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C00003 00002	truth[w83,jmc]		M.I.T. discussion about truth
C00010 00003		Reading the article "The coherence theory of truth" in the
C00014 00004	Subject: objective physical and mathematical worlds
C00022 00005	Subject: "your version of reality"
C00026 00006	Subject: correspondence theory
C00029 00007	Subject: Practical issues
C00032 00008		Chomsky and Piaget and others consider many aspects of human
C00040 00009	This rather long exposition is not intended primarily as an argument
C00068 00010		I have been silent (or rather its equivalent for written communication)
C00073 00011	I agree with Marvin that the idea of knowing as justified true belief
C00080 00012
C00084 00013	DAM:
C00088 00014		Philosophy owes science some debts.  In principle, this needn't
C00093 00015	possible worlds and elaboration tolerance
C00100 00016		I also once enumerated the 2 by 2 Turing machines, though not as
C00104 ENDMK
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truth[w83,jmc]		M.I.T. discussion about truth

∂12-Jan-83  2148	GAVAN @ MIT-MC 	rat psychology
Date: Thursday, 13 January 1983  00:42-EST
Sender: GAVAN @ MIT-OZ
From: GAVAN @ MIT-MC
To:   BATALI @ MIT-OZ
Cc:   phil-sci @ MIT-OZ
Subject: rat psychology
In-reply-to: The message of 12 Jan 1983  20:55-EST from BATALI
fragment:
In his message of 1983-jan-12, GAVAN says

"I'm tempted to ask just what TRUTH is and what makes you think there's
any such thing, but that's a little off the subject.  Maybe not.  To
me, there is no truth but only consensus.  What we call "truth" is
only what we have agreed upon, given certain conventions which we agree
are "rational."  It seems to me that the notion of coming to a consensus
brings us back to the problem which motivated the discussion.  How do we
in society and mental agents in a society-of-mind consensually validate
our beliefs and theories?"

	The above quote from Gavan strikes me as muddled and scientifically
unpromising.  It is similar to the Vienna circle ideas of the 1920s.
A young graduate student named Kurt Godel attended the Circle meetings
and had a different idea.  His idea was that truth was one thing conceptually
and what you could prove was another.  For his PhD thesis he proved that
in the case of first order logic the two coincided.  Later he was able
to show that in the case of the arithmetic of Principia Mathematica and
related systems they could not coincide.  Still later he was able to
show that the continuum hypothesis could not be disproved from the
Godel-Bernays axioms of set theory while maintaining his belief that
the continuum hypothesis is false.  Another young man named Alfred Tarski
was able to show around 1930 that truth in arithmetic was not arithmetically
definable.

	In my opinion, a person who makes a clear distinction between
truth and what is "consensually validated" will have a better chance of
advancing philosophy and/or artificial intelligence than someone who
muddles them.  He might, for example, be able to show that the notions
coincide in some cases and differ in others.

***the above was sent

good points - p. 116 from DAM (David Mc)
msg.msg[jnk,jmc]/116p

must defend DAM from Minsky's p. 117
msg.msg[jnk,jmc]/117p

DAM msg.msg[jnk,jmc]/118p

DAM p. 124 needs to distinguish his position from ...
msg.msg[jnk,jmc]/124p

	Here is an example of a possible payoff from distinguishing truth
from consensus.  Suppose we try to develop a formal "meta-epistemology"
based on a dynamical system (system evolving in time according to your
favorite formalism) called the "world" and a distinguished subsystem
called the "scientist".  We suppose that certain functions of the
"scientist" are to be interpreted assertions about the "world".
We can study the effects of various "scientific strategies" for
finding information about the world.  Some "worlds" are more knowable
than others.  Some strategies are more effective than others.  For
example, a realist might hope to prove that a strategy that confined
itself to relations among sense data would never learn certain facts
about the world that more liberal ontology could discover.  We might
even be able to prove that a "scientists" using consensual notions
of "truth" would be unable to formulate certain truths.  Probably,
before such a formal meta-epistemology can be developed, it will
be necessary to find a simpler yet relevant system to study.
To summarize, in order to model scientific and other knowledge seeking
activity, it will be necessary to distinguish what is true in
the model world from what the model scientist believes.

	My previous message was imprecise.  Godel proved that in first
order logic, validity (truth in all models) coincides with provability.
Even to formulate the result required keeping the concepts distinct.  I
should mention, however, that van Heijenoort informed me that Hilbert and
Ackermann formulated the problem in their book on logic even though
Hilbert's philosophy was nominally formalistic.
	Reading the article "The coherence theory of truth" in the
Encyclopedia of Philosophy and recalling Marvin's remarks about
sparsenes leads me to change somewhat my views expressed previously.
The article emphasizes the fact that we don't verify single statements,
but whole complexes of statements, i.e. theories and languages.
Moreover, within such a theory it is often, and perhaps necessarily,
unclear which statements are unadulterated observations, which are
definitions, and which are theoretical statements whose truth may
be verified.

	All this doesn't interfere with the correspondence theory
of truth as applied to single statements in a given language such
as English.  Nor does the fact that theories are verified as wholes,
rather than statement by statement, necessarily affect a viewpoint
to which truth has little to do with the method of verification.
However, it suggest we can do better.

	Suppose someone supplies us with a 50,000 word textbook on Newtonian
mechanics written in Martian.  Suppose that there are some errors
in the text and moreover we don't know the subject matter, there
are no diagrams, and we can't read Martian.  It may be very difficult
and take a long time to figure out what the document is.
Someone may initially advance the theory that the document is a cookbook
or a novel.  Nevertheless, it is extremely improbable, e.g. of the
order of the molecules rushing to the other side of the room, that
this textbook admits any coherent interpretation than as a textbook
of Newtonian mechanics with a few errors.  Whether cryptography
and linguistics are presently up to guessing it, I don't know.
Remember that the still undeciphered inscriptions in unknown
languages are almost certainly not narratives or exposition but
mostly lists, whether of kings or the contents of warehouses.

