Is the universe all there is? ‘Evidence’ for objects outside the universe...
Introduction
One of the topics that seems to come up from time to time on Lesswrong is the supernatural vs a naturalistic explanation for the universe.
I felt that I could make a contribution to this discussion as a theoretical physicist (now moved into a different area), which actually came about from a discussion I had with a particular esteemed professor from the University of Melbourne, in 2012. Prior to this moment, I had slowly (perhaps nascently) been developing a metaphysical philosophy that was a little closer to Functionalism than Physicalism (these two metaphysics are compatible with one another), but since Functionalism was shown by Prof. Searle to be ‘incomplete’ in a certain sense that I won’t go into right now, I continued my search as a side project, and I found that after much training both during Ph.D and in post-doctoral research in theoretical physics and pure mathematics, I found a ‘bug’ (or a ‘feature’) worth expounding that continued on from my initial thoughts on metaphysics many years prior. What I arrived at was a kind of reverse-Epiphenomalism, which I will explore below.
The ‘bug’ (or ‘feature’) is that while I found many scientists will typically attest to a kind of physicalism or completely naturalistic philosophy by lip-service, when in conversation and in daily work in their profession within science (or mathematics) I found that there was a tacit working-ethos of something more akin to Mathematical Realism. I want to defend this philosophy a little bit, as I would currently consider myself to fall into that category (would love to hear others’ view on this). What I mean is, when queried, many physicists and mathematicians would frame mathematical truths as actually true, ‘real’, that is, existing entities, and that there is a kind of Platonic ‘math world’, and in physics apply the process of Ansatz, where we apply a proposed mathematical object or principle and propose a theory, before beginning to query it and conduct experiments to see if we can falsify it. I found that a) this belief reminded me strongly of a talk by Richard Feynman where he explains the scientific enterprise as not really being so much a following of the scientific method per se (many great scientists have intuited great ideas prior to the experiment being conducted), but that it begins often with a kind of ‘special guess’ (Feynman’s terminology). This special guess seems to come from some deep place, some mental insight arrived at through an unclear process, some inspiration, and then the guess is applied (as an Ansatz) and the theory constructed from that point. Furthermore, I was reminded of b) my uncle’s former supervisor Roger Penrose a few years ago wrote Road to Reality: A Complete Guide to the Law of the Universe, and in it depicts a diagram (not reproduced here) that proposes a Platonic ‘math world’ and a ‘real world’ which follows a subset of these mathematical principles. Now I am aware of Penrose’s position that he doesn’t take this metaphysics as literally true, but I wondered why, and I decided to delve into it a little more, bear with me.
Mathematical Realism
I did a more thorough (and better cited) defence of Mathematical Realism in the manuscript I will refer to (which is here: https://arxiv.org/abs/1306.2266 - also, I know the current arXiv version has a typo in the first line—it is fixed in Peer-Review) but the point I wish to make (which I might not convince you all on) is that, if you think of any mathematical object: a straight line, the number ‘3’ (or any number) or any mathematical theory, there is a sense that these objects have a distinct existence, are ‘provable’ in a stricter sense than anything in science, specifically as the word ‘proof’ really has the format of an abuse notation in science—in science we infer, and collect evidence for or against things, but the word ‘proof’ really needs to be reserved for a mathematical procedure that is carried out (I know it has other definitions such as in copy-editing, or courts of law, but I am meaning only in the interface between science and mathematics in the context of Natural Philosophy). So, for example, if you were to have a map with a straight line marked on it, is it really there? It’s notional of course. but, is the line on the page really straight? Not really, it’s being compared to an ideal line that isn’t in the universe per se. If you rubbed out, or altered the line, would you destroy the actual concept of the straight line for everyone? Of course not, and furthermore, the concept of the straight line has a kind of objective existence, and doesn’t have the same properties as other objects in the universe—it doesn’t have a ‘location’ for a start, and seems eternal, immutable, static, but also provable in principle from any future race or alien, from anywhere in the universe, if they decided to replicate a definition of a concept of a straight line.
Now, I am keenly aware it can be argued (and often is) that these ideals can be thought of as a kind of ‘fiction’ agreed upon by humanity for a time, and this harmonises it with Naturalism. Because then, all these mathematical theorems are simply derivable from brain function. This has some troubling aspects as it has assumed structure being followed by brain function to start with, and assuming the thing to query doesn’t lead to good explanations. Furthermore, one is then in difficulty if asked whether molecules and atoms in the primordial universe moved, according to what equation, and how they were organised (in mathematical groups, for instance)? So we actually get a clear solipsism if we go too far with that approach. If atoms in the primordial universe can’t have followed any mathematical principles in their motion, then it’s all back-generated from our minds somehow. It’s certainly an irrefutable stance (I can’t disprove it), but most practicing physicists would kind of believe in a more straight forward ‘there is absolutely truth’ and ‘the universe existed before we did’ approach. That is, the atoms and particles in the early universe did undergo processes and fall into groups, and so forth, following mathematical principles. This is the stance that I am taking in this work but would love to hear feedback on missed alternatives. (For the Jordan Peterson followers out there, this view could be seen as an extension of Judeo-Christian ethos growing out of monastic tradition that learning, books, education and universities are important institutions built on a philosophical disposition that the universe is inherently reasonable and queryable. That also, is quite an assumption and we have no ability to prove it to be the case—but it has worked so far, as Dawkins has historically pointed out—though I differ on Dawkins that the philosophical underpinnings of science are scientific statements, they are in fact philosophical statements, so we need to assume this ethos to begin with prior to conducting science).
In that sense, the view I am taking is that mathematical principles are prior (they don’t have a constraint in time or location and are timeless), and that any physical interaction between two objects in the universe are governed by some principle—the ‘interaction’ itself is an abstraction, and so, the universe can’t really flow, evolve or function without the intersection of abstractions obtruding, and so phenomena are only linked via abstractions (and abstractions with themselves) but no two physical objects can be linked or related in any way without first defining an abstract entity called a ‘relationship’ - hence, a ‘reverse’ version of Epiphenomenalism.
Developing a formalism to be able to explore the process of Ansatz
Flash forward to my 2012 meeting with a particular professor (of String Theory, for reference), and we were discussing, lo-and-beyond, multiple universes. We were at a workshop for particle accelerator experimentation—the discussion was whether there would be any practical measurement in principle to show if there was anything outside of the universe. The typical position of many would be to dismiss it as impossible in-principle, because it could be assumed you could ‘draw a box’ around anything found, and define it as being in the universe. (In this post, I will refer to this work I put together afterwards that disproves this mathematically). But actually, this professor related an interesting anecdote.
The anecdote: let us imagine that life developed on earth, not when it did, but many millions of years later or more. One observation would be there would be no starlight. The universe would have expanded to such a degree that no stars would be visible except the sun, in fact, we would not (until telescopes were invented) even have a concept of a star, and we would only know the sun (moon) and an empty sky. A natural question for an astronomer in this fictional world, would be, that the sun seems fundamental to the universe and we would like to calculate the distance from the earth to the sun. Unfortunately, no matter what we do, we cannot derive from first principles this distance. The reason? Well, it isn’t fundamental, it’s kind of an arbitrary value, which works for us, and other earth creatures, to live at this comfortable temperature range, etc. So we are left with a situation where a person desires to find a fundamental physical answer to a physical phenomenon but cannot from first principles derive it from some mathematical principle. Now, consider the situation where the subatomic particles in our universe have certain masses, electric charges, and other properties. After half a century or more of trying, we haven’t got a method for deriving these values from scratch, but they need to be assumed from hand, as being values arrived at stochastically from some dynamical process (dynamic chiral symmetry breaking, or some other symmetry of the Standard Model, for this model, which is electroweak theory + QCD, is, as it has been known since Weinberg pointed it out, an Effective Field Theory). String Theorists (and other proposed methods of unifying General Relativity and the Standard Model) might propose a solution for generating these values mathematically—but, this is still speculative, as there is no firm evidence if (and which) of these theories are correct. (String Theory is not a single theory but covers an extremely broad range of parameters, and string phenomenologists will generally approach their art through methods of some kind of proposed compactification of dimensions to try to “get” an Ansatz for the universe but this as so far not been that successful).
