Alex,
I agree that the 'stuff' of the universe is mathematical. The existence of any particular physical entity I believe can be reduced to a mathematical description. For example, Newton's F=ma is mathematically describable. However, can't this description also be shown to be a special case of GR as well as Feynman's path integral method? And, isn't it expected by many cosmologists that GR will probably be shown to be a special case of some quantum theory of gravity (perhaps even incorporating the path integral)? Hence, it seems that there is often more than one layer of mathematical necessity. We often find that U is true and is a special case of V, and we find V is true and a special case of W, etc. As you said, either this goes on ad infinitum or there exists some necessary logical truth G which everthing is derived and everything is a special case of G. G becomes the ultimate truth so to speak.
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Since all of this 'stuff' has intrinsic mathematical/logical properties, can we reduce this 'stuff' to purely mathematical/logical relations and eliminate the 'stuff' picture of the world altogether and merely focus on the viewpoint called 'structuralism'? This is the view that all there is in the world are logical/mathematical structures and that *everything* (false vacuum, space, etc) ultimately reduces to these structures?
Warm regards, Harv |