With an abundance of views and perspectives available it is usually
possible to ground any (communicated) system in some other system.
This does not mean that, just because this is possible, this is the
'correct' view (I am not going to define 'correct' here).
For some 'systems' (the meaning of 'system' is somewhat problematic
here), it is very diffeicult to find such a perspective. Some
examples are: the universe (meaning everything that is, including
any God etc.), thought, language, mind, life, and free-will. In all
these cases it is difficult to find 'natural' *perspectives* which do
not seem to disort the intended interpretation unduely. In these
cases we may (almost by default) be forced to concede some sort of
self-production, but this is a matter of argument rather than
substance. Just because we have a choice of languages in other
cases does not mean there is NOT self-production (or, of course,
that there is).
Again, (I feel that I am becoming a bit repetative) the language of
representation you use needs to be appropriate for your ends. It is
very difficult to argue for an absolute use of language accross
contexts, aims, etc. Usually this is not useful (I am not going to
define that either!).
That is why, as Onar says, if meaning is inseperable (in *some*
ways) from the speaker, then we are led to self-production. This is
as much true of more traditional systems as hyper-sets etc. In
traditional mathematics we formalise sets in terms of other basic
concepts (such as logic and natural numbers) and alos formalise
logic and natural numbers in terms of sets. On paper these
formalisms are kept seperate, and used for seperate purposes. In our
minds they form part of a combined picture which is far more
self-referential, definitely self-reproducing and maybe
self-producing.
Hyperset theory is not special from this viewpoint. It is just
another formal system with its own advantages and disadvantages. (I
must admit I find it difficult to judge any formal system as special
in any vaguely impartial way). It is more expressive in some ways,
does not have quite the same set of assumptions as traditional set
theory, on the other hand its theory is less rich in some respects.
Both can be used to formalise the other.
All you are left with is judging which formal tool is appropriate for
what purpose. Your choice of formal tool does not effect the answers
to big philosphical questions.
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Bruce Edmonds
Centre for Policy Modelling,
Manchester Metropolitan University, Aytoun Building,
Aytoun Street, Manchester M1 3GH. UK.
e-mail b.edmonds@mmu.ac.uk
Tel no. +44 161 247 6479 Fax no +44 161 247 6802
WWW. http://bruce.edmonds.name/bme_home.html