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C00004 00002 REPRESENTATION AND PERCEPTION.
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C00016 00005 1. The Structure of the Theory
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C00039 00010 2. The Consequences of the Theory - Perception.
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C00057 00014 3. The Consequences of the Theory - other epistemological issues
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REPRESENTATION AND PERCEPTION.
Propose a general theory of mind - the mind as a computational
"Theory" of the world. The essence of the theory is that people do
(and robots should) construct Hypothetico-Deductive models. There is
a much stronger point though - we want to claim that this Theory is
the ONLY structure to which a cognisant being has direct access; it
is, so to speak, his experiential base. Experimemts are allowed, but
they do not involve straight-forward interaction with the "physical
world", for they are strongly mediated by this internal structure.
A central aim is to show that the major epistemological problem
is the analysis of raw information about the world in terms of the
construction of the internal model. There are, then, two distinct
but interrelated representational systems : one which is concerned
with the sensorily given, and another concerned with correlation
across temporal and spatial change. This second system, which we call
the observer's Theory, is an experimental one: within the Theory,
models of states of affairs are constructed, predictions are made and
compared to the sensorily given, in the traditional scientific way.
The manner of this experimentation is Popperian, ie. the concern is
with the setting up of hypotheses which are candidates for disproof
rather than for corroboration.
There are two distinct avenues for our discussion:
(a) examine the structure of such a Theory, and develop a
unified formalism for its expression. Particular points are:
(i) the internal structure of the theory is a set
of interrlated "models" of various states of affairs
(we can call them 'possible worlds` both for
convenience and because we want to use semantical
methods of modal logics in our discussion) These
models are "pictures of facts" in a rather strict
Wittgensteinian sense, and we want to make much of
this. In particular, we want to examine the
possibility of formalising and developing some of
the arguments about the "Picture Theory" developed
by W.(see Sect.3) We hope that we can make a
connexion here to the ideas of John McCarthy on the
use of explicit models of situations for planning
purposes. There is a common problem - the nature of
the correspondence between the states of the model
and the states of the world;and we propose a common
solution - the performance of experiments;
(ii) what kind of ontology does such a Theory
embody? This is directly connected with the problem
of methods of individuation which must be developed
in the treat-ment of (i).By "individuation" we mean
the process by means of which a person decides upon
the structure of his ontology - that is to say,
decides what the individuals in his universe are and
how he is to recognise them over space and time.
(b) examine the consequences of such an epistemology for
(i) perception - this is the major concern. We
shall be concerned to examine the consequences of
such a structural organisation for the design of a
possible vision system.
We will take as a detailed example the problem of
recognising complex curved objects, for example, a
set of tools and parts on a table. The low-level
technology already exists (Binford, Agin, Nevatia).
We want to see how a vision system should go about
making and corroborating hypotheses in this domain.
(ii) some other problems in the theory of knowledge
which face robots, e.g. causality; knowledge and
belief (esp. about other minds, and the reflexivity
problem - knowing that one knows); the frame and
qualification problems; belief consistency ( here we
want to suggest that a belief system must only be
consistent within a given model, not necessarily
across models); development of a semantics for
language.
Meta-comment:
All along, the thrust of the discussion will be three-fold
(a) to explore the analytic consequences of the basic thesis,
and its relationship to traditional issues in the philosophy of
perception and mind;
(b) to try to effect a contact with psychological reality and
suggest how the metaphysical points can lead to criteria for an
information-processing approach to a psychological theory of
perception;
(c) to evolve design criteria for a unified robot vision
system. But there will be a special concern to see how current ideas
and programmes fit in and where they might need modification or
extension.
There is an underlying symmetrical belief that
firstly, the nature of one's metaphysical beliefs actually can
and should affect the structure of the functional system that one is
designing, and secondly, that attempts to build a computational model
for a metaphysics can provide salutary insights into philosophical
inadequacies and errors. Even though Descartes used the notion of
"robot" to great philosophical effect, we believe that a
computational model has more to offer, because of its concern with
the internal (data and control) structures and with organisational
principles eg. epistemological primacy.
This is, of course, a Descriptive view of metaphysics, and can
be justified and analysed in a Strawsonian way. It is also Kantian,
in that we are searching for a priori synthetic and are happy to
allow empirical considerations to influence and refine the process.
