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Is Probability Real?

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Re: Is Probability Real?

#211

Post by kgwgk »

lottin wrote: post #210
kgwgk wrote: post #209

Earlier quoted context omitted.

And what I try to explain is that one way to define what it means to be X% sure about A is to say that - you put a number on it p(A) - which is between 0 and 1 - and allows you to compare how sure you are about different things p(A) and p(B) This number can be used to compute how sure you are about composite things: p(A or B) = p(A) + p(B) - p(A and B) p(A and B) = p(A given B) p(B) = p(B given A) p(A) That number p…

What do you mean "you put a number on it"? What number? If the number is arbitrary, which is what your explanation suggests, it cannot mean anything.

It's not completely arbitrary, it represents the degree of plausability you assign to the event.

These numbers have to obey some rules if you require that a set of beliefs is consistent.

The number you assign to the plausability of A and the number you assign to the plausability of not-A have to sum 1.

If you think A and B are equally plausible, you have to put the same number on them.

If you think that A and not-A are equally plausible, you have to assign the number 0.5 to both.

If you put the number p(head)=p(tails)=0.5 as your degree of plausability that the coin I just flipped (I actually did it!) is showing head or tails it's not an "arbitrary" number. It means that you think both (exhaustive) outcomes are equally plausible. Why do you say it cannot mean anything?

Re: Is Probability Real?

#212

Post by feanaro »

ikeboy wrote: post #128
feanaro wrote: post #126

Earlier quoted context omitted.

How do you resolve the problems raised by Bell's theorem?

Bell's theorem rules out local realism. I view realism as incoherent, so I'm certainly not committed to local realism.

You said the distinction between a probabilistic world and a deterministic one is incoherent. But if there is no local realism, wouldn't it be more accurate to describe your position as saying all events are probabilistic rather than none of them?

Re: Is Probability Real?

#213

Post by ikeboy »

feanaro wrote: post #212
ikeboy wrote: post #128

Earlier quoted context omitted.

Bell's theorem rules out local realism. I view realism as incoherent, so I'm certainly not committed to local realism.

You said the distinction between a probabilistic world and a deterministic one is incoherent. But if there is no local realism, wouldn't it be more accurate to describe your position as saying all events are probabilistic rather than none of them?

No. All events being probabilistic is still realism, just in a weaker sense than Bell.

Re: Is Probability Real?

#214

Post by lottin »

kgwgk wrote: post #211
lottin wrote: post #210

Earlier quoted context omitted.

What do you mean "you put a number on it"? What number? If the number is arbitrary, which is what your explanation suggests, it cannot mean anything.

It's not completely arbitrary, it represents the degree of plausability you assign to the event. These numbers have to obey some rules if you require that a set of beliefs is consistent. The number you assign to the plausability of A and the number you assign to the plausability of not-A have to sum 1. If you think A and B are equally plausible, you have to put the same number on them. If you think that A and not-A a…

It seems to me that if a probability is a quantity representing a degree of belief, and it's only meaningful in relation to another quantity representing another degree of belief, in the sense that we can only say than being X% sure is being more sure than being Y% sure, if X > Y, or equally sure, if X = Y, then such quantity only has an ordinal value, which is to say the quantity itself is meaningless. For it to be meaningful it has to have an interpretation that does not always refer us to another degree of belief. It also must not refer to a "degree of plausibility" since this is just another expression for "probability", and probability is what we are trying to define.

Re: Is Probability Real?

#215

Post by kgwgk »

lottin wrote: post #214
kgwgk wrote: post #211

Earlier quoted context omitted.

It's not completely arbitrary, it represents the degree of plausability you assign to the event. These numbers have to obey some rules if you require that a set of beliefs is consistent. The number you assign to the plausability of A and the number you assign to the plausability of not-A have to sum 1. If you think A and B are equally plausible, you have to put the same number on them. If you think that A and not-A a…

It seems to me that if a probability is a quantity representing a degree of belief, and it's only meaningful in relation to another quantity representing another degree of belief, in the sense that we can only say than being X% sure is being more sure than being Y% sure, if X > Y, or equally sure, if X = Y, then such quantity only has an ordinal value, which is to say the quantity itself is meaningless. For it to be…

I'm not sure I understand where do you see a problem.

In the example of the degree of belief (between 0 and 1) that you have that the coin on my desk is showing one face or the other, don't you agree that the right numbers that represent your indifference are 0.5 and 0.5? The quantity itself is not meaningless.

Re: Is Probability Real?

