Hello Armin,
I appreciate your comments and they are indeed useful.
Here are my comments:
"Concerning your axiom of motion, I must say, as metaphysical as "Force" is, it seems in some sense more concrete than Power. I don't know if this is an artifact of my education,"
It may be more concrete because it has already become common sense through education. But the notion of force is puzzling as much as power. However, in many cases people use power: "this car has a lot of power", "that was a powerful storm", etc.
"I would say that if there was a way to intuitively conceptualize Power as easily (or even more so) as Force, then your approach might attract more attention."
This is a good point. The way for people to conceptualize comes from education and solving problems. However, my intention was not to replace Newtonian mechanics but only to show that there can be alternative foundations. The key here is that the notion of force is compatible with a materialistic universe, where the notion of power sounds more "spiritual": Powerful God, powerful feelings, etc. Given that the goal of science is to preserve material autonomy, the notion of force is more appropriate for that, I agree.
"Your finding that the metaphysics of your approach permits a zero of the cause of motion to be associated with uniform circular motion reminded me of the fact that Galileo seemed to consider this type of motion to be inertial, which suggests that his metaphysics might have been closer to yours than to Newton's."
Actually in relativity such motion is also inertial because there are no forces that cause motion. One problem with circular motion is that it imposes stretched causality: If a stone is attached to a string and rotated, there is a centripetal force directed towards the center of motion. Does the force cause the motion of the stone, or the motion of the stone causes the force. Greenwood in his excellent textbook says he does not know the answer. More importantly, if power is the cause of motion, no fictitious causes must be considered in non-inertial frames as it is the case with force and centrifugal and Coriolis inertial forces.
"I have to think some more about the robustness of your arguments concerning the emergence of an arrow of time and the notion of spacetime as a substance. I tend to agree with the latter, but ascribe this more to the Lorentzian signature which leads to a geometry for which we do not have good intuitions (particularly the notion of a definite-negative metric interval). "
The arrow of time is a hypothesis that emerges from the notion of universal time in an occasionalist sense. I tend to look at geometry more as a convention rather than ontology.
"Regarding the notion of causal influences originating from outside spacetime, you may find Gisin's paper of interest. I believe that he is onto something, and in fact in my own work am (among many other things) attempting to formulate a firm mathematical grounding for such an idea (within the context of QM) in terms of something I call an "incomplete embedding"."
One problem here is to have a theory that generates some new and unique predictions based on this hypothesis.
"Returning to your current essay entry, I applaud your effort to make the metaphysical commitments of particular mathematical formulations of physical theories more explicit. This is a subject that I believe physicists in general do not spend enough time thinking about. As for the power of mathematics,bas far along as we have come since, say, Newton's epoch, I think we have still barely scratched the surface in terms of what is possible to do with mathematics."
Thank you and I agree about the power of mathematics.
" I am myself making an attempt in this direction by incorporating two non-classical logics into its foundation in the hope of increasing the expressive power of mathematics beyond what is possible at present, in order to arrive at a model of quantum mechanics that accomodates a distinction current theory doesn't and thereby illuminate what it says about the world."
This sounds interesting and the way to escape from the circle the same way that mathematicians escaped from Euclidean geometry after hundre4ds of years of trying to wither defeat or prove the fifth postulate. Good luck to you.
All the best.
Efthimios
