Changes

=====1.1.2.3.  The Trees, The Forest=====

=====1.1.2.3.  The Trees, The Forest=====

A sticking point of the whole discussion has just been reached.  In the idyllic setting of a knowledge field the question of systematic inquiry takes on the following form:

A sticking point of the whole discussion has just been

reached.  In the idyllic setting of a knowledge field the

question of systematic inquiry takes on the following form:

What piece of code should be followed in order to discover that code?

: ''What piece of code should be followed in order to discover that code?''

It is a classic catch, whose pattern was traced out long ago in the paradox

It is a classic catch, whose pattern was traced out long ago in the paradox of Plato's ''Meno''.  Discussion of this dialogue and of the task it sets for AI, cognitive science, education, including the design of intelligent tutoring systems, can be found in (H. Gardner, 1985), (Chomsky, 1965, '72, '75, '80, '86), (Fodor, 1975, 1983), (Piattelli-Palmarini, 1980), and in (Collins & Stevens, 1991). Though it appears to mask a legion of diversions, this text will present itself at least twice more in the current engagement, both on the horizon and at the gates of the project to fathom and to build intelligent systems.  Therefore, it is worth recalling how this inquiry begins.  The interlocutor Meno asks:

of Plato's 'Meno'.  Discussion of this dialogue and of the task it sets for

AI, cognitive science, education, including the design of intelligent tutoring

systems, can be found in (H. Gardner, 1985), (Chomsky, 1965, '72, '75, '80, '86),

(Fodor, 1975, 1983), (Piattelli-Palmarini, 1980), and in (Collins & Stevens, 1991).

Though it appears to mask a legion of diversions, this text will present itself at

least twice more in the current engagement, both on the horizon and at the gates

of the project to fathom and to build intelligent systems.  Therefore, it is

worth recalling how this inquiry begins.  The interlocutor Meno asks:

| Can you tell me, Socrates, whether virtue can be taught,

| or is acquired by practice, not teaching?  Or if neither

Can you tell me, Socrates, whether virtue can be taught, or is acquired by practice, not teaching?  Or if neither by practice nor by learning, whether it comes to mankind by nature or in some other way?  (Plato, ''Meno'', p. 265).

| by practice nor by learning, whether it comes to mankind

| by nature or in some other way?  (Plato, 'Meno', p. 265).

Whether the word "virtue" (arete) is interpreted to mean virtuosity

Whether the word "virtue" (''arete'') is interpreted to mean virtuosity in some special skill or a more general excellence of conduct, it is evidently easy, in the understandable rush to "knowledge", to forget or to ignore what the primary subject of this dialogue is.  Only when the difficulties of the original question, whether virtue is teachable, have been moderated by a tentative analysis does knowledge itself become a topic of the conversation.  This hypothetical mediation of the problem takes the following tack:  If virtue were a kind of knowledge, and if every kind of knowledge could be taught, would it not follow that virtue could be taught?

in some special skill or a more general excellence of conduct, it is

evidently easy, in the understandable rush to "knowledge", to forget

or to ignore what the primary subject of this dialogue is.  Only when

the difficulties of the original question, whether virtue is teachable,

have been moderated by a tentative analysis does knowledge itself become

a topic of the conversation.  This hypothetical mediation of the problem

takes the following tack:  If virtue were a kind of knowledge, and if

every kind of knowledge could be taught, would it not follow that

virtue could be taught?

