SUO: Re: Lifecycle Integration Schema
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LIS. Discussion Note 47
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JA = Jon Awbrey
MW = Matthew West
Matthew,
Well, it's Saturday, so let me kick back and
look at the big picture. We can get back to
the old grindstone soon enough on Monday.
Deleting points that seem covered well enough for now --
MW: In our wider architecture we recognise that there might be many views
of what abstract is. The architecture supports and expects any number
of models. The issue is how to translate between them. The model I
have presented here is the upper level of what the architecture calls
an Integration Model. That is, it is not so much itself intended to
represent every possible way of looking at the world directly, but to
be a way of representing the world that is sufficiently unambiguous
that people can map their own views of the world to it, and thus
to each other, with a high degree of precision. This is actually
what ended up driving us towards a 4D view for this purpose, since
it has seemed to us to have the greatest clarity.
This sounds good. I never get the 3d/4d thing, since most
state spaces that I worry about have far more dimensions than
that, even if they grow in leaps of 3 dims or bounds of 4 dims
at a time. But I do hear you saying stuff that sounds vaguely
system-theoretic, and that causes my ears to pointy up a bit,
Spockily speaking.
Again, one of the things that I notice is that many candidate ontologies,
at the starting gates of the SUO track or elsewhere, and no matter what
line they imagine they may be toeing at the moment, is a superficially
similar primal distinction between Abstract and Adstract, or whatever
the opposite of abstract may be in their local argot. So I would
like to try and get ahead of the pack a bit when it comes down
to the wire of comparative ontologizing, and I can do this by
comparing your idea of <abstract_object>/<possible_individual>
to the types of distinctions that others draw, or try to draw,
elsewhere.
There is a rather vast literature on abstraction that is currently extant
and actively in use. Understatement of the Millennium. Even if you keep
to the pointer-headed linkdom of computer science, the topic Abstraction,
along with its relations to Analogy and Modularization, have constituted
regular themes in the standard computer science curriculum, at least
since the days when I personally woke up and began paying attention
to such things. Progress, real comparative progress, on SUO will
critically depend on exploiting what bits of wisdom may happen
to have accumulated in these mountains of ocean floor sediment.
JA: One of the features that points to an abstract object or
a hypostatic abstraction is its being known by description,
in other words, by the predicates that are attributed to it
in remote reports of some variety, or in the various stories
and theories that are spun about it, instead of being known
more concretely and directly by acquaintance. That is one
of the marks of all of the things that I mentioned before:
dormitive virtues, egos, numbers, quarks, sweetness, the
Starship Enterprise, and last not not least, unicorns.
MW: Sweetness is a property that some individuals have.
Within our model that would make it a class which
is abstract. The things that were sweet would be
members of that class.
JA: I think that maybe it will be best to stick with this
shortest and sweetest of examples for a while, as it
appears to present the least number of distractions.
JA: I think that the critical thing for our purposes is to try and see how
the process of abstraction actually works in action, and here the best
description that I've seen is given by Peirce. So I recommend it for
continuing consideration:
CSP: | The most ordinary fact of perception, such as
| "it is light", involves 'precisive' abstraction,
| or 'prescission'. But 'hypostatic' abstraction,
| the abstraction which transforms "it is light" into
| "there is light here", which is the sense which I shall
| commonly attach to the word abstraction (since 'prescission'
| will do for precisive abstraction) is a very special mode of
| thought. It consists in taking a feature of a percept or percepts
| (after it has already been prescinded from the other elements of the
| percept), so as to take propositional form in a judgment (indeed, it
| may operate upon any judgment whatsoever), and in conceiving this fact
| to consist in the relation between the subject of that judgment and
| another subject, which has a mode of being that merely consists in
| the truth of propositions of which the corresponding concrete term
| is the predicate.
|
| http://suo.ieee.org/email/msg10966.html
CSP: | Thus, we transform the proposition, "honey is sweet",
MW: This is what we take to indicate set membership.