After thinking over the professor’s thoughts, I felt inspired to try to put some philosophical thinking down on paper to try to see if we could ‘prove’ multiple universes as arising from some stochastic process of abstract objects with a large configuration space—noting as a guess, the symmetry between the large and small scale Pareto distributions: of all the sperm, only a few lead to a foetus, of all the planets only a few seem habitable, of all the wealth, only a few have most of it, of all the space in the universe, only a small portion has a high concentration of mass (galaxies) - is it so much of an extension to imagine the same could apply to universes?
So, I set out to do a couple of things:
Write down a mathematical formalism for the process of an Ansatz so we can explore it, probe it, and under that formalism (at least!) make some conjectures about it;
Explore some simple properties of the large parameter space of mathematical objects and the constraint that only a few of them are ‘followed’ as mathematical principles that guide nature (ie how particles move, etc. not all theories are true!);
Make it as general as possible so as not to add superfluous structure that could add artefacts that would distort the discoveries that could be made;
As a key first step, I noted that any mathematical formalism of non-mathematical objects (physical objects) will inevitably lead to a ‘nesting’ structure (I called it the Labelling Principle), where a reference of an object is already a ‘pointer’ to ‘what is meant’ by the pointer, and what is meant by ‘what is meant by’ a pointer is also a pointer to the same object, etc. Of course, any physical object, in order to be referred to, needs to have a mathematical representation from within the mathematical framework being defined and there’s no way around that.
I then had to separate these two notions of existence. Mathematical objects that ‘exist’ in a real, or provable sense (I prove a theorem, for example) aren’t exhibiting the same kind of existence as ‘somewhere in the world a black swan exists’. It’s similar to how the word ‘causality’ can mean two distinct things: a physical property to do with the Minkowskian geometry of the universe (‘cause-and-effect’), and the ‘ground-consequence’ structure of a logical argument. To distinguish these two concepts existence, I call the mathematical one ‘exist’ and the physical one in the universe extant.
Then, I equated existence (in a mathematical sense) of objects in the formalism, to only occur for objects if they are extant, that is, I could query whether observed, extant phenomena constituted evidence for the extantness of a thing but setting up the formalism so that the mathematical theorem would be inconsistent (invalidated, and disproved by contradiction) so I could kind of model the process of an Ansatz and see it happen on paper. This was the main major constraint I added to the theory which otherwise isn’t too much more structured than good ol’ fashion Zermelo–Fraenkel theory with an axiom of choice (ZFC).
One of the first interesting discoveries was that this led to a very natural explanation of Eugene Wigner’s ‘Unreasonable Effectiveness’. It simply falls out of the theory from a simple cardinality argument.
Speaking of cardinality, I drew on Georg Cantor’s universality paradox that gave sudden, crucial insight on how there might be multiple universes.
First, I indeed needed to add some (reasonable) very general definitions of what a universe ‘is’ (in the Tegmark classification sense), and adopted a pose that the universe should at least be definable and practically usable—I am a physicist afterall—and also I needed to supply some clarification of what is ‘evidence’ in the context of this formalism.
Then, what I found is something very interesting, one is able to prove, using the theory and using a Cantor argument, that inclusion of mathematical principles leads to a Universal Set which can’t be consistently defined (a real problem for practising physicists) and so it is a proof by contradiction. In other words, If you want to define a universe in a consistent manner, it has to leave out certain objects. And these objects are the mathematical principles. So it’s fairly neat.
Putting all this together, as we talk of religion and spirituality, and taking the stance of a practising science where we are drawing on a philosophy that truth is important, we need to seek truth and that the universe is reasonable and queryable so that science can be done on it (a Judeo-Christian-derived view) I thought it worthwhile to show how this is kind of incompatible (or at least, not straightforwardly compatible) with Naturalism. And once the door is open, many other things outside the universe could be considered.
But I’ve been thinking of this for about 10 years, and then spent another 10 years developing it and thinking about it to myself (the actual writing down of this article was 1 year only), and I have struggled to get some real feedback on this proposal so I need to get some Lesswrong peer review happening.
Why now?
With recent works such as The Master and His Emissary, and the more ground-breaking works of Prof. Iain McGilchrist, together with the views on what is real, (what is meta-real) in deep narratives espoused by Jordan Peterson, it feels like people are coming to this particular same thought from different directions, this Mathematical Realism view that I had already held for a while, and can argue quite effectively for it. Now, when 2-3 fields (neurology/psychiatry, psychology, physics) converge on a similar thinking pattern, I think it’s worth taking notice as that doesn’t usually happen and it might indicate that we are onto something here. Therefore, I wanted to place here the work (it is currently going through Peer-Review) but is up as a pre-print:
On the existence of other universes https://arxiv.org/abs/1306.2266.
I wished to print some of the main theorems here in this post, but without knowing how to get a tex plugin, the typesetting doesn’t come across properly, so I will leave it here, with some concluding summaries regarding it:
Abstract
Natural philosophy necessarily combines the process of scientific observation with an abstract (and usually symbolic) framework, which provides a logical structure to the practice and development of a scientific theory. The metaphysical underpinning of science includes statements about the process of science itself, and the nature of both the philosophical and material objects involved in a scientific investigation. By developing a formalism for an abstract mathematical description of inherently non-mathematical (physical) objects, an attempt is made to clarify the mechanisms and implications of the philosophical tool of Ansatz. Outcomes of this style of analysis include a possible explanation for the philosophical issue of the ‘unreasonable effectiveness’ of mathematics as raised by Wigner, and an investigation into formal definitions of the terms: ‘principles’, ‘evidence’, ‘existence’ and ‘universes’, that are consistent with the conventions used in physics.
It is found that the formalism places restrictions on the mathematical properties of objects that represent the tools and terms mentioned above. This allows one to make testable predictions regarding physics itself (where the nature of the tools of investigation is now entirely abstract) just as scientific theories make predictions about the universe at hand. That is, the mathematical structure of objects defined within the new formalism has philosophical consequences (via logical arguments) that lead to profound insights into the nature of the universe, which may serve to guide the course of future investigations in science and philosophy, and precipitate inspiring new avenues of integrated research.
Summary
To summarise and encapsulate the final thesis and import of this work that will follow from the presentation of the formalism, we will find there is no logically consistent way to define a universe that includes all abstractions (such as mathematical objects), and that such a claim need only rely on logic to prove it. That is, objects outside the present universe can be proved to exist using a self-consistency definition, and that constitutes the only evidence that would be allowed in this case.
An attempt was made to classify other universes in a general fashion, and to clarify the characteristics and role of evidence for theories that provide at least a partial description of a universe. The connection between phenomena that constitute evidence and the theory itself was established in a proposed Duality Theorem. Instead of focusing on attempting an ad- hoc identification of extra-universal phenomena from experiment, the formalism was used to derive basic properties of objects that do not align with our universe. As a first example toward such a goal, a fundamental object was identified, which satisfies the necessary properties for evidence, and whose extantness does not coincide with our universe. This paves the way for future investigations into more precise details of the properties of objects and methods amenable to this type of formal inquiry.
Note that this proof demonstrates that, in principle, there are objects that exist in a universe different from our own, due to the constraints of logical consistency. The nature of the test-case object is quite rudimentary, but it serves as an initial example. The formalism as a whole, though, has been especially fruitful in producing the unanticipated results of immediate relevance to the scientific community; in particular, a possible explanation for the ‘unreasonable effectiveness’ of mathematics is put forward. This represents an important development in the philosophical understanding of physics. Furthermore, the clarification of Ansatz: the process of applying an hypothesis to the physical world, and then testing it against experiment, represents the main achievement of the work. The introduction of a framework within which one can interrogate the nature of how hypotheses are applied represents a long-term ambition, seemingly missing from the current literature, which future research can develop and refine.