For the present purpose, it should be recognized that this "trial factorization"

For the present purpose, it should be recognized that this "trial factorization" of a problem space or phenomenal field is an important intellectual act in itself, one that deserves attention in the effort to understand the competencies that support intelligent functioning.  It is a good question to ask just what sort of reasoning processes might be involved in the ability to find such a middle term, as is served by "knowledge" in the example at hand.  Generally speaking, interest will reside in a whole system of middle terms, which might be called a "medium" of the problem domain or the field of phenomena.  This usage makes plain the circumstance that the very recognition and expression of a problem or phenomenon is already contingent upon and complicit with a particular set of hypotheses that will inform the direction of its resolution or explanation.

of a problem space or phenomenal field is an important intellectual act in itself,

one that deserves attention in the effort to understand the competencies that

support intelligent functioning.  It is a good question to ask just what sort

of reasoning processes might be involved in the ability to find such a middle

term, as is served by "knowledge" in the example at hand.  Generally speaking,

interest will reside in a whole system of middle terms, which might be called

a "medium" of the problem domain or the field of phenomena.  This usage makes

plain the circumstance that the very recognition and expression of a problem

or phenomenon is already contingent upon and complicit with a particular set

of hypotheses that will inform the direction of its resolution or explanation.

One of the chief theoretical difficulties that obstructs the unification of

One of the chief theoretical difficulties that obstructs the unification of logic and dynamics in the study of intelligent systems can be seen in relation to this question of how an intelligent agent might generate tentative but plausible analyses of problems that confront it.  As described here, this requires a capacity for identifying middle grounds that ameliorate or mollify a problem.  This facile ability does not render any kind of demonstrative argument to be trusted in the end and for all time, but is a temporizing measure, a way of locating test media and of trying cases in the media selected.  It is easy to criticize such practices, to say that every argument should be finally cast into a deductively canonized form, harder to figure out how to live in the mean time without using such half-measures of reasoning.  There is a line of thinking, extending from this reference point in Plato through a glancing remark by Aristotle to the notice of C.S. Peirce, which holds that the form of reasoning required to accomplish this feat is neither inductive nor deductive and reduces to no combination of the two, but is an independent type.

logic and dynamics in the study of intelligent systems can be seen in relation

to this question of how an intelligent agent might generate tentative but plausible

analyses of problems that confront it.  As described here, this requires a capacity

for identifying middle grounds that ameliorate or mollify a problem.  This facile

ability does not render any kind of demonstrative argument to be trusted in the

end and for all time, but is a temporizing measure, a way of locating test media

and of trying cases in the media selected.  It is easy to criticize such practices,

to say that every argument should be finally cast into a deductively canonized form,

harder to figure out how to live in the mean time without using such half-measures

of reasoning.  There is a line of thinking, extending from this reference point

in Plato through a glancing remark by Aristotle to the notice of C.S. Peirce,

which holds that the form of reasoning required to accomplish this feat is

neither inductive nor deductive and reduces to no combination of the two,

but is an independent type.

   

   

Aristotle called this form of reasoning "apagogy" ('Prior Analytics', 2.25)

Aristotle called this form of reasoning "apagogy" (''Prior Analytics'', 2.25) and it was variously translated throughout the Middle Ages as "reduction" or "abduction".  The sense of "reduction" here is just that by which one question or problem is said to reduce to another, as in the AI strategy of goal reduction. Abductive reasoning is also involved in the initial creation or apt generation of hypotheses, as in diagnostic reasoning.  Thus, it is natural that abductive reasoning has periodically become a topic of interest in AI and cognitive modeling, especially in the effort to build expert systems that simulate and assist diagnosis, whether in human medicine, auto mechanics, or electronic trouble-shooting.  Recent explorations in this vein are exemplified by (Peng & Reggia, 1990) and (O'Rorke, 1990).

and it was variously translated throughout the Middle Ages as "reduction" or

"abduction".  The sense of "reduction" here is just that by which one question

or problem is said to reduce to another, as in the AI strategy of goal reduction.

Abductive reasoning is also involved in the initial creation or apt generation of

hypotheses, as in diagnostic reasoning.  Thus, it is natural that abductive reasoning

has periodically become a topic of interest in AI and cognitive modeling, especially

in the effort to build expert systems that simulate and assist diagnosis, whether in

human medicine, auto mechanics, or electronic trouble-shooting.  Recent explorations

in this vein are exemplified by (Peng & Reggia, 1990) and (O'Rorke, 1990).

