From: Andrew Brown (A.Brown@LUBS.LEEDS.AC.UK)
Date: Wed Nov 30 2005 - 03:24:10 EST
Paul,
You write:
The below misunderstands Chaitins point. It is that no
deductions can contain more information than is included
in the premises.
I reply: That is exactly the point I was making.
You wrote:
The claims of dialectical logic to be able to produce
information from nowhere hide the fact that hidden
presuppositions are sneaked in the back door, from
our existing knowledge of the world.
I reply: Who made such a claim? (I explicitly denied it in my post). Nobodying is 'sneaking' anything in! The point is that premises *are* necessarily interrelated to the rest of the world. We can learn something new by fathoming their interrelation. This is not sneaky, it's true. Formal logic abstracts form from content, and just studies form - so to base theory on formal logic is to presume that knowledge, and so presumably reality, is rooted just in manipulating symbols according to fixed rules of syntax. Knowledge and reality are not so rooted -Chaitin's argument applies to formal systems and shows their fundamental limitations. To overcome these, you have give up the abstraction made by formal logic, the abstraction of form from content and start to look at their interrelation as a whole (no doubt Chaitin wouldn't agree with this last which maybe your point). That's what dialectical logic does. It saves the word 'logic' from the unfortunate fate of being tied to formal systems.
Many thanks,
Andy
-----Original Message-----
From: OPE-L [mailto:OPE-L@SUS.CSUCHICO.EDU] On Behalf Of Andrew Brown
Sent: 28 November 2005 10:53
To: OPE-L@SUS.CSUCHICO.EDU
Subject: Re: [OPE-L] abstraction and surprise
We have discussed previously Chiatin's point that premises cannot
contain as much info as reality. This seems to me to make a research
program entirely based on linear logic doomed to failure. We have to
look elsewhere and dialectics, a logic of content, not just form, fits
the bill. The idea is that the starting point (the dialecical equivalent
of the 'premises') does *imply* its own further development, it has
implicit conditions of existence. This is not some sort miracle but it
occurs simply because the starting point is an abstraction from the
system as a whole, and cannot exist as such an abstraction. E.g. the
commodity as the general form of wealth implies money, which (arguably)
implies capital, which implies exploitation, etc.
Of course each development is a surprise. Any other way we wouldn't be
learning anything, beyond what we already know!
Andy
-----Original Message-----
From: OPE-L on behalf of Paul Cockshott
Sent: Mon 28/11/2005 09:14
To: OPE-L@SUS.CSUCHICO.EDU
Cc:
Subject: Re: [OPE-L] abstraction and surprise
And I take his point in appealing to a logic of
exposition is exactly to show that if we keep stumbling over surprises,
as VFT finds in Capital, ch. 1, then we have a problem. Or is that
just with a logic that is linear? That is, supposing a presentation
that was dialectical, could we find the insufficiency of each stage to
comprehend its presuppositions a kind of surprise that drove forward the
immanent logic of the argument so that it constituted a move from
surprise to surprise, dialectically sublated, so to speak?
Howard what do you mean by a linear logic?
Do you mean the same thing as a monotonic logic?
I am skeptical that the Hegelian arguments are logical
developments from a given
starting point. Wherever you have surprise, you have new
information.
This must have been introduced from outside as a hidden
additional
premise.
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