What does leaving out the mathematical principles achieve? If you are saying that the physical universe exemplifies the maximum set of consistent maths …then it doesn’t, observably. If you are saying that the mathematical universe is inconsistent if it exists at all...that’s a argument against realism. The epistemological role of mathematical realism is to finally settle questions questions which earthly mathematicians can’t settle.… which can’t be done if it is contradictory. A small but consistent MU has a uniqueness problem … there are multiple such. Multiple small but consistent MUs are no improvement on a large consistent ones..
Well, leaving out mathematical principles, as explained in the text, means that the universe can be defined in a consistent manner. That’s really useful for cosmologists, astrophysicists, and other people such as Prof Tegmark, trying to understand what universes could exist, if other universes existed before our own and generally do experiments to understand the scope of the universe. Maybe it’s not everyone’s trade, but for many people it really matters.
Putting it another way, adding mathematical concepts in the way described, without limiting the scope or doing something to handle the Cantor paradox, leads to a definition of the universe that’s logically inconsistent (ie it always leaves out something, so its a proof by contradiction, simply, the universe can’t be ‘large enough’ to encapsulate those entities.
Am I saying the universe exemplifies the maximum set of consistent maths? Not at all! Quite the opposite in fact—I’m not sure how you got that from this summary, as I’m saying the opposite, that many mathematical objects to not end up being exemplified, or related. The cardinality is the same but the set of things not mapping to anything in the universe is much much larger.
Am I saying the mathematical universe is inconsistent if it exists at all? Well, not really—I don’t know if there is a ‘mathematical universe’ per se. All we know is it’s too big to fit in our universe and stuff gets left out. We know that its not as large as ‘anything I make up’ because there are theorems that lead to contradictions and that limits the mathematical objects that are ‘real’ (in the mathematical sense). I imagine that it’s more like a ‘wood between the worlds’ or like a kind of meta language that is kind of between universes (if there are other universes) or otherwise simply exists outside (if there’s only one universe). So I don’t see this as an argument against realism—as realism was used to posit the notion of existence to ‘mathematically consistent’ in the first place, so it couldn’t go in that direction.
Totally agree that mathematics being a kind of encapsulated universe consistent with itself would undermine its own truth, and thereby be automatically false because one is relying on logic in the first place to posit it. So, indeed, that’s not a stance to take here. In fact, it’s a good argument for absolute truth, and one I’m fond of using.
‘Smaller but consistent’ MU—I’m not sure what you mean here—the ‘smallness’ would come from leaving out non-truths, ie contradictions, and that would be needed ti preserve a sense of truth in any framework. But also I think MU (does that mean ‘mathematical universe’) is a potentially misleading term as I just described above.
That is necessary, but insufficient , at best. If mathematical entities don’t have real existence, as fictionalists cliaim, then there is also no real inconsistency.
Comment: “That is necessary, but insufficient , at best. If mathematical entities don’t have real existence, as fictionalists cliaim, then there is also no real inconsistency.”
Response: Can you say that more precisely, what is necessary but insufficient, for what?
What I stated was, from this work, based on the assumptions as laid out in the manuscript, I can verbally summarise the result by the statement that ‘abstract objects can be demonstrated to be in a distinct universe from ours, as the set of both of them together cannot be defined in a consistent way logically.’
Do you mean that these assumptions, together with the steps, don’t show that these abstract objects to be in a universe distinct from ours, in the context of this formalism, and the definitions that I have supplied? OR do you mean that this statement, is necessary but insufficient to show a separate thing, ie to prove or to demonstrate some of the other concepts we have been discussing, such as MR, which I stated I did not try to prove? ie as an encapsulated logic I don’t see where I went wrong.
Based on your statement, “If mathematical entities don’t have real existence, as fictionalists cliaim, then there is also no real inconsistency.”, I don’t need to rely on there being a ‘real’ inconsistency for the steps to still work. What I mean is, what is ‘real’ or not is just the background metaphysic. A mathematical fictionalist would still hold that there are proofs and theorems, just that they don’t have a ‘real’ existence. But, I haven’t taken the assumption of mathematical fictionalism, in which I don’t know if I can talk about abstract objects at all—so it doesn’t apply here.
When I discuss mathematical fictionalism (note, this is not something I talk about in the manuscript), I have some questions I need to clarify about how it works, and seek guidance on, to be able to argue effectively on that topic as I haven’t had it fully described to me. As I keep mentioning, where I am at, provisionally, at the moment, is that I keep running into that said Solipsism (please note, as mentioned, this is not the argument from my paper which assumes MR). So, can we resolve it—in the primordial universe, how are we to understand the subatomic particles being arranged into groups, and so forth, if these structures required for our existence only are fictions occurring within the mind of people? (I assume that’s what fictionalism means)… if you can clarify
The assumption, alone, that the physical universe must be consistent is insufficient to show that there is a separate MU.
The assumption that the physical universe must be consistent, plus the assumption of MR, plus the assumption that consistency doesn’t matter for MU’s is sufficient to show that there is a separate MU.
But you have only shown that that follows from your assumptions, not that it is actually true, ie. your assumptions are actually true.
No, it’s valid, but it’s not sound. Valid but unsound arguments are ten a penny—you can show almost anything given three arbitrary premises.
https://en.wikipedia.org/wiki/Validity_(logic)
Fictionalism isn’t known to be true or false, neither is realism. It’s an open subject. You can make arguments against fictionalism, the fictionalist can make arguments against realism.
You seem to be hinting at an argument where an entity has to really exist in order to be talked about (an argument you haven’t brought before). But the plain fact is that we can talk about fictional entities, like Gandalf or Sherlock Holmes—so the fictionalist has a robust response.
Can you not learn that from books? How did you learn about realism?
Even now? But you’ve agreed that the existence of mathematically describable entities outside the mind doesn’t imply the existence of ontologically mathematical entities outside the mind .
Imagine the library of Babel. Since it contains every story, some stories will be history, whilst most will be fantasy. But the true stories are still stories in books.
Hi Tag, I didn’t hear back from you so I suppose I can assume that my explanations were satisfactory and I had now resolved the qualms as previously raised. Thank you for your attention.
Comment: 1: “The assumption, alone, that the physical universe must be consistent is insufficient to show that there is a separate MU.
The assumption that the physical universe must be consistent, plus the assumption of MR, plus the assumption that consistency doesn’t matter for MU’s is sufficient to show that there is a separate MU.”
Response 1: Thanks for clarifying what you mean here. I hear you, but I have been clear in the manuscript that I take the assumption of MR. And then, for assumption of the physical universe needing to be consistent isn’t really assumed, but it’s discussed, and I bring to bear a practicality argument—that it’s actually a semantic point (defining the scope of the term ‘universe’) and so I am clear here also. And the third item you mention, that it is required to assume that consistency doesn’t matter for MU: I’m not sure I agree here. I don’t think I made statements either way as to the consistency of a MU (or multiple MUs) in the work. We did discuss that consistency can be considered dependent on whether one holds one maximal MU or multiple separate MU, but I don’t think an assumption on that is needed with regards to the scope of the argument pertaining to objects being outside the scope of the (physical) universe.
Comment 2: “But you have only shown that that follows from your assumptions, not that it is actually true, ie. your assumptions are actually true.”
Response 2: Well, that’s something still. What would be required as an additional piece you would like to have available is a proof that MR is true. I’m not sure if such a thing exists, as it might be axiomatic. It’s definitely not in the scope I laid down in the manuscript but could be an interesting new topic. Hm, I wonder if it ends up being that multiple ontological views are proved valid, but it ends up being more convenient (ie less ‘epicycles’) to adopt one of them in particular and so from an Occam’s Razor perspective, one comes to the fore. But that’s speculation. Interesting point though!
