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| | well-documented (Hansel & Gretel, n.d.), but there are times when it provides | | well-documented (Hansel & Gretel, n.d.), but there are times when it provides |
| | the only means available. | | the only means available. |
| − | </pre>
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| − |
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| − | =====1.1.2.3. The Trees, The Forest=====
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| − |
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| − | <pre>
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| − | A sticking point of the whole discussion has just been
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| − | reached. In the idyllic setting of a knowledge field the
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| − | question of systematic inquiry takes on the following form:
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| − |
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| − | What piece of code should be followed in order to discover that code?
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| − |
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| − | It is a classic catch, whose pattern was traced out long ago in the paradox
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| − | of Plato's 'Meno'. Discussion of this dialogue and of the task it sets for
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| − | AI, cognitive science, education, including the design of intelligent tutoring
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| − | systems, can be found in (H. Gardner, 1985), (Chomsky, 1965, '72, '75, '80, '86),
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| − | (Fodor, 1975, 1983), (Piattelli-Palmarini, 1980), and in (Collins & Stevens, 1991).
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| − | Though it appears to mask a legion of diversions, this text will present itself at
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| − | least twice more in the current engagement, both on the horizon and at the gates
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| − | of the project to fathom and to build intelligent systems. Therefore, it is
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| − | worth recalling how this inquiry begins. The interlocutor Meno asks:
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| − |
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| − | | Can you tell me, Socrates, whether virtue can be taught,
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| − | | or is acquired by practice, not teaching? Or if neither
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| − | | by practice nor by learning, whether it comes to mankind
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| − | | by nature or in some other way? (Plato, 'Meno', p. 265).
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| − |
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| − | Whether the word "virtue" (arete) is interpreted to mean virtuosity
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| − | in some special skill or a more general excellence of conduct, it is
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| − | evidently easy, in the understandable rush to "knowledge", to forget
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| − | or to ignore what the primary subject of this dialogue is. Only when
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| − | the difficulties of the original question, whether virtue is teachable,
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| − | have been moderated by a tentative analysis does knowledge itself become
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| − | a topic of the conversation. This hypothetical mediation of the problem
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| − | takes the following tack: If virtue were a kind of knowledge, and if
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| − | every kind of knowledge could be taught, would it not follow that
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| − | virtue could be taught?
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| − |
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| − | For the present purpose, it should be recognized that this "trial factorization"
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| − | of a problem space or phenomenal field is an important intellectual act in itself,
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| − | one that deserves attention in the effort to understand the competencies that
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| − | support intelligent functioning. It is a good question to ask just what sort
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| − | of reasoning processes might be involved in the ability to find such a middle
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| − | term, as is served by "knowledge" in the example at hand. Generally speaking,
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| − | interest will reside in a whole system of middle terms, which might be called
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| − | a "medium" of the problem domain or the field of phenomena. This usage makes
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| − | plain the circumstance that the very recognition and expression of a problem
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| − | or phenomenon is already contingent upon and complicit with a particular set
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| − | of hypotheses that will inform the direction of its resolution or explanation.
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| − |
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| − | One of the chief theoretical difficulties that obstructs the unification of
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| − | logic and dynamics in the study of intelligent systems can be seen in relation
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| − | to this question of how an intelligent agent might generate tentative but plausible
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| − | analyses of problems that confront it. As described here, this requires a capacity
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| − | for identifying middle grounds that ameliorate or mollify a problem. This facile
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| − | ability does not render any kind of demonstrative argument to be trusted in the
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| − | end and for all time, but is a temporizing measure, a way of locating test media
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| − | and of trying cases in the media selected. It is easy to criticize such practices,
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| − | to say that every argument should be finally cast into a deductively canonized form,
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| − | harder to figure out how to live in the mean time without using such half-measures
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| − | of reasoning. There is a line of thinking, extending from this reference point
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| − | in Plato through a glancing remark by Aristotle to the notice of C.S. Peirce,
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| − | which holds that the form of reasoning required to accomplish this feat is
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| − | neither inductive nor deductive and reduces to no combination of the two,
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| − | but is an independent type.
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| − |
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| − | Aristotle called this form of reasoning "apagogy" ('Prior Analytics', 2.25)
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| − | and it was variously translated throughout the Middle Ages as "reduction" or
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| − | "abduction". The sense of "reduction" here is just that by which one question
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| − | or problem is said to reduce to another, as in the AI strategy of goal reduction.
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| − | Abductive reasoning is also involved in the initial creation or apt generation of
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| − | hypotheses, as in diagnostic reasoning. Thus, it is natural that abductive reasoning
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| − | has periodically become a topic of interest in AI and cognitive modeling, especially
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| − | in the effort to build expert systems that simulate and assist diagnosis, whether in
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| − | human medicine, auto mechanics, or electronic trouble-shooting. Recent explorations
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| − | in this vein are exemplified by (Peng & Reggia, 1990) and (O'Rorke, 1990).
