This looks fun! Do you plan on actually writing the paper? I
appreciate seeing that you are attempting a unified assault on the
problem of cognition from an abstract vantage point.
However, I am unsure about the bit concerning overcoming Godelian
limitations. Switching to relative complexity comparisons does not
obviously solve anything, at least to me. You will have to spell this
out in the paper! :) Along with everything else, like your notion of
analogy and so on.
On Wed, Jun 17, 2009 at 8:51 PM, marc.geddes<marc.ged...@gmail.com> wrote:
> I tripped over my own boot-laces and stumbled – whacking my head.
> Bent over to rub my head and retie the damn laces, all a sudden I had
> the following quick rough thoughts for a paper:
> 'Cognitive Reflectivity'
> Marc Geddes
> Melbourne, Australia
> 18th June, 2009
> "A change in the goal-system of an agent is equivalent to a change in
> the way in which knowledge is represented by the agent. It follows
> that it is equivalent to a change in the complexity of the program
> representing the agent. Thus we require a method of comparing the
> complexity of strings in order to ensure that relevant program
> structure is preserved with state transitions over time. Standard
> probability theory cannot be used because; (1) Consistent probability
> calculations require implicit universal generalizations, but a
> universal measure of the complexity of finite strings is a logical
> impossibility (fromGodel, Lob theorems); and (2) Standard measures of
> complexity (e.g Kolmogorov complexity) from information theory deal
> only with one aspect of information (i.e. Shannon information), and
> fail to consider semantic content. The solution must resolve both
> these problems.
> Regarding (2) the solution is as follows:, information theory is
> generalized to deal with the actual meaning of information (i.e . the
> semantics of Shannon information) .The generalized definition of the
> complexity of a finite string is based on the conceptual clustering of
> semantic categories specifying the knowledge a string represents. The
> generation of hierarchical category structures representing the
> knowledge in a string is also associated with a generalization of
> Occam’s razor. The justification for Occam’s razor and the problem
> of priors in induction is resolved by defining ‘utility’ in terms of
> ‘aesthetic goodness’, which is the degree of integration of different
> concept hierarchies. This considers the process through which a
> theory is generated; it is a form of process-oriented evaluation.
> Regarding (1); The Godel limitation is bypassed by using relative
> complexity measures of pairs of strings . This requires generalizing
> standard Bayesian induction ; in fact induction is merely a special
> case of a new form of case-based reasoning (analogical reasoning) .
> Analogical reasoning can be formalized by utilizing concepts from
> category theory to implement prototype theory, where mathematical
> categories are regarded as semantic categories. Semantic concepts
> representing the knowledge encoded in strings can be considered to
> reside in multi-dimensional feature space, and this enables mappings
> between concepts; such mappings are defined by functors representing
> conceptual distance; this gives a formal definition of an analogy.
> The reason this overcomes the Godel limitation and is more general
> than induction is because it always enables relative comparisons of
> the complexity of pairs of strings. This is because case-based
> reasoning depends only on the specific details on the strings being
> compared, whereas induction makes implicit universal generalizations,
> and thus fails.
> To summarize: Induction is shown to be merely a special case of a new
> type of generalized case-based (analogical) reasoning. Concepts from
> category theory enable a formal definition of an analogy, which is
> based on the notion of conceptual distance between concepts. The
> notion of complexity is generalized to deal with semantics, where the
> information in a string is considered to be a concept hierarchy. This
> enables comparisons between pairs of strings; relations between
> strings are defined in terms of the mappings between concepts, and the
> mapping is evaluated in terms of its aesthetic goodness. Godelian
> limitations are overcome, since analogical reasoning always enables a
> comparison of the relative complexity between any two finite strings.
> Further the new metric of aesthetic goodness ensures that the relevant
> program structure is preserved between state transitions and thus
> maintains a stable goal system."
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