	What this suggests is that a long enough document may
have certain statements in it true or false in an absolute,
language independent sense.  Of course, it may also assert
a myth in the same absolute sene of admitting that and no other
interpretation.  Some of the background for these assertions
is in Shannon's 1948 Bell System Technical Journal article
on the probabilistics of cryptography.  These ideas may be
combined with those of Solomonoff, Kolmogorov and Chaitin.
Subject: objective physical and mathematical worlds
In reply to: mainly GAVAN
	Whether the world should be regarded as a construct from
sense data and/or other experience or should be regarded as
existing independently of mind has been argued for centuries.
The same question arises about whether mathematical facts are
to be regarded as independent of the existence of human or other
minds.  I believe that I have convinced most of the participants
in the debate that I am an actual adherent of "realism" in both
cases, and this took some doing.  However, I haven't addressed
the issue itself, mainly because what little I can
add to the debate seems unlikely to change many minds.  However,
GAVAN keeps emitting rhetorical questions like "What world?", so
perhaps I should say something.

	Descartes tries to begin his consideration of philosophy
with a clean slate and argues "Cogito ergo sum".  He does not even
accept the existence of other minds a priori, but considers
their existence to be a consequence of his reasoning.  In order
to get such results, he adopts methods of reasoning so strong that
he can deduce the whole of the Catholic religion - which might raise
suspicions about his "rules of inference" among non Catholics.
Positivists often also propose to start from bare sense experience
and see what can be gotten from that.

	There is, however, another principle from which one might
start, and I'd like to give it the fancy name of "Principle of
philosophical relativity".  Consider taking as a starting principle:
"There is nothing special about me".  Unless there is positive
reason to believe otherwise about some aspect of reality,
I will assume that I am not in a unique position.  If I have
experiences and thoughts of a certain kind, very likely other
people have similar thoughts and experiences.  This corresponds
to common sense prejudice, and indeed we seemed to be programmed
that way.  A week old baby will open its mouth in response to its
mother's open mouth - presumably without having gone through the process of
deducing the existence of other minds and automatically making
a connection between the sight of its mother's mouth, and the
position of its own mouth, which it has never seen.  We may regard
the baby as jumping to mistaken conclusions.
If we refrain from overcoming this apparently built-in principle
of philosophical relativity, we get other minds, other physical
objects and lots more rather early in our philosophical investigation.

	Another argument that impresses me is the following: I
was taught in school about how the earth was formed from
the solar nebula, cooled off, developed life which evolved more
complicated forms, one form of which evolved intelligence, evolved
a culture, and eventually developed institutions of higher learning
in which some of us are even paid to think and argue about
philosophy.  Now I am asked to believe that all this about
life and intelligence evolving isn't to be taken seriously as
something that actually occurred but is to be taken merely as
a convenient way of organizing my experience and predicting
future experience.  I suppose I could manage this change of
viewpoint but am insufficiently motivated by any hope of benefit.

	The question of objective mathematical reality is harder (for me)
to argue about.  Would it be at all convincing to meet extra-terrestrials
and discover that while their mathematics had gone farther in some
directions than ours and less far in others, they talked
about the same basic systems of algebra, topology, analysis and
logic?  Does anyone expect something drastically different?
I'm inclined to take what apparently is a relatively extreme position
among mathematicians, although it was Godel's position, and say (for example)
that the continuum hypothesis is either true or false although it
is much less certain that humans will ever know or will ever even
have a strong opinion.

	There is also a question about what level of certainty
should be demanded before accepting the existence of other minds,
etc.  Many people profess uncertainty about whether the physical
world exists, but don't seem to give the slightest weight to the probability
that they don't in their practical actions.   This suggests that
a test be devised for the seriousness of sense data theorists.
It would involve offering a prize that could be won if there were
relations between sense data apart from those mediated by material
objects.  Someone who put effort into trying to win the prize would
be showing some seriousness about the sense data view.  Perhaps someone
can come up with a better way of formulating such a test.

	Well that's all I can come up with at the moment, though
there's lots more in the literature.
Subject: "your version of reality"
In reply to: GAVAN
    "Belief in OBJECTIVE reality is surely not pragmatically useful
    (depending upon what pragmatics means for you).  If you believe your
    version of reality is objective, then be prepared to beat your head
    against a wall for the rest of your life."

	The phrase "your version of reality" leads to two kinds
of confusion:

	1. Belief in the existence of objective reality, i.e. that
there are facts independent of human experience in general and one's
own in particular, does not require belief in a particular "version
of reality".  Thus I am prepared to learn that there is a wall
where I previously thought there was an opening.  Moreover, this
experience reinforces the doctrine that my beliefs are true only
if they correspond to reality.

	2. A person's beliefs cannot be summarized as a "version
of reality" for two reasons.  First a version of reality would involve
more detail than a human holds - the names of all the people in
the world to begin with.  Our opinions cover only a tiny part of
reality.  Second, even when an AI program's reality is restricted to a
tiny part of the world, e.g. a collection of blocks on a table, its
view cannot in general be regarded as a version of reality.  It may
not have an opinion about the location of some block or it may have
a disjunctive opinion: e.g. it may believe that a certain box
contains a red block or a green block.  This requires distinguishing
states of belief from belief in states of the world - or even in
partial states of the world.  Bob Moore in his M.I.T. master's
thesis emphasized how AI programs whose belief structures were
whole worlds or partial worlds are limited in their capabilities.
The first approximation to a state of belief is a THEORY in the
sense of mathematical logic.  A possible state of reality corresponding
to the state of belief would be a MODEL of the THEORY.  I'm
adopting a convention of capitalizing technical terms.  Unfortunately,
it may be that more sophisticated notions are required.
Subject: correspondence theory
In reply to: GAVAN

GAVAN: "Please remember that I am not denying the existence of
       reality, only the objectivity of anyone's experience of reality
       (and also the idea of a correspondence).  Sceptics have always been
       able to demonstrate that the existence of reality is unprovable but
       they've never been able to disprove its existence either.  Even the
       sceptics engaged in practice, so they did really assume that the
       world exists, as I do.  Their point and my point is not that the
       world doesn't exist.  The point is that there's no necessary
       correspondence between what's in the world and what's in your mind
       (or what's in your sentences)."