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| − |
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| − | But there is another reason why the factorization problem presents an especially
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| − | acute obstacle to progress in the system-theoretic approach to AI. When the states
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| − | of a system are viewed as a manifold it is usual to imagine that everything factors
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| − | nicely into a base manifold and a remainder. Smooth surfaces come to mind, a single
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| − | clear picture of a system that is immanently good for all time. But this is how an
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| − | outside observer might see it, not how it appears to the inquiring system that is
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| − | located in a single point and has to discover, starting from there, the most fitting
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| − | description of its own space. The proper division of a state vector into basic and
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| − | derivative factors is itself an item of knowledge to be discovered. It constitutes
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| − | a piece of interpretive knowledge that has a large part in determining exactly how
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| − | an agent behaves. The tentative hypotheses that an agent spins out with respect to
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| − | this issue will themselves need to be accommodated in a component of free space that
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| − | is well under control. Without a stable theater of action for entertaining hypotheses,
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| − | an agent finds it difficult to sustain interest in the kinds of speculative bets that
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| − | are required to fund a complex inquiry.
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| − |
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| − | States of information with respect to the placement of this fret or fulcrum can
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| − | vary with time. Indeed, it is a goal of the knowledge directed system to leverage
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| − | this chordal node toward optimal possibilities, and this normally requires a continuing
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| − | interplay of experimental variations with attunement to the results. Therefore it seems
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| − | necessary to develop a view of manifolds in which the location or depth of the primary
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| − | division that is effective in explaining behavior can vary from moment to moment.
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| − | The total phenomenal state of a system is its most fundamental reality, but the
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| − | way in which these states are connected to make a space, with information that
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| − | metes out distances, portrays curvatures, and binds fibers into bundles --
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| − | all this is an illusion projected onto the mist of individual states
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| − | from items of code in the knowledge component of the current state.
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| − |
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| − | The mathematical and computational tools needed to implement such a perspective
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| − | goes beyond the understanding of systems and their spaces that I currently have
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| − | in my command. It is considered bad form for a workman to blame his tools, but
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| − | in practical terms there continues to be room for better design. The languages
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| − | and media that are made available do, indeed, make some things easier to see,
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| − | to say, and to do than others, whether it is English, Pascal (Wirth, 1976),
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| − | or Hopi (Whorf, 1956) that is being spoken. A persistent attention to this
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| − | pragmatic factor in epistemology will be necessary to implement the brands
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| − | of knowledge-directed systems whose intelligence can function in real time.
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| − | To provide a computational language that can help to clarify these problems
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| − | is one of the chief theoretical tasks that I see for myself in the work ahead.
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| − |
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| − | A system moving through a knowledge field would ideally be equipped with
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| − | a strategy for discovering the structure of that field to the greatest extent
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| − | possible. That ideal strategy is a piece of knowledge, a segment of code existing
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| − | in the knowledge space of every point that has this option within its potential.
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| − | Does discovery mark only a different awareness of something that already exists,
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| − | a changed attitude toward a piece of knowledge already possessed? Or can it be
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| − | something more substantial? Are genuine invention and proper extensions of the
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| − | shared code possible? Can intelligent systems acquire pieces of knowledge that
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| − | are not already in their possession, or in their potential to know?
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| − |
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| − | If a piece of code is near at hand, within a small neighborhood of a system's place in
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| − | a knowledge field, then it is easy to see a relationship between adherence and discovery.
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| − | It is possible to picture how crumbs of code could be traced back, accumulated, and gradually
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| − | reassembled into whole slices of the desired program. But what if the required code is more
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| − | distant? If a system is observed in fact to drift toward increasing states of knowledge,
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| − | does its disposition toward knowledge as a goal need to be explained by some inherent
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| − | attraction of knowledge? Do potential fields and propagating influences have to be
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| − | imagined in order to explain the apparent action at a distance? Do massive bodies
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| − | of knowledge then naturally form, and eventually come to dominate whole knowledge
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| − | fields? Are some bodies of knowledge intrinsically more attractive than others?
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| − | Can inquiries get so serious that they start to radiate gravity?
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| − |
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| − | Questions like these are only ways of probing the range of possible systems that
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| − | are implied by the definition of a knowledge field. What abstract possibility best
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| − | describes a given concrete system is a separate, empirical question. With luck, the
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| − | human situation will be found among the reasonably learnable universes, but before that
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| − | hope can be evaluated a lot remains to be discovered about what, in fact, may be learnable
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| − | and reasonable.
| |
| | </pre> | | </pre> |
| | | | |