who we are and all, but still just grist
| for the mill of a normative study. But I digress ...
]
That seems simple enough, but you know there is more to be said.
There are in the idioms of ordinary discussion about these matters
just one or two or three things that are likely to cause confusion.
I called your attention to this overcharged property of -ionized words,
like "abstraction", that they equivocally denote both process and result,
both conduct and product, if you will. So we have a picture like this:
Abstraction
Abstractee (the process) Abstraction
(the object) •------->-------• (description)
But as you well know, or have come to accept, it gets worse.
Having invested so much in their partial descriptions, people
will tend to become, well, 'partial' to them. And, human nature
being what it is, it seems to be something of a sore annoyance to
keep thinking about something that you love so much as imperfect,
so people will come to imagine that there really is some object
that is perfectly described by their favorite description.
Comes the dawn of the hypostasis, the imaginary substance
that we shove under our abstraction to shore it up.
Abstraction
Abstractee (the process) Abstraction
(the object) •------->-------• (description)
\ /
\ /
\ /
\ /
\ /
\ /
\ /
•
Abstraction
(hypo-stasis)
And with this form of triple equivocality in the word "abstraction"
I think that the mathematician in all of us thinks to have achieved
a "form of perfection" (FOP).
And with that, I think that perhaps I should quit
while I still have my head, and take up the rest
of your note at a later time.
I leave you to contemplate the charge of our champion.
Jon
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