Dear Ben,
Thanks for your reply. I understand your lack of time. A few remarks to your remarks:
''It seems that these two possibilities are interchangeable: if you have redundancy, you can eliminate concepts one by one until the redundancy disappears and the remaining concepts are undefined. Conversely, you can define new concepts in terms of the fundamental (undefined) concepts and take these to be "equally fundamental."''
That´s the point. I was thinking that maybe we can define ''motion'' using ''time'', but then times becomes undefined... or we can define ''time'' using motion, but then motion becomes undefined... and so on. In the end, maybe all fundamental terms: space, time, motion, physical objects could have this ''duality''. The reason that points me for thinking this is that machian philosophy (which leads to GR) can be seen as a PART of this duality!
''2.It seems that "semantic completeness" as you define it requires redundancy, because if every concept can be defined in terms of others, then some of these concepts can be eliminated (at least, if there are a finite number of fundamental concepts).''
I don´t know if they could be eliminated... but the CHOICE of fundamental terms would not be unique! Again, we could consider that motion gains meaning from time, space and objects, OR that time gains meaning from motion, space and objects. Then, we could postulate that no matter how we choose to represent the universe, there should be no physical change upon a different choice of fundamental terms. Absolute and relational views of motion would be a part of the same structure... and there would also be the ''something else''!
Ultimately, what I propose is that by investigating the ''meaning'' of classical statements about motion, we can find new ways to conceive motion, and then build physics using this conceptions.
''What I am trying to get at is that the concepts of "change" or "motion" require that the "initial and final states" be identified as different states or configurations of the "same object" rather than two totally unrelated structures.''
We can also define motion without an absolute structure by introducing a ficticious ''background'' structure for the final and initial state and then eliminating it using barbour´s best matching: take for instance two configurations of point particles defined in cartesian frames, say (xi,yi,zi) and (x'i,y'i,z'i), representing distinct instants of time. Now hold the first frame fixed and perform rotations and translations of the second until some incongruence measure such as SQRT((xi-x'i)2+(zi-z'i)2+(yi-y'i)2) gets minimized. This is defined as the best-matched distance between these two configurations, and this value can be calculated using only information meaningful in the relational view of motion.
I´ll keep in touch for further discussion.
Best regards
Daniel
