Can something be of zero size and still exist?

[SanteriSatama]

Santeri wrote:
Zero is the identity element of addition. It has a clear mathematical meaning. It is also useful for positional writing of numbers.

Me:
Yes, but its relevance to this discussion is that it is considered to be an infinitely small quantity, which is why it presents difficulties for metaphysics.

A) Infinitesimal > 0
B) Infinitesimal = 0
Under classical logic, both can't be valid propositions. As standard definition of infinitesimal is A), those who consider that B) can be also true are wrong and/or dishonest, if they are making their claims under classical logic. But as Newton-Leibnitz calculus has some practical use for calculating approximations (by "making two wrongs right", to quote Bishop Berkeley), scientism keeps on telling that it a) follows classical logic and b) both A) and B) are somehow true.

Santeri:
Zeno proved physically that continua don't reduce to discrete quantification.

Me:
Really? He is often cited to show that the physical universe must be granular.

Yes, granular universe is the other possible interpretation. But from that follows that continua can't exist in any meaningful sense, which is equally bad news for calculus and scientism. On the other hand, discrete phenomena can be coherently derived from continua, as shown e.g. by foundational theory of mathematics that starts from relational operators (Relop, which I've discussed in many other threads). Ergo, under coherence theory of truth, the interpretation of continua is valid and granular interpretation is incoherent.

Quantal phenomena of Planck scale quantum physics only show that there are limits to quantifiable measurability, limits that are relative to the measuring tool used, ie. the formalist theory of mathematics presumed by scientism. Even though to a hammer everything looks like a nail, the perspective of a hammer can't make valid claims about "objective truth". The formalist theory of mathematics is a language game "hammer" built from counter-empirical and totally arbitrary make-believe axioms that have nothing to do with genuine science and scientific method of empirism and self-correcting of methodological presuppositions.

Criticism of the post-modern condition is and was directed against the arbitrary and counter-empirical language games of scientism. Post-modern condition refers to dishonest sophistry that keeps on playing a logically and empirically invalid language game even after it has been proven and shown invalid time after time.

Santeri:
a religious cult of materialism and obsessive quantitative measuring.

Me:
I won't argue for materialism. I personally do not engage in the materialist versus idealist argument. I see reality as a hierarchy, with its core an absolute, unknowable essence, which gives rise to all else. Holy Spirit, Creator, Creation.

Santeri:
Leprechauns are more real than nonsense about "completed infinity".

Me:
That is a bold statement that goes far beyond my level of comprehension.
Leprechauns are mythical, completed infinity has at least some geometric support.
However, I am not equipped to debate either.

"Completed infinity" is a self-contradictory number theoretical concept made up by Cantor. Geometry works naturally with continua, independent of number theory. "Completed infinity" is just a dishonest trick of trying to say "finite infinity" with so much fancy sophistry that the audience becomes utterly confused and believes in the BS of standard calculus, formalism and scientism.