Posted by
glen ep ropella on
URL: http://friam.383.s1.nabble.com/Robert-Rosen-tp525527p525533.html
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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.
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).
- --
glen e. p. ropella, 971-219-3846,
http://tempusdictum.comIn 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
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