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RECENT POSTS IN THIS TOPIC

James Hoover: on 5/11/20 at 6:33am UTC, wrote Andre, I have commented on you essay but discovered I have not rated it...

André Martins: on 5/9/20 at 21:54pm UTC, wrote There is a necessary correction in my abstract. Where it reads "There are...

André Martins: on 5/3/20 at 1:41am UTC, wrote Thank you for your kind words, Michael. I will take a look at your paper....

Michael muteru: on 4/30/20 at 9:32am UTC, wrote Dr Andre Your work on cognitive limitations is spot on,quite vivid in...

André Martins: on 4/23/20 at 7:18am UTC, wrote Hi, Jim I just came back to the page, I am planning to go and read some...

André Martins: on 4/23/20 at 7:14am UTC, wrote Dear Simon, Thanks for the comments. I just came back to check the thread...

André Martins: on 4/23/20 at 7:09am UTC, wrote Dear Israel, Thank you for your kind words, I am glad you enjoyed reading...

James Hoover: on 4/20/20 at 17:25pm UTC, wrote André, Lots of good points in your essay. A major point in your essay,...


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FQXi FORUM
September 17, 2021

CATEGORY: Undecidability, Uncomputability, and Unpredictability Essay Contest (2019-2020) [back]
TOPIC: Embracing undecidability: Cognitive needs and theory evaluation by André C. R. Martins [refresh]
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Author André C. R. Martins wrote on Feb. 10, 2020 @ 12:39 GMT
Essay Abstract

There are many ways we can not know. Even in systems that we created ourselves, as, for example, systems in mathematical logic, Goedel and Tarski's theorems impose limits on what we can know. As we try to speak of the real world, things get even harder. We want to compare the results of our mathematical theories to observations, and that means the use of inductive methods. While we can demonstrate how an ideal probabilistic induction should work, the requirements of such a method include a few infinities. Furthermore, it would not be even enough to be able to compute those methods and obtain predictions. There are cases where underdeterminacy can not unavoidable, such as the interpretation of quantum mechanics or the current status of string theory. Despite that, scientists still behave as if they were able to know the truth. As it becomes clear that such behavior can cause severe cognitive mistakes, the need to accept our limits, both our natural human limits and the limits of the tools we have created, become apparent. This essay will discuss how we must accept that knowledge is almost only limited to formal systems. Moreover, even in those, there will always be undecidable propositions. We will also see how those questions influence the evaluation of current theories in physics.

Author Bio

André C. R. Martins is an Associate Professor in the School of Arts, Sciences and Humanities (EACH) at Universidade de São Paulo (USP). He holds a PhD in Theoretical Physics and was Visiting Professor at École Polytechnique, at the Research Center in Applied Epistemology (CREA) in Paris. At EACH, he coordinated the creation of the Masters program in Modelling of Complex Systems.

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Jochen Szangolies wrote on Feb. 10, 2020 @ 17:53 GMT
Dear André,

there is a lot to unpack in your essay. I think your main question, however, is a simple one: when is it reasonable to believe something? This seems a straightforward question, but, as so very often, there are many subtleties that confound finding a straightforward answer.

You start out by noting that, contrary to mathematics, physical theory always includes an issue of...

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Author André C. R. Martins replied on Feb. 12, 2020 @ 06:29 GMT
Dear Jochen,

Yes, that is the main question. We actually have no logical support for believing in anything, except in a probabilistic way. While I agree there is theory-ladenness of data, I do not think it is an essential limit as many others I discuss. For me, in essence, it is a problem of translation. Different theories provide us with their own languages we use to interpret things. But we can always revert to the most basic description of the data if we really must. Suppose someone would propose some crazy theory with none of our fundamental particles. That would indeed make it hard to describe many basic experiments. But hard is not impossible. Instead of saying we have observed an electron, for example, we can say we have seen some patterns on a computer screen.

I do know about Solomonoff and have mentioned SI at the end of page 7. The essay size limits did not allow me to say more, however. I do discuss it in length, in a chapter by itself, in my coming book, "Arguments, Cognition, and Science" - https://rowman.com/ISBN/9781786615077/Arguments-Cognition-an
d-Science-Consequences-of-Probabilistic-Induction-in-Science


Hutter AIXI approach, however, is new, and I will need to check it. Thanks a lot for the reference.

I did take a look at your essay, and I found the concepts of finiteness and extensibility quite interesting. Quantum mechanics does seem to work as you describe. You also did an outstanding job of explaining the fundamental problems in measurement. I did enjoy reading it.

Cheers,

André

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Flavio Del Santo wrote on Mar. 11, 2020 @ 23:22 GMT
Dear Andrè (if I may),

Very clear and interesting essay. I find particularly inspiring your words, when you state: “However, we have to compare those predictions against what we observe, and predictions are never exact, even for deterministic theories. Experiments have errors. The constants in any theory are only known up to limited precision.” I could not agree more! I think you might have an interest in having a look at my essay, where I introduce the possibility an indeterministic alternative to classical physics. These present remarkable similarities.

Concerning the Bayesian model, are you familiar with QBism as an interpretation of quantum mechanics?

Meanwhile, good job, top rate!

