andrewk

The first question is about the prior distribution of X. My understanding is that most posters are assuming this is unknown to the player, and I have ...

Not if it is in two different games, which is what is happening here. In the first case, the game has envelopes with 5 and 10 in them, average 7.5, an...

I regard all computer simulations as irrelevant to the question at hand. The question is one of mathematics, and must be addressed by mathematics, not...

I'm afraid the table(s) is(are) still not showing. It may be a conflict between my system and the web-site. Perhaps you could enter the table as text ...

Indeed. You have written a program with repeated plays that shows it is best to switch, and Srap appears to have written one that is only slightly dif...

Good, so you are challenging line 0 of my proof. Why do you think it is an error? Do you not agree that, if I open the envelope and see 10, the possib...

That is a coherent response. Whether you realised it or not, you have sided with the Frequentist approach, and a Frequentist will indeed reject my cal...

We could get into a discussion of what's wrong with it, but we'd be discussing the wrong thing. Computer programs - with very few exceptions like dedi...

There is no long term in this setup. There is a single offering. If we want to consider a long series of such activities, it needs to be set up precis...

I agree with everything in that post. I too would love to see the world attain that state of having a single, trusted, global police force, and I feel...

That claim is not consistent with the following formal calculations from my earlier post: which say that, after opening the first envelope and finding...

Are you saying that you have reservations about my corrected version set out in that post? It is a fairly straightforward calculation based on conditi...

You've found me out. Please don't tell my employers that, or I'll lose my job.

The conclusion of symmetry is incorrect, because X is £5 in the first case and £10 in the second case. So we can't say that there's no difference beca...

That distribution is (1) unknown, as X is unknown and (2) not appropriate for estimating expected gains from switching, since it does not use all the ...

That is not consistent with your use of the term 'expected value' in the following: 'Expected value' only has meaning in the context of a probability ...

This is not well-defined. It needs re-stating to make it unambiguous. Here are some options. (1) A number X is drawn from a distribution f. A second n...

It was a good choice. In the version in wikipedia it is easy, and uncontroversial, to conclude that there is no reason to switch. Not so in this case.

You said this in reply to my pointing out that arguments based on expected values prior to opening an envelope are wrong because we don't even know if...

I am seeking to justify something - armed deterrence - that you call violence and that I do not. The state that results from that, I call peace and yo...

It occurs to me that, on my understanding of the two main interpretations of probability, and assuming no knowledge of the prior distribution of the l...

It appears we have different ideas of what constitutes violence and what constitutes peace. I doubt that difference can be bridged.

It's peaceful as long as the violence is only a threat. If violence actually happens then it depends on why it happened. If it happens in the name of ...

I tend to agree with Hanover, and with Hobbes, that it is the threat of violence on our behalf by the armed forces and police that allows people like ...

Interesting. The problem is different. Unlike in the OP, in the Wiki case, the envelope has not been opened before the option to swap. So the player h...

I am trained in mathematics, and use it in my work, but never studied formal logic until several years ago. I self-studied using what I could find on ...

It looks like an error to me. A set of truth assignments cannot satisfy both ¬? and ?x.? because the latter entails ?.

Do you have a link? It could just be an error. Universities tend to have fairly high error rates in their materials these days, because all the fee in...

It is hard to argue that armed forces are not necessary to a peaceful life, as Hanover pointed out. I think of them as a necessary evil. I admire thos...

It's necessary to distinguish between two cases, which is whether we know the distribution of X, ie the distribution for the lower of the two values. ...

That sounds correct. It sounds like you feel you've come up against something that is contrary to the above. I can't see it. What do you see that conc...

Yes, that was a mistake. 'is a block' is unary. Instead let it be 'is the same shape as', which is binary.

It looks like you're assuming the player's utility function is the identity function, which would be unusual and unrealistic. Even if we assume that, ...

It depends on my utility function U. Utility functions map one's wealth to levels of 'utility', ie satisfaction. They are generally assumed to be mono...

OK, with that information, we can conclude that it is consistent. One way to understand that is to consider the interpretation where above(x,y) is alw...

Are you saying that your axiom set is {<above axiom>, on(a,b), on(b,c)} where <above axiom> denotes the relation you wrote in the OP with the two fora...

We can take a feather that has fallen off a bird, and use it, in the absence of any legs, to establish the concept of a feather. Then we can develop t...

In mathematics properties are sometimes defined as the equivalence class of all objects possessing that property. For instance, once can define the cl...

I return to the distinction I started with - between rational meaning and emotional meaning. I think for many people the question of whether there are...

I would say yes, or at least all of physics that can be considered as science. In my lexicon other universes or events outside the light cone are meta...

It depends on what his argument is. If all it does is to point to the logical gaps in attempted constructive rational arguments then I think it would ...

The difference between these two is that it is hard to imagine any experience that would answer the question about whether universals are real, but on...

Some have made arguments that they thought were rational. I don't agree with them on that. If they were rational they would be conclusively persuasive...

I think it helps to make a distinction between rational meaning and emotional meaning. I tend to agree with Carnap that questions of ontology have no ...

I'm a bit bemused by this Ramsey business. I can't see what perceived imbalance they are trying to correct. It's a long time since I was at uni but, w...

Perhaps it turns on what is meant by 'switch genders' - specifically, whether the person in question declares that they are now of the gender that is ...

I've been thinking about this in terms of various universes that are limited as to what's in them. If we have only two objects, A and B, and they don'...

I'd rather not put it like that, as it seems to imply that we need to 'go to infinity' in order to make sense of the limit. Then before we know it, pe...

It seems to me that philosophers of law would tend, as in many other 'philosophies of...' (science, mathematics, ethics), to divide into those that th...

To engage in a philosophical discussion of mathematics and measure, it seems a good idea to first engage with the enormous branch of mathematics that ...