Code Meno Code

Cf: http://inquiryintoinquiry.com/2013/02/04/code-meno-code-1
NB. The copy on my blog should be a lot easier on the eyes.

Peircers,

The problem of Plato's “Meno” came up frequently in the AI and Cognitive Science
literatures of the 80s and 90s, and I encountered it once again as I turned to a
more system-theoretic framework for integrating the dynamic and symbolic aspects
of intelligent systems.  Here's a bit of the prospectus that I wrote at the time:

Adapted from “Prospects for Inquiry Driven Systems”
• http://mywikibiz.com/Directory:Jon_Awbrey/Essays/Prospects_For_Inquiry_Driven_Systems

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:

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 of Plato’s Meno. Discussion of this dialogue 
and of the task it sets for AI, cognitive science, and education, including the design of intelligent tutoring systems, 
can be found in (H. Gardner, 1985), (Chomsky, 1965, 1972, 1975, 1980, 1986), (Fodor, 1975, 1983), (Piattelli-Palmarini, 
1980), and (Collins and Stevens, 1991). Though it appears to mask a legion of diversions, this question 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
| 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 in some special skill or a more general excellence 
of conduct, it is evidently easy, in the understandable rush to “knowledge”, to forget or 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 is a kind of knowledge, and if every kind of knowledge can be be taught, would it not follow that virtue can 
be taught?

For the present purpose, it should be recognized that this “trial factorization” of a phenomenal field or problem space 
is a significant 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 field of phenomena. This usage makes plain the circumstance that the very recognition and expression of a problem or 
phenomenon is already contingent on 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 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) 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 and Reggia, 1990) and (O’Rorke, 1990).

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.

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.

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.

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?

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?

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.

Regards,

Jon

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