SUO: Abstractions, universals, and signs
In the following note, I discuss some issues concerning the top-level
ontology for abstract, information-like entities.
John Sowa
The SUO participants have characterized some basic issues in different
ways, using terms such as "information", "abstract, non-physical things",
"signs" or "sign types", and "universals" vs. "particulars". Following
are some quotations from recent discussions.
Adam Pease wrote:
> (comment Information "A class of abstract, non-physical things,
> which are object-like (rather than stuff-like) and atemporal.
> Important subclasses include numbers and mathematical theories.
> Since any string of characters can be represented as a number,
> and numbers are atemporal, then in an abstract sense, all the
> world's novels have always existed, just have not been committed
> to paper or human perception.")
Jon Awbrey wrote:
> The way I understand it, sign-tokens are physical things --
> they are actually another set of "outcomes" that "occur"
> in the real world, and so they have to have some sort of
> physical basis, but sign-types are classes of sign-tokens,
> what statistical folks called "events", that is, subsets
> of some sample space, and so they have an abstract quality
> to them. We "typically" intend the token as a representative
> of its class, and so there is almost always some ambiguity here.
>
> So when I hear people talking about a category of being that
> they call "information", I have to stop and say to myself:
> Okay, they mean a sign that is given in a setting where it
> posseses and potentially conveys a quantity of information.
From AAAI-2000 tutorial, slide 130, by Nicola Guarino and Chris Welty
http://www.cs.vassar.edu/faculty/welty/aaai-2000/sld130.htm
> A Minimal Top-Level Ontology
>
> Entity
> Particular
> Concrete
> Location
> Object
> Abstract
> Set
> Structure
> ...
> Universal
> Property
> Property kinds...
> Relation
We all seem to agree that if any distinction belongs in an "upper" level
of the ontology, the one that involves information, abstractions, or
universals certainly qualifies. The main question is how to define it
precisely and how to reconcile the divergent views.
At the MIT Media Lab, they describe the distinction with the succinct
phrase "atoms vs. bits". The following quotation from the director
of the lab, Nicholas Negroponte, illustrates the point:
> Thomas Jefferson introduced public libraries as a fundamental American
> right. What this forefather never considered was that every citizen
> could enter every library and borrow every book simultaneously, with
> a keystroke, not a hike. All of a sudden, those library atoms become
> library bits and are potentially accessible to anyone on the Net.
> This is not what Jefferson imagined. This is not what authors imagine.
> Worst of all, this is not what publishers imagine.
This quotation comes from an article in _Wired_ magazine:
http://www.media.mit.edu/people/nicholas/Wired/WIRED3-01.html
The terms "atoms" and "bits" are fairly good ways of describing the
distinction, but they are too closely tied to a particular technology.
Besides atoms, physicists talk about photons, quarks, and hypothetical
superstrings, which might someday be observable or might be replaced by
some totally different hypothesis. And bits are the units of digital
encodings, but analog encodings, such as grooves on a vinyl record or
FM radio transmissions, can represent the same information or a close
approximation to it. A more general pair of terms, which do not depend
on any particular technology, are "physical" vs. "abstract".
The next question that comes up is how the physical and abstract entities
are related. Plato called the abstractions the eternal forms or ideas,
of which the physical things are imperfect copies. Aristotle adopted
Plato's terminology, but he maintained that the physical things are
the ultimate reality, and the abstractions exist only insofar as they
are embodied in some physical entity. Alfred North Whitehead based
his philosophy on Plato "as corrected by Aristotle". He used the
term "actual entity" for the physical things, and "eternal object"
for the abstractions. For the relationship between the physical and
the abstract, Whithead coined the word "ingression", which roughly
corresponds to "encoding" (but with further qualifications in W's
own highly specialized and technical vocabulary).
In the ontology of my KR book, I used "physical" vs. "abstract" with
the term "characterize" for the relation between the two: the abstract
entity x characterizes the physical entity y. For example, one could
say that the abstract form "sphere" characterizes the earth to a good
approximation. If you need a better approximation, you could use the
form "oblate spheroid" to characterize the earth. And if you need an
even better approximation, you could use satellite data to construct
a topographical map that would characterize the earth's surface to
an accuracy of a meter or so. The general term "characterize" would
have to be specialized to a family of more specific terms, such as
"x has a one-to-one mapping to y that preserves metrical relationships
to a tolerance z" or "x can drive a sound system that can recreate a
pattern of sound waves that approximates y within a tolerance z(f)
for frequencies f within the range 20 to 20K hertz".
I would make essentially the same distinctions as Nicola G. and Chris W.
in their slide #130. The differences would be in the choice of terms
and in the arrangement of subtrees in the diagram. Following is my
rearrangement of slide #130 (with my terms on the left and the terms
used by NG & CW in parentheses):
> Entity (also Entity in #130)
Physical (Concrete particulars only)
> Object (also Object in #130))
> Process (not listed in #130)
> Nexus (space-time locations, as well as situations...)
> ...
Abstract (including universals and abstract particulars)
> (Universal)
> Property
> Property kinds...
> Relation
> (Abstract particulars)
> Set
> Structure
> ...
The major difference between this diagram and slide #130 is that
abstract particulars are grouped with universals instead of concrete
particulars. (There are also other differences in the subtrees, but
that is another topic.) The reason for that move is that I would say
that all abstractions correspond to predicates. If an abstraction x
characterizes a physical entity y, you can define a monadic predicate
(lambda (y) (x characterizes y))
The difference between a universal and an abstract particular is similar
to the distinction that Bertrand Russell drew between a general predicate
that applies to zero or more entities and a "definite description" that
applies to exactly one entity. The idea of grouping universals with
abstract particulars was also common among the medieval logicians (who
invented the terminology of "universal" vs. "particular"). They made
the observation that the individual named Socrates could be described
by a predicate socratizes(x), which is true of exactly one x (although
they didn't use the modern notation "socratizes(x)").
Suggested distinction: A universal corresponds to a predicate that may
be applied to a class of zero or more physical entities. An abstract
particular corresponds to a predicate that applies to only one entity.
As an example, the form "oblate spheroid" would characterize all the
major planets and moons in the solar system, but a satellite map of the
earth would uniquely characterize our planet (with a nearly zero chance
that it would have an equally close resemblance to any other planet
in the universe).
My category "abstract" is very close to the category "information"
that Adam Pease gave above, but I would take exception to the phrase
"object-like (rather than stuff-like)". I would prefer to say that
the digital information in a CD is more "object-like" and the analog
information in a vinyl recording is more "stuff-like", and I would
call them both "abstract". We could, for example, translate the bits
on a CD to analog information for an FM radio broadcast and then
record the reception on another CD. With current technology, we would
probably lose some bits along the way, but with a sufficiently broad
bandwidth on the FM broadcast, it would be possible to get a recording
that was identical to the original.
I also agree with Jon Awbrey's comments about signs. A sign type x
is abstract, and a sign token y is physical. The sign type contains
the information that is "encoded in" or "characterizes" the sign token.
C. S. Peirce had a lot more to say about signs, which I tried to
accommodate in my KR book. But I would be the first to admit that
the 23 pages of Sections 2.2 and 2.3, in which I tried to summarize
the philosophies of Peirce and Whitehead among others, cannot begin
to do justice to the many volumes that they wrote on the subject.
Bottom line: I believe that we can reconcile the various views
that have been put forth in these discussions, but there is still
more work to be done.