Simon

There’s a general consensus that, although quantum theory has changed our understanding of reality, Newtonian physics remains a reliable short term guide to the macro world. In principle, the vast majority of macro events that are just about to happen are thought to be 99.9999% inevitable, as opposed to 100% like Newton thought.  From that I deduce that if a coin is shortly to be flipped, the outcome is unknown but, is as good as determined as makes no odds. Whereas if a coin is flipped farther into the future from a point of prediction, the outcome is proportionately more likely to be undetermined. 

I’m willing to concede debate about this. What I do recognise is that Beauty’s answer of 2/3 Heads, after she learns it’s Monday, depends on it being an already certain but unknown outcome.... (read 424 more words →)

Well in that case, it narrows down what we agree about. Mathematical propositions aren’t events that happen. However, someone who doesn’t know a specific digit of Pi would assign likelihood to it’s value with the same rules of probability as they would to an event they don’t know about. I define credence merely as someone’s rational estimate of what’s likely to be true, based on knowledge or ignorance. Credence has no reason to discriminate between the three types of reality I talked about, much less get invalidated.

I would also highlight that almost all external outcomes in the macro world, whether known or unknown, are already determined, as opposed to being truly random. In that sense, an unknown coin flip outcome is just as certain as an unknown mathematical proposition. In the case of Sleeping... (read 625 more words →)

Hi Dadarren. I haven’t forgotten our discussion and wanted to offer further food for thought. It might be helpful to explore definitions. As I see it, there are three kinds of reality about which someone can have knowledge or ignorance.   

Contingent – an event in the world that is true or false based on whether it did or did not happen.

Analytic – a mathematical statement or expression that is true or false a priori.

Self-location – an identity or experience in space-time that is true or false at a given moment for an observer. 

I’d like to ask two questions that may be relevant.

a) When it comes to mathematical propositions, are credences valid? For example, if I ask whether the tenth digit of... (read more)

Ok that’s fine. I agree MWI is not proven. My point was only that it is the absolute self-location model. Those endorsing it propose the non-existence of probability, but still assign the mathematics of likelihood based on uncertainty from an observer. Forgive me for stumbling onto the implications of arguments you made elsewhere. I have read much of what you’ve written over time. 

I especially agree that perspective disagreement can happen. That's what makes me a Halfer. Self-location is at the heart of this, but I would say it is not because credences are denied. I would say disagreement arises when sampling spaces are different and lead to conflicting first-person information that can’t be shared. I would also say that, whenever you don't know which pre-existing time or identity applies to you, assigning subjective likelihood... (read more)

Ok here's some rebuttal. :) I don’t think it’s your communication that’s wrong. I believe it’s the actual concept.  You once said that yours is a view that no-one else shares. This does not in itself make it wrong. I genuinely have an open mind to understand a new insight if I’m missing it. However I’ve examined this from many angles. I believe I understand what you’ve put forward.

In anthropic problems, issues of self-location and first person perspective lie at the heart. In anthropic problems, a statement about a person’s self-location, such as ‘'”today is Monday” or “I am the original”, is indeed a first person perspective. Such a statement, if found to be true, is a fact that could not have been otherwise. It was not a random event that had a chance of not happening. From this, you’ve extrapolated – wrongly in my view - that normal... (read more)

I’ll come back with a deeper debate in good time. Meanwhile I’ll point out one immediate anomaly.  

I was genuinely unsure which position you’d take when you learnt the two envelopes were the same. I expected you to maintain there was no probability assigned to Envelope A. I didn’t expect you to invalidate probability for the contents of Envelope B. You argued this because any statement about the contents of Envelope B was now linked to your self-location – even though Envelope B’s selection was unmistakably random and your status remained unknown. 

It becomes even stranger when you consider your position if told that the two envelopes were different. In that event, any statement about the contents of Envelope B refers just as much to self-location. If the two envelopes are different, a hypothesis that Envelope B contains ‘copy’ is the same hypothesis that you’re the original - and... (read more)

I’ve allowed some time to digest on this occasion. Let's go with this example.  

A clone of you is created when you’re asleep. Both of you are woken with identical memories. Under your pillow are two envelopes, call them A and B. You are told that inside Envelope A is the title ‘original’ or ‘copy’, reflecting your body’s status. Inside Envelope B is also one of those titles, but the selection was random and regardless of status.  You are asked the likelihood that each envelope contains ‘original’ as the title.

I’m guessing you'd say you can't assign any valid probability to the contents of Envelope A. However, you’d say it’s legitimate to assign a 1/2 probability that Envelope B contains ‘original’. 

Is there a fundamental difference here, from your point of view? Admittedly if Envelope A contains 'original',... (read more)

I doubt we’ll persuade each other :) As I understand it, in my example you’re saying that the moment a self-location is ruled out, any present and future updating is impossible – but the last known probability of the coin stands. So if Beauty rules out Heads/Peter and nothing else, she must update Heads from 1/2 to 1/3. Then if she subsequently rules out Tails/Peter, you say she can’t update, so she will stay with the last known valid probability of 1/3. On the other hand, if she rules out Tails/Peter first, you say she can’t update so it’s 1/2 for Heads. However, you also say no further updating is possible even if if she then rules out Heads/Peter, so her credence will remain 1/2, even though she ends up with identical information. That... (read 638 more words →)

Ok let’s see if we can pin this down!  Either Beauty learns something relevant to the probability of the coin flip, or she doesn't. We can agree on this, even if you think updating can't happen with self-location. 

Let’s go back to a straightforward version of the original problem. It's similar to one you came up with. If Heads there is one awakening, if Tails there are two. If Heads, it will be decided randomly whether she wakes on Monday or Tuesday. If Tails, she will be woken on both days with amnesia in between. She is told in advance that, regardless of the coin flip, Bob and Peter will be in the room. Bob will be wake on Monday, while Peter is asleep. Peter will be awake on Tuesday, while Bob asleep. Whichever of... (read 538 more words →)

Interesting Dadarren. 

I sense that you’re close to being converted to become a ‘pure halfer’, willing to assign probability to self-locations.  Let me address what you said.  

“Your latter example: after seeing Red/Blue, I will not say Heads' probability is halved while Tails' remain the same. I will say there is no way to update. “

I assume you mean that the probability of 1/2 for Heads or Tails – before and after she sees either colour –  remains correct. We can agree on that. What matters is why it is true. You’re arguing that no updating is possible after she sees a colour. I invite you to examine this again.

The moment she sees – for example – blue, we can agree that Tails/Red and Heads/Red are definitely ruled out. The difference is that Tails/Red reflects a self-location whereas Heads/Red does not. You’re claiming that because Tails/Red reflects a self-location... (read more)