Mathematical Platonism and Idealism

[DavidSchuy]

Would you say that mathematical platonism and metaphysical idealism are compatible? If yes, to what extend are they compatible and how exactly?

Mathematical platonism argues and postulates that mathematical objects/entities exist objectively in a platonic realm of existence.

Idealism argues and postualtes that all is one consciousness - so does cosmopsychism (which is the same view; only another term) - and that the subjective inner experience that we call consciousness is the ontological primitive of existence.

But it is postulated as an axiom. As everyone knows, axioms are unprovable truths. And my questions is whether and to what extend are mathematics and consciousness interrelated? Is mathematics just like the bones and consciousness like the living organism/flesh around the bones?

Does a mathematical realm exist in addition to the one consciousness? And what role does the hypothesis of the mathematical universe play here? See Max Tegmark.

Thank you very much for all answers!

[Starbuck]

Wow, I was just about to post something on this, once I had worked out an angle. Just making my way through Roger Penrose's Road to Reality, where he goes into the relationship between maths and physical reality.

I kept thinking as I was reading that there is a relation to idealism, particularly BKs comment in his Schopenhaur book about ideal forms being 'distorted' by the impingement of the dissociated mind. in the same way, numeric concepts are always distorted in the physical world (ie there is no such thing as a perfect circle in physical reality, but it can be contemplated momentarily in mind.

Recommend the Penrose book (certainly the first few chapters) which goes into the early history of greek mathematics, who were at the same time being influences by Platos ideas.

[AshvinP]

Would you say that mathematical platonism and metaphysical idealism are compatible? If yes, to what extend are they compatible and how exactly?

Mathematical platonism argues and postulates that mathematical objects/entities exist objectively in a platonic realm of existence.

Idealism argues and postualtes that all is one consciousness - so does cosmopsychism (which is the same view; only another term) - and that the subjective inner experience that we call consciousness is the ontological primitive of existence.

Cosmopsychism is not identical to idealism, but one subset of idealist ontology. (but that may not be relevant to your questions)

Idealism is compatible with Platonism - objective idealists generally accept the reality of "archetypes", which are similar to Plato's ideal forms. They are meta-patterns of 'immaterial' thoughts which manifest uniquely in particular 'material' forms ('immaterial' and 'material' both fall under the ontic category of consciousness).

But it is postulated as an axiom. As everyone knows, axioms are unprovable truths. And my questions is whether and to what extend are mathematics and consciousness interrelated? Is mathematics just like the bones and consciousness like the living organism/flesh around the bones?

Does a mathematical realm exist in addition to the one consciousness? And what role does the hypothesis of the mathematical universe play here? See Max Tegmark.

Thank you very much for all answers!

The first one (bones of living organism) is most accurate IMO. There are no 'mathematical objects' or 'realm' which are ontically different from conscious activity.

[SanteriSatama]

Intuitionist school of philosophy of mathematics is idealist. Intuitive aspect is considered primarily ontological, construction of mathematical languages secondary. Nuanced difference between intuitionism and platonism could be that former has more dynamic and evolutionary view of mathematics, participatory evolution of mathematical cognition, platonism is associated with eternalism and immutability of mathematics.

[ScottRoberts]

Would you say that mathematical platonism and metaphysical idealism are compatible? If yes, to what extend are they compatible and how exactly?

Mathematical platonism argues and postulates that mathematical objects/entities exist objectively in a platonic realm of existence.

I'm not sure about "a platonic realm of existence" in the sense of it being distinct from this realm, but yes, idealism is compatible with there being mathematical objects/entities existing objectively, that is, independently of human existence.

Idealism argues and postualtes that all is one consciousness - so does cosmopsychism (which is the same view; only another term) - and that the subjective inner experience that we call consciousness is the ontological primitive of existence.

One might disagree with that definition of idealism (problem of subjective vs. objective idealism, for instance), but never mind.

But it is postulated as an axiom. As everyone knows, axioms are unprovable truths. And my questions is whether and to what extend are mathematics and consciousness interrelated?

Mathematical objects, like all objects, exist within consciousness.

Is mathematics just like the bones and consciousness like the living organism/flesh around the bones?

