File spoon-archives/marxism2.archive/marxism2_1996/96-07-31.055, message 3

Date: Thu, 11 Jul 96 08:32:02 GMT

>      It has long been argued that dialectics involves
> allowing "fuzzy boundaries" between categories.  This
> would be consistent with intuitionistic math which allows
> for the "excluded middle" to hold.  It could also be
> thought to hold for "fuzzy logic," now used by Japanese
> manufacturers in washing machines and air conditioners.
> Some claim that Japanese philosophy is more conducive 
> to accepting such "it is both true and false" logics.
> Barkley Rosser

Barkley is confusing boundaries unnacceptably.

i) intuitionistic logic and the excluded middle.

Basically, intuitionistic logic dissallows proof by contradiction.
So arguments of the form :

not A -> B
not A -> not B
therefore not not A
therefore A

are disallowed.

intuitionistic logic stops at

"therefore not not A".

Classical ( ie non intuitionistic ) logic by implication has a rule

A or not A.
so it can deduce from 
not not A

But what this has to do with dialectics, I have no idea.
Intuitionsistic logic is VERY firmly a two state logic. If anything, it is
irritatingly more consistent about it than classical logic.

In a way, the difference between Intuitionsistic and Classical approach to
Logic is like the difference between the way a Computer and a Mathematician
approach arithmetic. Suppose we want to know if there is a solution to
the equation F(x) = 0.

The Mathematician proves that there is a solution.
The Computer says, "well, what is the solution then ?"
The Mathematician replies "All I know is that there is a solution. But I can't
tell you what it is".
The Computer says "well at least tell me how to construct the solution then".
The Mathematician says "Look, I've no idea how to construct the solution. But
I know there is one".
The Computer says, "OK, so you have disproved the theorem that there is no solution.
But you have not told me anything about whether there is a solution".

Now, IMO, the Computer is just thick. 

ii) Fuzzy Logic.

Well, what a load of bollocks fuzzy logic is.
As far as I am concerned, it ranks below neural networks, and that's pretty low.

In fuzzy logic, states aren't true and false, they're on a grey scale. But it's
grey scale can only answer questions like "to what extent is the light bulb on" ?
In fuzzy logic, you just get the light meter out and read the result.
Not exactly earth shattering, I hear you say. Well exactly.

iii) There ARE all sorts of logics which can talk about a world more interesting than
the world imagined by classical, particularly mathematical logic. They are all
derivatives of modal logic, particularly the various temporal logics. They can
at least express ideas like "The sun is shining on Thursday in Manchester". They 
form a potential logical background to analysing some aspects of electronic circuits,
for instance.

But my basic attitude to all these formal logics is that if something can be expressed
in any way in terms of formulae, then you have simplified what that thing is
beyond recognition. Dialectical Materialism allows us a framework to comprehend this
totallity. So what if some bizarre logic can express the functionality of an 
electronic circuit ? That doesn't get close to explaining what I use by PC for.
It's like using the Chemistry of an internal combustion engine to explain what
cars do.


Adam Rose


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