It's not as if a star would have absolutely no effect from a Boltzmann cake suddenly appearing inside of it. A civilization with a good enough model of how this star zigs and zags, they would be able to find facts about the star which would force a bayesian to move from the ridiculously tiny prior probability of the hypothesis :

On August 1st 2008 at midnight Greenwich time, a one-foot sphere of chocolate cake spontaneously formed in the center of the Sun; and then, in the natural course of events, this Boltzmann Cake almost instantly dissolved.

to some posterior distribution. Some pieces of evidence might increase the probability of the hypothesis, some might decrease it.

This is not a cheap objection in anyway. To misinterpret verifications such as early Wittgenstein and W.V. Quine as claiming that only those sentences which we can currently test are meaningful is a mistake. A common mistake, and one that some using the term positivist to describe themselves have made.

If logical positivism / verificationism were true, then the assertion of the spaceship's continued existence would be necessarily meaningless, because it has no experimental consequences distinct from its nonexistence. I don't see how this is compatible with a correspondence theory of truth.

This is another sort of mistake. Because a hypothesis can't be tested by me does not mean that it is meaningless. Vereficationists would agree with this because they think verification works everywhere, even on the other side of the universe. If some alien race over there could have seen the spaceship, or seen something which made the probability of there being a spaceship there high, or not have, then the claim is not meaningless.

What vereficationists like Quine are saying is that science is done through the senses. In the matrix code, way above the level of the machine language, our senses are the evidence nodes of our Bayes nets, and our hypotheses are the last nodes. The top layer of nodes consists of the complete set of states that some beings sensory apparatus can be in, any node in this mind containing a belief which is independent of all of the evidence nodes, contains a belief which is meaningless for that mind. But showing subjective meaninglessness of some hypothesis in one being is not enough to show that a belief/hypothesis is meaningless for all minds.

I think the critiques of this article apply to the worse of the worse of positivism. But many of those critiques are critiques that were made by hard verificationists such as Quine. But the simplest form of versificationism can be traced to Edmund Husserl belief it or not. The core of what the first movement of phenomenologists, and Quine, were saying is that only stimulus sentences can ever be used as initial evidence. Some stimulus may increase the probability of some other belief which may then be used as evidence for some other belief in turn, but without evidence from stimulus there wouldn't be enough useful shifting about of probability to do anything. Certainly a human brain, or even a replica of Einsteins brain, would have a hard time figuring out the theories of relativity if they only had a 4by4 binary black and white pixel view of the world, and could move around the camera providing them the input around freely as they like.

If no constructable mind could ever get any result from any instrument, natural, current or wildly advanced, that would force a rational mind to update its probability about a given sentence, a la bayes, then that sentence is not a scientifically meaningful belief. This is to be senseless for Wittgenstein, or literally meaningless, this is only to be scientifically meaningless for Quine. Both positions have been called vereficationism and I think both are useful, and true-ish at least.

Lastly,I've always thought of positivism as going perfectly with a correspondence theory of truth. We can treat "senseless" or "meaningless" as just meaning "un-entangle-able beliefs", as in beliefs which make no restrictions on experience.

It seems to me that Yudkowsky and the whole lot of LW staples are plainly positivists. And I have always thought of this as a good thing. Positivism plus LW style Bayesianism plus effort, form an epistemology which at least gives you a stronger fighting chance than you would have otherwise. Forming stupid belifs is harder after reading lesswrong, and harder after reading Quine, or Goodman, or even the most basic vereficationists texts. Many people have made philosophical mistakes which can then be avoided by reading vereficationists. Such as LW. Give credit where it is due, to yourself and Quine.

"fixed". I'm genuinely sorry for being inconsiderate, I'm young and still have a tendency to use provocative language if I feel emotionally stimulated.

On a lighter note... I'm curious how some of you may have estimated a very low probability of say... the likelihood that one religion is a very good approximation to the truth. I doubt that there really is any way in which someone could give a sensible estimate, unless one were to put years of work into it to weigh all the (non)evidence meticulously (and as we know religions tend to dress their stories in a LOT of colorful detail, because hearing details makes things appear more true, since they assist our human imagination).

How could one of us, in a practical way, come up with a roughly realistic number? I used something like 0,0000000000000000001% probability because that's what it -feels- like to me. I can only imagine how unlikely it would be, by comparing it to something very unlikely... like winning the lottery twice in a row. Which still doesn't feel as surprising as discovering that our world is formed out of the body of a slayed giant. But then again my feeling of surprise upon winning the lottery (I'm not actually playing) is of course in no way directly proportional to the actual odds of winning either. What kind of thought process went through your head when you had to answer this question? (I'm asking everyone in general, not just Alicorn).