1. The Structure of the Theory
" For there is a massive central core of human thinking
has no history - or none recorded in histories of thought; there are
categories and concepts which, in their most fundamental character,
change not at all. Obviously these are not the specialities of the
most refined thinking. They are the commonplaces of the least
refined thinking; and are yet the indispensible core of the
conceptual equipment of the most sophisticated human beings. It is
with these, their interconnexions, and the structure that they form,
that a descriptive metaphysics will be primarily concerned."
(P.F.Strawson, `Individuals')
(In many ways, this is the least well thought out part of the
summary proposal. This is more by design than accident, for it is the
very nature of this work that it be an excercise in `experimental
metaphysics' (term due to Yorick Wilks) rather than the slavish
working out of the consequences of an immutable theory delivered ex
cathedra at the beginning.)
In constructing our metaphysical position we shall be
influenced by three philosophers Kant, Strawson and Wittgenstein.
The former two were concerned with the a priori synthetic knowledge
which underlie our ability to perceive and, in the case of Strawson,
to identify the particular individuals whom we take as existing in
our world. Wittgenstein was (in his early work) concerned with the
relationship between (logical) language and the way that we analyse
the world. He was, in particular, interested in analysing the
propositions:
dismiss past philosophical insights in a cavalier way; rather we
intend to see how various of these insights can be combined in an
overall philosophical system. In this way, value may be gained by
both sides. Obviously then, our effort is directed more to some grand
design than to the solution of particular problems in some limited
domain. We hope that this can be a strength, not a weakness.
There are three central issues which must be faced in this
section:
(i) is there reason to believe that representational
problems for robots can be solved by the use of an unified
formalism? John McCarthy, particularly, has been the
champion of first-order predicate calculus for this purpose.
Opponents (particularly of a Plannerish bent) have argued
that LPC (and by induction other well-understood logical
systems) isn't a rich enough language, and doesn't have a
sufficiently powerful control structure. Now while I can
appreciate these criticisms, I want to suggest that they can
be at least partly overcome by using a richer, more
interesting logic. My justification is three-fold:
(a) The whole point about having a well-understood
logical system as the basis of one's representation
is precisely that it is well-understood. It's
strengths and limitations are known before one
starts;
(b) the Planner people in particular seem either to
have failed to grasp, or simply repressed, the point
that a language like Planner is itself a formal
system which may be an implementation of well-known
logics (something close to Gentzen systems)(I'm
grateful to Richard Weyhrauch for this point.)
Implicit in their approach are the notions of
`hypothesis', `possible state-of-affairs' which are
in wide-spread use by logicians. There's lots more
to be said on this issue, all of it controversial!
(c) the issue of control structures is cloudy: John
McCarthy in particular has argued cogently for a
separation of the epistemological and heuristic
factors in a language for planning and problem-
solving language. I agree with this.
4
(ii) " This suggests approaching the ordinary non-modal
logic as the logic of world-descriptions, and approaching
modal logic as a study of the properties and interrelations
of different possible worlds" (Hintikka).
If we accept the possibility of using some formal system
for our representation theory, then what kind of language
should it be? Here I take my cue from the semantics for
modal logics developed by Kripke, Hintikka and Scott over
the last decade. These logicians have been particularly
concerned with exploring the philosophical implications of
their formal work, and have, I think, shown that the systems
they have dealt with are sufficiently powerful to act as
tools for the analysis of the nature of knowledge, belief,
tense, action and causality. In the recent work of Hintikka
there are the beginnings of an attempt to use them in the
context of perception as well. One of the features of this
work which is particularly important from our point of view
is the natural wy in which it captures the notion of CHANGE
which is at the centre of the representation problem. Over
and over again we will stress the constructive nature of
action.
I have already done some work along the lines of
implementing the methods for the construction of model
systems developed by Hintikka. A model system is a
collection of model sets, each of which is itself a
description of a possible world. The constructing of a model
set is rather similar in principle to Herbrand techniques
and the semantic tableaux method of Kripke, ie. it is of a
rather standard and well understood model-theoretic form. A
formula,F, is said to be satisfiable iff and only if it can
be a member of some model set in a model system, and valid
iff its negation is unsatisfiable. The importance of the
concept of model system lies in the fact that it is a
collection of different kinds of states of affairs,related
by a dyadic alternativeness relation. The fundamental notion
is then of accessibility of one world from another.
