Bernado's Mathematical Universe

[SanteriSatama]

"Every flowing point moves according to the Euler formula, and since there are as many flowing points as there are complex numbers, it follows that every monad is akin to a container of infinitely many concentric circles of flowing points.

Real numbers and real complex plane don't compute. No matter how many axioms your mystical formalist makes up, real numbers don't compute, can't do arithmetic and hence can't form form a field. I'm sorry but I don't see the invisible clothes of your naked emperor. The invisible clothes made of non-demonstrable and non-computable "flowing points" of "real numbers" don't exist. Because they don't compute, they can't offer the continuity and causality that physicalism of point-reductionism claims and desires in it's futile, absurd and powerless attempt to argue against Zeno.

The truncated approximations do compute, because they are rational numbers. But because they are not the actual infinities, neither they can provide the desired continuity and causality of physicalism.

So what is the option that is left for point-reductionists? Theology. Actually I do agree that mathematics and theology can't be separated, but mysticism of "flowing points", "infinite sets", "substance" etc. incoherent mumbo jumbo computing beyond time and place, in some Eternal Platonia or what ever, sucks also as theology. By coherent and ethically sound theology I mean that we should not make mathematics into yet another mystical religion, that would be blasphemous against beauty, honesty and communicability of mathematics, the core values of constructing mathematical languages. Which as such are a continuous process withoug any "final truth" of a dead god of any static model forcing itself over process ontology and evolution of mathematics as living spirit.

***

As for Brouwer, I agree that his "solipsist" subjectivism would be insufficient, but since Brouwer intuitionism has been moving towards more cosmic and process philosophical idealist ontology.

[Squidgers]

"Every flowing point moves according to the Euler formula, and since there are as many flowing points as there are complex numbers, it follows that every monad is akin to a container of infinitely many concentric circles of flowing points.

Real numbers and real complex plane don't compute. No matter how many axioms your mystical formalist makes up, real numbers don't compute, can't do arithmetic and hence can't form form a field. I'm sorry but I don't see the invisible clothes of your naked emperor. The invisible clothes made of non-demonstrable and non-computable "flowing points" of "real numbers" don't exist. Because they don't compute, they can't offer the continuity and causality that physicalism of point-reductionism claims and desires in it's futile, absurd and powerless attempt to argue against Zeno.

The truncated approximations do compute, because they are rational numbers. But because they are not the actual infinities, neither they can provide the desired continuity and causality of physicalism.

So what is the option that is left for point-reductionists? Theology. Actually I do agree that mathematics and theology can't be separated, but mysticism of "flowing points", "infinite sets", "substance" etc. incoherent mumbo jumbo computing beyond time and place, in some Eternal Platonia or what ever, sucks also as theology. By coherent and ethically sound theology I mean that we should not make mathematics into yet another mystical religion, that would be blasphemous against beauty, honesty and communicability of mathematics, the core values of constructing mathematical languages. Which as such are a continuous process withoug any "final truth" of a dead god of any static model forcing itself over process ontology and evolution of mathematics as living spirit.

***

As for Brouwer, I agree that his "solipsist" subjectivism would be insufficient, but since Brouwer intuitionism has been moving towards more cosmic and process philosophical idealist ontology.

This is all just strawman now.

Mystical formalist? There is a whole chapter refuting formalism. Maybe just stop arguing against your own made up assertions?

[SanteriSatama]

Mystical formalist? There is a whole chapter refuting formalism. Maybe just stop arguing against your own made up assertions?

Emphasis on the word "mystical". Where else does he get real complex numbers and point-reductionism from?

Is his book a matter of belief and worship for you?

[Soul_of_Shu]

Inspired by the neologism 'eidomorphism', word junky that I am, I did investigate the very generous preview/sample of the book to discover that what the author is proposing is a version of dual-aspect cosmopsychism, wherein some mathematical ideation is fundamental. However, I too balk at the notion of this being based in a proto-substance, however 'minded' such a substance may be, for any such substance seems also an idea conceived by mind, in the version of idealism that I resonate with. But for anyone who can still hold to the existence of such a substance, then surely there's not much to lose by forking over the 99 cents for the kindle edition, and delving into the details—hey, even this math-challenged bloke may give it a try.

[Squidgers]

Mystical formalist? There is a whole chapter refuting formalism. Maybe just stop arguing against your own made up assertions?

Emphasis on the word "mystical". Where else does he get real complex numbers and point-reductionism from?

What does it matter? You wont be able to understand because you refuse to move out of your own paradigm to learn the framing. Not that you should, though its weird to be arguing against it considering you know nothing about the framing and context of the ideas.

It's the same as a materialist getting worked up over an idealists version of mind and consciousness. If the materialist stays within their frame then of course these concepts will be interpreted a particular way and the materialist will never know what the idealist means by these ideas (especially if they only read a blurb to form their understanding).