FWIW: I agree with you that:

• my beliefs are always the outputs of real-world embodied algorithms (for example, those associated with remembering previously proven axioms) and therefore not completely reliable.
• there exists a non-empty set S1 of assertions that merit a sufficiently high degree of confidence that it is safe to call them "true" (while keeping in mind when it's relevant that we mean "with probability 1-epsilon" rather than "with probability 1").

I would also say that:

• there exists a non-empty set S2 of assertions that don't merit a high degree of confidence, and that it is not safe to call them true.
• the embodied algorithms we use to determine our confidence in assertions are sufficiently unreliable that we sometimes possess a high degree of confidence in S2 assertions. This confidence is not merited, but we sometimes possess it nevertheless.

Would you agree with both of those statements?

Assuming you do, then it seems to follow that by "what I truly believe" you mean to exclude statements in S2. (Since otherwise, I could have a statement in S2 that I truly believe, and is therefore definitionally true, which is at the same time not safe to call true, which seems paradoxical.)

Assuming you do, then sure: if I accept that "what I truly believe" refers to S1 and not S2, then I agree that truth is what I truly believe, although that doesn't seem like a terribly useful thing to know.

I think he will have a strong feeling that pi is about 3.141...

That's the key issue. Reality is doing something here. And you know, in advance what his model will move to. You don't think he will succeed at his event. At the end of the day, you are pretty sure that there's something objective going on.

More starkly, I can give you mathematical examples where your intuition will be wildly at odds with the correct math. Some of those make fun games to play for money. I suspect that you won't be willing to play them with me even if your intuition says that you should win and I shouldn't.

Not even mathematical facts necessarily hold since there could always be a magical demon blurring your mind, making you make errors and making you blind at them.

That's a much weaker statement than the one you originally stated. This new statement says, basically, "you can never be 100% sure of anything", whereas before you seemed to be saying, "there exist no objective standards of truth at all, any story is as good as any other".

I think I can still take part in rational debate by embracing the definition of rational truth during that debate

I don't think it will work in this case, because we're debating the very notion of rational truth.

However, I now realise this wasn't exactly the right place to tell about my idea of subjective truth.

I personally didn't mean to give you that impression at all, I apologize if I did. Just because I happen to think that using reason to debate with someone who does not value reason is futile, doesn't mean that I want to actively discourage such debate. After all, I could be wrong !

I am not Randolf, but I've met people who would answer this question thusly:

Ultimately, you are still relying on faith, intuition, or some other objective criterion in order to construct all of these logical proofs. I could choose different axioms and construct some proofs of my own, which would differ from yours. Furthermore, the very value you place on axioms and logic is subjective; I, on the other hand, place a much higher value on feelings and intuitions. Therefore, even though your arguments may be entirely logical and therefore important in your subjective worldview, they hold very little value in mine (though the reverse is also true).

I don't think it's possible to use logic to convince someone of the importance of logic, unless he happens to be convinced already.

Hehe, I knew someone would pick up on my reference, I just didn't realize how fast it would happen :-)

But my point was this: if Randolf really does believe that truth is subjective, and that it is arrived at mostly through feelings and intuitions, then he has effectively removed himself from rational debate. There's nothing I can say that will persuade him one way or another, because there's no useful mechanism by which my subjective beliefs can influence his subjective beliefs. So, there's little point in arguing with him on this (or any other) topic.

Randolf, my apologies if I seem to be putting words in your mouth; the above paragraph is simply my personal interpretation of your claim, taken to its logical conclusion.

I think he will have a strong feeling that pi is about 3.141...

Why ?

Like I said, in my definition truth is subjective and may chance since it's tied to the person's beliefs / feelings.

Hmm, well, if you truly believe that truth is subjective, then there's nothing I can do to dissuade you, by definition -- since my subjective opinion is as good as yours. Now if you'll excuse me, I've got to go build some hula-hoops, and then maybe take to the skies by will alone.

Ok, so consider what happens when this person does indeed attempt to construct a physical hula-hoop. After failing a few times, assuming he doesn't give up altogether, he'll be forced to accept (however provisinally) that pi is not 3, but approximately 3.14159265 (in our current physical reality, at least). He now has two conflicting models in his mind: one of an abstract hula-hoop made with pi == 3, and another one made with pi ~= 3.14159265. Which one will he "have a strong feeling / intuition / belief" about, do you think ?