John said:
> 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.
So, I ask a follow-up question: Would the greater generality of
information theory with respect to probability theory imply something
concerning the even more general question of whether or not logic is more
general than mathematics? Some seem to think that Goedel showed the
opposite.
STAN
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Received on Sat Jun 10 21:34:28 2006