A particularly valuable feature of this formalism is that
it provides compact, PARTIAL descriptions of states of
affairs. At least one reason why the frame and qualification
problems arise in the situation calculus is the attempt to
describe the WHOLE world under the guise of a situation.
They fall into the same problems as Carnap State-
descriptions. Model sets not only provide a much more
compact description, but have the powerful reflexive feature
5
that they not only say what there is, but also that that is
ALL there is. This has important consequences for
epistemology which are discussed in detail in section 3.
The logic is basically like LPC+the Godel/von Wright
system. If the alternativeness relation is transitive, then
we get S4; symmetric gives Brouwer's system; both Trans. and
Symm. gives S5.
In our ideas for implementation, the basic representation
is is follows:
(a) a Model System MS is a triple {Q}⊗R≡MS where Q
is a set of model sets, and R is a procedure
defining the alternativeness relation;
(b) a Model Set is a set of predicates (in
negational miniscope normal form) each of which is
represented by a triple. The truth value of a
predicate within a possible world,WORLDn, is defined
by the triple
WORLDn⊗[X⊗Y≡Z]≡ one-of{TT,FF,UU}
We might then proceed as follows:
(i) if the triple [X⊗Y≡Z] is already assertted TT
or FF in WORLDn then we succeed/fail immediately;
(ii) if UU then see whether it follows analytically
from other assertions. Important point here: we
don't want to indulge in large scale theorem-proving
in this situation, because we are interested in an
experimntally-biassed system, rather than a purely
analytic/logical one. So if the triple cannot be
proved/disproved by rather simple manipulation
(transitivity,etc) we go on to actually do an
experiment. For example, in trying to evaluate
WORLDn⊗[SUPPORT⊗A≡B]
we might actually RUN the item(secretly a procedure
item),SUPPORT. So we have a chance to have a
"theorem prover" which actually communicates with
the exploratory machinery. Rather than running
through a vast data base (something that I just
don't believe that people do in the kindds of
situation we shall want to deal with) we will be
content to stop and activate a process which can
look at the world in some direct way.
6
Two sub-issues arise here:
(a) we must decide on cost-effectiveness measures for
giving up an analytic approach and actually embarking upon
an experiment. This is part of the more profound issue:
(b) what are the measures one should use for guiding
experimentation. Here is connexion with Feldman ideas on
Bayesianism.
In section 2 I show some examples of the operation of such
a system within a visual context.
(iii) we must explore the ontology of our proposed
representational system. Here I am particularly concerned
with what Simon has called Pragmatic Wholism. For any
cognisant being, it really is a problem (as Strawson has
shown) to decide what are the individual particulars to
which he assigns existence in his universe. For one thing,
he may want to change such an assignment from time to time:
individuals may combine with each other or separate
according to circumstance. This issue is closely related to
that of perceptual attention, and I'll talk about that in
section 2.
One central conclusion of philosophical discussion has been
that the concept of actor is of great import. I think it is natural
to discuss actors and action within the framework I set out in (ii
and iii) above, and within our general thesis. One can see that the
problem of deciding about the consequences of other people's actions
is considerably simplified if, as we suggest in our design, every
individual has a theory of how other people behave. I intend to
discuss this in more detail in section 3.
2. The Consequences of the Theory - Perception.
In this section, I set out some ideas for using the formal
techniques described above to construct a hypothesis-making vision
system. The central idea is very simple: possible worlds whic are
alternatives to the current state of affairs reflect the structure of
hypothetical worlds. Such a hypothetical world must be compatible
with all that is known at present, but need not be compatible with
all that is believved at present. When a choice point is reached, say
in a scene analysis, a number of alternative(disjoint) possible
worlds can be generated. The internal structureof these worlds
contains the much needed "clues" about how to verify (or more
accurately, falsify) them experimentally. This is I think a direct
product of an "advice taker" strategy. When building hypotheses, we
build in the assertoric tests.
Before giving an example of how this might work, I want to make
some important asides: asides which aim to show how our basic
epistemological notions can in some smooth way capture well known
features of perception.
***** Hintikka and the two quantifier (individuation methods)
business.
