Re: Sci-Am: Ladders of Effective Theories

["Tim Gwinn" <***>]

Title: Message

Roberto,

 

Ok, I think we are thinking along similar lines.  Rosen describes in the beginning of AS how it was his involvement in a group that was attempting to better understand social organizations that led to his inquiry into anticipatory systems and their consequences. Such systems or "social phenomena", to use your term, are full of self-referential structures, as you point out. Certainly, impredicative, or self-referential, structures are one of the defining characteristics of Rosennean complexity, and as such, those systems have both the richness of that complexity, as well as the difficulties associated with attempting to model and understand them.

 

I'd greatly appreciate if you could email your article - I'd be very interested in reading it. :)

 

Regards,

Tim

 

-----Original Message-----
From: ROSEN Forum [mailto:***On Behalf Of Roberto Poli
Sent: Saturday, June 14, 2003 8:57 AM
To: ***
Subject: Re: Sci-Am: Ladders of Effective Theories

Tim,

the idea of resorting to self-referential structures goes obviously against the infinite regress advocated by the sci-am article. This doesn't exclude the possibility of a number (I am not saying series) of self-referential structures, variously interconnected one another. Consider "social phenomena": politics, language, art, law, etc etc. Each of them constitute a self-referential system, which at the same time is partially independent and partially dependent from other systems. Biology shares the same picture. I have analyzed a number of the connected issues in a paper of mine published a couple of years ago: “The Basic Problem of the Theory of Levels of Reality”, Axiomathes, 2001, 12, 3-4, pp. 261-283. Please note that at that time I did'nt know Rosen's work. You may retrieve the paper from http://www.kluweronline.com/issn/1122-1151. If not, let me know and I will mail it to you.

r

   

Roberto,

 

The formalism and math part is definitely an area where I am weak in understanding. :)  I think I did adopt the set-theoretic view only because I am used to seeing it from Rosen.

 

Yes, I  think that a self-referential structure would be a possible solution.  But would that satisfy the view presented in the sci-am article, of some deepest theory with no inputs? I am not sure, myself, but it seems that self-reference is a different way of avoiding the infinite regress than what the author proposes in the article, since each theory still receives inputs in the self-referential case. Perhaps this is what you meant, I am not sure.

 

Wouldn't the self-referential structure make the sequence of (mathematical) theories essentially noncomputable, since - as a dynamic system - they must all be solved simultaneously?

 

Regards,

Tim