SUO: RE: Direct and Indirect Use of Axiom Systems
Dear Jon,
See comments below.
Matthew West
Principal Consultant
Shell Information Technology International Limited
Shell Centre, London SE1 7NA, United Kingdom
Tel: +44 20 7934 4490 Other Tel: +44 7796 336538
Email: matthew.west@shell.com
Internet: http://www.shell.com
> -----Original Message-----
> From: Jon Awbrey [mailto:jawbrey@att.net]
> Sent: 03 September 2003 20:20
> To: West, Matthew R SITI-ITPSIE
> Cc: SUO
> Subject: Re: Direct and Indirect Use of Axiom Systems
>
>
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> JA = Jon Awbrey
> MW = Matthew West
>
> JA: After some thought, I think that it might be
> good to elaborate on a few of these points,
> especially to point out certain implications
> of the indirect approach.
>
> JA: There are two different ways of using axiom systems to
> describe an object system,
> like common sense, domain knowledge, intelligent conduct,
> linguistic competence,
> linguistic performance, and so on. It has taken three
> years for this recognition
> to precipitate out of a suspension of nagging senses that
> we are talking in ways
> that are radically skew to one another, but I think that
> I can safely describe it
> now as a difference between the "direct" and the
> "indirect" use of axiom systems.
>
> JA: For example, consider the case of common sense belief systems
> and the performance systems that depend on them for guidance.
>
> JA: 1. Common sense belief and behavior might be represented directly
> as an axiom-based inference system, where the axioms give us
> the starting points of belief and behavior and the inference
> rules and proof chains provide us with literal simulations
> of the processes that apply this knowledge in practice,
> whether occurring "in the head" or in external action.
>
> JA: 2. Common sense belief and behavior might be regarded as arising
> from the states and transformations of an object system, and
> this object system might be described by an axiomatic theory,
> and yet the relationship of theory to model is more indirect,
> in that the axioms and inferences occurring in the theory are
> not the axioms and inferences occurring in the object system.
>
> MW: This sounds closer to what we are attempting.
>
> I muffed up the point a bit the first time, but think I said
> it better on the second try below. But I get the impression
> that many people are taking the "direct and literal" approach
> for granted as being the only one that comes to mind. I don't
> think this path has much chance of success with either creative
> literature or full-blown scientific theories, mostly on account
> of the unavoidability of indexical, metaphorical, and genuinely
> symbolic modes of communication with multiple levels of meaning
> or "poly-hermeneutic interpretation", if you will take the coin.
>
> JA: As a matter of fact, the indirect approach allows us to deal with
> a much wider range of object systems than just those that conduct
> themselves like literal deductive systems. For instance, we might
> be dealing with systems of belief and behavior that are configured
> at several different levels and that are composed of many diverse
> components, not all of which are consistent with each other, and
> that interact in non-deterministic ways. Indeed, many of these
> components may not even have all the structure of axiom systems
> but may operate more like automatic associative complexes or
> even very primitive reactive processes.
>
> MW: But I think we are trying to produce one consistent system,
> rather than many different views.
>
> I think that our theories of what's going on in the object system have
> to be empirical, rational, and as consistent as we can make them, but
> it's kind of like abnormal psych -- one wants a theory that explains
> the phenomenon, but the phenomenon itself may persist in appearing
> inconsistent and irrational in all terms that make sense to us.
> Closer to home, if we need a theory that describes and explains
> the persistence existence of many different views of the world,
> then we may hope to settle on one satisfactory theory about it,
> but the objective phenomenon is the simple fact of diversity,
> distribution of opinion, entropy, indeterminacy, uncertainty,
> or whatever privative condition we have in view at the time.
MW: Yes. All theories are wrong, some ares useful.
>
> JA: For instance, systems of heuristics often have this
> structure, with
> one sage maxim contradicting the next deep truth, it all depending
> on practical judgment, what the Greeks called
> "phronesis", I think,
> to decide which rule of thumb applies in which immediate instance.
>
> JA: In light of these possibilities, it might be better
> to revise my description of the indirect approach
> in something like the following way:
>
> JA: 2. Common sense belief and behavior might be regarded as arising
> from the states and transformations of an object system, and
> this object system might be described by an axiomatic theory,
> and yet the relationship of theory to model is more indirect,
> in that the axioms and inferences occurring in the theory are
> not literal representations of the initial conditions and the
> transitional processes that take place in the object system.
>
> MW: OK.
>
> JA: I think that it would help to clarify many of our discussions
> if we able to reflect on which implicit model we were using
> in each case, and to make a point of making that explicit.
>
> JA: Of course, it is also perfectly conceivable that we will be
> using a mixture of both direct and indirect modalities in
> our models and theories.
>
> MW: I think what we are attempting is a single consistent
> indirect model --
> from your description above.
>
> I hope so, or I'd hope that we'd eventually get around to that,
> as I think it's the only chance we have with complex phenomena,
> but I'm not so sure that we'll get to that penultimate resort
> until the slots in the back of the our medicine cabinets are
> filled to overflowing with rusty occam's razor blades.
>
> Jon Awbrey
>
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