Re: Category Theory and Rosen - some clarifications (i hope 8-))

[Mark P. Line]

glen e. p. ropella wrote:
> 
> Mark P. Line writes:
>  > So the limits of theory are the limits of compression?
> 
> Basically, yes.  Theoretical constructs are the compression
> of observed data.

Are you speaking normatively, or descriptively?

Normatively, I would say that your statement represents one possible
opinion. Another possible opinion is that the link between theory and
observation need not be expressible in terms of compression -- in terms
of relative length of statements of generalizations and statements of
the data being generalized.

Descriptively, I don't believe your statement for a minute. It may often
be true that a theoretical construct compresses the union of its
empirical database and its prediction space, but I think it is very
seldom the case that a theoretical construct compresses the empirical
database -- and only at the most generalized levels of theory.


I think one of the things that drives major theoretical upheavals is the
tendency for scientists to treat predictions as though they were data.
Data collected under no assumption that the theory is "true" are not
distinguished from data collected under the assumption that it is --
especially after the theory has been reified (removing some of its
important assumptions from easy and objective criticism).

I wonder what would happen if we started requiring all published
theories to be associated with a published corpus of empirical data.


> Now, like all compressions, some way (algorithm) for
> uncompressing the data is necessary.  This is where formal
> systems, simulations, logic, etc. play a significant role.

Even if I thought that theories are (or should be) compressions of
observed data, I don't think I'd be likely to assume that the
compression or decompression operations are necessarily computable.


> The liar's paradox is basically presented by
> the unparsable nature of the statement, "This statement is
> false."

<nit>
Uninterpretable, not unparseable, right? The statement can be _parsed_
(grammatically decoded) just as easily as "This cumquat is orange."
</nit>

> What this provides is an English statement to which a truth
> value cannot be deduced.

>From which one should conclude that English statements don't necessarily
have "truth values" -- maybe they _never_ have "truth values", in fact.
I wonder why that conclusion isn't always drawn.


> English language, the sentence is *easily* understood as
> "The person presenting the sentence is casting doubt on his
> own credibility." It's simply pointing out that human
> language is not logic.

Preeeeeeecisely. 

Unless you define logic in terms of human language, that is. But no, we
have to have something that "transcends" the foibles of mere verbal
expression, don't we... :)


> (However, it *could* be appropriate to say that the liar's
> paradox is an example of the incompleteness theorem....
> But, I would object to that, as well.)

Me too, because it would imply that human language is a formal system.
And them's fightin' words where I come from, boy!



> Now, to move on, I would again posit that in order to
> develop a theory of Alife, we need a formalization of Alife
> systems.... i.e. some formal system that is common to all
> or, at least, large subsets of the set of systems we call
> Alife systems.

Do you posit the following as well?

"In order to develop a theory of life, we need a formalization of living
systems.... i.e. some formal system that is common to all or, at least,
large subsets of the set of systems we call living systems."



> I'm not suggesting that the purpose of
> formalization of Alife is to make Alife more analyzable. 
> But, I *do* want to be able to make statements about Alife
> systems.  Not only that, I want to be able to state
> *theorems* of Alife systems.

Do you believe that biologists should want to be able to state
*theorems* about living systems?


-- Mark

(Mark P. Line  --  Bellevue, Washington  --  <address@hidden>)



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