Comment 3: “No, it’s valid, but it’s not sound. Valid but unsound arguments are ten a penny—you can show almost anything given three arbitrary premises. https://en.wikipedia.org/wiki/Validity_(logic)”
Response 3: Ah, but that’s all I an supplying. I am sorry the work was not all you would hope it to be, right now. But these things take time and effort and that’s as far as we have got so far, unless you wish to collaborate on an extension as described above—though, I’m not sure there is an easy resolution especially if there’s a semantic component described above.
Context: But, I haven’t taken the assumption of mathematical fictionalism, in which I don’t know if I can talk about abstract objects at all—so it doesn’t apply here.
Comment 4: “Fictionalism isn’t known to be true or false, neither is realism. It’s an open subject. You can make arguments against fictionalism, the fictionalist can make arguments against realism.
You seem to be hinting at an argument where an entity has to really exist in order to be talked about (an argument you haven’t brought before). But the plain fact is that we can talk about fictional entities, like Gandalf or Sherlock Holmes—so the fictionalist has a robust response.”
Response 4: Ah you have misunderstood me, what I meant was I don’t have a detailed knowledge of how to construct a framework in mathematical fictionalism, and if I can define an object in that framework and refer to it in quite the same way. I don’t mean that a Sherlock Holmes or Gandalf can’t be referred to in a fictionalism, it’s just that I don’t know enough about how it set up (what os the nature of the ‘fiction’ from an ontological perspective, to know what properties it should have, or if the target of the reference is the sort of thing that can have properties (I’m assuming it can?). In MR, it seems more straightforward that if I can define an entity, it can be given an existence in an abstract sense, for the object referred to to have properties (including non-extantness) but without requiring that the object have a related extant object in the universe (such as a Sherlock Holmes who is clearly not extant even though his concept exists).
Context: I have some questions I need to clarify about how it works, and seek guidance on, to be able to argue effectively on that topic as I haven’t had it fully described to me.
Comment 5: “Can you not learn that from books? How did you learn about realism?”
Response 5: Well yes, I can, but it would be a new research topic and these things take time, as mentioned. One has to start somewhere and one can’t expect all parts of a project to be done right away, especially as research topics need to unfold incrementally to build a body of knowledge. But what you say here goes beyond just reading—I don’t know the body of literature of fictionalism/realism contains a systemisation in the way I have described in order to compare the variants that could be done. I think I would have to do that work, and so I have started here: but I picked realism because it’s a more natural starting point as mentioned, from a physics perspective and a view (at least tacitly) held by colleagues and even if not admitted, is operated under when doing daily life in the world of physics research.
Context: As I keep mentioning, where I am at, provisionally, at the moment, is that I keep running into that said Solipsism
Comment 6: “Even now? But you’ve agreed that the existence of mathematically describable entities outside the mind doesn’t imply the existence of ontologically mathematical entities outside the mind .”
Response 6: I mean, I haven’t investigated down to the very bottom what precisely a ‘mathematically describable entity outside the mind but not leading to an ontological mathematical entity’ really is, and if it doesn’t lead to other issues, contradictions, etc down the track. I can see that it’s something that can be proposed but I don’t know if such a thing is sound, hence why the investigation as I mentioned is taking place. It sounds like it is resolved in your mind but I haven’t understood it or had it presented to me yet. It’s not enough to state a thing could be so, we need to check the consistency through and through and I haven’t seen a detailed presentation of such a thing yet (if it exists).
Context: So, can we resolve it—in the primordial universe, how are we to understand the subatomic particles being arranged into groups, and so forth, if these structures required for our existence only are fictions occurring within the mind of people? (I assume that’s what fictionalism means)… if you can clarify
Comment 7: “Imagine the library of Babel. Since it contains every story, some stories will be history, whilst most will be fantasy. But the true stories are still stories in books.”
Response 7: Thank you for this metaphor, it is helpful—here in the library of Babel, which contains every story, only some of the stories will be history, and some are various other non-historical genres. This is similar to the statement in the work I was doing, where ‘extantness’ means ‘history’ ie the abstraction projects down to relate to an actual object in the real world. Whereas there might be many abstractions (existing but not ‘extant’ and also non-existing entities means that defining them leads to a contradiction and can’t be defined consistently). So indeed only a small portion of the abstractions have the ‘extant’ property (using the world extant to distinguish it from ‘exist’ in the mathematical sense), and what I did in my formalism was to create a meta-language scoped so that the objects only ‘exist’ if they are ‘extant’, which places some limits and also structure and properties for the formalism. But anyway, the true stories (the ‘histories’) or the ‘extant’ items, are still abstractions we refer to, it’s just that they have this special projective relationship with a physical object. The fact that the formalism can only ever speak in abstractions is part and parcel of having a self-contained meta-language (and also useful as we can do inquiries on it), but the fact that you always need a ‘pointer’ to be able to included in the formalism was precisely why the Labeling Principle was imposed, which defines this property. So, here in your metaphor, it seems very consistent with the view I have, and relied upon in the work, so I don’t quite follow why the metaphor is against the view expounded somehow. I agree with the metaphor, and it is the same as my view.
The universe meaning the physical universe? But that’s an argument against MR.
Which universe? Are you talking about a single maths+physics universe? (as opposed to Platonism)
You can specify which kind of MU you are talking about, as a hypothesis. (although at this point I am not even clear whether you are for or against MR.
I didn’t say that. The problem is that it doesn’t make any difference to our activities—we can’t tell whether the axiom of choice is true by peaking into Plato’s heaven. So it’s a huge amount of additional entities that don’t do anything, in practice.
...and there isn’t a unique non contradictory MU either.
The argument is that the MU is either maximal and inconsistent, or non-unique., ie indefineable. Both are problems.
Plus the Occam’s razor problem.
It would come from leaving out one side of a contrdiction, ie. there are two smaller universes for every contradiction.
So.,,,have you a better one?
Responses to questions, also thank you for your patience—there seems to be a misunderstanding under the surface that we are both approaching, perhaps in terms of terminology that is causing some of the disagreement:
Comment 1: “The universe meaning the physical universe? But that’s an argument against MR.”
Response 1: Yes, the universe meaning the physical universe, and I am taking Mathematical Realism to mean that the mathematical statements are real (they exist) but not in the physical universe. If one defined Mathematical Realism as compelling the inclusion of mathematical objects into the physical universe, then I don’t hold that. This position is about demonstrating how the putting together of mathematical objects in the physical universe means the new composite universe can’t be consistently defined. So the real mathematical objects have to be outside the universe.
Comment 2: “Which universe? Are you talking about a single maths+physics universe? (as opposed to Platonism)”
Response 2: Leading to a definition of a universe that is a single maths+physics universe, which can’t be defined consistency. Which means we end up dispensing with it and then having something closer to Platonism.
Comment 3: “You can specify which kind of MU you are talking about, as a hypothesis. (although at this point I am not even clear whether you are for or against MR.”
Response 3: I don’t specify a MU as I don’t assume such a one exists, in an encapsulated way. I specify that we hold that mathematical truths are real (exist) and show that they need to lie outside the physical universe. I think this must be the heart of the confusion—there must be a definition of MR that is different from the way I am using it. It appears as though, in your view, that having something ‘exist’ means it needs to be encapsulated either in a) a universe, or b) the physical universe so they ar combined together. (Not sure which you are assuming), whereas I had not taken MR to mean this, otherwise the work wouldn’t make sense. Apart from the terminology, I rely on the definition of the physical universe in the manuscript, ie Eq(68).
Comment 4: “I didn’t say that. The problem is that it doesn’t make any difference to our activities—we can’t tell whether the axiom of choice is true by peaking into Plato’s heaven. So it’s a huge amount of additional entities that don’t do anything, in practice.”
