Re: inequivalent complmentary models

[Howard Pattee <***>]

Tim wrote:
I am familiar with the term "complementarity", and I personally do not find
it an acceptable substitute for "inequivalent". "Complementarity" seems to
me to have a very specific meaning in physics that "inequivalent" would not
capture.

HP: You are right that the term complementarity was first coined by Bohr to describe 
quantum models, where it was never stated formally with precision. However, he later 
generalized the concept when he realized that it applied in many wider contexts. Rosen 
preferred inequivalent because of its meaning in formal model theory. Neither word is 
very good.

In our discussions Rosen and I understood complementary models and inequivalent models to 
mean the same thing in context, namely, to  characterize models of systems in which a 
single model was fundamentally inadequate and that required one or more additional models 
none of which could be derived from, or reduced to, the other. In other words, the models 
could not be formally combined without being inconsistent.

Zeno?s paradox of the hare and tortoise is an early case. It arises because of the 
complementarity of discrete and continuous models. Even though Aristotle pointed out the 
problem (?That which moves does not move by counting?), logicians are often disturbed by 
the concept. Historically, Newton?s argument with Huygens over whether light is discrete 
particles or a continuous wave was the same type of problem. Today physicists recognize 
the necessity of many such complementary models. Bohr quipped that there were simple 
truths whose opposite was false, and there were great truths whose opposite was also true.

Tim:If modern physics is a program, as you stated in your previous post, that
begins with "epistemic principles" that "support the ideal of objectivity
which simply means that these aspects or laws do not change when the
observers change, nor can they be changed by the observer", then physics is
tacitly asserting a world-as-mechanism view, whether it acknowledges it or
not. And such a world is coincident with one described in state-based terms.

HP: I don?t follow your logic here. The symmetry principles and the Hertzian 
correspondence condition lead to no such conclusion. This is demonstrated directly by the 
great variety of physical models that are not Newtonian (memoryless, path-independent) 
state-determined and that are also not considered by physicists to be conceptually 
mechanistic in the Newtonian sense.

Howard