Posted by
Phil Henshaw-2 on
URL: http://friam.383.s1.nabble.com/Robert-Rosen-tp525527p525531.html
That's nice, describing informality as sneaking in new axioms (or 'understandings', perhaps) in a series of assertions. Of course it's all but impossible to not do that,... given the complex way that ideas arise out of feelings and intents. What then about the invisible assumptions that tend to be numerous in any attempt at making formal statements. Would the likely presence of hidden assumptions make all formal statements presumably informal?
Phil
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-----Original Message-----
From: "Glen E. P. Ropella" <
[hidden email]>
Date: Wed, 02 Jan 2008 10:59:52
To:The Friday Morning Applied Complexity Coffee Group <friam at redfish.com>
Subject: Re: [FRIAM] Robert Rosen
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Nicholas Thompson on 01/01/2008 10:59 PM:
> thus, to be a good formalism, a formalism has to be in
> some sense informal, right?
This is a difficult question phrased in a misleadingly simple way.
We now know that mathematics is _more_ than formal systems (thanks to
Goedel and those that have continued his work). I.e. we cannot
completely separate semantics from syntax. The semantic grounding of
any given formalism (regardless of how "obvious" the grounding is)
provides the hooks to the usage of the formalism. Hence, by the very
nature of math, any formalism can be traced back to the intentions for
the formalism (though the original intentions may be so densely
compressed or that uncompressing them may be hard or impossible).
And in that sense, including your statement above, all formalisms will
then be good formalisms because they all have a semantic grounding.
But just because all formalisms assume a semantic grounding doesn't mean
they're "informal". The hallmark of a formalism is that it encompasses
all the assumptions in axioms that are well-understood and clearly
stated up front. I.e. a good formalism won't let new axioms slip in
anytime during inference. So, that's what it now means to be "formal".
An informal inferential structure loosens that constraint and will
allow one to introduce new semantics as the inference chugs along.
- --
glen e. p. ropella, 971-219-3846,
http://tempusdictum.comIt's too bad that stupidity isn't painful. -- Anton LaVey
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