Re: Inconsistency, etc.

[Tim Gwinn <***>]

(from below)
> HP: I am in full concordance with Rosen, although I may prefer
> slightly different expressions. I also treat von Neumann?s and
> Chaitin?s concepts of complexity as complementary to this one.

Those two are indeed concepts of complexity entirely different from, and
inequivalent to, the concept of Rosennean complexity. This discussion list
is about Rosennean complexity.

Tim


> -----Original Message-----
> From: ROSEN Forum [mailto:*** Behalf Of Howard
> Pattee
> Sent: Friday, June 04, 2004 12:56 PM
> To: ***
> Subject: Re: Inconsistency, etc.
>
>
> Tim, Judith, Dan,
>
> Here are some Rosen quotes that may help answer concerns you
> raised about my views of complementarity, non-equivalent models
> and Rosen?s concept of complexity.
>
> > H.Pattee wrote: Inconsistency can arise only in formal symbol
> systems. Nothing in nature can be inconsistent (What would that
> mean?). It is only in our > formal models that inconsistency can
> occur. Only in the formal sense can they [models] be
> inconsistent. Two well-defined valid models can describe
> properties of reality even though the models if combined formally
> would be inconsistent. For example, the microscopic laws of
> motion are reversible, that is, formally symmetric in time. A box
> of gas obeys these laws. The second law of thermodynamics is
> irreversible, and the same box of gas also obeys this law. You
> cannot formally combine these two models consistently, but to
> fully understand a box of gas you need both [complementary] models.
> >
> Judith: I see a great deal to argue with in the above paragraph
> (which may or may not surprise the list!), however, since the
> above is not couched in terms of what Robert Rosen did or did not
> believe, I see little need to challenge it.
>
> Rosen (AS, p 83, Case 3): ?In this case no mathematical relation
> can be established between F1 and F2. Thus, these encodings are
> inadequate in principle to represent any linkage in N between the
> families or qualities encoded into them. Into this class, we
> would argue, fall the various complementarities postulated by
> Bohr in connection with microphysical phenomena [He later
> generalized the concept]. Here again, it must be stressed that it
> is the mathematical character of the encodings which determined
> whether or not relations between them can be effectively
> established; in this sense, complementarity is entirely a
> property of formal systems, and not of natural ones.?
>
> ?We are subsequently going to relate our capacity to produce
> independent encodings of a given natural system N with the
> complexity of N (See 5.7).?
>
> AS, 5.7, p. 322: ?Thus, for us, a system will be complex to the
> extent that it admits non-equivalent encodings; encodings which
> cannot be transformed or reduced to one another.?
>
> HP: I am in full concordance with Rosen, although I may prefer
> slightly different expressions. I also treat von Neumann?s and
> Chaitin?s concepts of complexity as complementary to this one.
>
> Howard