The human perceptual machine seems to have two
epistemologically and functionally distinct parts:
(a) an egocentric system - essentially depends only upon
the observer, and is independent of his beliefs about the
fundamental nature of the physical world. Mainly concerned
with position in visual space.
We identify this with Hintikka's perceptual individuation
and, to a lesser extent, with Russell's knowledge by
acquaintance. That is to say, it is concerned with seeing
things simply as objects in a given perceptual field,
without seeing WHAT they are.
(b) an allocentric system- depends upon the nature of the
observer's theory about the nature of the physical world.
Concerned with relative positions of objects within the
external-world-frame.
We identify this with Hintikka's physical individuation
and, to a lesser extent, with Russell's knowledge by
description. This involves seeing things for what they are,
and thereby involves a re-identification across space and
time (and the attachment of a label).
8
There are distinct neuro-psychological correlates with this
classification.
(i) Pohl's work shows that ego- and allo-centric vision are
mediated by quite distinct areas of the nervous system, the former by
the prefrontal neocortex and the latter by the posterior parietal
neocortex.
There is some cause for thinking that the egocentric system is
also the one primarily concerned with visuo-motor coordination (at
least at the lowest level) mediated by the infero-temporal cortex;
(ii) studies on the development of perception and cognition in
children (esp. Piaget) suggest that children have access originally
only to an egocentric representation, which is concerned only with
the topological features of the visual field. They need time and
experience to encode the physical knowedge essential to the
allocentric representation, which is concerned with the Euclidean
geometric relations and with object identification and
reidentification.
(iii) a very tentative suggestion - mental imagery, at least of
the Shepard type, ie. involving actual spatial transformations of
images of physical objects, might be mediated by an ego-centric
system. Studies show that people do not seem to be able to
manipulate the spatial framework itself(Cooper). All they can do is
detect transformation with respect to the visual field position; More
peripherally,
(iv) there is good psychological evidence (e.g. Posner) for a
dual representation in memory - one based on imaginal properties, the
other on more semantic properties;
We also might want to suggest that this dichotomy of visual
representation reflects computational structure. One of the things
which has been neglected in robot vision is the issue of just what
division of labour there is between number-crunching and symbolic
methods for achieving vision. This is epitomised by the failure to
use depth as a powerful segmentational cue. Stereo (but perhaps not
other depth cues) can be achieved by simple correlational methods
involving no semantical knowldedge, simply some low- level feature-
detection (cf. Blakemore) (or possibly none at all! - Julesz)
So a suggested design for a vision system must make it clear
what is to be done at low-level and what at high level. To this end,
we suggest the following representational classification:
9
(a) an egocentric visual representation built essentially
on the basis of position in the world w.r.t. the eye/camera.
An open issue is what kind of resolution such a
representation should have. Marr has suggested that it be
based on a small set of simple labels e.g.
long/medium/short, near/intermediate/far-away. I'm not sure
that this is good enough. Minsky is certainly wrong when he
says that people aren't very good at metrical judgements
(people are very good at detecting distortions in cubes
(Attneave) and in cubical corners (Shepard)). So we
certainly will want a representation which is Cartesian 3D
in a very concrete sense.
(b) the allocentric representation must be much more
symbolic, since it is the place where real contact with
memory and with non-perceptual knowledge takes place. Below
are some suggestions for the structure of this
representation.
For a vision system , there are two very difficult problems :
(a) the attention problem : in any given task situation, a
vision programme must decide upon the level of detail to
which it is going to attend. For example, a vision system
for driving a motor-car must attend closely to the central
field of view, but maintain high-priority demons for objects
moving in the peripheral field. From an epistemological
point of view, this is the problem of changing from a
general model of a situation to a more detailed sub-model.
This is, of course, a part of the more general problem:
(b) of how to enter the appropriate model for a given
scene. This can be arranged by having low-level predicate
demons for, e.g. Inside/Outside,
Urban/Countryside,Room/Table-top etc. Actually this is
something of a peripheral problem, since usually an observer
already has some knowledge of where he is and what he is
likely to see simply because it was he who performed the
action of changing his position. This is a very important
issue, and one to be dealt with in some detail. The
interrelation between action and perception is central to a
hypothetico-deductive machine, for it is at the core of the
process of experimentation.
