Speculation About the Discovery of Ideal Forms

[AshvinP]

I am curious as to how mathematical objects could be "invented" under idealism? As Cleric pointed out, this is generally the wrong question to even be asking because it makes no difference in our practical existence, but it is still a curiosity. How could an ideal form not exist before it is "discovered"? Perhaps the question turns on the meaning of "discovered", because no ideal form can exist until it is thought by someone (under idealism), and since ideal forms have always existed (also under idealism), they have always been thought by someone. Although "discovery" seems to imply that it was not only thought, but someone becomes aware it was thought. This also relates to the Shermer-Peterson interview I just posted - JP points out one way to distinguish between "invention" vs. "discovery" of meanings attached to ideal content is to see how much evidence from different methodologies, like philosophy, evolutionary theory, neuroscience, etc., converge on a specific phenomenon. If we truly exist in a unified realm of shared meanings, and the meaning at issue is valid, then all methods (perspectives) should converge on that meaning.

You are voicing Platonism again, so we are going in circles. There is 2.5 millennia of history behind the Platonic and non-Platonic versions of idealism and a dispute between them, with no resolution whatsoever.

"and since ideal forms have always existed (also under idealism), they have always been thought by someone. "

- not necessarily true. There is an uncountably infinite variety of mathematical forms that are impossible to exhaust and think all of them. Refer to Hoffman's "Gödel candy shop". Even if we assume for a sec that the number of the individual minds in the universe of Cosnciousness is infinite, it would be only a countable infinity. But the variety of mathematical forms and ideas is uncountable infinity, so it is impossible for all the minds in the universe to think all the possible mathematical ideas. For example, there is uncountable infinity of possible geometrical shapes, and so uncountable infinity of the possible ideas of all possible geometrical shapes (I hope you are familiar with the difference between countable and uncountable infinities per Kantor's infinite set theory). But yes, once some of those ideas become "invented" or "discovered" (whatever we want to call it) by one of the minds (whether it can be one of the divine minds or one of the human ones), then they become shared and spread between the minds and become part of the shared content.

"Platonism" is generally used to mean a realm of ideal forms which is totally beyond the world of appearances (even though I would take issue with that interpretation of Plato). That is not what we are asking about here; rather we are asking about ideal forms which are very much existing within the world of appearances, i.e. mathematical objects. We could call them "archetypal forms", but I think my question applies to all ideal forms. And I am not asking what Western v. Eastern traditions say about invention vs. discovery, but what is actually consistent with idealism if we think it through for ourselves.

Hoffman's reference of Godel's "candy shop" is precisely to show how consciousness may be in the process of exploring all of its possible relations. An interesting question under idealism, then, is whether some ideal form can exist without being thought, or whether forms only come into existence when they are thought (and vice versa). We do not need to assume infinite number of minds, countable or uncountable, but only One mind as necessitated by idealism. How can the One mind fail to encompass all possible forms? What does it even mean for an ideal form to "not exist"? Those are my questions.

[Eugene I]

How can the One mind fail to encompass all possible forms?

Because, as I said, the set of all possible forms is an uncountable infinity, it is impossible to encompass all of them. It is the same as to have all ideas about every single point on the line. It is impossible, the amount of points on a line is an uncountable infinity.

Or, can One mind encompass all possible pieces of music, including all possible ways of performing each of these piece of music. As a hobbyist musician, I can tell that one rendition of the same piece of music can be quite different from another rendition of the same piece, and each rendition is actually a very different piece of music. so there is uncountable infinity of all possible renditions of even one piece of music and it is impossible to imagine them all.

[AshvinP]

How can the One mind fail to encompass all possible forms?

Because, as I said, the set of all possible forms is an uncountable infinity, it is impossible to encompass all of them. It is the same as to have all ideas about every single point on the line. It is impossible, the amount of points on a line is an uncountable infinity.

Or, can One mind encompass all possible pieces of music, including all possible ways of performing each of these piece of music. As a hobbyist musician, I can tell that one rendition of the same piece of music can be quite different from another rendition of the same piece, and each rendition is actually a very different piece of music. so there is uncountable infinity of all possible renditions of even one piece of music and it is impossible to imagine them all.

So it seems you are then using a quantitative argument to limit that which is qualitative, i.e. ideal forms. Is that a valid approach? Remember we are only asking in the context of idealism. Originally I said that maybe it turns on whether we take "discovery" to mean prior existence of ideal form or rather awareness of prior existence of ideal form. I am still wondering if that is the most important distinction.

[Eugene I]

So it seems you are then using a quantitative argument to limit that which is qualitative, i.e. ideal forms. Is that a valid approach?

Yes, because the amount of possible qualities of ideal forms is uncountably infinite. Every rendition of a piece of music is qualitatively different (It bears a unique ideal qualitative content) in the space of all musical forms, so this qualitative space of all possible musical forms is uncountably infinite and impossible to fully ever encompass by consciousness.

In mathematical set theory trying to define "the set of all sets" as a mathematical object leads to so-called Russel's paradox - "does the set of all sets includes itself?" The "set of all sets" is mathematically self-contradictory concept. And so is the set of all possible ideas - does the set of all possible ideas includes itself?