Response 4: Ok, we can’t tell if an axiom is true (by definition of what an axiom is) as its one of the building blocks for a particular computational logic we may choose to define, L. Now, if L is embedded in some other framework, a meta language, we may be able to make some statements about the axioms, but not from within L itself. But, for a given L, and its axioms, the truths would be statements that are formatted as theorems, which can either be proved or take the format of a Goedel sentence (ie only proved from outside L but not from within, unless the consistency of L is undermined). In other words, the mathematical truths and realities that we can ‘peek into Plato’s heaven’ to see, aren’t the axioms, of a given L (in the context of L, unless we go outside of L), they are of the format “given a and b” (where we can make ‘a’ and ‘b’ anything we want), “then c follows”. So I am stating that such a truth holds true, for my selection of ‘a’ and ‘b’, regardless of whether one is in a physical universe or any other speculated other physical universe. ie I am asserting that these mathematical truths hold in any physical universe as a meta language, as I can choose anything I want for ‘a’ and ‘b’, then logic of ‘c’ holding up in the context of the system ‘L’ I have defined, is immutable and true.
Comment 5 ”...and there isn’t a unique non contradictory MU either.”
Response 5: Fair—indeed there wouldn’t be, as there are many different systems of logic, say, I could define (different L’s, as mentioned above, for instance) that could all be internally consistent. I don’t however state that there is such an MU encapsulated. I only really explore the physical universe and whether we can bolt-on mathematical truths to it or not. Believing mathematical theorems are real truths that hold everywhere (regardless of what universe), and finding that we make the definition of the universe tricky if we definite as the physical universe + mathematical truths, I concluded that, adding mathematical all truths enters a Cantor universality paradox. However, you could for example, argue for a subset of mathematical truths (just the ones that apply to the physical universe in some way) and bolt it on to the physical universe to make a new type of MR. I haven’t seen a prescription for how this could be done though in practice. e.g. it’s not clear a given phenomenon can even have a single mathematical prescription applied to it. I could use complex numbers, or matrices, or other types of vector spaces, to achieve a similar end—the mathematical machinery isn’t necessarily unique when applied to their relevant targets in the physical universe, and yet all these mathematical theorems and the objects they operate on are different entities—so where does it end? (ie how can we prescribe how to limit the mathematical theorems that might get bolted on to the physical universe to make a new universe including them all, so as not to run into a Cantor paradox)?
Comment 6: “The argument is that the MU is either maximal and inconsistent, or non-unique., ie indefineable. Both are problems.
Plus the Occam’s razor problem.”
Response 6: If i understand correctly what MU means here, that is some set that includes at least enough mathematical objects to encounter a Cantor paradox), then I agree an MU being maximal makes it undefinable consistently. But the other case that, if it is split into smaller/limited subsets that don’t encounter that, then there are a multiplicity of them, and not a unique MU, I don’t know if this second option is a separate problem though. If I arbitrarily separate them out into different components, and I select one of them (perhaps a candidate to bolt onto the physical universe to define a phys+math universe), I can still ask if the remaining ones I left out are ‘true’ or ‘real’ and whether they are in this newly defined universe.
I don’t know of any prescription for selecting such a limited candidate subset though.
Comment 7: “It would come from leaving out one side of a contrdiction, ie. there are two smaller universes for every contradiction.”
Response 7: Ok, which amounts to defining a smaller calculus, like an ‘L’, which has only certain axioms, contains only certain structures and is limited to only certain theorems.
Comment 8: “So.,,,have you a better one?”
Response 8: I was actually going to ask you the same question, but for MR—if it appears my definition of MR is different from what you had in mind, what should I call my thing, if the naming convention is causing confusion? Essentially what I meant was the math I wrote—the words are hard to get right as people come at the problem with different background of terminology usage.
For your question here about a better term for MU, I think we can retain it but clarify the different concepts. In one case, MU could be used to mean an encapsulated system (ie a universe) of mathematical theorems. Or in one case, it could mean one of the completely consistent definable subsets of it. In another case, it could mean the physical universe + a bolt on of either all or a consistently definable subset of mathematical theorems (ie both physical + math together). Maybe we should call the latter, ‘PMU’?
From the paper:
Should be tenets?
Why would mathematical ideas match non-mathematical entities at all? Or was that supposed to read:
“matching mathematical ideas to non-physical entities”
Are you assuming mathematical is the only kind of “abstract”?
Yes as mentioned in the body, there’s a typo on the arXiv version that’s fixed as it’s going through peer-review.
mathematical ideals would not in general map to non-mathematical (physical) entities, hence why it’s a non-trivial constraint added to the formalism—essentially making a kind of an ‘avatar’ of the physical entity labeled within the formalism. There wouldn’t be any other way of referring to a non-abstract entity within an abstract formalism. In this case, I adopted a ZFC mathematics as it was convenient for the formalism, bringing me to:
No, I am not assuming that. For a start, much of logic would qualify and that wouldn’t necessarily be encompassed by mathematics (as Gödel showed) and many abstractions may have very little extra structure. But in this formalism, I choose a way of casting the problem and adopt a minimal amount of structure to add these constraints, it adopts a ZFC set theory.
Trying again, “non mathematical” means “not having mathematical existence”, rather than “mathematically indescribable”..? (Example of the former, electrons; example of the latter qualia, ghosts)
But then , why not just say
“matching mathematical ideas to physical entities”
Yes—fair enough — to clarify that, in that quoted sentence, when I said ‘non-mathematical entities’ I actually meant physical entities, rather than eg non-truths/falsehoods within mathematics (eg contradictory theorems and so forth).
That is a good pickup, and a good fix as I try to describe it in english language terms.
Your sentence is clearer.
Most maths doesn’t describe the physical world. No maths automatically describes the physical world .. you have to look.
Mathematics isn’t all that effective for the reasons given above.
Equations describe motion, they don’t cause it. Note that for every correct equation of motion, there are an infinite number of wrong ones.
Huh?I thought you were arguing for mathematical realism.
Responses:
1. “Most maths doesn’t receive the physical world. No maths automatically describes the physical world .. you have to look.”
-absolutely agree. The configuration space of all mathematical objects (if that could even be characterised consistently) is far larger than the space of all mathematical objects or theorems that describe actual events in the universe. Otherwise, we couldn’t have any wrong theories!
2. “Mathematics isn’t all that effective for the reasons given above.”
-Mathematics has been very effective so far at describing the universe and I do suggest looking up the context of Eugene Wigner’s comment here. What reasons given above? That the space of all mathematics is much larger? This isn’t what’s being said—let me clarify: it’s not at all obvious prima facae that the universe should, at rock bottom, be describable by mathematics or reasonable at all. (We still don’t know for sure if it is, but it has been the working ethos of science for a while).
3. “Equations describe motion, they don’t cause it. Note that for every correct equation of motion, there are an infinite number of wrong ones.”
-Agree, the equations are not causing anything. I don’t state that they do. But definitely the particles/atoms/etc are following specific trajectories or patterns, which are derivable from laws that we don’t know quite why they are the form that they are. Certainly the format is very specific—the particles and atoms don’t do anything, they do certain things (ie with constraints). [Yes, they can follow a lot of trajectories at once, and exhibit non-locality and all those multiple processes can be summed together) but it’s not “no structure” it has structure and constraint the pre-existed before we ‘discovered’ the laws, that’s my point.
4. “Huh?I thought you were arguing for mathematical realism.”
-I am. I don’t try to prove it though. In Mathematical Realism, abstract objects ‘exist’ and are real. I then go on to demonstrate that they also must exist outside the universe. You might have assumed that the universe is all there is, and that is what I am claiming to have disproved.
We can imagine a situation where it is more effective, ie. where mathematical truth is automatically physical truth. So the maybe the unreasonable effectiveness of mathematics isn’t that big a deal.
Also, it’s hard to see how mathematical realism—the claim that all maths exists—explains it, since what you need to explain UEM is a reason to believe only maths exists. If there is a physical universe and a separate mathematical universe, then the physical universe need not even be mathematically describable.
That isn’t a gotcha against mathematical anti-realists, though, because they are well aware of it. Why did you bring it up?