10
Given a random scene, the sequence of appropriate actions is
approximately as follows:
(a) find some quite localised and crude features on the basis
of some low-level segmentation, eg. using depth
(b) on the basis of these, postulate a global context
(c) one the basis of this context, search for further crucial
identifying features which confirm or invalidate my suggestion.
Failing this, postulate a new context.
In general I shall come to the scene already armed with some
clues which restrict my choices in (a) and (b).
In the light of our general theory, expressed in section 1, we
might suggest that what is involved in the vision problem is the
construction of descriptions of possible worlds compatible with what
is already known. Such construction is to be corroborated in two
ways: firstly, during the actual construction process, analytic
consequences of what is already known will manifest themselves
automatically. In the second stage, given a hypothesised possible
world, experiments must be performed by collecting and analysing
sensory data.
Now it's time for an example. Consider a domain consisting of a
table-top and a set of tools ( o known structure). The problem is to
find appropriate tools for, say, an assembly task. We assume that the
low-level technology would be that of Binford-Agin-Nevatia, ie. a
depth-based volume representation.
*****
11
3. The Consequences of the Theory - other epistemological issues
for robots.
In this section ,we want to take up and develop some of the
epistemological issues which we touched upon in section 0 and 1. In
particular, we want to explore the consequences of the claim that
cognisant beings have direct acquaintance only with models of their
worlds (and models of those models). We also want to explore some of
the philosophical problems underlying the notion of correspondence
between a model and the world; this will involve some discussion of
the views of L Wittgenstein and his later commentators.
a. Our formalism and some traditional epistemological problems.
(i) knowledge and belief The use of modal logical
techniques for analysis of problems in epistemic logic is
too well known to require discussion here. The only topic
that we want to explore in depth is that of "knowing that X
knows", where X is either oneself or someone else. I think
that we should then be able to handle statements about
John's knowing that Bill knows Jack's phone number, etc. We
can also naturally handle problems like, if p⊃q does K[a].p
⊃ K[a].q.
The logic of belief has not been so closely studied. Within
our model formalism there sems to be a natural place for
thinking about belief consistency in terms of consistency of
assertions within but not across the models within a being's
Theory.
(ii) tense and change
Tense logics have been an area of great activity in model
theory, and are clearly central to any robot representation
theory which involves the notion of change. Here of course
the situational calculus has already made some
contributions, but I want to claim that my formalism gives a
natural frame-work for handling the semantics of tense and
change operators.
(iii) action (esp. frame & qualification problems) By
extension from what I said in (ii), we should also be able
to handle action in a natural way. The central point is that
any action on the part of a robot must get a grip on the
predicted consequences of that action. But, unlike the
situation calculus, we aren't forced to try to predict the
state of the whole world after any action or change. The
reflexive nature of our models puts a constraint on what we
12
bother to predict. In general, we simply don't worry about
things which we havn't explicitly calculated, and the frame
and qualification problems are much mollified.
(iv) causality
The semantical framework that we have set out was
originally developed to deal with the traditional necessity
and possibility operators, and so it should be easy to
extend it to cover causality. Dana Scott has proposed a
Kripke-type model theory for causality involving a ternary
alternativeness relation between models (say, possible
worlds indexed by time, space-time etc) in the normal kind
of way. The causality operator then has a semantics much
like the necessity operator, and various conditions upon the
alternativeness relation induces nice axioms. Chellas has
reformulated the Stalnaker-Thomason semantics for
conditionals in these terms. The real insight is that
causality (as Kant suggested) can be regarded as a logical
operator much like necessity. Not much has been done yet on
the choice conditions on the alternativeness relation, but
this is clearly worth exploring from our point of view.
b. The correspondence problem - models and the world.
In this section, we are concerned to suggest that a fundamental
feature (and associated problems) of our epistemology, the nature of
the correspondence between a model and the world it purports to
describe, is a reflection of the discussion by Wittgenstein and his
later commentators on the way in which a logical language reflects
the structure of the reality of which it speaks. So this section will
begin by being exegetical, and go on to suggest an avenue for a
further exercise in philosophical analysis (one of some importance).
