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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