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..."
AAndré Martins
- Joined Feb 9, 2020
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.
Yes, it was Smolin's idea. Much easier to track now, thanks.
I am not saying simplicity does not work, it did in the past, and it will probably work well in the future also. But there is a clear bias we introduce in explanations as we do start looking at the simpler ones. Assuming there are several equally good explanations (probabilistic underdeterminancy), we would find the simpler ones first, just because we are looking there first. That does fit nicely with your #3.
The world is explainable might mean different things, as you know. It might even be just partially correct, in that we can get part of the answer but not the complete version, in principle. And yes, avoidance of overfitting is important. In principle, Bayesian methods do penalize more complicated models, so you would not need that. But, even in simple cases of model comparison, you crash into problems with the priors.
In any case, I think it is essential not to assume more than we actually can say from observation. Introducing new theories is fundamental, even metaphysical ones, but we must withdraw judgment far more often than it is done in the physics community.
Yours,
André
Dear Simon,
Great piece, I am glad you mentioned it in my own entry, as I had some time to read essays today and came soon to yours. Let see what it does to my primacy effect (I'll love to know what my own article does with your effect also). And, indeed, there are nice similarities in our opening sentences.
Your description for a possible KC-universe generating scenario is intriguing and reminds me of something similar I heard about some time ago. I can't recall the source, but it was about universes being created as consequences of other universes and there was some kind of evolutive pressure on the process. I need to hunt that one down.
Anyway, I must say I have a problem with the suggestion that simplicity might be a good way to pick correct theories. You do not say that explicitly but you do suggest that as an argument. I do like simplicity and I think it does have a role in science. But, unlike other physicists, I think the role simplicity (and, with that, measures of complexity) does play is based on human limitations. Simple, assuming human language and knowledge, is easier to use and that makes it preferable. But that is not the same as claims of truth - which should not be made - or even probabilistic truth.
Best,
André
Dear Izrael,
Interesting essay. The message mathematics is an amazingly useful tool but that we do need to talk about the real world is an important one. Indeed, claiming the universe is made of mathematics is pure untestable metaphysics, a claim quite beyond our abilities. At the very least, our current ones.
Best,
André
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
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
Dear Israel,
Thank you for your kind words, I am glad you enjoyed reading it.
Best,
André
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
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-and-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
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.