But there is another reason why the factorization problem presents an especially

But there is another reason why the factorization problem presents an especially acute obstacle to progress in the system-theoretic approach to AI.  When the states of a system are viewed as a manifold it is usual to imagine that everything factors nicely into a base manifold and a remainder.  Smooth surfaces come to mind, a single clear picture of a system that is immanently good for all time.  But this is how an outside observer might see it, not how it appears to the inquiring system that is located in a single point and has to discover, starting from there, the most fitting description of its own space.  The proper division of a state vector into basic and derivative factors is itself an item of knowledge to be discovered.  It constitutes a piece of interpretive knowledge that has a large part in determining exactly how an agent behaves.  The tentative hypotheses that an agent spins out with respect to this issue will themselves need to be accommodated in a component of free space that is well under control.  Without a stable theater of action for entertaining hypotheses, an agent finds it difficult to sustain interest in the kinds of speculative bets that are required to fund a complex inquiry.

acute obstacle to progress in the system-theoretic approach to AI.  When the states

of a system are viewed as a manifold it is usual to imagine that everything factors

nicely into a base manifold and a remainder.  Smooth surfaces come to mind, a single

clear picture of a system that is immanently good for all time.  But this is how an

outside observer might see it, not how it appears to the inquiring system that is

located in a single point and has to discover, starting from there, the most fitting

description of its own space.  The proper division of a state vector into basic and

derivative factors is itself an item of knowledge to be discovered.  It constitutes

a piece of interpretive knowledge that has a large part in determining exactly how

an agent behaves.  The tentative hypotheses that an agent spins out with respect to

this issue will themselves need to be accommodated in a component of free space that

is well under control.  Without a stable theater of action for entertaining hypotheses,

an agent finds it difficult to sustain interest in the kinds of speculative bets that

are required to fund a complex inquiry.

States of information with respect to the placement of this fret or fulcrum can

States of information with respect to the placement of this fret or fulcrum can vary with time.  Indeed, it is a goal of the knowledge directed system to leverage this chordal node toward optimal possibilities, and this normally requires a continuing interplay of experimental variations with attunement to the results.  Therefore it seems necessary to develop a view of manifolds in which the location or depth of the primary division that is effective in explaining behavior can vary from moment to moment. The total phenomenal state of a system is its most fundamental reality, but the way in which these states are connected to make a space, with information that metes out distances, portrays curvatures, and binds fibers into bundles — all this is an illusion projected onto the mist of individual states from items of code in the knowledge component of the current state.

vary with time.  Indeed, it is a goal of the knowledge directed system to leverage

this chordal node toward optimal possibilities, and this normally requires a continuing

interplay of experimental variations with attunement to the results.  Therefore it seems

necessary to develop a view of manifolds in which the location or depth of the primary

division that is effective in explaining behavior can vary from moment to moment.

The total phenomenal state of a system is its most fundamental reality, but the

way in which these states are connected to make a space, with information that

metes out distances, portrays curvatures, and binds fibers into bundles --

all this is an illusion projected onto the mist of individual states

from items of code in the knowledge component of the current state.

   

   

The mathematical and computational tools needed to implement such a perspective

The mathematical and computational tools needed to implement such a perspective goes beyond the understanding of systems and their spaces that I currently have in my command.  It is considered bad form for a workman to blame his tools, but in practical terms there continues to be room for better design.  The languages and media that are made available do, indeed, make some things easier to see, to say, and to do than others, whether it is English, Pascal (Wirth, 1976), or Hopi (Whorf, 1956) that is being spoken.  A persistent attention to this pragmatic factor in epistemology will be necessary to implement the brands of knowledge-directed systems whose intelligence can function in real time. To provide a computational language that can help to clarify these problems is one of the chief theoretical tasks that I see for myself in the work ahead.

goes beyond the understanding of systems and their spaces that I currently have

in my command.  It is considered bad form for a workman to blame his tools, but

in practical terms there continues to be room for better design.  The languages

and media that are made available do, indeed, make some things easier to see,

to say, and to do than others, whether it is English, Pascal (Wirth, 1976),

or Hopi (Whorf, 1956) that is being spoken.  A persistent attention to this

pragmatic factor in epistemology will be necessary to implement the brands

of knowledge-directed systems whose intelligence can function in real time.