     Can it be that most of our arguments have been based on mere
misunderstanding?  The correspondence theory does not require the
correctness of anyone's opinion of reality.  Correspondence is instead the
criterion for the truth of a belief.  In this interpretation I claim to
also speak for the authors referred to in the Encyclopedia article on the
correspondence theory.

     There used to be a further issue about the "objectivity of
observation", i.e. whether trees (directly observed) are as real as
elementary particles, but I think arguments on this subject have died down
- both are real.
Subject: Practical issues
	Are there any practical consequences for AI in the debate on
the correspondence theory of truth vs. coherence or consensus.

Maybe yes, maybe no, depending on what one supposes adherence to
one of these theories would suggest.

1. A consensus theory might suggest that a program look for a consensus
in deciding what to believe and how to act.  For example, it might
choose to abandon what it thinks it saw with its own eyes for no
other reason than that public opinion is different.  Issues might
arise involving whether a consensus among copies of itself would
count.  Rather than me speculating, it might be better if an
adherent of the consensus theory would tell us what consequences
it might have for the design of programs.

2. An adherent of a coherence theory who doesn't think there is
anything for beliefs to correspond to might look for models that
simply predict experience.  I am not sure what its motivation would
be to seek experiences that don't cohere with previous experience.
However, an AI researcher who upheld a non-correspondence theory
merely out of stubbornness might find a version which was isomorphic
with a correspondence theory in its suggestions for research
strategy.

3. An adherent with the correspondence theory with an objective
reality will make programs that are never sure their current
picture of reality is correct and which will seek tests of it.
It will go quite far out in its speculations.
	Chomsky and Piaget and others consider many aspects of human
behavior to be innate, often disagreeing about just what is innate.
Even if each of them has defined, as exactly as he can, what he means
by innate, we may be too lazy to find the precise reference.  It is
unsound, however, to attribute the silliest meaning we can think of,
even though it may temporarily massage the ego.  It is a much better
approximation to attribute the most sensible meaning we can think of,
although if precision is sought, there is no substitute for reading
the literature.

	Piaget, I think, thought that certain concepts were innate
in the sense that they arise at a certain stage of development of
all normal humans.  I don't know what qualifications he made about
how normal the environment had to be.

	With regard to sentences, Minsky's off hand reference to
what I said was correct - if I interpret him correctly.  I doubt
that sentences are innate in the following sense.  1. If adults
brought up a child never uttering sentences, the child might not
come to use them.  2. A population of children initiallized without
sentences would develop them in time.  I have no opinion about whether
this development would take place at the age of ten in the first
generation or would be an invention after several generations.  I
suspect this differs from Chomsky's opinion, because his ideas about
innate universal grammar involve sentences.

	To the extent that I understand Chomsky's argument I consider
it faulty.  He argues that an innate universal grammar is required,
because a child acquires the grammars of their native language from
a small amount of experience, and this grammar permits judging
the grammaticality of an indefinitely large collection of sentences.
It seems possible to me that a major evolutionary step towards
human intelligence occurred when the output of a pattern recognition step
could be fed back into the input and combined with early data.
This is a step beyond the simple chain suggested by anatomy, where
the first visual or auditory cortex passes signals to the second,
which transforms them and passes them on but never back to its own
inputs.  However, this capability is needed for thought processes
apart from language and might be a general intellectual mechanism
developed earlier than language.  The Chomsky strategy of studying
grammar first and thought later wouldn't uncover it.  Perhaps I
misrepresent Chomsky's point of view.  In principle, the point is
testable by looking for either behavioral or anatomical evidence
for such feedback processes.  For example, mental goal-seeking is
often a top down
process analogous to top down parsing.  "In order to achieve  C, I
need to perform an action that has preconditions  B and B', which requires
actions that have preconditions ... ".

	DAM interprets me correctly as believing that some early written
languages lacked sentences, although the oral languages of the
same people included sentences.  In fact this is known.  The oral
language of the Aztecs included sentences, although their inscriptions
didn't.  Much that is known of their culture was written by Aztec
priests, etc., after the Spanish taught them to write their own
oral language in the Latin alphabet.

	I am even willing to entertain the possibility that the first oral
languages didn't have sentences.  I would also suspect that some present
day primitive oral languages are impoverished in some respect, especially
in the way they are ordinarily used.  The anthropologists and bible
translators who study these languages may mistakenly impose European
linguistic categories on them.

	"I bet GAVAN make big fella mistake Friday" in his speculation
about the Creole languages - for any of the possible meanings of "Creole".
Consult Webster's Collegiate for at least four.  The Creole languages
weren't invented by masters for the use of slaves.  Moreover, I'll bet
that all of them can distinguish past events from present events when this
is necessary for the communication without ever using tenses.

	Apart from that it would be a mistake for GAVAN to suppose that we
advocates of the correspondence theories consider ourselves defeated.  We
merely have trotted out all the arguments we care to and don't want to
repeat ourselves.  Therefore, it is pointless for him to repeat flat
assertions he has made already about the meaningless of
correspondence statements.
This rather long exposition is not intended primarily as an argument
for the correspondence theory of truth, although it presents my
position on the relations among CORRESPONDENCE, COHERENCE and CONSENSUS.
It is addressed primarily to people who are already base their thinking
on some kind of correspondence theory and outlines some research ideas.
The primary idea is that abstract meta-epistemology is worth studying.
By abstract I mean that we consider a knowledge seeker in a world,
and we consider the effectiveness of strategies as functions of the
world.  For this purpose, it is often appropriate to consider model
worlds that are not candidates as theories of the real world.
By studying strategies in abstract worlds, both theoretically and
experimentally, we may develop candidate strategies for application
to the real world.  These candidate strategies may discussed as
philosophies of science and imbedded in programs interacting with
the incompletely known physical and mathematical worlds.

