[nonneta] “So you claim that all “real” masses are ultimately composed of “unreal” entities with zero mass, and hence something comes from nothing. This is blatent “creation ex nihilo”. Likewise you assert that all real entities of positive volume are composed of unreal entities of zero volume, and that all real entities of positive radius are composed of unreal entities of zero radius. Needless to say, no finite number of zeros (real or unreal), nor even a countably infinite number of zeros, can sum to a positive value, so you are proposing that the finite (zero) somehow becomes infinite (a continuum). All this is in blatent violation of the principles that you claim to espouse.”
My apologies, I was sure I mentioned that no real (physical) thing is made of substance.
It exists as a concept. Kind of like a coordinate axis. I suppose this kind of thing can be said to be real in a way, but not in the same way as a ruler.
[nonneta] “ ... you haven’t defined “radius” or “mass” ... “
Perhaps a dictionary should be added to the list of references Tom suggested earlier. If we cannot rely on at least some of the work others have done in the past we are going to be at this for a long time.
Hmmm. Is there something about the dictionary definitions that you see as incompatible with “physical” entities?
[nonneta] “By the way, neither of the two mutually exclusive definitions of “primitive” you mentioned is correct. A primitive element of a conceptual framework need not be “small, and conversely the smallest things need not be primitive.”
My apologies again. I could have sworn I discussed examples of this sort of thing, like galaxies being some of the primitive entities comprising galactic clusters. And substance, the “conceptual” smallest possible thing, not being the “physical” smallest thing.
[nonneta] “ ... is there some objective distinction between mathematical descriptions and physical explanations?”
Since you’ve mentioned this several times, I guess it is significant to you. Hmmm, “objective”? I hope you are not a solipsist. If you are, we will never be able to see eye to eye.
To me the distinction seems so obvious that I forget it is not that way for everyone. And that means it needs to be nailed down. I’m not sure what you are looking for, so I’ll just pick what seems (to me) like an obvious starting point.
Can we agree that there is a difference between a mathematical object and a physical object?
Consider a sphere and a soccer ball as examples, respectively, of a mathematical object and a physical object. They have some similarities. Three dimensional, very symmetrical (“round“), their ratios of surface area to volume are smaller than for other three dimensional “things”.
The same equation can be used to describe both of them. Exactly in the case of the sphere, approximately in the case of the soccer ball. It would take a fairly complicated set of equations to describe the soccer ball exactly.
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And they have some differences. Suppose I place a soccer ball in the center of a soccer field, and suppose I also write some equations that describe a sphere of the same size in the same place.
I can kick the soccer ball. but not the sphere. The soccer ball can be used to move another soccer ball. The sphere cannot move a soccer ball
The sphere is a concept. I can visualize it, but not kick it. I can even visualize the conceptual version of the soccer ball. the one described by the aforementioned set of equations. In my mind, or rendered on a monitor, it looks a lot like a physical soccer ball. But I still can’t kick it. Until I feed those equations into a Santa Clause Machine and build a physical soccer ball (one that I can kick), it is “just” a set of equations.
I suspect, however, that this is not going to satisfy your definition of “objective”.
