That suggests that there *are* smaller particles that dictate those attributes and their combinations. I don't deny that there is at least one additional incremental step in the microcosm: that's what the Unimid Theory is all about. But, I can only claim that Unimids [Bill’s finite particles] *need not be* divisible and offer my logical arguments on the evidence.
TSW: "One scientist felt sure that 'matter is not infinitely divisible,' while another reiterated that 'no ‘ultimate’ individual or partless particle is known to science.'
BW: Both were correct, based on the available evidence. Democritus was right for 2,200+ years ... until new evidence mitigated that truth. The other statement will also be true, until UT is validated by evidence.
TSW: "... there are now at least three different kinds of electrons, some of which emit neutrinos."
BW: My Kindle version doesn't have footnotes, so I have no idea what you're talking about. There is only one "kind" of electron. There are three types, or "flavors", of neutrinos (which have no charge), but their names do not imply that they are the same as electrons (which have charge): electron neutrinos, muon neutrinos and tau neutrinos. Each of them is a distinct particle, even if they're in the same class.
BW: An amusing semantic twist, but invalid. An ultimate particle would be solid mass, not empty. To assert that it doesn't have constituent parts (no smaller things) is not saying it contains nothing. It isn't "of a sort" with the proposition of an eternal nothingness (void) *outside* of the known cosmos.
TSW: "The philosophical purpose of finity, whether it be construed as microscopic, macroscopic, or both, is at some point to call a halt to materialism."
BW: A microcosmic fundamental particle IS matter, not immaterial. Of course, it can always be argued that the Unimid is not "fundamental", but that's a different question.
TSW: Lakatos: "As the universe is infinitely varied, it is very likely that only statements of infinite length can be true."
BW: ... because Imre Lakatos says it, or because Lakatos was a dialectical materialist?
BW: In essence, he's just restating Karl Popper's characterization of the "uncertainty" of inductive reasoning. What Popper says about induction is correct, but irrelevant, simply because he offers a standard of impossible human omniscience, rather than "unmitigated truth".
TSW: "Thus, the infinite hotel with the infinite number of rooms can always accommodate an infinite number of guests."
BW: It's a funny story, which ignores the fact there is no room available for the first guest, since there are no predecessors.
TSW: Planck: "... calculation shows that an infinitely long time passes ..."
BTW: Planck was also wrong about his "quanta" being discrete particles of light. It's just a conversion factor. Ask if you want an explanation.
TSW: Paul Davies: "The infinities that occur in QED (quantum electrodynamics) are clearly symptomatic of some profound shortcomings in our understanding of physics."
BW: He's right: any time a theoretical mathematical description "goes to infinity", it is probably false. But that's a conclusion at odds with your observation:
TSW: "We invariably give up contact with the real world whenever we use mathematical axioms that 'somehow avoid the concept of infinity."
BW: On the contrary, It is THAT the mathematical axioms DO go to infinity that makes them invalid. It's a good argument *against* infinities in math, not *for* infinity in nature.
TSW: "This model, unfortunately of a piece with mere enumeration, is nonetheless an improvement in that it provides a three-dimensional framework for beginning a description of the real, infinite universe."
BW: Nonsense. There is no such thing as a "point", "line", or "plane" in reality: they are abstractions *from* reality, which always has three dimensions. A primary fault of the Big Bang Theory is the proposition of a "singularity", with no dimensions, as the origin of everything.
TSW: Robin Collingwood: "Since modern science is now committed to a view of the physical universe as finite, certainly in space and probably in time ... the physical world as a whole must ultimately depend for its existence on something other than itself."
BW: You're comparing an obscure British professor with Aristotle??!! I discussed Aristotle's apparent "sop" to mystics earlier, explaining why it wasn't anything any mystic could love.
BW: Anytime anybody pursues a "reason" for all of existence, they have committed a logical fallacy: reason is a human *product* of reality, not its creator. In the absence of a body, supporting a brain, there can be no thought, nor any motive. Reality does what it does, without the slightest "concern" about the consequences or its effect on our understanding of why it does what it does.