Bernado's Mathematical Universe

[SanteriSatama]

Would you say that reality is mathematical ontologically?

If reality is not at all ontologically mathematical, how would math map to reality at all? What is mathematics actually showing us about nature?

World has mathematical aspects, but there are also non-mathematical qualia. By the definition I'm using, the mathematical aspect is the more-less relation, the comparative.

In that sense mathematics shows us measurements, nothing less, nothing more. A measurement is not the thing measured, a measured thing is a measurement. The thought "about nature" is just an objectifying relation, not nature.. In nature-creation, more-less relation of mathematics is a driving of evolution.

[Squidgers]

Would you say that reality is mathematical ontologically?

If reality is not at all ontologically mathematical, how would math map to reality at all? What is mathematics actually showing us about nature?

World has mathematical aspects, but there are also non-mathematical qualia. By the definition I'm using, the mathematical aspect is the more-less relation, the comparative.

In that sense mathematics shows us measurements, nothing less, nothing more. A measurement is not the thing measured, a measured thing is a measurement. The thought "about nature" is just an objectifying relation, not nature.. In nature-creation, more-less relation of mathematics is a driving of evolution.

I don't think you fully answered my second question (and/or i didn't fully understand your answer), but I'll try and rephrase it.

If the measurements are at all accurate (which scientists assume they are), what exactly is being measured (is it reality or something else?) and how does mathematics "measure" any part of reality, if reality is in no way mathematical?

Or perhaps more simply: what makes reality measurable?

Qualia would be the "inside" or "subjective" component of a mathematical structure. Similar to how music is both a collection of waveforms (an objective mathematical structure) and the subjective experience of said waveforms

[SanteriSatama]

If the measurements are at all accurate (which scientists assume they are), what exactly is being measured (is it reality or something else?) and how does mathematics "measure" any part of reality, if reality is in no way mathematical?

Or perhaps more simply: what makes reality measurable?

Qualia would be the "inside" or "subjective" component of a mathematical structure. Similar to how music is both a collection of waveforms (an objective mathematical structure) and the subjective experience of said waveforms.

Your question presupposes a thing called "objective reality". As long as we formulate the question in terms of subject-object division, it does not make any sense.

Accuracy of a measurement is relative to the measurement stick aka metric. When physicalists measure with the metric of real numbers, the measurments are always infinitely inaccurate by definition, because that is how that metric works.

[Squidgers]

If the measurements are at all accurate (which scientists assume they are), what exactly is being measured (is it reality or something else?) and how does mathematics "measure" any part of reality, if reality is in no way mathematical?

Or perhaps more simply: what makes reality measurable?

Qualia would be the "inside" or "subjective" component of a mathematical structure. Similar to how music is both a collection of waveforms (an objective mathematical structure) and the subjective experience of said waveforms.

Your question presupposes a thing called "objective reality". As long as we formulate the question in terms of subject-object division, it does not make any sense.

Accuracy of a measurement is relative to the measurement stick aka metric. When physicalists measure with the metric of real numbers, the measurments are always infinitely inaccurate by definition, because that is how that metric works.

Still not really answering the question. Even if there was no "objective reality" (which is a presupposition itself) the question of why reality can be measured at all still lies unanswered.

[Squidgers]

The reason i think this is an interesting, if not important discussion has been addressed in my op. There is a missing link between metaphysics and mathematics, and i find it is often to do with the assumptions people have on what mathematics is whete the philosophy of mathematics is presumed.

The formalist position weds mathematics to logic. But formalists, similar to materialists, will define something by their own framework and then claim it as limited without considering that it is the framework that is limited, not the thing being defined. Define it a different way and those limits disappear

[ScottRoberts]

Would you say that reality is mathematical ontologically?