I then go on to demonstrate that they also must exist outside the universe.
If there is a material universe as well, obviously maths is outside it. But what does that have to do with the supernatural (particularly in the Carrier sense)? Plenty of naturalists believe in mathematical realism.
Responses:
“We can imagine a situation where it is more effective, ie. where mathematical truth is automatically physical truth. So the maybe the unreasonable effectiveness of mathematics isn’t that big a deal.”
“Also, it’s hard to see how mathematical realism—the claim that all maths exists—explains it, since what you need to explain UEM is a reason to believe only maths exists. If there is a physical universe and a separate mathematical universe, then the physical universe need not even be mathematically describable.”
If there is a physical universe separate from the mathematical universe, it is exactly my point that it need not be mathematically describable. I make this point in the OP, if you read. In fact, we just hold it as a belief that the universe is inherently (or maybe only mostly) reasonable and structured. It’s worked quite well so far. But whoMs to stop it from being, rock bottom, having even a single component thatMa completely immune to it? I venture to suggest there are some aspects of even non-rel QM that suggest as such, and once of my friends Cael who did his PhD in mathematical physics got quite deep in this area, and was starting to feel that the whole idea of there being objects that ‘have attributes’ might subtly break down at some point.
Anyway, I’m not sure what you are pointing it as I agree with you here, in fact it was one of the points I was making.
What extra step are you suggesting needs to be done?
(Cont’d)
“That isn’t a gotcha against mathematical anti-realists, though, because they are well aware of it. Why did you bring it up?”
“If there is a material universe as well, obviously maths is outside it.”
“But what does that have to do with the supernatural (particularly in the Carrier sense)? Plenty of naturalists believe in mathematical realism”
I’m not sure I know what a Carrier sense for supernatural is, but what this has to do with the supernatural is purely the literal definition of the universe and if something can be outside of it, supervening (ie structure and equations that sit outside it).
If plenty of naturalists believe in mathematical realism, as I have argued, there’s an inherent contradiction that’s always unspoken—and by that I mean, people will say one belief, but then operate with a totally different modus operandi—it just seems simpler to adopt the working ethos of physics as truth, no?
No , because a Tegmark level IV mathematical Universe—where the apparent physical universe is just a small.part of the mathematical one—isn’t obviously contradictory. (It might be better to say physical objects aren’t inherently non mathematical).
To argue for realism against anti realism, you need to show that “ansatz” can’t work under anti realism, which you haven’t done. If the physical universe is at least partly describable mathematically, , then random guessing at mathematical models will work occssionally. So you dont need to assume more for Anstatz than for UEM.
It doesn’t because, as I explained, the existence of a mathematical.universe implies nothing about the mathematical describability of a separate physical universe. (A Tegmark solution does, but you have rejected it!)
Which result?.If it’s not a solution to UEM, why bring it up?
Well, it might, but I don’t quite.see what that has to everything else.
Im trying to find out why you even mentioned UEM. Solips ism?
“That isn’t a gotcha against mathematical anti-realists, though, because they are well aware of it. Why did you bring it up?”
I don’t see how it leads to solipsism. “So we actually get a clear solipsism if we go too far with that approach” doesn’t explain it either. It isn’t clea r.
“If there is a material universe as well, obviously maths is outside it.”
You seem to be blurring “whether mathematical realism is true” and “what are they implications of MR”. If MR is true , then the mathematical universe is obviously bigger than the physical universe,just because most maths isn’t physical.
Assuming realism...?
The first google match for “Carrier supernatural” is
[https://www.richardcarrier.info/archives/7340(https://www.richardcarrier.info/archives/7340)
Well, maybe aren’t using, or don’t care about the literal definition.
Between mathematical realism and mathematical fictionalism , or between mathematical realism and naturalism?
Re: the latter.. If they think of the supernatural as gods and ghosts, as most people to, then there isn’t because mathematical realism doesn’t entail anything like that. I think the ghosts and ghoulies definition is what people care about.
“No , because a Tegmark level IV mathematical Universe—where the apparent physical universe is just a small.part of the mathematical one—isn’t obviously contradictory. (It might be better to say physical objects aren’t inherently non mathematical).”
And a point here not mentioned is your comment is that these mathematical objects if coupled to a normal universe still exhibit different properties: they don’t have a location, they are timeless, they don’t exhibit many of the usual attributes of physical objects etc.
The statement of physical objects not inherently being non-mathematical is a good one—I like that. Clearly there is a deep link between mathematics and nature as the mathematical attributes get exhibited in many places.
“To argue for realism against anti realism, you need to show that “ansatz” can’t work under anti realism, which you haven’t done. If the physical universe is at least partly describable mathematically, , then random guessing at mathematical models will work occssionally. So you dont need to assume more for Anstatz than for UEM”
(Cont’d) apologies, this is taking some time and I will do this in parts as I will run out of time here and there. Bear with me.
“It doesn’t because, as I explained, the existence of a mathematical.universe implies nothing about the mathematical describability of a separate physical universe. (A Tegmark solution does, but you have rejected it!)”
Did you read the paper? It’s not the existence of a mathematical universe that is used to show it, but, given the framework, I use a cardinality argument—so there’s more work and proofs and theorems in the paper—I just summarise the cliff notes in this post for the lay audience. What I do is use a very general statistical observation only, rather than trying to link up individual objects to theorems, I look at the relative size of the spaces. What I have explored is the connection between a separate universe in a framework where the mathematical principles can be used to describe things in many universes, the reverse-Epiphenomenal view. Also, I haven’t totally rejected a Tegmark view, it just needs to be subtly qualified—ie the mathematical parts tied together with the universe can’t be unscoped, one is limited by Cantor’s Theorem here.
“Which result?.If it’s not a solution to UEM, why bring it up?”
The result: Equation (54) in the paper. I brought it up because it was interesting, and I hadn’t seen a cardinality argument before. If by UEM you mean Universal Existing Mathematics, well that’s not what the work is trying to demonstrate. It seems like you intended this work to be about proving UEM, and are frustrated that it doesn’t. I’m confused because that’s not what I set out to do and it’s interesting, but not the topic I am looking at.
“Well, it might, but I don’t quite.see what that has to everything else.”
The reason for my aside, was it was an example of what could be true—I’m trying to say I don’t necessarily hold that the universe is always structured and reasonable, it might not be. What I did was assume it, and show the result. I certainly don’t prove it. It would be interesting to get more data and explore these things. But in the case where the universe is reasonable all the way down, then this would hold. It seems like you wanted me to prove or disprove something which isn’t the topic I set out to do. You can do it if you want. (Cite my paper though :)
“Im trying to find out why you even mentioned UEM. Solips ism?”
I’m really not following you now. I adopt Mathematical Realism for the reasons stated, its a philosophy that’s reasonable and also aligns with the working ethos of physics and mathematics. What other popular flavor should I have chosen?
“I don’t see how it leads to solipsism. “So we actually get a clear solipsism if we go too far with that approach” doesn’t explain it either. It isn’t clea r.”
Ah ok, so the solipsism goes as follows. Note that this does not constitute a proof, it’s really more pointing out a metaphysical convenience, where physicalism on the other hand needs to jump through some more subtle hoops and goes a little against Occam’s Razor. That is: in the specific version of physicalism that seems mathematical entities as nonreal, and fictions that exist in the human mind, then structures that pre-date humanity, like the mathematical groups associated with particle behavior in the early universe, couldn’t’ve existed back then. So I intuit that the actual structure is timeless and not incorporated easily into the universe that way. It’s not the only way, there are other versions of physicalism.
Cont’d (2)
8. “You seem to be blurring “whether mathematical realism is true” and “what are they implications of MR”. If MR is true , then the mathematical universe is obviously bigger than the physical universe,just because most maths isn’t physical.”
