Re: [OPE-L] abstraction and surprise

[Paul Cockshott <wpc@xxxxxxxxxxxxx>]

Andrew Brown wrote:


 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.-
------------------------------
Paul

I think it might help me here if you were to give an example of a premise
that was necessarily interrelated to the rest of the world, and show
how this is different from the method of successive approximation.

I admit to having been prejudiced against dialectical logic after
reading Hegels book on it years ago. In the context that you are
using it may mean something different.
-------------------
Andrew

 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. --
--------------

Paul
I am not sure that I agree with this. The kind of work that Ian Wright is doing
involves rigourously applying a few simple fixed rules and investigating
the implications of this - deriving for example the law of value from
such simple assumptions.

I also think that paradoxically Marx's method of exposition with
the circuit notations in Capital is actually very similar to formal
syntax. One should not be so ready to dismiss formal synatax

Consider
m-> C -> m'

Split this into two rules

m -> C

C -> m'

This looks very like a simple Chomsky grammar notation.
It corresponds to what Chomsky in 1957 was calling a non-terminating
transformational grammar.
It defines a language of which the following are valid sentences

M
C
M'
C'
M''
C''
M'''

etc

This models the self expansion of capital over time.

I find it quite striking that Marx was using notational
formalism that did not come into general use until the 1950s
I am not sure whether in Chomsky's terms this is a finite state
grammar or a phrase structure grammar, I am currently engaged
in an off-list debate on what sort of grammar marx was using.


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). ----
--------------
Paul

When you 'look at their interrelation' as you put it, is this:

a) a heuristic for investigation
b) a didactic tactic for explanation
c) a rigourous procedure to be followed in investigation
-


That's what dialectical logic does. It saves the word 'logic' from the
unfortunate fate of being tied to formal systems.
 ---------------------------



--
Paul Cockshott
Dept Computing Science
University of Glasgow



0141 330 3125