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Vladimir Fedorov: on 5/18/20 at 5:46am UTC, wrote Dear Michael, I greatly appreciated your work and discussion. I am very...

David Jewson: on 5/9/20 at 8:49am UTC, wrote Dear Michael, You might find the following approach interesting as regards...

Jochen Szangolies: on 5/8/20 at 16:15pm UTC, wrote "If so, then yes, there is only one 'natural numbers' there..." ...

Jochen Szangolies: on 5/8/20 at 16:05pm UTC, wrote "incidentally, I'm not quite clear on the distinction you seem to draw...

Michael Dascal: on 5/6/20 at 15:06pm UTC, wrote Dear Stefan, Thank you for the comment! That's a nice way of putting it:...

Satyavarapu Gupta: on 5/5/20 at 10:34am UTC, wrote Dear Dr Michael Dascal, Yours is a smooth flowing essay with a very nice...

Yutaka Shikano: on 5/4/20 at 22:13pm UTC, wrote Dear Michael Dascal, As you are young brilliant student, this essay...

John Vastola: on 5/3/20 at 23:21pm UTC, wrote Lovely essay! I really appreciated the main idea that models are not...


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FQXi FORUM
October 20, 2020

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Learning from Theories by Michael Dascal [refresh]
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Author Michael Dascal wrote on Apr. 25, 2020 @ 01:32 GMT
Essay Abstract

We typically take a theory’s predictive power to indicate representational success. In this essay I argue that this is unjustified, particularly in the case of physical theories. Looking to Gödel’s theorem as a guide, I show that it demonstrates how a theory can prove sentences that are true ‘merely within’ the theory - not true of the theory’s subject matter. Given this, I explain that in cases where we don’t have a clear pre-theoretic knowledge about a theory’s subject matter it can be difficult or impossible to know into which category a given sentence falls. Applying this to physical theories, I first explain how this implies certain limitations on what we can learn from classical and relativistic representations of physical systems and laws. I then look to quantum mechanics, where a complete obscurity of the theory’s subject matter makes it nearly impossible to learn anything from how it represents the universe.

Author Bio

Michael Dascal is a doctoral candidate in the Department of Philosophy and the Joint Center for Quantum Information and Computer Science at the University of Maryland. His research focuses on perspectival quantum mechanics and on quantum computational efficiency and supremacy.

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Luca Valeri wrote on Apr. 29, 2020 @ 16:16 GMT
Dear Michael,

what an intriguing, interesting and clearly argued essay. Of what I have read until now, it is the one, I was the most attracted. If I criticize it now, it is not to invalidate, what you wrote. But in my essay I somewhat take the opposite view.

Let me make an example. A square can be seen as a representation of the rotation group with rotations generated by 90° rotations. Or as a representation of the rotation group including the 4 mirror symmetries. For both groups the representation is the same, but a square, that can only be rotated, seem to me something quite different than one, that also can be turned upside down. So it seams that the possible operations, the physical laws or the axioms that axioms convey the meaning of what a square is and not so much the square as the object on which one operates.

In that sense if the natural numbers might be identified by some counting operation. The different axioms would express different additional possible operation and hence physical laws that might or might not be realized in the world.

In my essay there is also an underdetermination. If we identify objects (ie. the square), on which one operates, with the subject of matter, but only the possible operations are knowable (expressed as relations between objects), then the subject of matter is underdetermined by laws hence the axioms.

I don't know, if this makes sense for you or maybe I just twist the words a bit. I would like to know, what you think of my essay called: 'Semantically Closed Theories and the Unpredictable Evolution of the Laws of Physics'.

Luca

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Author Michael Dascal replied on Apr. 30, 2020 @ 00:38 GMT
Dear Luca,

Thank you for the comment! I'm not certain that I follow all of this, but please let me know if there's something I've misunderstood.

First, I should say that I just read your essay and you seem to adopt a number of positions that I sympathize with, if not in my essay here then in my other work. (My dissertation defends "perspectival" theories of quantum mechanics, which fall under the "subject interpretation" umbrella - though I think this is a bit of a misnomer! Just as you hint at here, I look to the universality of unitary evolution to explain how Wigner and his friend can consistently observe their own measurement results while they disagree about whether the friend evovles unitarily. I do have some questions about what you say about this, but I'll post these in your essay's discussion thread shortly.)

