John_Taverner wrote on Sep 4
th, 2022 at 10:24am:
Frank wrote on Sep 4
th, 2022 at 9:52am:
This is why mathematics is necessary for theories of big bangs and black holes: Ordinary language, sense data and minds built on them cannot 'compute' and comprehend and express them without paradox.
Conversely, mathematics (and black holes and big bangs) lacks explanatory power when it comes to I and Thou.
Thou canst speak for thyself.
I'll let Einstein answer your last point:
Ahem.....Wachet auf Herr Doktor Professor!
Quote:An enigma presents itself which in all ages has agitated inquiring minds. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?
In my opinion the answer to this question is, briefly, this: as far as the propositions of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality
Albert Einstein, 1921
Albert knew his Immanuel:
First of all, we must observe that all proper mathematical judgments are a priori, and not empirical, because they carry with them necessity, which cannot be obtained from experience. But if this be not conceded to me, very good; I shall confine my assertion to pure Mathematics, the very notion of which implies that it contains pure a priori and not empirical cognitions.
...
But it happens fortunately, that though we cannot assume metaphysics to be an actual science, we can say with confidence that certain pure a priori synthetical cognitions, pure Mathematics and pure Physics are actual and given; for both contain propositions, which are thoroughly recognised as apodeictically certain, partly by mere reason, partly by general consent arising from experience, and yet as independent of experience. We have therefore some at least uncontested synthetical knowledge a priori, and need not ask whether it be possible, for it is actual, but how it is possible, in order that we may deduce from the principle which makes the given cognitions possible the possibility of all the rest.
He goes on. I think you would enjoy reading it.
https://www.gutenberg.org/files/52821/52821-h/52821-h.htm#__RefHeading___Toc3103KANT'S Prolegomena, although a small book, is indubitably the most important of his writings. It furnishes us with a key to his main work, The Critique of Pure Reason; in fact, it is an extract containing all the salient ideas of Kant's system.