According to BK's idealism, are Mathematics invented or discovered?

[PHIbonacci]

^this.

Some resources:

Platonism in the Philosophy of Mathematics
https://plato.stanford.edu/entries/plat ... thematics/

Philosophy of mathematics - Wikipedia
https://en.wikipedia.org/wiki/Philosoph ... jor_themes

Structuralism (philosophy of mathematics) - Wikipedia
https://en.wikipedia.org/wiki/Structura ... #Varieties

Max Tegmark - Wikipedia
https://en.wikipedia.org/wiki/Max_Tegmark

Our Mathematical Universe (Max Tegmark) - Wikipedia
https://en.wikipedia.org/wiki/Our_Mathematical_Universe

According to Max Tegmark:

In Tegmark’s view, everything in the universe — humans included — is part of a mathematical structure. All matter is made up of particles, which have properties such as charge and spin, but these properties are purely mathematical, he says. And space itself has properties such as dimensions, but is still ultimately a mathematical structure.


Mathematical Structure is involved in Everywhere

“If you accept the idea that both space itself, and all the stuff in space, have no properties at all except mathematical properties,” then the idea that everything is mathematical “starts to sound a little bit less insane,” Tegmark said in a talk given Jan. 15 here at The Bell House. The talk was based on his book “Our Mathematical Universe: My Quest for the Ultimate Nature of Reality” (Knopf, 2014).

“If my idea is wrong, physics is ultimately doomed,” Tegmark said. But if the universe really is mathematics, he added, “There’s nothing we can’t, in principle, understand.”

What does BK think and what do you think?

[Starbuck]

From Bernardos interviews, I will be brave and step up. I would say he makes the following claims.

All there is is phenomenal consciousness and its excitations. Just like a guitar string, those excitations have 'natural' modes of expression. Manifestation (including the meta-conscious 'us' that can communicate about such matters) is just those modes and their 'interference patterns'. We could equate those natural modes with ratios and relationships, and from there we could infer that Tegmark is correct in assuming that there is a kind of ultimacy to mathematics (in their purest platonic and transcendent form). However, Bernardo would argue that Tegmark misses the ontological basis within and out of which that mathematics resounds in - vis-a-vis consciousness.

I would agree with Bernardo, in the sense that the pure abstraction of Tegmark's dream will never directly account for nature's sole given - phenomenal awareness.

[SanteriSatama]

BK makes clear, from his background in computer science, that qualia can't be reduced to quanta. On the other hand, BK is also suggesting that at least on some level, the boundary of an alter is a mathematical structure, ie. Markov Blanket.

Empirically, mathematics is both invented and discovered. What mathematicians do, and how they experience mathematics, involves both intuition and language games.

Before we can move further, we need to first clarify what we mean by mathematics, is it even valid to question what is mathematics, and if so what is it?

Is mathematics just quantifcation? Phenomenally, no, if geometry, topology etc. are branches of mathematics. What is the relation of continuum and quantification? Is mathematics closed and eternal, or open and evolving process? What is the relation of pure mathematics and applied mathematics, which should follow which?

As a practice, mathematics is a general study of abstract relations, with many open questions and disagreements.

In my own view, continua are more foundational than quanta, and I can build a coherent argument for that view. I subscribe to Intuitionist philosophy of mathematics, and I'm very critical of Hilbert's formalism. Intuitionism naturally presupposes some sort of idealism. So does Tegmark's Platonism, which is conclusion from physicalism, not from pure mathematics and empirical intuitionism. What are main differences between Intuitionism and Platonism?

Platonism suggest something transcendental, eternal and immutable, and as far set theory of physicalism is claimed to best reflect that Eternal Platonia, the argument is easy to shoot down with mathematical and philosophical criteria, and becomes a matter of theology. Intuitionism considers that also the idealist ontology of mathematics is an open and evolving process, in which also human scale mathematical cognition creatively participates. Intuitionism has more strict conditions for linguistic constructions of mathematics than Formalism, and the type of Platonism motivated by Formalism and Physicalism, which allow non-constructible and non-demonstrable and non-computable theological argumentation. With recent development of computation theory and it's implication to proof theory (undecidability of Halting problem with Curry-Howard correspondence), Intuitionism rejects eternalism of mathematical proofs, at least in most cases.

[ScottRoberts]

I would say, like Santeri, that mathematics is both discovered and invented. It is all invented by some mind or other, with the mathematics used to construct physical reality being invented by MAL. Which we discover, though no doubt what we discover only dimly resembles that of MAL. Meanwhile, we can invent our own.

My definition of mathematics, for what it is worth, is that it is the study of non-referential form. One can distinguish between mathematical thoughts, and, say, the thought of a house, where the difference is that, for example, the thought of a triangle is the triangle, while the thought of a house is not the house.

[SanteriSatama]

My definition of mathematics, for what it is worth, is that it is the study of non-referential form. One can distinguish between mathematical thoughts, and, say, the thought of a house, where the difference is that, for example, the thought of a triangle is the triangle, while the thought of a house is not the house.

That's a very poetic definition, also in the etymological sense of the word. I like it very much.

IMHO the answer to the Wigner's question in his classic article "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" is that mathematics is poetry.