Re: [Fis] Reply to Ted Goranson: levels of description

With respect to definitions of information
(Shannon, Von Neumann, Kolmogorov, etc.)
there is the completely opposite approach
of Michael Leyton. He defines information as
causal explanation. This is very powerful
because it is driven by a meaning-making
system, i.e., a cognitive system.

With respect to quantitative issues, his work
uses his group-theoretic methods based on
levels of wreath-product sequences.
The wreath products come from structural
characterizations of intelligent causal explanation.

best
Jim Johnson

  ----- Original Message -----
  From: John Collier
  To: FIS
  Sent: Saturday, June 10, 2006 2:22 PM
  Subject: Re: [Fis] Reply to Ted Goranson: levels of description

  At 08:20 AM 6/7/2006, Andrei Khrennikov wrote:

    My comment:
    Yes, >> deeply about the nature of information>>
    This is the crucial point. But as I know there are only two ways to
    define information rigorously, classical Shannon information, and
    quantum von Neumann information. In fact, all my discussion was about
    the possibility (if it would be possible at all) to reduce the second
    one to the first one.

    I understood that very often people speak about information in some
    heuristic sense, but we are not able to proceed rigorously with a
    mathematical definition of information. And I know only definitions
    which are based on different kinds of entropy and hence probability.

  Hmm. You should read Barwise and Seligman, Information Flow: the logic of distributed Systems. Very important for understanding Quantum Information. Also, I assume that you are familiar with algorithmic complexity theory, which is certainly rigourous, Minimum Description Length (Rissanen) and Minimum Message Length (Wallace and Dowe) methods that apply Kolomogorov and Chaitin's ideas very rigourously. If you don't like the computational approaches for some reason, then you might want to look at Ingarden et al, (1997) Information Dynamics and Open Systems (Dordrecht: Kluwer). They show how probability can be derived from Boolean structures, which are based on the fundamental notion of information theory, that of making a binary distinction. So probability is based in information theory, not the other way around (there are other ways to show this, but I take the Ingarden et al approach as conclusive -- Chaitin and Kolmogorov and various commentators have observed the same thing). If you think about the standard foundations of probability theory, whether Bayesian subjective approaches or various objective approaches (frequency approaches fail for a number of reasons -- so they are out, but could be a counterexample to what I say next), then you will see that making distinctions and/or the idea of information present but not accessible are the grounds for probability theory. Information theory is the more fundamental notion, logically, it is more general, but includes probability theory as a special case. Information can be defined directly in terms of distinctions alone; probability cannot. We need to construct a measure to do that.

  John

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  Professor John Collier collierj@ukzn.ac.za
  Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South Africa
  T: +27 (31) 260 3248 / 260 2292 F: +27 (31) 260 3031
  http://www.nu.ac.za/undphil/collier/index.html

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Received on Sat Jun 10 21:33:37 2006