[Inquiry] Re: Questions Involving Pure Symbols -- Discussion

[Jon Awbrey]

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QUIPS.  Discussion Note 8

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Re: QUIPS-DIS 7.  http://stderr.org/pipermail/inquiry/2005-May/002608.html
In: QUIPS-DIS.    http://stderr.org/pipermail/inquiry/2005-May/thread.html#2602

Ben,

Here are some random thoughts on the information associated
with logical operators.  The way that I would think about the
information associated with "and" is like this.  Information is
a concept that only makes sense in a certain context, and so the
the type of setting that we have in mind makes all the difference
in what we come up with.  The question that I'd be asking is this:
How much is our uncertainty reduced when we learn a specific law,
say that one of three boolean variables is the conjunction of the
other two?  Since this is a theoretical example, not an empirical
situation, we assume equal likelihood or maximum entropy for our
prior uncertainty, namely, that any one of the 8 triples in B^3
is equally likely, of 3 bits of uncertainty.  When we learn that
the law of the land is x = y and z, there are only 4 triples that
satisfy that equation, and so our uncertainty is now just 2 bits.
This means that knowing the law reduces our uncertainty by 1 bit.
It seems like the next question is this:  How do we conceive this
law to be communicated, that is, what is the language or channel?
If we could say that the reduction of uncertainty was associated
with the reception of a single sign, then that sign would convey
one bit of information, but that doesn't seem like a likely case.
To make this example more realistic, we would have to think of a
specific language for the propositional forms on three variables.

Far as I get ...

Jon Awbrey

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inquiry e-lab: http://stderr.org/pipermail/inquiry/
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