[SanteriSatama]

What does it matter? You wont be able to understand because you refuse to move out of your own paradigm to learn the framing. Not that you should, though its weird to be arguing against it considering you know nothing about the framing and context of the ideas.

Why do change the discussion from math to personal? I mentioned Badiou, whom I love as "worthy enemy" to steelman my case.

[Squidgers]

Inspired by the neologism 'eidomorphism', word junky that I am, I did investigate the very generous preview/sample of the book to discover that what the author is proposing is a version of dual-aspect cosmopsychism, wherein some mathematical ideation is fundamental. However, I too balk at the notion of this being based in a proto-substance, however 'minded' such a substance may be, for any such substance seems also an idea conceived by mind, in the version of idealism that I resonate with. But for anyone who can still hold to the existence of such a substance, then surely there's not much to lose by forking over the 99 cents for the kindle edition, and delving into the details—hey, even this math-challenged bloke may give it a try.

How do you define "substance", and what does using the notion imply to you?

Here is an explanation from Eido - curious if it matches yours.

". . . while we can posit that substance is that whose essence is existence, it doesn’t tell us what substance is or what its exact properties are. For this, we need to examine our perceptions and also our reason in order to give an account of the necessary properties of substance. Our ontology proceeds by abductively inferring a small set of properties as the sine qua non of everything we see and know. Then, we a priori infer the necessary substance and hence deduce from its properties everything we can and will ever possibly know.

Eidomorphism first and foremost concerns itself with the study of substance. By substance, it is meant that which does not require another thing from which it can be formed. If a substance could be formed of something else, then it would not be called a substance, since it would have to consist of something else. Substance is what forms the basis of reality and is knowable as what can only be explained through itself, and as what can explain everything else.

Were there no substance, then nothing could be explained in terms of anything. Without substance, when we explain something, then we would always need recourse to another thing, and for that thing, another as well, and so on ad infinitum. Further, if we were to stop explaining a thing in terms of another thing at some point without positing a substance, then there would be no sufficient reason for one cut-off point rather than another, hence explanation in this context is either infinite regress or no explanation at all."

[Soul_of_Shu]

How do you define "substance", and what does using the notion imply to you?

Here is an explanation from Eido - curious if it matches yours.

". . . while we can posit that substance is that whose essence is existence, it doesn’t tell us what substance is or what its exact properties are. For this, we need to examine our perceptions and also our reason in order to give an account of the necessary properties of substance. Our ontology proceeds by abductively inferring a small set of properties as the sine qua non of everything we see and know. Then, we a priori infer the necessary substance and hence deduce from its properties everything we can and will ever possibly know.

Eidomorphism first and foremost concerns itself with the study of substance. By substance, it is meant that which does not require another thing from which it can be formed. If a substance could be formed of something else, then it would not be called a substance, since it would have to consist of something else. Substance is what forms the basis of reality and is knowable as what can only be explained through itself, and as what can explain everything else.

Were there no substance, then nothing could be explained in terms of anything. Without substance, when we explain something, then we would always need recourse to another thing, and for that thing, another as well, and so on ad infinitum. Further, if we were to stop explaining a thing in terms of another thing at some point without positing a substance, then there would be no sufficient reason for one cut-off point rather than another, hence explanation in this context is either infinite regress or no explanation at all."

What is being referred to by the term 'substance' according to the above, I would refer to as the uncaused, irreducible ontological primitive. My issue with the term is mainly that in referring to consciousness as such a substance, it evokes more physicalist connotations of substance, whereby it might be conceived to be equatable to some universal field of quantum vacuum energy, or perhaps so-called dark energy/matter, that being representational rather than fundamental under idealism. So for that reason, I prefer to avoid it.

[SanteriSatama]

Were there no substance, then nothing could be explained in terms of anything. Without substance, when we explain something, then we would always need recourse to another thing, and for that thing, another as well, and so on ad infinitum. Further, if we were to stop explaining a thing in terms of another thing at some point without positing a substance, then there would be no sufficient reason for one cut-off point rather than another, hence explanation in this context is either infinite regress or no explanation at all."

In the quote "substance" is explained by other meanings, which can be further looked upon in a dictionary where words are explained by other words. Reading a dictionary, meaning arises from how dictionary entries relate to each other. The above is an attempt to prove "substance" by assumed absurdity of "infinite regress". Potentially infinite regress, however is not a problem, as completeness is not necessitatated nor assumed beyond axiom of reductionism. And with axiom of reductionism, say hello to Gödel's incompleteness theorem.

Only actually infinite regress of "completed infinity" (such as real numbers) is a genuine problem and absurdity, but nothing a priori necessitates such absurdity, as axiom of reductionism is totally arbitrary metaphysical choice.

