Re: Inconsistency, etc.

[Howard Pattee <***>]

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