All the best,

Flavio

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Author André C. R. Martins replied on Mar. 13, 2020 @ 16:30 GMT
Dear Flavio,

You have written a very nice piece there. Yes, misconceptions among physicists are common, even if most of your conclusions have always been quite obvious, your information treatment makes yours a rather nice paper. There is no way to be certain about the real world, even when using deterministic theories, and you show that clearly. I don't actually see that as an alternative to classical physics but the only way to do it right, everything else is an approximation.

On QBism, I am quite curious about it, but still need to study it seriously. That is something I MUST do soon.

Best,

André

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Israel Perez wrote on Apr. 17, 2020 @ 18:04 GMT
Dear André Martins

I enjoyed reading your essay, specially the discussion on cognition and Bayesian methods. It is well written and fluid. I am afraid I have no criticism, your discussion is well argued and aligned with the topic of this contest.

Good luck!

Regards, Israel

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Author André C. R. Martins replied on Apr. 23, 2020 @ 07:09 GMT
Dear Israel,

Thank you for your kind words, I am glad you enjoyed reading it.

Best,

André

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Member Simon DeDeo wrote on Apr. 19, 2020 @ 23:44 GMT
Hello André,

Very nice to see this piece in the mix (the first one this year I've read, so I guess I now have primacy bias.)

One thing I really like here is the hidden (recursive) problem of knowing for Bayesians: errors are distributed how? And according to what prior? And what's the prior on that, and the errors, and so on.

The standard story (for the Bayesian who want to "ground") is Jaynes' Max-Ent priors story which can't work once the system has unrestricted state space. I think. One hopes to construct a Max-Ent story that's invariant under system symmetries, but even there, there's a need to specify the symmetries and constrain one's beliefs in them. e.g., some Loop Quantum Gravity people want to violate Lorentz invariance, which means that a prior that is invariant under LI is wrong.

PS: amusingly, our opening sentences have rather a lot of parallelism. There are many things we can not know, indeed!

Simon

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Author André C. R. Martins replied on Apr. 23, 2020 @ 07:14 GMT
Dear Simon,

Thanks for the comments. I just came back to check the thread and have not still read entries for a while, I am planning to do it next. And check the parallel between our opening sentences, for sure!

And yes, using Bayesian methods fully is impossible. I still feel we should know what it would take so that we can guess a direction to move forward. After all, we can demonstrate, as Jaynes did, we should use Bayesian probabilities to work with plausibilities. There is just this pesky problem of a few infinite requirements to do it right...

André

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James Lee Hoover wrote on Apr. 20, 2020 @ 17:25 GMT
André,

Lots of good points in your essay. A major point in your essay, keeping an open mind, is one which I also emphasize in mine. Confirmation bias is a danger when setting out to prove a hypothesis which also often guides the methodology used. As you say, we need to diminish the influence of human subjectivity in our conclusions. When you say that computational models are more reliable than human cognition, it calls to mind the algorithym that the Soviet Union used to detect incoming ICBMs that failed due to detection errors programmed into it. An attending engineer was a planet-saving check on the system. So as you know in your field, human cognition can error with inputs, something you mentioned "understanding our limitations is crucial.

Hope you get a chance to read mine.

Jim Hoover

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Author André C. R. Martins replied on Apr. 23, 2020 @ 07:18 GMT
Hi, Jim

I just came back to the page, I am planning to go and read some essays tomorrow. I will include yours in the list.

And yes, our cognition can cause quite a few problems and we should be wary of our own reasoning, I obviously fully agree. Computational models can certainly go wrong, as they depend on who is implementing them. But they should provide a more reliable account of the consequences of a set of assumptions than we could get otherwise. Just as any kind of logical or mathematical tools would do.

André

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Michael muteru wrote on Apr. 30, 2020 @ 09:32 GMT
Dr Andre Your work on cognitive limitations is spot on,quite vivid in placing indeterminacy on a mathematical scale by implementing Bayesian analysis.Perfectly done. Are basic cognitive mechanisms which give rise to our world preconditioned by our environment? kindly read/review how it all impedes on our knowledge here https://fqxi.org/community/forum/topic/3525.thanks all the best.

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Author André C. R. Martins replied on May. 3, 2020 @ 01:41 GMT
Thank you for your kind words, Michael.

I will take a look at your paper. Anyway, it does seem our cognitive mechanisms are heavily influenced by the environment of our ancestors. Mercier makes a very strong case that we reason and argue not to find the best answers but to fit in a group because that is far more important from an evolutionary point of view. That is very strong conditioning by environment.

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Author André C. R. Martins wrote on May. 9, 2020 @ 21:54 GMT
There is a necessary correction in my abstract. Where it reads "There are cases where underdeterminacy can not unavoidable..." it should be "There are cases where underdeterminacy might be unavoidable..."

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James Lee Hoover wrote on May. 11, 2020 @ 06:33 GMT
Andre,

I have commented on you essay but discovered I have not rated it yet. Time grows short so I am now rating it, being your 10th rating. My reason for mentioning this is that many ratings are 1s or 2s w/o comments. I remember I enjoyed reading your essay a few weeks ago.

Jim Hoover

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