Question

This is the third part of our discussion dealing with the question of whether there can be three-dimensional bodies that have no center, and I feel, to my surprise, that we have reached some agreements, so it is possible to move forward. I will try to summarize your position as fairly as possible and then lay out my argument (if I described something incorrectly—please correct me).
As I understand it, you claim that such bodies could exist, at least in principle, in physical reality. We also agreed that mathematics is separate from physics, and therefore even if it allows for the possibility of their existence, that is only a necessary condition, not a sufficient one. We still have no proof that they actually exist. We also agreed that as long as we have not found a law of nature (an empirical law) that forbids this, the possibility remains on the table, although here too this is only a necessary condition and not a sufficient one.
Let us move on: the question I am raising is why, despite all this, there are those who think that such bodies are possible (like you). After all, it is not enough that we cleared the mathematical hurdle and the empirical hurdle. There has to be some positive external justification. What is it? You brought the example of debt, but it seems that there too we agreed that debts are not physical entities (and cannot be), even though their mathematical description is completely valid and even though there is no “law of nature” preventing their existence. And yet, contrary to what you said regarding debt, with respect to the existence of finite three-dimensional bodies, you express a different position. Why? Note that here you cannot recruit mathematics again as a justification, since even on your view it is only a necessary condition. I also find it hard to see how you could base your position on the physical consideration for that very same reason.
In my view, the only way left to us to deal with the question can come from the a priori philosophical arena. Indeed, you yourself used a philosophical “method” when you brought the analogy between the universe and a balloon (assuming the universe has a finite size, like other bodies). There I argued against you that even if the analogy is valid (in my opinion it is not), it proves the opposite of what you meant to show; namely, it shows that there must be a center to a finite three-dimensional body (and probably to the universe as well). When you used that analogy, you spoke about the balloon’s surface, which is only two-dimensional. In my opinion this claim confuses the mathematical description of the surface with a philosophical description. In mathematics the ability to manipulate is much greater precisely because in such cases it does not apply to physical and metaphysical reality. You made illegitimate use of the great freedom that mathematics gives us and tried to force it and its properties onto real, physical, and metaphysical reality. More specifically: you argued that a balloon’s surface is a two-dimensional structure that stands on its own, as it were separately from the balloon’s inner volume, which the surface encloses. As stated, this is a legitimate and useful move so long as it is carried out with purely mathematical tools. But you then tried, absentmindedly, to apply this description to real reality. By doing so, you maneuvered yourself into the absurd position according to which, in reality, a surface could somehow exist floating in the air without a center enclosed by it.