Even meta-level questions such as the appropriate theory of truth may
be studied in these abstract systems.

Here are my views on the relations between CORRESPONDENCE, COHERENCE,
and CONSENSUS baldly stated.  Arguments are later.

1. The truth of a statement about the world is defined by its
CORRESPONDENCE to the facts of the world.  The truth of a statement about
mathematical objects is determined by its correspondence to the facts
about these mathematical objects.  Of course, both of these presuppose the
existence of the world and of mathematical objects.  Tarski says: "Snow is
white" is true if snow is white.  This has an unfortunate but inevitable
circularity, because we use language for talking about the world, and
we're talking about sentences in the same language.  The circularity has
the consequence that the definition doesn't itself provide a means of
determining facts about the world.  Unfortunate but inevitable.

2. Our means of trying to determine the truth involves the COHERENCE
of large collections of statements including reports of observation.
We do not take COHERENCE as the definition of truth, because we always
want to admit the possibility that a collection of statements may
be coherent but wrong.  Naturally, we will only come to believe that
it is wrong if some other collection of statements is found to
be more COHERENT, but the new one may be wrong also.

3. CONSENSUS is a mere sociological phenomenon whereby groups of
people come to more or less agree about the truth of somm collection
statements.  At any given time there may or may not be CONSENSUS in
various groups of people.

Meta-epistemology again:

A Toy mathematical example illustrating use of the above concepts:

	Consider a mathematical system consisting of a computer
C, a language L, and a collection D of interacting automata
to which C is connected.  We suppose that the language L includes
a predicate symbol  holds, and we interpret  holds(i,s,t)  as
asserting that the  i th subautomaton of  D  is (was) in state
s  at time  t.  We further interpret a certain list B
of sentences in the memory of the computer as the list of what
the program BELIEVES.  Sentences elsewhere in memory are considered
mere data.  We suppose that the automaton system, including the
computer part is started in some initial configuration.  At some
times during the operation of the system, certain sentences will
be in the list  B.  Suppose  holds(17,5,200)  is in that
list at some time  t1.  We regard it as true, and the program as
BELIEVING it correctly if subautomaton 17 is in state 5 at time 200.
In fact, whether the program BELIEVES it is irrelevant to its truth,
since its truth depends on the evolution of the automaton system,
in interaction with the program, and not on the contents of the list
B.  However, our interest is in designing knowledge seeking programs,
and we are interested in what programs connected to what automaton
worlds will have lots of true beliefs.

	One important class of programs, to be compared in effectiveness
with others, are programs that use data structures interpretable
as sentences about the world, mathematics, goals, etc. - in short
the kind of program now used in much AI research.  The program
may be provided with an initial stock of sentences.  Some of these
sentences may be regarded as presuppositions about the kind of
world to which the program is connected.  Of course,
it wouldn't be interesting to include such assertions as  holds(17,5,200)
in the presuppositions, and then admire the result if
the program moves the sentence to the list  B.  In evaluating
programs, it would be most interesting to consider connecting them
to a variety of automaton systems in a variety of initial states.

Remarks:

	1. There will be programs that can be ascribed more true
beliefs if we use a different language and some other location
than in the list  B.  Indeed programs that evolve intelligence
are unlikely to use this specific langauge.  However, since we
are talking about DESIGNING the program, it is difficult enough
to make it smart in the way we intend and quite unlikely that
it will turn out to be smart in some entirely different interpretation.
Therefore, we'll stick to the language  L  and the list  B.

	2. Finite automaton worlds are discussed as an example only.
If I were smarter and I thought your patience were greater, I would
have the program interacting with systems more like those discussed
by current theories of physics.  Even within the automaton model,
there are more interesting kinds of assertions than  holds(i,s,t)
which is rather like an assertion that a particular molecule
has a certain position and velocity at a given time.  Assertions
about the structure of the system of automat, e.g. what is connected
to what more closely resemble present day scientific assertions.
Indeed the "obstacles and roofs" world that I mentioned earlier
is EPISTEMOLOGICALLY and HEURISTICALLY more like our own world.
The automaton model is only METAPHYSICALLY ADEQUATE for our present
purpose.  (These terms are used in the sense of McCarthy and Hayes "Some
Philosophical Problems from the Standpoint of Artificial Intelligence").

	3. What kinds of programs should we design?  This depends
on what kinds of automaton systems we intend to connect to the
program.  If we connect it to worlds that behave like those
that behaviorist psychologists were in the habit of connecting to
their rats and sophomores stimulus-response models of the world
will be fine.  Indeed the sentences of the form  holds(i,s,t)  may
be quite superfluous for success in worlds designed by behaviorists,
and sentences like  responds(s,r)  interpreted as "If I give it
the signal  s  I will get back the response  r"  may be more
appropriate.  In terms of its ability to predict, a correspondence
concept of truth will be irrelevant, because the behaviorist will
have designed his automaton system to give the intended responses
to the stimuli, and the actual mechanism whereby this is done
will be hidden from the program.

	However, we might consider designing programs of a different
kind.  These programs would hypothesize very large systems
of interacting simple automata connected in a regular way and
such that the inputs to the program were the result of averages
of large numbers of "microscopic" events.  The states and transitions
of the individual microscopic automata would not affect the
inputs of the program, i.e. would not be observable.
Nevertheless, the laws connecting the individual "microscopic"
automata would be permanent features of the world and could
be used to explain and predict otherwise unpredictable events
that were more directly observable.

	In worlds that I would design, such strategies would
be more effective than strategies hypothesizing stimulus-response
laws.  I would design such worlds for my program, because I
believe such worlds are moe like the world to which I am connected
and of which I am a part.

