RE: Hierarchy/Hierarchies of Scientific Knowledge

Theoretical models of Nature and the predictions that follow from them are exactly like mathematical systems with axioms and theorems like Euclidean geometry. However, logical connections, which may or may not correspond to causal physical influences, propagate equally well in either direction. Therefore, the choice of what constitutes an axiom or a theorem is arbitrary. For instance, if one considers the quantum description of an electron and a proton together with the Coulomb force between them, then a hydrogen atom emerges as a consequence of the theory. I suppose one can do an inverse sort of problem and deduce the Coulomb interaction from the knowledge of the existence of the electron, the proton and all the energy levels of the hydrogen atom. Accordingly, one may be surprised of the occurrence of the hydrogen atom but it is a logical consequence of the assumed theory. There are other examples where the consequence of the theory is quite surprising. For instance, when !
P. A. M. Dirac unified quantum mechanics and the special theory of relativity, the spin of the electron popped out of the theory. Quite a remarkable emergent quantity but it was always contained in the theory but we did not know it. It seems clear to me that there are quantities that may certainly not emerge from a purely physical theory. I think life, consciousness, and rationality will never emerge from a purely physical theory.

Moorad

________________________________

From: asa-owner@lists.calvin.edu on behalf of Gregory Arago
Sent: Sat 5/6/2006 9:10 PM
To: asa@calvin.edu
Subject: Hierarchy/Hierarchies of Scientific Knowledge

In the thread on emergent properties, the words 'hierarchy' and 'hierarchical' have come up. This seems to suggest something that comes before or after, below, higher or above, primary, secondary, etc. Could folks at ASA help by describing/explaining what kind of hierarchy or hierarchies are said to exist in scientific knowledge?
 
I found the paragraph by Keith Miller below and also Randy's opening post quite fascinating.
 
Kind Regards,
 
Greg
 
 
"For me one of the fundamental perspectives is that an internally
complete description of a system at one level does not in any way
deny the validity of another different and non-contradictory
description at another level. There can be several internally
complete levels of description within the broad umbrella of science.
At a yet higher level, the whole hierarchy of scientific descriptions
become one type of understanding of reality that can be (at least
theoretically) complete, but yet cannot exclude the existence of
another equally valid, equally true, and non-conflicting understanding." - Keith Miller

________________________________

Share your photos with the people who matter at Yahoo! Canada Photos <http://photos.yahoo.ca>
Received on Sat May 6 21:41:12 2006