From: Howard Engelskirchen (howarde@TWCNY.RR.COM)
Date: Wed Nov 30 2005 - 01:24:44 EST
Hi Paul, Andrew, and all,
Paul asked what I meant by linear logic. I was just using the term as Chris
Arthur used it in his Chapter 2 where he critiques the sequence of models
method -- the method of successive approximations which "consists in moving
from the more abstract to the more concrete in a step by step fashion,"
removing simplifying assumptions to take account of wider phenomena. The
special target is the idea that the early chapters of Capital present a
model of simple commodity production which is then made more complex by the
more or less arbitrary introduction of labor power, money, organic
composition, etc.
I agree with Paul that there is no magic to dialectical logic. If reality
needs to be followed dialectically, then this has to do with the nature of
the reality studied and this must be shown.
For example, unless commodity exchange is limited to the instantaneous
exchange of performances, promises are necessary. But if, given self
interest, one person is going to perform in reliance on another's promise of
performance, then if exchange among strangers is to be reliably reproduced,
force is necessary. That is, the insufficiency of the economic structure
demands a legal superstructure. Here, as elsewhere in science, the logic of
the exposition, which may be presented dialectically, follows causal
explanation. Notice that the causal explanation given does not offer a
historical account, but instead explains what is required for the
reproduction of a totality.
But the bare statement that a starting point abstracted from a whole has the
whole implicit in it does not in itself show anything about the nature of
the reality to be studied. Moreover, the abstraction with which we start
may be a methodology, a way of picking out features of reality we otherwise
would not have access to, or it may be an ontology, that is, we refer to
some abstract mode of being.
There are lots of self-reproducing systems, totalities, that are the object
of scientific investigation. We ourselves are one and could begin by
investigating some causal mechanism, e.g., the heart, lung, axon, etc.,
essential to our own persistence.
Assume then a social totality. When we start with value by abstracting from
the relation of exchange, what is it to which we refer?
Howard
----- Original Message -----
From: "Paul Cockshott" <wpc@DCS.GLA.AC.UK>
To: <OPE-L@SUS.CSUCHICO.EDU>
Sent: Tuesday, November 29, 2005 5:59 PM
Subject: Re: [OPE-L] abstraction and surprise
The below misunderstands Chaitins point. It is that no
deductions can contain more information than is included
in the premises.
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.
-----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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