	4. If we give the program worlds composed of interacting
parts, sentences interpreted as asserting that the world is so
constructed would be true.  Moreover, research programs aimed at
discovering such parts, their internal structures and their interactions
would be likely to generate true beliefs, and would be more successful
than other strategies in predicting the experiential consequences
of actions.  This is almost tautologous, since if we connected a
program a world constructed of interacting parts, its beliefs will
be true if they assert this fact, and its predictions of the experiential
consequences of actions are more likely to be correct if the strategy
takes into accoun the facts.  Therefore, this is not evidence for
the appropriateness of a correspondence theory of truth in dealing
with human experience.  However, if humans have in fact evolved
in a world composed of interacting parts, then considering
epistemological models of the kind proposed here can help us
devise intelligent strategies for learning programs.

	5. Besides its "official beliefs" which I would have the
program exhibit for my inspection on the list  B, the program
would keep on various lists many other kinds of sentences "about" the laws
of interaction of the automata making up the world.  We could inspect
these lists and try to interpret the sentences as assertions about
its world.  Sometimes we would succeed and interpret the sentences
as true or false.  Sometimes we would fail and say that a certain
sentence has no clear interpretation because the concepts are
confused.  For example, some sentence might be analogus to one
about how much phlogiston a rat produces per day.

	6. In certain kinds of world, the best strategy for
accumulating beliefs would be a COHERENCE strategy.  The strategy
would have collections of assertions about large numbers of aspects
of the world, some of which would be alternatives to each other.
A strategy that put in the list  B  of official beliefs the
most COHERENT collections of assertions would probably be
most effective in generating beliefs that CORRESPOND to its
world.  It would also be most effective in predicting the experiential
consequences of actions.

	7. If the knowledge seeking program were composed of many
semi-independent subprograms, each connected to the automaton world
in a different way, strategies of co-operation might well develop.
Such strategies might involve inter-knower lists of of beliefs
obtained by CONSENSUS.  This is especially likely if the individual
knowers were limited by short lives from independent access to the
phenomena and so were forced to develop collective institutions
of science.

	8. So far our epistemological statements have all been at
the meta level.  We have discussed the beliefs and truth seeking
strategies of the programs in the automaton world from outside
that world.  If the world is complex, and complex worlds are the
primary interest, it will sometimes be effective for the program
itself to have theories of truth and belief and use these theories
in its knowledge seeking strategy.  We might, for example, include
sentences expressing such meta-beliefs in the initial supply of
sentences we give the program.  We might include the whole general
theory including a CORRESPONDENCE theory of truth, a COHERENCE
strategy of search and a CONSENSUS theory of co-operation
in the initial stock of sentences provided we could formalize
it suitably.  We might try out rival theories, suitably formalized.
Alternatively, we might leave out any theories and see if they
develop.

	9. As long as we provide a language  L  and examine what
sentences in it appear in the list  B,  we minimize our problems
of interpretation.  However, if the system develops other languages,
or if we adopt some more "natural" approach than having a  L  and
B,  we will have problems of whether certain data structures can
be interpreted as sentences making assertions about the world, i.e.
in inventing a translation rule into the language  L  or whatever
language we use for describing the world.  However, I don't think
we will face a problem of having to alternate translations that
both "make sense".  As I said in a previous message, cryptography
experience and the Shannon theory suggest that such problems are
extremely unlikely provided we take symmetries and isomorphisms
into account.  My paper "Ascribing Mental Qualities to Machines"
discusses some of these points.

	10. Symmetries and isomorphisms of the world or parts of
it raise interesting problems.  The world to which we connect
the computer may have symmetries and it may be isomorphic to
structures other than those we design.  The program may consider
rival theories and then discover that they are isomorphic.
If we consider final theories of the whole world, the preferred outcome
is clear.  It should find the isomorphic theories and
recognize their isomorphism.  Moreover, many isomorphisms
can be kept implicit by using a formalism that is canonical
with respect to the transformations involved.

	However, we are not primarily interested in programs
that will create a final theory of the world write it in list
B  and then stop.  More facts may break an isomorphism, so the
machine must be more sophisticated.  On the one hand, it can't
spend time trying to decide between theories isomorphic with
regard to the means it has for interacting with the phenomenon
involved.  On the other hand, it needs should keep the equivalent
theories on hand just in case the equivalence breaks down later.

	11. All this is methodology intended as a guide to research.
There are two directions in which research might proceed, theoretical
and experimental.  On the one hand, we can develop theories of
what can be found out about what kinds of worlds.  E. F. Moore's
"Gedanken Experiments with Sequential Machines" in Automata Studies
should be read by anyone who contemplates research in this area.
Its merit is that it makes important distinctions and proves some
theorems about investigating automaton worlds.  Its fault is that
these worlds have too little structure for a sophisticated research
strategy to be effective.  They aren't as bad as the stimulus-response
worlds, however, since at least they contain memory.

	I fear that it is beyond our present knowledge to formulate
sophisticated conjectures about the effectiveness of different theories
of truth in guiding research in automaton worlds.  I suppose the
theoretical state of meta-epistemology is that we need to work on
establishing interesting conjectures.

	Experimental research in this area seems inappropriate at
present until there are some conjectures.  For example, a program
for solving "obstacles and roofs" worlds might turn out to be just an
exercise in programming.  I would also be uninterested in a proof
that "obstacles and roofs" is NP-complete.

	12. It might be interesting for an adherent of the COHERENCE
theory of truth to attempt a meta-epistemological model.  I wouldn't
know how to begin.  He might start in the same way as I did - consider
systems consisting of a computer program connected to something with
which it interacts.  My knowledge seeker attempts to find out the
structure of the something.  However, just considering the knowledge
seeker connected to something involves a something, i.e. a world,
and makes the problem one of finding out about the world.  Someone
who rejects "the world" and an associated correspondence theory
might well consider that these have already been presumed by
connecting the program to something.  Well, that's their problem.
Perhaps even Gedanken experiments are inappropriate from their
point of view.