Regarding the comment you posted here though, I'd like to push back a bit. (Though again, if I've misunderstood then please let me know!) You wrote, "A square can be seen as a representation of the rotation group with rotations generated by 90° rotations. Or as a representation of the rotation group including the 4 mirror symmetries. For both groups the representation is the same, but a square, that can only be rotated, seem to me something quite different than one, that also can be turned upside down." (emphasis added). My concern here is that you seem to suggest that there are two distinct objects - one square that can be reflected and one that can't. However, this seems to me to imply that what's true of the square - whether it admits certain reflective symmetries, in this case - depends on whether some rational agent has a theory that performs these operations. This can't be right though - if someone were to introduce a theory that includes a completely novel kind of operation, O, and it turns out that O is a symmetry operation on all squares, we wouldn't say that we discovered "a new type of square", nor that the squares our old theories discuss were necessarily different objects than the ones described by O-symmetry.

This might be a tricky case because it's difficult to picture abstract mathematical objects as existing outsides of our theories, but it may be clearer if we think about a physical example. When we learn that stars are governed by relativistic (not Newtonian) physics, we don't think of this as replacing Newtonian systems with relativistic systems out in the world. Rather, we think about this as learning a new feature about physical systems that we didn't know about before. That is, things that we thought were Newtonian systems turned out to be relativistic ones. (We can further contrast this with cases where we have learned that certain objects in our theories didn't exist, such as phlogiston or caloric, for example.)

Now that said, I certainly don't think that fundamental ontology is remotely transparent to us! All I mean to push back on here is whether operational differences should be seen as representative of ontological ones. As long as we accept that multiple theories can describe different operations over a single domain of objects then we can certainly talk about the domain of objects independently of the theories. For example, I'm perfectly happy to talk about fundamental particles while acknowledging that I'm not clear on their ontological nature. Whatever this nature is, it seems clear that there must exist something in the physical world that our theories at least try to represent (to varying degrees of success!).

Does this clarify - maybe I've made this more confusing than it needs to be!

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Luca Valeri replied on Apr. 30, 2020 @ 15:07 GMT
Hi Michael,

I replied to your questions in my blog. There I also touched the ontological question about the "subject of matter" a bit, that underlies my view.

In fact I would say "this is a different square" or object if an observable symmetry operation O is present or not. We can do completely different stuff with it.

Your physical example about the Newtonian or relativistic star reminds me an argument by Hilary Putnam that the reality of an electron did not change because we have today a totally different theory than many years ago. But it is not about our theories that descibe things.

As you nicely wrote: "whether operational differences should be seen as representative of ontological ones". I would say yes. This has nothing to do with our theories that can be wrong or inaccurate. But what operations can be performed depends on the laws. And the properties can be assigned to objects also depends on the laws. The separation of objects and laws that is manifest in simplistic realist interpretations is very artificial. They build a unity. Besides there are conceptual dependencies on the definability of objects and laws. That cannot be conceptualized done independently.

In my essay I make the bold claim that objects and laws are emergent and changeable. And I think it could be fruitful to take such a view. And the decision whether such a view will be accepted will be a pragmatic one. Can such widening of the ontology and conceptual framework help to explain phenomena like consciousness, free will or help to develop a theory for quantum gravity etc.

I acknowledge that the fundamental ontology is not knowable, but manifested, emergent and changeable relations between things are. Without holding the things as fixed, as we mostly do.

Hope this makes my point a bit clearer?

Luca

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Edwin Eugene Klingman wrote on Apr. 29, 2020 @ 17:46 GMT
Dear Michael Dascal,

What a wonderful essay (which means it largely agrees with me!)

My drumbeat in this contest has been that physicists project mathematical structure on the world and then come to believe that the physical universe actually has this structure.

For example, qubit structure is appropriate for spins in magnetic domains and statistical analysis, but very inappropriate for Stern_Gerlach spins traversing an inhomogeneous magnetic field, as seen in the famous postcard data. Instead, a 3D spin yields exactly the correct deflection distribution. Yet Bell forces the qubit in his 1st equation: A,B = +1,-1 and goes on to prove ‘nonlocality’, whereas the 3D spin yields exactly the correlation that Bell claims is impossible.

I love the following quotes from your essay:

“...our theories may contain provable sentences which have nothing to do with their subject matter.

The point is that our theories contain provable sentences which might not reflect anything about the structure of the physical universe.