I wouldn't say so, as it implies that mathematical objects can exist independently of consciousness.

Does a mathematical realm exist in addition to the one consciousness?

No. All realms are within consciousness.

And what role does the hypothesis of the mathematical universe play here? See Max Tegmark.

Consciousness is not possible under Tegmark's hypothesis, so it needs in addition, at minimum, a divine Mathematician.

[ScottRoberts]

Intuitionist school of philosophy of mathematics is idealist. Intuitive aspect is considered primarily ontological, construction of mathematical languages secondary. Nuanced difference between intuitionism and platonism could be that former has more dynamic and evolutionary view of mathematics, participatory evolution of mathematical cognition, platonism is associated with eternalism and immutability of mathematics.

They can be combined by assuming there is divine mathematics in addition to our own, some of which we have discovered. We can even add formalism, regarding it as just an interesting mathematical exercise, but not fundamental to other mathematical endeavors.

[Simon Adams]

They can be combined by assuming there is divine mathematics in addition to our own, some of which we have discovered.

This does seem the most natural and rational conclusion. There may be some areas of maths that are pure invention, but most of maths must be an uncovering of something fundamental to nature. Any sophisticated enough aliens we came across could have very different looking maths, but there would have to be a core that was directly equivalent.

I find the “non Platonic” position confusing, as they say that the axioms of maths are just invented by humans. But if the axioms were wrong, we wouldn’t be able to use it so successfully in physics etc. So we were never free to just invent any axioms we fancied. Something like imaginary numbers, where we don’t have a clue what they’re describing, and yet they clearly are describing something fundamental in nature, doesn’t really make sense if maths is not fundamental to nature.

The non Platonic argument seems to get caught up in this obsession with the limits of language, which people spend a lot of time on just to get to the self evident conclusion that there are always limits and subjectivity with using language. I guess there are areas of maths like this, but that’s where our maths doesn’t overlap with the platonic realm - as you say, just an interesting excercise.

[SanteriSatama]

They can be combined by assuming there is divine mathematics in addition to our own, some of which we have discovered. We can even add formalism, regarding it as just an interesting mathematical exercise, but not fundamental to other mathematical endeavors.

Formalism can be considered game theory, yes. Brouwer was solipsist, but Heyting and some other intuitionists held more general MAL-type idealism. Platonism in the sense of archetypal mathematics is not a problem for intuitionism, philosophy of time is the big question.

Qualia are not reducible to quantification, hence archetype(s) of quantification can't be ontologically prior to conscience with flow of qualia. This denies quantification as eternal and immutable Platonia. Quantitative archetypes can manifest as haltings of and in time, relative to flow of processes, but they are not absolute Platonia. Quantitative archetypes are evolutionary, not immutable.

Supposing LNC we can deduce that dynamic tetralemma of halting problems, written as relational operators is more fundamental than quantification:

More <
Less >
Both <>
Neither ><

<> corresponds with notions of interval and Bergson duration. This justifies naming it 'Self'.

Suggesting that qualia are reducible to dynamic tetralemma would be too bold, but codependent relation between sentience and mereology of Bergson durations seems plausible. In this view awareness as unitary continuum, single duration of all durations is not necessary or well justified. Platonic 'One' is just an archetype.

Presupposition of LNC and deriving undecidability of halting problem from that is the game theoretical 'if-then' point of view in this approach. That can of course be problematized and thought differently, no final philosophy of time is suggested.

[SanteriSatama]

I find the “non Platonic” position confusing, as they say that the axioms of maths are just invented by humans. But if the axioms were wrong, we wouldn’t be able to use it so successfully in physics etc. So we were never free to just invent any axioms we fancied.

It can be argued that theoretical physics has reached dead end because of wrong axioms in the underlying theory. Point-reductionism of Hilbert's axioms of geometry is arbitrary and wrong.

Something like imaginary numbers, where we don’t have a clue what they’re describing, and yet they clearly are describing something fundamental in nature, doesn’t really make sense if maths is not fundamental to nature.

Complex numbers and complex plane can be done wholly rationally and with clear definitions, as shown by NJ Wildberger.