I wasn’t able to perceive the blur between these two items in my quote: ”!!!! That’s not at all obvious, in fact, I’d never heard it before until I began looking into this. If it’s obvious now to many people, that’s great! Perhaps the cultural mindset is different compared to my younger days. Certainly the most common view I run into among academics ‘spoken’ is that maths is included in the physical universe as a kind of ‘convenient fiction’ and the physical universe is there is, but then in reality they often kind of tacitly adopted this kind of mathematical realism—I wanted to explore why there’s some unwillingness to face this hypocrisy… (etc)”
I’m simply relating to you what my experience has been in regard to the conversations I have had. The observation that some people will state they adopt a view, and then operate with another view, is not a commentary on whether MR is true or not, or whether I believe it to be true. It’s something that I noticed, and I have in this work taken a stance of MR being true.
I’ve tried to be as clear as I can, and I havent deviated from the same point that I, A) adopt MR (I give some context as to why I think it’s reasonable and a natural view, for my own part), and then B) I develop a formalism assuming it, in the format that I describe (there may be other variants) and then I work through some of the implications of the formalism. I feel like I’m repeating myself over and over to you, I’m not quite sure why it’s not clear.
When you state ‘If MR is true, then the mathematical universe is obviously bigger than the physical universe,just because most maths isn’t physical’ doesn’t follow, in my view. Why would MR being true mean that the mathematical universe is necessarily bigger than the physical universe? The only way I can see it being obvious is if you are defining the ‘mathematical universe’ as the physical universe and the mathematical part altogether. Perhaps that’s what you mean, but you didn’t state it.
In the work I have put together, you can see that what I am showing from the formalism is that extending the physical universe to encompass the mathematical truths runs into some practical issues, and instead defining the universe as being smaller than this, necessarily leaves out some objects that are now not in the universe.
9. “Assuming realism...?” As mentioned, yes the formalism takes MR as a backing metaphysic as previously stated.
10. “The first google match for “Carrier supernatural” is… https://www.richardcarrier.info/archives/7340# ”
Ah, I haven’t read this author before and didn’t realise Carrier was the name of an author, I had assumed it was a jargon coined on here perhaps. But having a brief look, I’m honestly not sure how to match my work to this definition of supernatural. Do I have to? I am anticipating my work can be standalone and not to try to use another person’s definition of supernatural. Here, I use it purely as ‘not in the universe’ where I’ve defined the universe in the way I describe in the work.
I mean, it’s interesting, but one thing that makes it difficult to do matchup with another work is some of the terms don’t appear to be carefully defined enough, e.g. “Tautologically a natural world is a world with nothing supernatural in it, and a supernatural world is a world with at least one supernatural thing in it.” It’s not clear to me what a ‘world’ is, here, or how it is intended to relate to the kinds of realities I am talking about.
11. “Well, maybe aren’t using, or don’t care about the literal definition.”
In that case, umm. I got nothing. If people are using different definitions or don’t care about the literal definition, it doesn’t really impact the meaning of the work I am trying to do here.
12. “Between mathematical realism and mathematical fictionalism , or between mathematical realism and naturalism?
The inherent contradiction I was meaning here was more the former: a Naturalist is bound into believing that the natural laws, mathematical principles governing nature (and so forth) are part of nature or an emergent reality, in some versions, it is present in our mind, and yet with the other hand, will operate as though there was a ‘math land’ where only some items from that apply to our universe. Both valid points of view but incompatible.
In the latter case, you could totally have a Naturalism that extends the physical part to encompass the abstract and mathematical part, as described above, though it need to be done carefully and some methods of doing that can result in contradictions (the ‘draw a box around everything’ scenario). I apologise for the confusion that these are two separate points.
13. “Re: the latter.. If they think of the supernatural as gods and ghosts, as most people to, then there isn’t because mathematical realism doesn’t entail anything like that. I think the ghosts and ghoulies definition is what people care about.”
I hear you, but then that mixes in some folklore aspects adding another dimension of complexity. In this post (ie not the article, but the post) what I noted was that this opens the door—once you admit one supernatural supervening, it demonstrates at least one case where it can occur. I’m of the view that the folklorish aspects in humanity don’t come from nothing, and while many of the folklore stories may not be true, they keep coming up in every culture. I’ve been thinking for a while that the difference between a ‘demon’ and a ‘mindset’ seems slight, and there might be some truth to the idea that the abstract has a more ‘real’ aspect and dimension than people are in the habit of believing right now. That the mind is participating in real, genuine discovery and creation when it deals with mathematics.
And also, it doesn’t matter what people think or care about, let’s work out the truth first, and then we need to believe it, regardless of how uncomfortable it is, or what previous propaganda says, or it has a bad reminding taste of some folklore. So many weird physics things that seem unbelievable and seem crazy I have had to accept over the years as truth. If it’s true it’s true, and I think these aspects are also talked about in the neurology book The Master and His Emissary by Iain McGilchrist and his follow up book ‘The Matter with Things’, which argues that both the ‘Reality-Out-There’ and the ‘Made-Up-Miraculously-By-Our-Minds’ views of reality are both false, and that there is a contribution from both the observer and the environment at the same time in creating reality. The reductionist view of nature to boil it down to something more objective, you can see, is actually highly stylized, attitude driven and not objective at all.
Because most maths isn’t physically applicable, as I stated, and you agreed.
You have a communication issue, because you are not using “supernatural” in the expected way, and a PR issue, because a lot of your intended audience are going to reject the supernatural out of hand. Whence the downvoting.
You need to communicate clearly , and you don’t need to repell the reader
Again, that’s not the same thing. The existence of X-ishly describable entities doesn’t imply the existence of free-standing X’s. For instance, we can describe the colours of external objects using the trichromic RGB system , but it’s definitely not out there.
Comment 1: “Because most maths isn’t physically applicable, as I stated, and you agreed.”
Response 1: I do agree that most maths isn’t physically applicable, but that doesn’t mean that for MR, the MU is obviously bigger (to clarify, for MU here, do you mean physical+maths, I am assuming not). For example, I might have many physical objects in my universe, and not all being mapped to by a mathematical abstraction. I have no way of ensuring that the universe is all totally mapped to. I make a supposition that in physics, we hold a view that it can (or should be). But I don’t know for sure, and so the relative sizes of physical + mathematical parts is hard to define. It may be the case the the mathematical part is indeed larger, but the fact that most maths isn’t physical doesn’t guarantee it, it would be something to do with limits on the size of the physical universe, and/or the scope of mathematics obtruding into it. Maybe most physical doesn’t get mapped to (though, I don’t believe that currently, it could definitely be proposed).
Comment 2: “You have a communication issue, because you are not using “supernatural” in the expected way, and a PR issue, because a lot of your intended audience are going to reject the supernatural out of hand. Whence the downvoting.”
Response 2: Thank you for the view. The way I see it though, it is actually a good communication method, in that I have excited some commentary and engagement from the community—such as yourself—you have been very generous with your engagement. The rejection out-of-hand though accidentally demonstrates that the audience might not have been as attentive as they might pride themselves on, however, which itself is a useful insight to note.
Comment 3: “You need to communicate clearly , and you don’t need to repell the reader”
Response 3: I am attempting to communicate as best I can, and am limited of course by my competence. Apologies if it doesn’t come up to scratch—I am doing my best. I also am not intending to repel the reader, but get some engagement, which was successful.
Also, the ‘do I have to’ was in the context of whether i need to match my work to this definition of supernatural, not based on communicating clearly, per se. I wasn’t aware of the work, but how else do I generate discussion to get some improvement from the lesswrong community? I have to start somewhere. I was as clear as my faculties allow. I tried to define the supernatural the way I see it. A comparison of that view and another work seems like a different topic beyond the scope of this post.
Comment 4: Again, that’s not the same thing. The existence of X-ishly describable entities doesn’t imply the existence of free-standing X’s. For instance, we can describe the colours of external objects using the trichromic RGB system , but it’s definitely not out there.