To provide a computational language that can help to clarify these problems

is one of the chief theoretical tasks that I see for myself in the work ahead.

A system moving through a knowledge field would ideally be equipped with

A system moving through a knowledge field would ideally be equipped with a strategy for discovering the structure of that field to the greatest extent possible.  That ideal strategy is a piece of knowledge, a segment of code existing in the knowledge space of every point that has this option within its potential. Does discovery mark only a different awareness of something that already exists, a changed attitude toward a piece of knowledge already possessed?  Or can it be something more substantial?  Are genuine invention and proper extensions of the shared code possible?  Can intelligent systems acquire pieces of knowledge that are not already in their possession, or in their potential to know?

a strategy for discovering the structure of that field to the greatest extent

possible.  That ideal strategy is a piece of knowledge, a segment of code existing

in the knowledge space of every point that has this option within its potential.

Does discovery mark only a different awareness of something that already exists,

a changed attitude toward a piece of knowledge already possessed?  Or can it be

something more substantial?  Are genuine invention and proper extensions of the

shared code possible?  Can intelligent systems acquire pieces of knowledge that

are not already in their possession, or in their potential to know?

If a piece of code is near at hand, within a small neighborhood of a system's place in

If a piece of code is near at hand, within a small neighborhood of a system's place in a knowledge field, then it is easy to see a relationship between adherence and discovery. It is possible to picture how crumbs of code could be traced back, accumulated, and gradually reassembled into whole slices of the desired program.  But what if the required code is more distant?  If a system is observed in fact to drift toward increasing states of knowledge, does its disposition toward knowledge as a goal need to be explained by some inherent attraction of knowledge?  Do potential fields and propagating influences have to be imagined in order to explain the apparent action at a distance?  Do massive bodies of knowledge then naturally form, and eventually come to dominate whole knowledge fields?  Are some bodies of knowledge intrinsically more attractive than others? Can inquiries get so serious that they start to radiate gravity?

a knowledge field, then it is easy to see a relationship between adherence and discovery.

It is possible to picture how crumbs of code could be traced back, accumulated, and gradually

reassembled into whole slices of the desired program.  But what if the required code is more

distant?  If a system is observed in fact to drift toward increasing states of knowledge,

does its disposition toward knowledge as a goal need to be explained by some inherent

attraction of knowledge?  Do potential fields and propagating influences have to be

imagined in order to explain the apparent action at a distance?  Do massive bodies

of knowledge then naturally form, and eventually come to dominate whole knowledge

fields?  Are some bodies of knowledge intrinsically more attractive than others?

Can inquiries get so serious that they start to radiate gravity?

Questions like these are only ways of probing the range of possible systems that

Questions like these are only ways of probing the range of possible systems that are implied by the definition of a knowledge field.  What abstract possibility best describes a given concrete system is a separate, empirical question.  With luck, the human situation will be found among the reasonably learnable universes, but before that hope can be evaluated a lot remains to be discovered about what, in fact, may be learnable and reasonable.

are implied by the definition of a knowledge field.  What abstract possibility best

describes a given concrete system is a separate, empirical question.  With luck, the

human situation will be found among the reasonably learnable universes, but before that

hope can be evaluated a lot remains to be discovered about what, in fact, may be learnable

and reasonable.

====1.1.3.  Reality and Representation====

====1.1.3.  Reality and Representation====