[AshvinP]

So it seems you are then using a quantitative argument to limit that which is qualitative, i.e. ideal forms. Is that a valid approach?

Yes, because the amount of possible qualities of ideal forms is uncountably infinite. Every rendition of a piece of music is qualitatively different (It bears a unique ideal qualitative content) in the space of all musical forms, so this qualitative space of all possible musical forms is uncountably infinite and impossible to fully ever encompass by consciousness.

In mathematical set theory trying to define "the set of all sets" as a mathematical object leads to so-called Russel's paradox - "does the set of all sets includes itself?" The "set of all sets" is mathematically self-contradictory concept. And so is the set of all possible ideas - does the set of all possible ideas includes itself?

I am not following...

How can something be said to exist if it is not "encompassed by consciousness"? Put another way, if the choice is between claiming the set of all ideal forms falls outside of Consciousness or the set of all ideal forms includes itself, why are we preferring the former choice over the latter? Is it only because the latter turns out to be "mathematically self-contradictory"? Isn't the simplest resolution to such a contradiction to claim that mathematics cannot possibly describe all that exists (which is also result of Godel's incompleteness theorem)?

[Eugene I]

And I'm not following you, we lost each other in philosophical debris

What I'm simply saying is that we have no evidence that Consciousness can encompass and experience the actual uncountable infinity of all possible ideas. From our own experience we only know that consciousness can experience a limited set of ideas. To me experiencing the actual infinity is unimaginable. The actual infinity is a mathematical abstraction, and many mathematicians still reject the Kantor's theory of infinite sets and argue that the idea of infinity is mathematically illegal and self-inconsistent and should be excluded from "healthy" mathematics.

[AshvinP]

And I'm not following you, we lost each other in philosophical debris

What I'm simply saying is that we have no evidence that Consciousness can encompass and experience the actual uncountable infinity of all possible ideas. From our own experience we only know that consciousness can experience a limited set of ideas. To me experiencing the actual infinity is unimaginable. The actual infinity is a mathematical abstraction, and many mathematicians still reject the Kantor's theory of infinite sets and argue that the idea of infinity is mathematically illegal and self-inconsistent and should be excluded from "healthy" mathematics.

I get that part and I agree that we, as limited alters of Deep M@L, cannot experience all possible ideas. There are many aspects of M@L that we cannot experience right now, such as omnipotence and omnipresence. But how can we say M@L does not experience "all possible ideas" under idealism? It seems to me that, if an idea is possible, then it is already known in some manner. Think about it this way - as soon as you experience an idea, it exists and is known. So does that mean you "invented" the idea? I find it hard to accept that under idealism.

Again, the question is just a curiosity rather than anything that will make a practical difference. And perhaps it cannot be answered for that reason.

[Eugene I]

Exactly, it can not be answered, and I think it is irrelevant. There are versions of idealism that include this assumption that M@L actually experiences "all possible ideas", as wells as the assumptions of "omnipotence and omnipresence" (those are mostly known as theistic versions of idealism), and there are versions that do not do that. I simply do not subscribe to the former versions, they are too inconsistent and too non-parsimonious with their over-stretching assumptions of "omnipotence, omniscience and omnipresence" of the MAL. Don't you know the paradox of omnipotence: "can god create a rock that he can not lift?".

[AshvinP]

Exactly, it can not be answered, and I think it is irrelevant. There are versions of idealism that include this assumption that M@L actually experiences "all possible ideas", as wells as the assumptions of "omnipotence and omnipresence" (those are mostly known as theistic versions of idealism), and there are versions that do not do that. I simply do not subscribe to the former versions, they are too inconsistent and too non-parsimonious with their over-stretching assumptions of "omnipotence, omniscience and omnipresence" of the MAL. Don't you know the paradox of omnipotence: "can god create a rock that he can not lift?".

The standard answer to that is God cannot do that which is logically impossible (under any formulations of logic). Like He can't choose to not exist. I'll go with that for now.

What is the form of idealism that rejects omnipotence. omniscience and omnipresence? As far as I understand, Eastern spiritual traditions do not restrict Consciousness to only limited powers, knowledge, or locations, unless we are considering meta-cognition a "power", but even then our meta-cognition must be included in the One Consciousness.

[Eugene I]

The standard answer to that is God cannot do that which is logically impossible (under any formulations of logic). Like He can't choose to not exist. I'll go with that for now.

What is the form of idealism that rejects omnipotence. omniscience and omnipresence? As far as I understand, Eastern spiritual traditions do not restrict Consciousness to only limited powers, knowledge, or locations, unless we are considering meta-cognition a "power", but even then our meta-cognition must be included in the One Consciousness.

Omnipotence and omniscience are exactly those logically impossible things that God just cannot do. Unlike the omnipresence, because in idealism there is nothing existing outside consciousness, which is the same as to say that consciousness is "omnipresent".

Knowing the Eastern traditions quite well, I've never heard them mentioning "omnipotence and omniscience", that is a Western theological invention.