The view I'm developing is that numbers and universals and the like are real, but not manifest or existent. — Wayfarer
But I am tempted by the possibility of mathematics being reified at the quantum levels. — jgill
Nicholson showed that the angular momentum of a rotating electron ring could only be h/2π or 2(h/2π) or 3(h/2π) or 4(h/2π) … all the way to n(h/2π) where n is an integer, a whole number. For Bohr it was the missing clue that underpinned his stationary states. Only those orbits were permitted in which the angular momentum of the electron was an integer n multiplied by h and then divided by 2π. Letting n=1, 2, 3 and so on generated the stationary states of the atom in which an electron did not emit radiation and could therefore orbit the nucleus indefinitely. All other orbits, the non-stationary states, were forbidden. Inside an atom, angular momentum was quantised. It could only have the values L=nh/2π and no others. — Kumar, Manjit. Quantum (pp. 98-99). Icon Books. Kindle Edition.
it doesn't seem to follow that mathematics is embedded in nature at all, but rather that it is embedded in the human understanding of nature. — Janus
I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
'Scientists tend to be empiricists; they imagine the universe to be made up of things we can touch and taste and so on; things we can learn about through observation and experiment. The idea of something existing “outside of space and time” makes empiricists nervous: It sounds embarrassingly like the way religious believers talk about God, and God was banished from respectable scientific discourse a long time ago.
Platonism, as mathematician Brian Davies has put it, “has more in common with mystical religions than it does with modern science.” The fear is that if mathematicians give Plato an inch, he’ll take a mile. If the truth of mathematical statements can be confirmed just by thinking about them, then why not ethical problems, or even religious questions? Why bother with empiricism at all?'
Do we view the same phenomena or view similar phenomena that we call the same for the convenience of fabricating the kinds of objects that are amenable to mathematical calculation?
Karen Barad is among those who suggest that the geometric notion of scale must be supplemented with a topological notion of it. What this means is that scales interact each other to produce not just quantitative but qualitative changes in material forms.
That’s because the presuppositions concerning the irreducible basis of objectness which underlie mathematical logic guarantee that it will generate a world of excellently established facts. It fits the world that we already pre-fitted to make amenable to the grammar of mathematics. The very prioritization of established facts over the creative shift in the criteria of factuality demonstrates how the way mathematical reasoning formulates its questions already delineates the field of possible answers.
I think the sciences are slowly moving away from the idea, exemplified by the periodic table, of pre-existing forms that reappear throughout nature. They are coming to realize that such abstractions cover over the fact that no entity pre-exists its interaction with other entities within a configuration of relations. The ‘entities’ are nothing but the changing interactions themselves, which tend to form relatively stable configurations. According to this approach, the world is not representation but enaction.
In this sense, it seems like mathematics must be "embedded in the universe." So the question seems to be more "how did our mathematical intuitions and those of other animals emerge and did mathematics not exist in any sense prior to the first animal that possessed mathematical intuitions?" — Count Timothy von Icarus
So, math is just a measuring and calculating tool using numbers applied to describe and predict the measurable properties of the external objects and movements. — Corvus
I believe that the only way to make sense of mathematics is to believe that there are objective mathematical facts, and that they are discovered by mathematicians,” says James Robert Brown, a philosopher of science recently retired from the University of Toronto. “Working mathematicians overwhelmingly are Platonists. They don't always call themselves Platonists, but if you ask them relevant questions, it’s always the Platonistic answer that they give you.”
My belief has always been that numbers are real but not physical. Of course, that contravenes physicalism, for which everything must be reducible to the physical, so it can't cope with that idea. It has to reject it. So I think those comments are revealing of the real philosophical issue at stake: that mathematical realism, the idea that numbers and mathematical relations are real but not physical can't be allowed to stand. — Wayfarer
I have long thought that mathematics is both invented and discovered. — Janus
But mathematicians are very imaginative people. What they have done goes far beyond what you describe. — jgill
Mathematics — Corvus
I say prelinguistic because apparently some animals can do simple counting. — Janus
Which animals can count? — Corvus
Anyhow simple counting is not mathematics. — Corvus
If mathematics is embedded in the universe, then why don't the other animals with high intelligence such as Monkeys, Apes and some dogs make use of mathematics? Surely they exist in the universe just like humans do? Why is it that only humans use mathematics? What have humans got, the other species haven't got? — Corvus
I think that there are regularities to the way things occur in the universe, due to the universe having such regularities biological evolution could and did occur. — wonderer1
What have humans got, the other species haven't got?
— Corvus
Symbolic language. — Janus
r. If the regularities are there, then "what mathematics describes," is everywhere in the universe, even if "mathematics" is not. If we take mathematics only to be the descriptions, not the things described, then mathematics is still "embedded in the universe — Count Timothy von Icarus
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