Posted by
Phil Henshaw-2 on
URL: http://friam.383.s1.nabble.com/Robert-Rosen-tp525527p525536.html
Glen,
>
> sy at synapse9.com on 01/02/2008 05:27 PM:
> > That's nice, describing informality as sneaking in new axioms (or
> > 'understandings', perhaps) in a series of assertions. Of
> course it's
> > all but impossible to not do that,... given the complex way
> that ideas
> > arise out of feelings and intents. What then about the invisible
> > assumptions that tend to be numerous in any attempt at
> making formal
> > statements. Would the likely presence of hidden
> assumptions make all
> > formal statements presumably informal?
>
> Well, with the stronger form of the word "formal" and the
> expansion of the word "informal" to refer to formal systems
> that allow the introduction of new axioms at will, we'd have
> to be careful to distinguish ill-formed systems from
> well-formed but open formal systems.
>
> Since adding new axioms as you go along might result in an
> inconsistent formal system (where the new axiom contradicts
> another axiom or a theorem derived from previous axioms),
> it's right to _mistrust_ the truth value of any formal
> statement unless one can demonstrate that:
>
> 1) no new axioms were added since consistency was demonstrated, or
> 2) if new axioms were added the resulting system is shown to
> be consistent.
That's about where I get too, that we need to accept that formal systems
are all embedded in informal ones. Introducing new principles in a
formal argument is then just an error in constructing the argument from
accepted principles. It that occurs it means you need to 'get to know'
the new principle or go back to the old ones.
> But, such mistrust is not the same as declaring the formal
> statement (or the system in which it's written) to be
> informal.... just not worthy of blind trust. In the case of
> (1), we would NOT accuse the statement or system of being
> "informal" in this new sense. In case (2), the _statement_
> might not be informal but the system in which it's stated
> would become "informal" (in this new softer sense of the word).
But then going back to the thread, Rosen's theorem seems to be offered
as proof that life requires gaps in efficient causation. Could those
gaps be regions? Would it be a corollary to say no formal system can
explain emergent organization of self-referencing causal loops, and so
maybe make ordinary complex systems which develop by growth a typical
case example for Rosen's idea? That would imply a map of the
deterministic plane sort of like Swiss cheese, with all individual
emergent systems defining 'dark matter' islands of self-organization
isolated from efficient causation by the 'white matter' of 'the cheese
itself'... ..Whew!... ;-)
> - --
> glen e. p. ropella, 971-219-3846,
http://tempusdictum.com> In all affairs it's a healthy thing now and then to hang a
> question mark on the things you have long taken for granted.
> -- Bertrand Russell
>
> -----BEGIN PGP SIGNATURE-----
> Version: GnuPG v1.4.6 (GNU/Linux)
> Comment: Using GnuPG with Mozilla -
http://enigmail.mozdev.org>
> iD8DBQFHfVU6ZeB+vOTnLkoRAjesAKDO7DsLZ4HNxF18iWU7cPNQOlnxywCcCm/T
> Ga+wkjMxw0uYaXsgIzmFPyM=
> =FQt3
> -----END PGP SIGNATURE-----
>
>