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

From: John Collier <[email protected]>
Date: Sat 10 Jun 2006 - 20:22:09 CEST

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

---

Professor John Collier                                     [email protected]
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 20:24:19 2006