	Here is another way of putting the question.  Are Gedanken
experiments or real experiments with knowledge seeking programs
appropriate from the point of view of any non-correspondence
theory of truth?  If so, what is the experimental environment of
the program, and what kinds of sentences does it attempt to ascribe
truth to?  Would an obstacles-and-roofs world be appropriate,
or does it presume to much of a "real world"?

	13. Finally, I hope for some reaction, which is why I wrote
this. The reaction I hope for, isn't primarily further debate on
the correctness of the CORRESPONDENCE theory or even applause for
stoutly maintaining it, although I am willing to take part in limited
further debate.  Aside to GAVAN: I have not specifically attacked
coherence or consensus theories, because I have not formulated straw
men to be attacked.  However, if you formulate something to attack,
I'll attack it if I disagree with it.

	I mainly seek reaction to the idea of research in
abstract meta-epistemological models, i.e. the theory of knowledge
seeking programs connected with abstract worlds.  Are there interesting
conjectures about what strategies and what presuppositions
will succeed in what worlds?  Are experiments and appropriate,
and which?

	Also, I would like to know if people find the ideas clear and/or
interesting or whether they require more detailed exposition to be even
comprehensible.  This length is my limit for this forum, but it may be
appropriate to try to develop more specific research questions if there is
interest.
	I have been silent (or rather its equivalent for written communication)
for a while, partly because of net problems, and partly because of having
undertaken to make a considered comment on coherence and consensus theories
on the basis of some references GAVAN gave me.  Habermas isn't here yet,
and I haven't got through Putnam's "Reason, Truth and History" in which
he seems at least partly to go back on his earlier realist positions.

	However, the colloquy on Robby and Tarskian semantics is too
much for me to stay out of.

1. What use is the predicate  true(<sentence>)?  It is of little use
applied only to constant sentences, because in almost every
place where  "true("Snow is white")" appears, you might as well write
"Snow is white".  Its real usefulness is in quantified assertions,
such as

	1. Whatever JMC says is true, formalized as:

(all (x) (implies (says jmc x) (true x)).

	2. If Smith says something he knows is not true, Smith is a liar.

	3. Any true assertion about the blocks on Robby's table follows
from those listed in the variable  FACTLIST  in Robby's program.

	4. Any assertion about LISP programs "proved" by the Boyer-Moore
theorem prover is true.

	A common use of the predicate  true(<sentence>)  will involve
substituting a particular sentence in a general statement involving
true  having the form of an implication, then proving the antecedent
(which may involve only a syntactic computation or lookup
in a database on the sentence), concluding by modus ponens that
the sentence is true, and then using the Tarski equivalence to
assert the sentence itself.

Informalized example:  Whatever Tarski says is true.  I just heard
Tarski say "Snow is white".  I believe my ears are working, so
Tarski said "Snow is white".  Hence, "snow is white" is true.  Hence,
Snow is white.

	Therefore, to answer DAM's question, if Robby has to reason
from the form of sentences or has to reason from the source of sentences,
he will have use for the predicate  true(<sentence>).

2. In our discussion of Robby's function we may conclude that Robby's
beliefs about what is on the table is COHERENT but not true or that
all the robots have come to a CONSENSUS that snow is black, but they're
all wrong.

3. Question for clarification.  Does the CONSENSUS theory of truth
apply to assertions like "The E key on this damn terminal
was sticking for a day last week, and I really should have complained
about it while it was happening, because they can't investigate
a problem that has gone away temporarily"?
I agree with Marvin that the idea of knowing as justified true belief
has bugs, but I also think that it is a useful idea.  The point is
to avoid claiming that a single formalism captures all useful ideas
of knowing.  I have a paper in which knowing is axiomatized in such
a way that it is closed under inference.  It will have a footnote
suggesting that the reader replace each occurrence of KNOW in the
paper by KNOW7, formalizing KNOW1 thru KNOW6 to suit himself.
When we have a flexible system of handling contexts, then KNOW
itself can be used in its different senses without confusion.

It seems to me that outlawing approximate concepts such as knowledge used
in ordinary language is not likely to be fruitful for either AI or
philosophy.  Moreover, simplified versions of these concepts are
likely to be useful.  Consider the afore-mentioned Robby:

We may find it advantageous to include in his database that Pat knows
Mike's telephone number and that travel agents know airline schedules.

Notice the following facts about English.  We can say, "Pat knows
that Mike's telephone number is 333".  We can also say, "Pat believes
that Mike's telephone number is 333".  We can say, "Pat knows Mike's
telephone number", and this is a different use of the verb "knows"
than in the previous sentence.  English doesn't have a parallel
use of "believes", i.e. we can't say, "Pat believes Mike's telephone
number", but have to say "Pat believes that he knows Mike's telephone
number".  In my formalization of concepts as objects (reported in Machine
Intelligence 9), I was tempted to introduce a parallel usage of
"believes", i.e. believes(pat, Telephone Mike).  There is no obvious
reason why such a locution shouldn't be present in some natural
languages.

Marvin complains that we can't give an operational definition of "knows".
It would be nice if we could, but the world isn't as we would like
it to be, and I think that confining robots to operationally definable
concepts won't work.  In fact, I hope it will be a theorem of abstract
meta-epistemology that systems only using operationally definable
concepts in their thinking will be ineffective in finding out about
their worlds, i.e. perhaps Life World physicists would be unable to
define "glider" and "puffer train" operationally.

Marvin seems to propose dropping "knows" from scientific
language and use "believes" combined with asserting  p  itself.
However, there are large areas of usage, such as most use of the
above sentences, in which this would be inconvenient, and we would
promptly introduce a term for justified true belief, perhaps not
even defining it precisely.  Even so, I might go along with Marvin
if making this concession to his scruples would make it likely
that epistemology for robots would thereby avoid future crises
of the same sort - attacks on approximate concepts.  However,
"believe" is also subject to the same kind of attack.