One way to think of all this is that a theory's axioms all stand on equal footing. There's no differentiation between those that capture the subject matter's structure and those that build on top of it. (Moreover, there's no guarantee that such a delineation exists in the axioms.) This means that we can't expect a theory to ‘indicate' which of its theorems are about its subject matter and which aren't. This may not be worrisome in the case of arithmetic, but the consequences of this are troublesome when our knowledge of the subject matter is at all obscured, as is the case in physics.

In other words, if we wish to accept our experience and empirical data (of single measurement outcomes) without ‘breaking' quantum mechanics or adding new measurement dynamics to it, then we must give up any attempt to learn metaphysical or ontological lessons from the theory.


I invite you to read my essay, Deciding on the nature of time and space.

My best wishes to you in your career, and good luck in the contest.

Edwin Eugene Klingman

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Author Michael Dascal replied on Apr. 30, 2020 @ 01:06 GMT
Dear Edwin,

Thank you for the kind comment! I'll be sure to look at yours too. (If you haven't already, you should read the paper I cite by Curiel. From what you've said here it sounds like you'd like it.)

All my best,

Mike

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Edwin Eugene Klingman replied on May. 1, 2020 @ 01:18 GMT
Mike,

Thanks for your response. I found Curiel very relevant (but wordy). A recent paper of mine relates, I believe, to Curiel and to my essay: A Primordial Spacetime Metric

I look forward to any comments on my essay.

Warmest regards,

Edwin Eugene Klingman

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H.H.J. Luediger wrote on Apr. 29, 2020 @ 21:12 GMT
Dear Michael Dascal,

I'm still trying to figure out whether you added anything to Tarski's theory of truth:

The truth of sentences of an object-language (here: e.g. QM) can only be judged in meta-language.

However, the crucial questions you bypass are:

- what is meta-language?

- what is a legitimate object-language?

- what's the relation between object- and meta-language?

thanks for an courageous essay,

Heinz

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Author Michael Dascal replied on Apr. 30, 2020 @ 01:33 GMT
Dear Heinz,

Aha! You've caught some of the material I had to cut out of my last draft due to length restrictions!

In brief, part of what my essay is trying to highlight is that when a theory can represent itself, the formal distinction between object and meta-language blurs or fades away completely. As such, without a second 'source' for identifying the object language (i.e. some pre-theoretic knowledge of the theory's subject matter, or perhaps a simpler theory to refer to), we can't know how to judge a sentence in the theory.

For instance, say a theory (capable of self-reference) proves some sentence P. If we don't have a clear grasp of the theory's subject matter then this means that we don't have a clear idea of whether P is a sentence in the object language, the meta-language, or a meta-meta-language.

This is the problem, of course, as without being able to distinguish these cases means that we can't detemine which sentences are about the subject matter and which aren't.

I hope this helps - and thank you for the opportunity to say this, albeit quickly!

All my best,

Mike

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Author Michael Dascal replied on Apr. 30, 2020 @ 01:39 GMT
Apologies - the above should read:

"...we don't have a clear idea of whether "P is true" is a sentence in the object language, the meta-language, or a meta-meta-language."

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Stefan Weckbach wrote on May. 1, 2020 @ 06:17 GMT
Dear Michael,

you wrote an extraordinarily informing and deep essay and by reading and enjoying it as well as by thinking about it I must say that this is a brilliant piece of work that accurately nails the current essay themes. So thanks for that!

The only thing I would *add* as a probable interpretative result of the hole issue would be to state that obviously - very obviously indeed in my humble opinion -, formal systems can't completely capture what you call at page 8 the 'true nature'. As such, the overall lesson of Gödel and of your complete essay in my opinion is that the formalizability of the limits expressed therein at least epistemologically (if not ontologically as well) point to some profound *limits of formalizability*.

The latter is the theme of my own essay. I would be happy if you liked to check it out and eventually leave a comment there!

Best wishes,

Stefan

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Author Michael Dascal replied on May. 6, 2020 @ 15:06 GMT
Dear Stefan,

Thank you for the comment! That's a nice way of putting it: Insofar as the structure of reality is at least as rich as to reqire a representation of arithmetic with recursive addition and multiplication, there must be a limit to how formalizable it is!

I'll be sure to look at yours as well!

Best,

Mike

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Jochen Szangolies wrote on May. 1, 2020 @ 13:05 GMT
Dear Michael,

you start your essay by noting what could be reformulated as a tension between three classical arguments in the philosophy of science---Putnam's 'no miracles'-argument, Quine's 'indispensability'-argument, and Laudan's 'pessimistic meta-induction'. The 'no miracles'-argument tells us that theories must get something about the world right, as otherwise, their (predictive)...

