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All of Michael Carey's Comments + Replies

Let's talk about Impostor syndrome in AI safety
Michael Carey70

The best advice I ever heard for Imposter Syndrome, was

"It's okay, by definition nobody is qualified to do something- if it is truly cutting edge"

Thank you for this article.

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2MiguelDev
This is a thought that frequently crosses my mind too, especially in the field of AI safety. Since no one really has definitive answers yet, my mantra is: keep asking the right questions, continue modeling those questions, and persist in researching.
Why I Don't Believe The Law of the Excluded Middle
Michael Carey10

Thank you for clarifying, I misunderstood your post. 

Yes, you're right. "essentially" arbitrary problems would be free game. 

There is a hierarchy of questions one can ask though. That is, whatever oracle you introduce, you can now ask more complex questions and would require a more complex oracle to answer ( basically, you can ask the first oracle, questions about itself, which require another more complex oracle to answer). 

When I saw you use the word "computer" I thought you meant, a literal computer that we could in principle build. 

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3Noosphere89
My focus was on the more philosophical/impractical side, and the computers we can actually build in principle, assuming the laws of physics are unchangable and we are basically correct, we can't even build Universal Turing Machines/Turing Complete systems, but just linear bounded automatons, due to the holographic principle. Also, the entire hierarchy can be solved simply by allowing non-uniform computational models, which is yet another benefit of non-uniform computational models.
Would You Work Harder In The Least Convenient Possible World?
Michael Carey51

If in World A, the majority was an Alice ... not doing the job they loved ( imagine a teacher who thinks education is important, but emotionally dislikes students) , unreciprically giving away some arbitrary % of their earnings, etc...

Is that actually better than World B? A world where the majority are Bobs, sucessful at their chosen craft, giving away some amount of their earnings but maintaining a majority they are comfortable with.

I'm surprised Bob didn't make the obvious rebuttals:

  1. Alice, why aren't you giving away 51% of your earnings? What metho

... (read more)
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Polarization is Not (Standard) Bayesian
Michael Carey10

My immediate thoughts ( Apologies if they are incoherent): The predictability of belief updating could be due in part to what qualifies as "updating". In the examples given, belief updating seemed to happen when new information was presented. However, I'm not sure that models how we think. 

What if, "belief updating" is compounded at some interval, and in the absence of new information, old beliefs, when "updated" don't actually tend to change?   Every moment you believe something even in the absence of new information, would qualify as a moment o... (read more)

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Why I Don't Believe The Law of the Excluded Middle
Michael Carey10

You would be right in most cases. But, there is still the issue of independent statements. " ZF is consistent" can not be shown to be true or false, if ZF is consistent, via the Incompleteness Theorems. 

So, some statements may not be shown to halting, or not halting. Which, is the famous halting problem. 

Any algorithm would be unable to tell you, if the statement halts or doesn't halt. So, not all statements can be expressed as true/false or halt/not-halt 

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3Noosphere89
There are 2 things to be said here: 1. I didn't say that it had to return an answer, and the halting problem issue for Turing Machines is essentially that even though a program halts or doesn't halt, which in this case can be mapped to true or false, we don't have an algorithm that runs on a Turing Machine that can always tell us which of the 2 cases is true. 2. Gödel's incompleteness theorems are important, but in this context, we can basically enhance the definition of a computer philosophically to solve essentially arbitrary problems, and the validity problem of first order logic becomes solvable by introducing an Oracle tape or a closed timeline curve to a Turing Machine, and at that point we can decide the validity and satisfiability problems of first order logic. You also mentioned that oracles like oracle tapes can provide the necessary interpretation for set theory statements to be encoded, which was my goal, since a Turing Machine or other computer with an Oracle tape, which gets around the first incompleteness theorem by violating an assumption necessary to get the result.
Reflexive decision theory is an unsolved problem
Michael Carey30

As far as I know for know, all of standard Mathematics is done within ZF + Some Degree of Choice. So it makes sense to restrict discussion to ZF (with C or without).  

My comment was a minor nitpick, on the phrasing "in set theory, this is a solved problem". For me, solved implies that an apparent paradox has been shown under additional scrutiny to not be a paradox. For example, the study of convergent series (in particular the geometric series) solves Zeno's Paradox of Motion. 

In Set Theory, Restricted Comprehension just restricts us from asking ... (read more)

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Reflexive decision theory is an unsolved problem
Michael Carey72

Saying that Set Theory "solved the problem" by introducing restricted Comprehension is maybe a stretch.

Restricted Comphrension prevents the question from even being asked. So, it "solves it" by removing the object from the domain of discourse.

The Incompleteness Theorems are Meta-Theorems talking about Proper Theorems.

I'm not sure Set Theory has really solved the self-reference problem in any, real sense besides avoiding it. ( which may be the best solution possible)

The closest might be the Recursion Theorems, which allow functions to "build-themselves" by ... (read more)

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3Richard_Kennaway
I was painting with a broad brush and omitting talk of alternatives to Limited Comprehension, because my impression is that ZF (with or without C) is nowadays the standard background for doing set theory. Is there any other in use, not known to be straightforwardly equivalent to ZF? (ETA: I also elided all the history of how the subject developed leading up to ZF. For example, in Principia Mathematica Russell & Whitehead used some sort of hierarchy of types to avoid the inconsistency. That approach dropped by the wayside, although type systems are back in use in the various current projects to formalise all of mathematics.) Any answer to Russell's question to Frege must exclude something. There may be other ways of avoiding the inconsistencies, such as the thesis that Adele Lopez linked, but one has to do something about them.
3Adele Lopez
There's some interesting research using "exotic" logical systems where unrestricted comprehension can be done consistently (this thesis includes a survey as well as some interesting remarks about how this relates to computability). This can only happen at the expense of things typically taken for granted in logic, of course. Still, it might be a better solution for reasoning about self-reference than the classical set theory system.
Why I Don't Believe The Law of the Excluded Middle
Michael Carey10

I imagine you are refering to a Turing Machine halting or not halting.

There are statements in Set Theory, which Turing Machines cannot interpret at all ( formally, they have a particular complexity), and require the introduction of "Oracles" in order to assist in interpreting. These are called Oracle Turing Machines. They come about frequently in Descriptive Set Theory.

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2Noosphere89
So we can, in a manner of speaking, encode them as programs to be run in a Turing Machine with a oracle tape. That's not too hard to do, once we use stronger models of computation, and thus we can still encode set theory statements in more powerful computers. So I'm still basically right, philosophically speaking, in that we can always encode set theory/mathematics statements in a program, using the trick I described of converting set theory into quantified statements, and then looking at the first quantifier to determine whether halting or not-halting is either true or false.
Why I Don't Believe The Law of the Excluded Middle
Michael Carey00

What do you mean by "believe in the Law of Excluded Middle"

Do you need to believe it applies to all conceivable statements?

Usually, when one is working within a framework assuming the Law Of Excluded Middle, it's only true for their Domain of Discourse.

Whether it's true outside that domain is irrelevent.

The Law of Excluded Middle is obviously false, in the framework of quantum bits, where 1 = true, 0 = False. So, I doubt anyone believes it applies Universally, under all interpretations.

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