Some philosophers have responded to the demand to base epistemology
on the facts as discovered by quantum mechanics by pointing out
that even the physicists don't think that present quantum mechanics
provides the last word.  They advance the slogan, "It shouldn't be
necessary to solve all the problems of science before doing
epistemology".  I agree, and advance the further slogan, "It shouldn't
be necessary to solve all the problems of philosophy in order
to do artificial intelligence.  My goal is to formalize common
sense epistemology, not to engage in disputes with philosophers.
However, avoiding disputes isn't so easy, when one also wants to
interact with philosophers in order to get some help and when
certain recently discovered philosophical concepts, e.g. "natural
kinds" are of genuine use for AI.

I have been continuously disappointed in the direction this discussion
has taken.  I had hoped that a discussion of philosophy of science
undertaken in an AI/computer science environment would concentrate
on identifying usable formalisms, and that the discussants would
advance their own positive ideas of what formalisms might be
useful.  In fact, there has been much too little of this, and
much of the discussion is based solely on pre-computer philosophical
ideas.  Again let me recommend Aaron Sloman's "The computer revolution
in philosophy" or even Daniel Dennett's "Brainstorms".

Unique factorization is an interesting case.  It doesn't take much
experience with factoring numbers to develop an intuition for the
uniqueness of factorization.  The reasoning from Peano's axioms
or other first principles is non-trivial.  Also the statement
of unique factorization as a formula is non-trivial, and I would
suppose that natural language was used until fairly late.  It
is a rather direct consequence of "If  p  divides  ab,  then  p
divides  a  or  p  divides  b".  This in turn is proved by applying
the Euclidean algorithm to  p  and  whichever of  a  and  b  which
p  is assumed not to divide (say a), getting  1 = xa+yp, which we
then multiply by  b  getting  b = xab+ybp.  Since  ab  is assumed
divisible by  p, this shows that  b  is divisible by  p.  The
Euclidean algorithm is gotten from the division algorithm, and
the latter depends on the fact that any  m  can be divided by
any  n  leaving a remainder less than  n.  This depends on the
ordering properties of the natural numbers.  A simpler proof is
not to be expected, because the theorem isn't true in many rings
of algebraic integers that don't have division algorithms:
e.g. 6 = 3x2 = (1+sqrt(-5))(1-sqrt(-5)), and both are primes
in R(sqrt(-5)).  Have I got that right?  The point, if any, is that
mathematical experience can lead to intuitions that may be non-trivial to
verify from what one is inclined to take as the basic facts.
DAM:
	In particular why can't we think of "P is true" as being
     equivalent to (unquote P) where "unquote" is a particular syntactic
     operator which takes a quotation and removes the quotes.  This does
     not seem to me to depend on Tarskian semantics.  Of course the
     function "unquote" will have a recursive definition with rules like
     (unquote "P and Q") iff (unquote P) and (unquote Q). But I do not
     consider such recursive rules to have much to do with Tarskian
     semantics.

	My formalizations of knowledge and, incidentally of truth,
were formulated axiomatically at first, and didn't explicitly use
the Tarskian semantics, although any first order theory has Tarskian
semantics that anyone if free to discuss.  However, when I began
to try to formalize puzzles involving non-knowledge, such as a
strong version of the puzzle of the three wise men or the puzzle
of Mr. S and Mr. P, I had to use the Kripke semantics of modal
logic in an explicit way, and no modal logician has been able to
show how to solve either of these problems purely within modal
logic.  The strong version of "Three wise men" requires that the
king tell his wise men that he will put white or black spots on
each of their foreheads at least one of which will be white.  In
fact all three spots are white.  He then asks "Do you know the
color of your spot?" three times.  The formalization must express
these conditions, and the strong problem is to be able to prove
from the formalization that they answer know the first two times
the king asks, and yes the third time.  Unfortunately, these results
haven't been yet put in publishable form, but anyway the semantic
formalization involving possible worlds as objects does the strong problem
nicely.

	Your proposed formalization involving unquote isn't described
well enough for me to tell whether it will be more like a modal
formalism or like a first order formalization of the predicate  true.
In any case, your proposal has the advantage that arguments about
the meaning of "unquote" may not get as emotional as those about truth,
and such sayings as "Unquote is Beauty, and Beauty is unquote" will
more clearly seem to demand explanation on the part of those who
utter them.
	Philosophy owes science some debts.  In principle, this needn't
be the case if philosophy were to confine itself to what could be
determined by thinking, but it seems that we humans aren't smart
enough and have too much tendency to run in intellectual herds.  Here
are some examples:

1. Before approximately the time of Galileo, there wasn't much separation,
but most philosophy, and much science, attempted to explain the world
in terms of purpose, i.e. the purpose of the ant is to teach us not
to be lazy, and the purpose of the rainbow is to remind us that God
told Noah that the next time he would destroy the world by fire not
by water.  It was only by providing explanations that, as Laplace
put it, had no need of that hypothesis, that science rescued philosophy
from its concern with explanation by purpose.

2. Kant's notions of a priori facts, e.g. Euclidean geometry, were
determined by introspection and later proved wrong.  It would be
interesting to know whether it was noted that non-Euclidean geometry
proved him wrong or whether it had to wait for the theory of
relativity.

3. Before Einstein, just about anyone, scientist or philosopher, wouldn't
have noticed that distant simultaneity needn't be axiomatic and that
expressing space-time as the Cartesian product of space and
and time, was possible in many ways, none of which was
canonical.  If you don't know what "canonical" means
here, read some mathematics.  Hint: the dual of a finite dimensional
linear space is isomorphic with it but not canonically, while the
dual of the dual is canonically isomorphic with the original space.

4. Quantum mechanics tells us that common sense notions of causality
are only an approximation to reality and leaves us with
basic problems about causality that have remained unsolved since
the 1920s.

5. Daniel Dennett's "Can a computer feel pain" in his Brainstorms
points out that the question, "Can a person feel pain without
knowing it?" is a scientific question rather than a philosophical
question.

6. Mathematics has also taught philosophy some lessons.  Before
Godel and Tarski, no-one distinguished clearly between truth and
provability.  Cauchy destroyed philosophical nonsense about
calculus by Berkeley, and pre-destroyed similar nonsense by Marx.
Cantor destroyed the philosophy of the infinite.

