Picking up where I left off on the last article, “Math Masquerading as Empirical: The lie of the “smallest particle”, there is a bit more to add. So here goes:
To speak technically, or rather, specifically, the idea of a smallest praticle—a dimensionless object with no sub parts (that is, no left side, no right, up, down, inside, outside, etc.)—would be an object which is infinitely finite.
Now, to be clear, it doesn’t take much more than a rudimentary understanding of rational and logical consistency to see that “infinitely finite” has…well, a few problems.
Something which is infinitely small is, by definition, limitless in its smallness. In other words, its smallness is so large that it cannot be measured.
So, it would appear that that to be infinitely small implies a corollary of infinitely large. And, well…that just doesn’t make much sense, does it?
Put pointedly, the claim of “infinitely finite” implies the tautology “infinitely infinite”, and as I am sure you astute readers know, tautology is an overt logical fallacy. At any rate, both “infinite finity” and “infinite infinity” are irrational and impossible because the fact remains, and will remain forever, that infinity cannot be objectively and non-contextually qualified or quantified without introducing a rational error which undermines the quantification/qualification entirely. These notions may be quantified and qualified mathematically, but this is, at the very least, to implicitly concede that all qualifications/quantifications of infinity are purely abstract, and by no means empirical or empirically verified. In other words, are non-actual (non- empirical/physical/material).
Furthermore—and this may be a bit arcane and difficult to grasp, so you may need to dwell upon this for a while—the claim that there an “absolute small”, or a smallest particle, and that that denotes a limitation to objective physical reality, rather than proof of its limitlessness, is to conflate the smallness and bigness of the universe. In other words, “big” and “small” cease to be relative terms, instead becoming corollary (which is irrational; for by definition opposites are not corollary) where the absolute smallness of physical reality is the singular limitation of its size. In other words, it is a logical fallacy to claim that the irreducible smallness of the physical universe implies an irreducible bigness, as if “big” and “small” are bookends with the physical universe existing between them. If the smallness is infinite, then it simply cannot be known as distinct from the infinite bigness. Both are infinite. Both are limitless qualifications and quantifications of size. And so what is the difference between “small” and “big” here? And how would you know the difference in the first place?
You wouldn’t. You couldn’t.
In other words, there is no rational, nor is there even a mathematical, way to ever know the actual size of the universe, nor to claim that there is a size to it at all. By asserting “big” and “small’ as fundamental, absolute (infinite), and therefore non-relative characteristics of the universe, they lose all meaning completely. And thus, the claim that there is such a thing as a “smallest particle” is a lie. For the smallest particle is also the biggest. And that…is an entirely meaningless claim.