It is possible to work out a mathematical ontology, but like any ontology there are explanatory gaps to deal with. The basics, though, are pretty straightforward. Assume that all things are thoughts (idealism), and speculate that all thoughts are mathematical objects, or reducible to mathematical objects. One needs to define "mathematical object" which I do as: a mathematical object is a non-referential form. A non-referential form contains its own meaning, as distinct from a referential form like the thoughts "I'm hungry", or "Paris is the capital of France", which refer beyond themselves, while the thought of a Euclidean triangle is the triangle. I would also suggest that instrumental non-programmatic music is another case of non-referential form.

However, mathematical forms alone cannot constitute reality, since from forms alone one cannot derive awareness of forms (this is, basically, the hard problem of consciousness). Hence one must also postulate at least one Mathematician. (The lack of which is what makes Max Tegmark's Our Mathematical Universe a failure as an ontology).

But even with that there are (at least) two problems that must be addressed. One is explain the existence of feeling, willing, and sense perception, as well as thinking. Another is to explain the origin of referential forms. Here is a partial way toward addressing these problems that I wrote up a while ago, if one doesn't mind some repeating of points already mentioned:

Thinking and Feeling, Language and Perception

In the "Divine and Local Simplicity" essay [in which I argue for conflating thinking and willing], I left open a question, that if fundamentally thinking and feeling are identical, how did it come about that we now distinguish them? I do not have a satisfactory answer to this question, but I think that the answer is tied to the answer to another question: how do referential forms come about, which is to say, how did language come about?

Recall that in that essay I distinguished 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. The thought of a house refers beyond itself, while the thought of a triangle does not. The former is referential, and the latter is non-referential. A referential form points to something else, which could be another referential form, a non-referential form, or formlessness. Excluding the last case, what we have is that one form "brings to mind" another. This implies that the second could lie outside of mind. Assuming that nothing is outside of Ultimate Mind, this could only happen in a localized consciousness such as ours. Thus the need for referential form is correlated with the localization of consciousness.

Sense perception is also correlated with localization, and it is not that hard to see that sense perception is by and large a language (or many languages), that is, is referential. It is generally accepted, once one has moved beyond naive realism, that the objects of perception are referential, although the more commonly used term is that they are 'representations'. Even, or perhaps especially, the critical realist must acknowledge that what is actually seen is not what is "really there". Instead, according to the materialist sort of critical realist, what is actually seen is a product of electro-chemical activity of the brain. For the idealist, what is actually seen is the result of a "meeting of minds", the mind of the perceiver, and the mind whose conscious activity is communicated to the perceiver through what is perceived.

There is, however, a broad range of "readability" in sense perception. Words, assuming one knows the language, are obviously "read through" -- it takes an effort to actually notice them as sense objects. Rocks, on the other hand, if one is not a nature mystic, are not read through at all. But to return to the present topic (the relation between thinking and feeling), I think it is instructive to consider music. "Music is feeling, then, not sound" says Peter Quince in Wallace Stevens' poem Peter Quince at the Clavier. We "read through" the sounds and in doing so are moved, to what we might call sadness or to joy. However, the word "sadness" does not quite make sense, for we may greatly enjoy hearing a slow, minor key piece. Music, one might say, gives us the pure emotion without the bad stuff.

On the other hand, it has been known since Pythagoras that music is highly structured. It can be analyzed mathematically. This makes it, as I see it, also expression of pure thought. And so, one could say that a pure thought is a pure feeling, and a pure feeling is a pure thought. How, then, did impurity arise?

In a localized consciousness, as noted above, not everything is "in mind", and so we need referential forms to bring what is not in mind into mind. This means that a referential form carries an additional purpose than just "being", however lovely it may be, in the way that a mathematical object or a musical passage "just is". And so, we can distinguish the referral to another form from the feeling of the form. That referral to another form is a thought.

As said at the start, this does not solve the question of how thought and feeling became distinguished. It just states that this question is tied to the question of how localized consciousness came about.

