The facts of arithmetic, addition, subtraction, multiplication and division are independent of a material substrate, they hold whatever is being counted, they hold when nothing is being counted. That is true of every bit of mathematics, from the most humble to the most complex and esoteric. They work in conditions in which there is no possibility of a one-to-one relationship with any physical objects that could be counted, as in operations dealing with numbers so big, they exceed the number of all objects in the universe, in measurement of intervals invented by human beings which don't exist anywhere but in our minds. That's not unknown, it's as known as anything is in mathematics. While it would be sort of interesting to go through Eugene Wigner's famous, lauded, and often ignored essay, The Unreasonable Effectiveness of Mathematics In The Natural Sciences, I've got garden work to do today. It's harvest season, for Pete's sake. And Pete isn't helping much. I wonder if they still put that in the required reading of university Frosh. Or did that, alas, go with requirements in rigorous Frosh Rhetoric.
Some mathematicians have posited that mathematical "objects" exist in an independent realm of reality outside of the realm of physical objects which science deals with* but that's a philosophical and logical problem, not a scientific statement. You can't come to that belief except through a choice to believe. What you can know is that 1+1=2, though as Bertrand Russell and Alfred North Whitehead found, especially after their work was rigorously criticized, you don't really know that, you believe it.
But it is a truth universally acknowledged. It's true no matter what physical substrate it has in what is being counted, it is true when nothing is being counted, which proves its independence of material objects in any rational meaning of the word "proves" or, really, any of the terms involved in your denial. It's true or science, a far more tenuously asserted body of universal and reliable knowledge, is not true.
* Though, as I've pointed out recently, huge swaths of science under the hegemony of scientistic materialist monism has escaped that one-time requirement for something to be a scientific endeavor. It is one of the most ridiculous and hilarious of all of the follies of contemporary academia, really of the ideology of modernism, that it is exactly the most ardent of materialists who have insisted on exempting science from its attachment to observable, measurable physical objects and phenomena and from the requirements that the conclusions asserted by such science be, as well, held up to properly scientific replication of their work. I've noted before that Stephen Hawking, in his last book, made that demand very explicitly, that his cosmological speculations which have no possibility of confirmation by observation or even reasonable expectation of that in some future be considered science on the basis of mathematics, alone. But that's true for any so-called science which purports to deal with "things" that not only cannot be observed but which, in many cases, may be made up by the would-be scientist.
That practice is most obvious in the obvious pseudo-sciences dealing with the invisible things that go on in our minds, which cannot be known to others except by our own reporting of that invisible experience - we can't even confirm our own experience in any "objective" or even rigorous manner, never mind generate reliable data on which to perform mathematics.
When the academic field of study, psychology, was new, as good a philosopher as William James made the rather incredible statement that the vulnerability of minds to the methods of science created to measure and describe the unconscious movements and transformations of observable physical objects was to be taken as a given. He was making an incredible and totally unwarranted leap of faith, the landing of that leap has not happened and I doubt ever will. It was a leap away from the gravity of honest, rational consideration of the limits of science imposed by the requirement of observation (not to mention the continual and habitual, and near universal sin of such "sciences" not only the requirement to replicate, they often don't even try to. And that's not counting when the frequent other obvious sins of totally invalid methodology and, often, of the most outlandish and extravagant claims that alleged phenomena that are reported have relevance to other (often merely alleged) phenomena when there is no demonstrated link between them.
Psychology, though, is not alone in those scientific sins, the study of things in the lost past which cannot be seen or known cannot be honestly subjected to scientific methods. The faith of scientistic materialism that insists you can extrapolate speculations infinitely BECAUSE, DAMN, IT, IT HAD TO HAVE BEEN THAT WAY! has produced huge piles of formerly held science that has, since, gone out of fashion or been disconfirmed or merely replaced by other speculations. There are huge areas of past speculation about evolution which go into that category.
While it might frustrate legitimate evolutionary scientists that the vast majority of what they would need to make their science anything like complete or rigorous or accurate is and is certainly forever lost to science, they have allowed their fellow scientists to get entirely out of hand. In no area is that more obvious than when evolutionary science must depend on the behavior of organisms which cannot be counted or even known to have existed, the nature of those behaviors or their results totally unknowable through observation or measurement, Sociobiology and Evolutionary Psychology are charcteristic of that, made more so through the mixing the worst excesses of psychology with just those areas in legitimate evolutionary science most vulnerable to the kind of ideological extension I just mentioned. I am on record as expecting that that greatest of all such speculations, natural selection, will increasingly be seen as an illusion of that kind. I don't think any universal explanation of the origin of species will ever be found, I'm skeptical that there is any one such mechanism.
I think natural selection is a product of the economic class interests of its inventors and those who have, successively, over its entire history, tweaked and changed and modified and trimmed and fitted it and pasted stuff to it to make it at all plausible as THE GREATEST SCIENTIFIC THEORY IN HISTORY, DAMN, IT! though that very history shows that, no, it really isn't. It's nothing compared compared to the durability, the universality and the usefulness of the facts of arithmetic. And those are about what might be entirely imaginary objects of the simplest kind. It's an irony that only about such simple objects that reside in our imagination that you get the most durable and reliable information.
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