(i)The potted Wittgenstein
The picture theory defines a sentence as a legitimate
picture when it is an `isomorphic representation' of the
state of affairs which it purports to describe. For a
sentence, A, to be an isomorphism of a state of affairs, B,
they must both be articulate fields (Stenius), ie. both must
be a structured set of individuals, a number of properties
defined on these individuals, and a number of relations
between them. Two such fields are isomorphic with respect
to a "key" which establishes the isomorphism; the key must
respect categories, ie. it must correlate individuals with
individuals and properties with properties. The key remains
the same for all sentences of the same language - indeed, it
13
is what (in a sense) characterises the language; it is what
one must know in order to understand the sentences of the
language. The theory does not hold that all sentences of the
language are pictures of actual facts, but that TRUE
sentences are isomorphic representations of the reality of
which they speak.
(ii) relation of the picture theory to truth-function
theory
(iii) Stenius on modal and descriptive components
(iv) Hintikka on the Picture Theory:
Hintikka has suggested several important modifications and
extensions to the original Wittgensteinian Picture Theory:
He modifies the category criterion mentioned above by
pointing out that generally in sentences individuals are
correlated not with real-world individuals but also with
predicates. This is not really a category violation when we
realise that what really corresponds to a relation in a
sentence is not the word which is usually said to correspond
to it, but rather the relation-symbol and its associated
argument places. Isomorphism cannot apply between relations
except when thair arguments fill the appropriate argument
places. This is pattern-matching of a simple kind; its
result is the correlation of a predicate symbol P (with n
argument places) with a predicate α(P) with the same number
of arguments. This leads naturally to a a connexion with
model theory which can be made by asserting that "a set of
sentences, λ, is imbeddable in a model set just in case it
has a model, ie. iff there is an articulate field and key(α)
which maps a set of free singulat terms onto the set of
individuals in the field, and also maps all the predicate
symbols occurring in λ onto predicates of the filed, so that
λ is true." By virtue of the fact that members of a model
set can stand for themselves, model sets are actual models
of the state of affairs in which all their members are true.
The problem, obviously, is the discovery of the key. If we
use a model set as a model of itself, and define the
individuals of the articulated field as the free singular
terms occurring in the model set, then we have the field. It
is important to grasp that, since model sets are only
partial descriptions of worlds, they admit the possibility
that the mapping is a homomorphism, in that they do not
preent us with as a single picture of the world. They only
14
present us with a set of alternative possibilities at this
stage. Pinning down the isomorphism is the difficult
exercise which holds the most interest for us. It is of
interest for two reasons: firstly, the discovery that there
may indeed be sometjing more fundamental than logic
(contrary to Tractatus 6.123 and Notebooks, p4) and secondly
that we are led to a constructive (in the non-intuitionistic
sense) view of the semantics of quantification theory.
Compare "If one thinks of sentences as directions for
building models, their pictorial character becomes still
clearer" (Phil.Bemerk. )
So we see that an attempt to extend the original
Wittgensteinian picture view to languages with
quantification leads to the realisation that model set like
descriptions are no longer capable of being compared with
reality in the straightforward way that W. envisioned (" It
is laid against reality like a ruler"). Rather model-set-
like pictures are compared with reality in a constructive
kind of way - the models are (to use Hintikka's phrase)
"recipes for the construction of pictures". phrase)
"recipes for the construction of pictures". The
constructive techniques that we have talked about above may
form the beginning of a development of this view. From an
exegetical point of view, it may also be a clue to the
continuum of the early and late philosophies - by virtue of
the connexion between the Picture Theory and Language Games
(vi) In the latter philosophy, W was concerned to point out
what he regared as an error in his earlier view - the notion
that the primitives of logic gain their meaning by being
correlated in some way with sensible experience (or at least
with the denotation of objects). He thought that such a
theory of meaning would leave no place for public criteria
of the meanings of names. In the light of what has been said
above both about the descriptive/modal distinction and the
constructive nature of the picture view, I want to suggest
that this was an over reaction, and that there is a natural
place in our descriptive metaphysics for public criteria.
But the place is a somewhat curious one. In our view, of
course, there is no real problem of correspondence of the
models that divers people hold, for they are all represented
within the observers model of those models. This is, in
abstracto, a highly solipsistic view of course, but we can,
if we wish temper it by allowing public criteria to enter in
the guise of experimental results. This is really an open
question at the moment.
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