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wedrifid comments on Syntacticism - Less Wrong Discussion
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No I don't. I remember hardly anything about stuff that has passed out of my future light cone. Especially about small dark objects. And since actual information is lost when stuff goes out of my future light cone some of those objects no longer have enough evidence about them in the entire light cone to be able to reconstruct what they are. Although I suppose there is a probability distribution over possible combinations of object-going-out-of-the-light-cone that could be constructed based on remaining evidence.
Things existing has nothing to do with me being able to detect them or to remember them or to in principle be able to deduce their existence based on evidence.
As for "a proof exists", that is something that can sometimes be proven to exist or not exist. I'm told that sometimes that you can even prove that a proof exists without having a proof. Which seems to rely on a bizarre definition of proof but hey, mathematicians are into that sort of thing.
My position: Any ways of defining terms such that assigning probabilities to "a proof exists" is forbidden is a broken way to define such terms. It neither matches the intuitive way we use the language nor constitutes a useful way to carve up reality.
I'm not bluffing anything. Nor am I writing a treatise on logical uncertainty. But I'll tell you this: If I'm locked in a room, someone reliable generates a random 40 digit number from a uniform distribution right in front of me and I'm not given a computer and I'm asked to bet at even odds that it is not a prime number I am going to take that bet. Because it probably isn't a prime number. That's right, probably not.
It's not because I'm clever and prestigous and am claiming to have deep wisdom about logical uncertainty. It's because I'm not am not stupid and I assign probabilities to stuff so I can win. If being impressive and insightful requires me to only assign 0% and 100% to things like that then I don't want to be impressive and insightful. Because that is literally for losers.
There's very little in that I disagree with. In particular I think "winning" is a fine summary of what probability is for. But there is nothing for you to win when assigning a probability to a claim that has no testable consequences--winning is a testable consequence.
Just the most fundamental part:
Serious question: what's special about the phrase "a proof exists" that requires you to assign a probability to it? Presumably there are some grammatically correct assertions that you don't feel should have numbers attached to them.
I don't consider "can have probabilities assigned" to be an exception that requires a special case. It gets treated the same as any other logical uncertainty. You can either handle logical uncertainty or you can't.
I don't understand. You're saying you do have a prior probability for every grammatically correct assertion?
No, that isn't something I've said.
Then what is it about the assertion "a proof exists" that calls out to have a number attached to it? Why is it similar to "a written proof will exist by tomorrow noon" and not similar to "the exquisite corpse will drink the new wine"?
In case it wasn't clear, I rejected this line of reasoning. "A proof exists" is not a special case that needs justification.
Please refer to my first few comments on the subject. They constitute everything I wish to say on the (rather unimportant) subject of whether "a proof exists" is permitted. I don't expect this conversation to produce any new insights.