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Author Michael Dascal replied on May. 1, 2020 @ 18:24 GMT
Dear Jochen,

Thank you for the detailed comment!

I think that there are a few points here that you’ve misunderstood (or that we simply disagree about!) Before I address these though I must make a concession. You pointed out a genuine error on my part. My original draft included Peano, Presberger, Robinson and Skolem arithmetic. When I was editing I meant to cut out Robinson...

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Jochen Szangolies replied on May. 2, 2020 @ 07:48 GMT
Dear Michael,

thanks for your clarifications; I think I understand the point you're making a little better now.

As for my point regarding pessimistic meta-induction and the like, that was merely me trying to outline another way as to how one might come to doubt the notion that 'a theory's predictive power indicates representational success'---we have theories of unparalleled power,...

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Jochen Szangolies replied on May. 8, 2020 @ 16:05 GMT
"incidentally, I'm not quite clear on the distinction you seem to draw with the Dedekind-Peano axioms; to me, those would've been the same, and thus, just as susceptible to the Gödel argument"

I realize now that you were talking about second-order arithmetic here (right?). If so, then yes, there is only one 'natural numbers' there, for which the Gödel sentence is true (but unprovable since second-order logic has no completeness theorem, that is, doesn't derive every valid sentence). In this case, we would rather have a theory that fails to tell us everything about its domain, while still fixing that domain fully. But where does that leave us?

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John Joseph Vastola wrote on May. 3, 2020 @ 23:21 GMT
Lovely essay! I really appreciated the main idea that models are not necessarily the same as the things they're trying to represent, and the arguments that this is true even in math (the one place you'd expect this not to be true). Hard to read in some places though.

A bit of semantics: you take N to mean the numbers themselves, along with addition and some other things, but not...

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Yutaka Shikano wrote on May. 4, 2020 @ 22:13 GMT
Dear Michael Dascal,

As you are young brilliant student, this essay included the wonderful context. I really enjoyed reading this. From the viewpoint of the Godel theorem, you summarized this essay.

On the other hand, as the computational resource, quantum mechanics is often used. Especially, the Godel theorem is often cited in the context of computation. Therefore, I would like to know the relationship to quantum computation as well. For reference, my essay focused on history of computation related to the random number generation.

Best wishes,

Yutaka

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Satyavarapu Naga Parameswara Gupta wrote on May. 5, 2020 @ 10:34 GMT
Dear Dr Michael Dascal,

Yours is a smooth flowing essay with a very nice discussion. Very good.

Many people discussed about Godel theorem and its applicability to Quantum Mechanics. Will this theorem be applicable to theories in Cosmology?

For example Dynamic Universe Model is a theory see my essay(A properly deciding, Computing and Predicting new theory’s Philosophy)gave lots of results in Cosmology and many of its predictions came true.

Can we apply Godel's theorem there?

Best wishes to your essay

=snp

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David Jewson wrote on May. 9, 2020 @ 08:49 GMT
Dear Michael,

You might find the following approach interesting as regards some of the very thought-provoking questions you pose in your essay.

So, you could start with the things that we do know about, i.e. the things we perceive, such as colours and shapes. Then think about the qualities they share. Let’s say they share the qualities of amount (or quantity), position, direction (if moving) and change. If it was then possible to build a theory of physics out of just these things, then it would be a theory about things that we do know about.

Rather surprisingly it would appear possible to do just that, build a theory out of these things alone; but not just any old theory – the theory of Quantum Mechanics. This suggests that Quantum Mechanics is really about things we know about. Of course, this is carefully disguised: most people would say Quantum Mechanics is about photons and electrons and ‘physical things’ and not about the quantity and change of the things we perceive.

This theory is itself is just a list of instructions (an algorithm). But the discovery of that list of instructions is the discovery of something we didn’t know about the world.

What do you think? If you interested there are some more details in my essay.

All the best,

David

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Vladimir Nikolaevich Fedorov wrote on May. 18, 2020 @ 05:46 GMT
Dear Michael,

I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

"It doesn’t seem that this is what physics isfor– it feels like it’s meant torepresent and inform usabout the structure of the physicalworld, not merely to predict our observations of it".

While the discussion lasted, I wrote an article: “Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus”, due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 “Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability”.

I hope that my modest results of work will provide you with information for thought.

Warm Regards, `

Vladimir

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