I should note that I consider all this as just an interesting ontological exercise -- like any ontology, the claim "Reality consists entirely of a Mathematician creating mathematical objects" cannot be proven. But I am not aware of any empirical or rational reason to reject it out of hand.

[Squidgers]

I should note that I consider all this as just an interesting ontological exercise -- like any ontology, the claim "Reality consists entirely of a Mathematician creating mathematical objects" cannot be proven. But I am not aware of any empirical or rational reason to reject it out of hand.

What would "proof" even look like? Surely that would also depend on the epistemology and ontology assumed by the one asking for proof.

For example, if a complete theory of everything that positied a mathematical substance was presented, assuming it covered all the "gaps" and presented it's case with rigor and precision, would that then be enough of a proof? An empiricist would still say no to this. But that is like demanding proof of the matrix from inside the matrix

[ScottRoberts]

What would "proof" even look like? Surely that would also depend on the epistemology and ontology assumed by the one asking for proof.

For example, if a complete theory of everything that positied a mathematical substance was presented, assuming it covered all the "gaps" and presented it's case with rigor and precision, would that then be enough of a proof? An empiricist would still say no to this. But that is like demanding proof of the matrix from inside the matrix

Right. I judge ontologies on the criteria: plausibility, parsimony, adequacy (completeness), and coherence. All I am saying is that one can conceive of reality as just mathematics (and a Mathematician), and that doing so scores ok on these criteria, though one has to do some argumentation in the cases of plausibility and adequacy. And it neatly answers the "effectiveness of mathematics in the natural sciences" issue.

[SanteriSatama]

The reason i think this is an interesting, if not important discussion has been addressed in my op. There is a missing link between metaphysics and mathematics, and i find it is often to do with the assumptions people have on what mathematics is whete the philosophy of mathematics is presumed.

The formalist position weds mathematics to logic. But formalists, similar to materialists, will define something by their own framework and then claim it as limited without considering that it is the framework that is limited, not the thing being defined. Define it a different way and those limits disappear

Intuitionism and idealist ontology of mathematics can offer the "missing link", and a chance to to find a coherent answer to Wigner's wonder of efficiency of mathematics. Brouwer's solipsism, however, is not sufficient. Ramanujan said he received his insights from his Goddess. The idealist ontology of mathematics is beyond subjective, but it's also evolutionary. Evolution of mathematics is not limited to evolution in unilinear time, which is already clear from CPT symmetry of quantum mechanics.

The formalist-physicalist paradigm of point-reductionism is an absurd cult of Emperor's New Clothes. Stephen Wolfram's ideas of computational universe are very interesting, but I have also some philosophical differences with him.

[Squidgers]

The reason i think this is an interesting, if not important discussion has been addressed in my op. There is a missing link between metaphysics and mathematics, and i find it is often to do with the assumptions people have on what mathematics is whete the philosophy of mathematics is presumed.

The formalist position weds mathematics to logic. But formalists, similar to materialists, will define something by their own framework and then claim it as limited without considering that it is the framework that is limited, not the thing being defined. Define it a different way and those limits disappear

Intuitionism and idealist ontology of mathematics can offer the "missing link", and a chance to to find a coherent answer to Wigner's wonder of efficiency of mathematics. Brouwer's solipsism, however, is not sufficient. Ramanujan said he received his insights from his Goddess. The idealist ontology of mathematics is beyond subjective, but it's also evolutionary. Evolution of mathematics is not limited to evolution in unilinear time, which is already clear from CPT symmetry of quantum mechanics.

The formalist-physicalist paradigm of point-reductionism is an absurd cult of Emperor's New Clothes. Stephen Wolfram's ideas of computational universe are very interesting, but I have also some philosophical differences with him.

Have you tried Neven Knezevic's take on an ontological mathematics? His arguments are well formulated but also long winded (which might be necessary for this kind of mapping).

https://www.goodreads.com/book/show/521 ... domorphism

This is his first attempt, although i know he is working on a more independent model since he fell out with the authors of some of his sources