"Flowing points", what ever that is supposed to mean, substantial or not (and I'm genuinely curious), at least refers to motion. In the standard canon of Western philosophy, as exemplified e.g. by Kant, substance is supposed to be diachronically permanent, temporally immutable. I'm guessing, but the argument of the book seems to fall into the category of mathematical platonism, immutable and eternal Platonia as the "substance"?

Problem with immutable Platonia is that as historical phenomenon, mathematical languages and thinking have been changing and evolving, and there are passionate foundational disputes between various philosophies and perspectives. Empirically, mathematics is not only found, but also created evolutionary process.

Gödel's incompleteness theorem is just a specific case of the more general Halting problem, as Chaitin explains:

”So, argued Turing in 1936, if there were a FAMT (Formal Axiomatic Math Theory) that always enabled you to decide whether or not a program eventually halts, there would in fact be an algorithm for doing so. You’d just run through all possible proofs untily ou find a proof that the program halts or you find a proof that it never halts. So uncomputability is much more fundamental than incompleteness. In-completeness is an immediate corollary of uncomputability. But uncomputability is not a corollary of incompleteness. The concept of incompleteness does not contain the concept of uncomputability.”

Motion, continuity and time coincide with computability, and as Chaitin's article shows, real numbers and their point-reductionism are not computable. Without both computability and continuity, the supposed mathematical substance cannot have causal force, and hence any explanatory power.

[Squidgers]

Inspired by the neologism 'eidomorphism', word junky that I am, I did investigate the very generous preview/sample of the book to discover that what the author is proposing is a version of dual-aspect cosmopsychism, wherein some mathematical ideation is fundamental. However, I too balk at the notion of this being based in a proto-substance, however 'minded' such a substance may be, for any such substance seems also an idea conceived by mind, in the version of idealism that I resonate with. But for anyone who can still hold to the existence of such a substance, then surely there's not much to lose by forking over the 99 cents for the kindle edition, and delving into the details—hey, even this math-challenged bloke may give it a try.

How do you define "substance", and what does using the notion imply to you?

Here is an explanation from Eido - curious if it matches yours.

". . . while we can posit that substance is that whose essence is existence, it doesn’t tell us what substance is or what its exact properties are. For this, we need to examine our perceptions and also our reason in order to give an account of the necessary properties of substance. Our ontology proceeds by abductively inferring a small set of properties as the sine qua non of everything we see and know. Then, we a priori infer the necessary substance and hence deduce from its properties everything we can and will ever possibly know.

Eidomorphism first and foremost concerns itself with the study of substance. By substance, it is meant that which does not require another thing from which it can be formed. If a substance could be formed of something else, then it would not be called a substance, since it would have to consist of something else. Substance is what forms the basis of reality and is knowable as what can only be explained through itself, and as what can explain everything else.

Were there no substance, then nothing could be explained in terms of anything. Without substance, when we explain something, then we would always need recourse to another thing, and for that thing, another as well, and so on ad infinitum. Further, if we were to stop explaining a thing in terms of another thing at some point without positing a substance, then there would be no sufficient reason for one cut-off point rather than another, hence explanation in this context is either infinite regress or no explanation at all."

It sounds like a semantic issue rarher than an issue with the model? i think that, despite using the term 'substance', the model supports Bernado's since it also centralises experience. Although I suspect the author hasn't read Bernado's work

"I deliberately avoid the term ‘consciousness’ because consciousness is just as poorly defined as energy and matter, or ontological space and time. Dozens of definitions of consciousness float around without an adequate distinction between mind and experience, thus for the sake of of reductionism I only adopt experience and avoid consciousness. Consciousness is a rather complex definition that has not been properly analyzed, and though it will later appear in this book, it will only appear as a compound concept formed out of simpler concepts such as experience. By experience, I mean the basic ‘aboutness’ of subjectivity, or the capacity for having mental and physical sensations. For instance with qualia, we define a quale as what it feels like to be in a particular state of mind, or to experience a particular state of mind.

We must be careful, however, to avoid assuming that mind and sentience are by necessity the same thing."

"This is not to say that I will argue that reality is solely based on experience, but rather that experience takes centre-stage. Mere mind is insufficient to explain solidity, nor is the conflict of wills sufficient to explain why there is a universe with this specific structure. It doesn’t explain why anything is the way it is, but merely that this is the result of some cosmic psychological fiat resulting from an unconscious mind. Further, Berkeley may have shown that ‘matter’ is as empty a word as ‘jabberwocky’, but in no way should we believe that we can reduce form purely to mind or mind and form purely to formless matter. In no way can form be simply a matter of content, nor should content just be another type of form. A quale cannot become a quantum, nor is the converse possible. What will be demonstrated later is the need for a double-aspect monist theory."