Response 4: I didn’t say that the existence of X-describable entities implies free standing X’s. The idea of free standing X’s, ie a kind of Platonism is not something i set about to prove. I believe I assumed it as a starting point, and wanted to see how far I could get with it, as an exercise. So I wouldn’t argue it that way. I do state in the above quote that the Naturalist was bound to believing natural laws (by definition) and that I take it to mean that mathematical principles governing nature emerge from this same (physical) universe, as opposed to a more Platonic view of Mathematical Realism (ie. “out there” as you put it). Is that untrue? In regard to such a Platonic view, I would take it that the colours of objects using an RGB system, which are both concepts (the colours, and the RGB system) are abstractions that have an existence, and would be included as one of the abstractions in my formalism, that then get projected down in a reverse-epiphenomenal way, onto the physical-world object. (ie they are attributes of it, and attributes are abstractions).
I have. There’s almost nothing to it, if Ansatz means nothing more than some guessed-at mathematical descriptions turning out to be right.. and that is the . description of Ansaztz you give here:-
(We don’t know where Ansatze come from in a detailed way, but it’s hard to see why that would need a supernatural/metaphsyical explanation, since we don’t know where “think of a number comes from”, but don’;t doubt that it is an ordinary psychological process. The whole rhetoric surrounding Ansatz, or guessing as I like to call it, is overblown, IMO).
But Wigner brings in further issues—the issue that a guessed-at mathmaticlal structure which is intended that is intended to describe one phenomenon, can be applicable to others. And you mention , in relation to Dirac’s relativistc wave equation, the ability to make successful novel predictions..
The various sub-problems have various possible solutions.
An ontology where the universe is based on a set of small set of rules explains the unreasonable effectiveness well enough: since each rule has to cover a lot of ground, each rule has multiple applications. And such an ontology is already fairly standard.
There’s also an underlying problem that saying “I can solve X” has two meanings: “My assumptions are the only solutions to X” and “I have the latest in a long line of putative solutions” It is not enough to succeed, others must fail.
Responses:
Comment 1: “I have. There’s almost nothing to it, if Ansatz means nothing more than some guessed-at mathematical descriptions turning out to be right.. and that is the . description of Ansaztz you give here:- (etc) ..then, so long as some things are mathematically describable, some mathematical descriptions will describe them, even if guessed randomly”
Response 1: Hang on, what I mean is, constructing an Ansatz completely from scratch, without any assumed structure doesn’t sound like something there would be ‘nothing to it’ - I would expect that if you have one, you’d need to be careful not to accidentally smuggle in an assumed concept from the get-go, which hasn’t been demonstrated yet—it’s hard to come to any logical machinery or systems from scratch without assuming something, without any structure or rules or symbols at all. Even if it is very simple, you have to start from somewhere. I tried to keep mine very general, and a few items of structure were added as minimally as possible. But what I mean is, the very concept of an Ansatz itself is automatically couched in some framework—I don’t think one can have a concept unless one at least has a framework for the concept to be part of, or to exist in, so I would assume to even invoke the concept, a framework (even a skeleton one) has been assumed.
Comment 2: “(We don’t know where Ansatze come from in a detailed way, but it’s hard to see why that would need a supernatural/metaphsyical explanation, since we don’t know where “think of a number comes from”, but don’;t doubt that it is an ordinary psychological process. The whole rhetoric surrounding Ansatz, or guessing as I like to call it, is overblown, IMO).”
Response 2: In terms of where Ansatze come from, I don’t think we do know quite where it comes from but we don’t need to know for the purpose of this investigation yet—it’s simply enough that we require logic to exist, and for there to be an abstract concept that can be invoked—very little else in the proof was assumed. The supernatural explanation (again, being careful to define what I mean here by supernatural, that is being outside the physical universe) comes about naturally, with only some minimal rules of logic being invoked. We might not know ‘where’ “think of a number” comes from, but we do know that the number is consistently definable, it ‘exists’ (that’s taken based on an MR viewpoint though), and it gets instantiated a lot, in the physical universe—ie the physical objects obey (and have an intimate relationship with) these mathematical objects.
In terms of the psychological process by which we access it, the psychology would be developed from brain structures, and those are based on proteins, based on info from genes, on chemistry, on physics, down to the smallest particle, so at every level, we have seen a great deal of natural processes are respecting mathematics, and we can write down these laws. So it would come at no surprise that our brains are also structured and follow processes. But, you wouldn’t argue that if the brain was destroyed, that the concepts being referred to by some maths would be destroyed, nor would an atom being destroyed mean the concepts of mathematical groups an equations of motion would be destroyed. Surely those are just all instances but not the thing being referred to itself. (ie they are not the mathematical truths themselves, as those truths turn up in all sorts of places).
Apologies if the rhetoric seems overblown—can you specify in what way? As above, I haven’t quite got your view in mind re mathematical truths. It seems you can’t have no metaphysic, we all have a metaphysic in mind, just it might be undeclared or unexamined—so I am interested to learn yours—it seems yours, to you, seems preferable, but I am unclear of your statement of it.
Comment 3: “But Wigner brings in further issues—the issue that a guessed-at mathmaticlal structure which is intended that is intended to describe one phenomenon, can be applicable to others. And you mention , in relation to Dirac’s relativistc wave equation, the ability to make successful novel predictions.. The various sub-problems have various possible solutions. ”
Response 3: What are the issues raised by Wigner issues for? ie it seems consistent with the metaphysic I have adopted. Many different mathematical mechanisms can be applied to describe processes. It happens all the time in particle physics. There’s a concept of a ‘Representation’ of a group. Subatomic particles are arranged into Groups, which have a certain mathematical structure. But a group is quite general, and you can represent a group in different ways. One particular group might have many different representations, one using matrices, one using complex exponentials, all sorts. These representations have the group structure, but they add more, adding specificity, and are called vector spaces. You could use one machinery to look into a physical phenomenon, or you could use another. Both could apply. Hence why it is hard to have a prescription for how to ‘select just the mathematical truths’ applicable to the physical universe so as to bolt them on and get a consistent P+M Universe (hence why I don’t go down that route).
Comment 4: “An ontology where the universe is based on a set of small set of rules explains the unreasonable effectiveness well enough: since each rule has to cover a lot of ground, each rule has multiple applications. And such an ontology is already fairly standard.”
Response 4: The universe being ‘based’ on a set of rules is an interesting phrase, as it does seem similar to my version of MR—ie that there are rules, and those can be talked about in a meta way, regardless of physical universe, and then the physical universe can be talked about as following those rules. I also agree, since it is the view I was expounding, that this leads to an explanation of the unreasonable effectiveness, but the way I said it was different—I just counted the countably-infinite number of possible abstractions that could apply to a phenomena in a physical universe, and the seemingly ‘smaller’ (more restricted) countably-infinite number of abstractions applying to phenomena that also are extant in a universe, and found them to be of the same Cantor cardinality.
Comment 5: “There’s also an underlying problem that saying “I can solve X” has two meanings: “My assumptions are the only solutions to X” and “I have the latest in a long line of putative solutions” It is not enough to succeed, others must fail.”
Response 5: It is true that a phrase like ‘I can solve X’ can have an ambiguity. I take it to mean the latter though, in other words, taking some assumptions, and working through some steps, one can arrive at a valid solution—which in and of itself has merit, without stating whether other approaches can get to the same point. One might point out the neatness (less ‘epicycles’) or more (or less) in line with Occam’s Razor to evaluate a purported solution after it is given—but I wouldn’t say that means a solution hasn’t been given. Certainly in my work I don’t state it’s the only way, it’s much smaller than that, as a claim—just that this way seems to hold up, seems neat, a lot of things fall out of it ‘for free’ (ie it solves the problem with low entropy, without over-engineering extra unnecessaries) and it also seems to align with thinking drawn from multiple different fields of knowledge which is usually a detective’s ‘hint’ in the right direction, during an investigation.
Wow this is getting down-voted quite a bit! And yet not really much feedback as to why...