CSP: | into "honey possesses sweetness".
MW: We take possesses to be a synonym for classifies.
Many things to do today, will pick it up at this point when
I can concentrate better and go through it more carefully.
Jon Awbrey
CSP: | "Sweetness" might be called a fictitious thing, in one sense.
| But since the mode of being attributed to it 'consists' in no
| more than the fact that some things are sweet, and it is not
| pretended, or imagined, that it has any other mode of being,
| there is, after all, no fiction. The only profession made is
| that we consider the fact of honey being sweet under the form
| of a relation; and so we really can. I have selected sweetness
| as an instance of one of the least useful of abstractions. Yet
| even this is convenient. It facilitates such thoughts as that the
| sweetness of honey is particularly cloying; that the sweetness of
| honey is something like the sweetness of a honeymoon; etc.
|
| C.S. Peirce, CP 4.235, "The Simplest Mathematics",
| Chapter 3 of the "Minute Logic", Jan-Feb 1902.
|
| http://suo.ieee.org/email/msg10966.html
JA: Referring to a few of Peirce's standard discussions
of "hypostatic abstraction" (HA), the main thing
about HA is that it turns an adjective or some
part of a predicate into an extra subject,
upping the arity of the main predicate
in the process.
JA: For example, a typical case of HA occurs in the transformation
from "honey is sweet" to "honey possesses sweetness", which we
could choose to represent in several different ways as follows:
JA: | Sweet(honey) ~~~> Possesses(honey, sweetness)
|
| S(h) ~~~> P(h, s)
|
| S P
| o o
| | ~~~> |
| o o
| h <h,s>
|
| ^
| [S] ~~~> /P\
| | o->-o
| | | |
| o o o
| h h s
JA: The chief thing about this form of grammatical transformation is that we
abstract the adjective "sweet" from the main predicate, thus arriving at
a new, increased-arity predicate "possesses", and as a by-product of the
reaction, as it were, precipitating out the substantive "sweetness" as a
new subject of the new predicate.
cf: http://suo.ieee.org/email/msg10967.html
JA: I think that I can point out at this juncture that the HA process,
as Peirce describes it, and as I try to picture it here, is akin
to the process of lambda abstraction that provides us with one
very successful model of computation, underpinning the tongue
of Lisp, just for a taste.
MW: The starship enterprise does exist in space-time, but not
necessarily ours. I can see that this is abstract in the
sense that it may never be real in our world, and certainly
isn't a present or historical object, but it does not fit our
definition of abstract.
MW: Unicorns are fictional animals that do not exist in our world
but could exist in some other possible world, and would exist
in space-time therefore they are individuals and not abstract.
JA: The first thing that we have to decide here is what real use we want
to make of these examples. If they're just intended as entertaining
examples of fictitious entities, that's one thing. Any other example
of a parabolic or theoretical term will do. If we have an application
in mind where we would need to talk intelligently about the meaning of
literary and mythical symbols, which is what many serious people would
see as giving these examples a modicum of real interest, that's another
thing. I once took courses in Literature and Film where we spent whole
years on the study of themes like Archetype, Myth, Science Fiction, and
Surrealism. There are lots of people out there who are interested in
using logical representations and ontologies for just such things --
many recent conversations with folks like Murray Altheim continue
to remind me of this -- but spinning the gold of Arts and Letters
into the hay of literal FOL travesties is not an intelligent way
to address these interests and applications.
JA: The maxim is: Logic should not make us stupid.
Ergo, if it's making us stupid, it ain't logic.
MW: My mapping so far between your abstract and our model is that
your abstract is our abstract plus all possible_individuals
that are not actual (in our world). I am uncertain about
quarks and egos. You may be uncertain about my analysis.
JA: But when you think about it, you will probably realize
that this is yet another one of those distinctions that
is more a matter of degree than an absolute dissection,
since all data of perception is to some degree remote.
JA: This has certain implications.
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