7. Scientists have also helped mislead philosophy.  Behaviorism
and logical positivism are just as much the creation of scientists
as of philosophers.

	Now that dialectics has been mentioned, I cannot resist
the following quotation, which I believe is from Schopenhauer.

"But the height of audacity in serving up pure nonsense, in stringing
together senseless and extravagant mazes of words, such as had previously
been known only in madhouses, was finally reached in Hegel, and became the
instrument of the most bare-faced general mystification that has ever
taken place, with a result that will appear fabulous to posterity, and
will remain as a monument to German stupidity".
possible worlds and elaboration tolerance
	What Robby needs to know about depends on how smart we are trying
to make him, and I think that our first efforts have to be rather
modest, because we don't understand epistemology well enough.
I have been trying to develop an idea I call "elaboration tolerance".
We want Robby to use simple formalisms and then elaborate them
when he has to.  One way to do this is to use predicates that
can be "elaborated" into more comprehensive predicates.  Thus we
begin with  at1(Robby, desk)  and suitable axioms for  at1.  Later
we need  at2(Robby,desk), which is an object rather than a truth
value.  We say things like  knows(Robby, at2(Robby,desk)) and have
an axiom

	(x y).at1(x,y) iff true1(at2(x,y)).

Successive elaborations may involve such expressions as
true2(at2(x,y),s) where  s  is a situation,  true4(true2(at(x,y),s),w)
where  w  is a possible world, etc.  The possible worlds can in turn
be be mere objects whose values depend on more comprehensive
possible worlds.  If you think this idea is half-baked in its present
form, I agree with you.

	However, the AI and philosophical point is that we can use
a possible worlds formalism without having to commit ourselves to
a philosophical doctrine about what (if anything) possible worlds
"really" are.   As a mathematical object, a possible world is a
member of a space of possible worlds.  Such a space may be a set
the set of equivalence classes of a subset of outer level possible
worlds.  Thus in the wise men puzzle, the possible worlds are
characterized by the colors of the spots on the foreheads of
the three wise men.  However, we aren't really committing ourselves
to this as the only distinction worth making in the world as a
whole, and it is only in certain outer possible worlds that there
is a wise men puzzle at all.

	I think the best strategy is to develop the possible
worlds idea for use in AI, and then to figure out what we have
got.  If we try to pin down the idea now, it is likely to turn
out that we will want a somewhat different concept than the
one we have made precise at considerable trouble.

	I will look at my numerous files on the wise men and
Mr. S and Mr. P puzzles and decide what to transmit.  Since they
are lengthy and many won't be interested, I'll transfer copies
once to OZ and then give a reference in  phil-sci.  The S and P
puzzle is as follows:

	Two numbers  m  and  n  are chosen such that  1 < m =< n < 99.
Mr. S is told their sum and Mr. P is told their product.  The following
dialogue ensues:

Mr. P:	I don't know the numbers.

Mr. S:	I knew you didn't know.  I don't know either.

Mr. P:	Now I know the numbers.

Mr. S:	Now I know them too.

In view of the above dialogue, what are the numbers?

The point is that to formalize Robby's reasoning in solving the
puzzle, we need to express the original ignorance in the form
of the existence of sufficient possible worlds.

	Incidentally, DAM, if you meant that a possible world
in the wise men problem was fully characterized by the colors
of the spots, you were mistaken.  In the Kripke formalism, a
possible world is characterized not only by the colors of the spots,
but also by what other possible worlds are "accessible" (possible)
from it.  My own formalization uses a four term accessibility
relation  A(world1,world2,person,time), and we can express
"person  pp  knows proposition  p  at time  t  in world  w" by

	(w1)(A(w,w1,pp,t) implies true(p,w1).

Here's that old devil  "true"  again.

	My axioms for S and P were modified by Ma Xiwen, a visitor
from Peking, and he gave a proof in Weyhrauch's FOL proof checker of the
reduction of the knowledge problem to a mathematical problem.
Unfortunately, I found a bug in his axioms; they don't describe
the problem correctly.  While I have fixed that bug I haven't
redone the proof, because I am dissatisfied with the expression
of the axioms for learning.  Anyway, I'll shortly transmit
something.
	I also once enumerated the 2 by 2 Turing machines, though not as
completely as Marvin did, in the hopes that the simplest machines with
universal or other interesting behavior would lead to some new ideas about
what are the simple computing mechanisms.  Maybe carrying the enterprise
further would turn up something interesting.  However, it reminds me of
the last sentence in a Government pamphlet that gave all the known
techniques for panning for gold in streams.

     "A strong man, who isn't afraid of hard work, can make as much as
     fifty cents a day doing this".

My informant claimed that while Chinese laid off from building railroads
in the beginning of this century had panned out all the streams in
California, enough years had elapsed since even they gave up for enough
gold to wash down from the mountains so that one could make twenty dollars
a day.

	Maybe there are enough new ideas about what might be interesting
to justify another look at small Turing machines and other tiny computers.
Is it interesting that Conway's Life, invented for an entirely different
purpose, can support self-reproducing universal computers?  See reference
1.  I don't see any justification for dogmatism either way about the
possible reward from this enterprise.

	About numbers:

	I'm not sure there is much to be gained by studying the concept of
number itself, whether philosophically, mathematically or psychologically.
The probability of empty profundity is rather high.  Let me point out
(allege) that a child's first use of numbers is not to state the
cardinality of small sets.  Rather it is to count, i.e. recite the number
sequence - a singularly useless achievement in itself.  Presumably,
however, the rules for forming the numeral sequence, at first arbitrary
and then having increasing regularity, give a child the notion of
algorithm or at least the idea of a sequence formed by rule.  Pleasure in
this exercising this algorithm seems to motivate feats of counting that
require a span of attention longer than a child of that age usually
devotes to such activities.

References:

1. Unsubstantiated M.I.T. rumor.