#216

Post by feanaro »

ikeboy wrote: post #213
feanaro wrote: post #212

Earlier quoted context omitted.

You said the distinction between a probabilistic world and a deterministic one is incoherent. But if there is no local realism, wouldn't it be more accurate to describe your position as saying all events are probabilistic rather than none of them?

No. All events being probabilistic is still realism, just in a weaker sense than Bell.

Yeah, I'm grasping at straws because I don't really understand what your position is from the things you said in this thread.

Re: Is Probability Real?

#217

Post by samatman »

st1x7 wrote: post #8
enriquto wrote: post #5

Earlier quoted context omitted.

A simple sentence that I've found useful for pedagogy: "the probability of that coin toss being 50% does not talk about the coin; it talks about you , and about your partial knowledge of the universe." You can add: "The coin toss itself is deterministic and the result can be computed if you know the initial position and speed." They will inevitably bother you about the physical impossibility to measure the starting p…

> the probability of that coin toss being 50% does not talk about the coin; it talks about you, and about your partial knowledge of the universe. But it does talk about the coin - a weighted coin would have a different probability. Same in the example with the white/black balls - if they weren't 5 white and 5 black but 6 white and 4 black, the probability you would assign to the top one would be different. Again, the…

Thought experiment: you're presented a jar, and offered the chance to bet ten bucks on drawing a white ball. You know nothing about the content of the jar. What odds would you take?

Now, you see ten white balls get added, then are blinded while other balls are added (maybe). You estimate the jar can't hold more than about a hundred balls. What odds would you take?

Now, you see ten white and ten black get put in, and saw it was empty before. What odds?

Now, you see ten white and fifty black, but the whites are larger, and you get to draw a ball. What odds?

The difference between the second-to-last and the last is the missing information we usually think of when we talk about randomness being missing information.

And you'll see that the previous scenarios don't change anything about that.

Re: Is Probability Real?

#218

Post by lottin »

kgwgk wrote: post #215
lottin wrote: post #214

Earlier quoted context omitted.

It seems to me that if a probability is a quantity representing a degree of belief, and it's only meaningful in relation to another quantity representing another degree of belief, in the sense that we can only say than being X% sure is being more sure than being Y% sure, if X > Y, or equally sure, if X = Y, then such quantity only has an ordinal value, which is to say the quantity itself is meaningless. For it to be…

I'm not sure I understand where do you see a problem. In the example of the degree of belief (between 0 and 1) that you have that the coin on my desk is showing one face or the other, don't you agree that the right numbers that represent your indifference are 0.5 and 0.5? The quantity itself is not meaningless.

You say indifference, but indifference with regards to what? In economics, an individual is said to be indifferent between two alternatives if those alternatives result in the same level of utility for him or her, utility being an abstract concept representing well-being. But you don't say why this person is indifferent to the coin showing one face or the other. Because if it's because he or she thinks both options are equally likely, then we again have a problem, since we don't know what "likely" means.

Re: Is Probability Real?

#219

Post by kgwgk »

lottin wrote: post #218
kgwgk wrote: post #215

Earlier quoted context omitted.

I'm not sure I understand where do you see a problem. In the example of the degree of belief (between 0 and 1) that you have that the coin on my desk is showing one face or the other, don't you agree that the right numbers that represent your indifference are 0.5 and 0.5? The quantity itself is not meaningless.

You say indifference, but indifference with regards to what? In economics, an individual is said to be indifferent between two alternatives if those alternatives result in the same level of utility for him or her, utility being an abstract concept representing well-being. But you don't say why this person is indifferent to the coin showing one face or the other. Because if it's because he or she thinks both options a…

At what point does the following argument derail for you?

0) I tossed a coin, it lies flat on my desk

1) You have some degree of belief about the statements H:“the coin shows heads” and T:“the coin shows tails”

2) You want to quantify that degree of belief

3) You postulate that you can put a number on your degree of belief about some statement A with the following properties:

3a) p(A) it is between 0 (false) and 1 (true)

3b) p(A or B) = p(A) + p(B) - p(A and B)

3c) p(A and B) = p(A given B) p(B) = p(B given A) p(A)

4) p(H) + p(T) = 1

5) Unless your degree of belief about H is higher than your degree of belief about T

or your degree of belief about T is higher than your degree of belief about H ...

6) ... it follows that p(H) = p(T) = 0.5

Re: Is Probability Real?

#220

Post by lottin »

lottin wrote: post #218
kgwgk wrote: post #215

Earlier quoted context omitted.

I'm not sure I understand where do you see a problem. In the example of the degree of belief (between 0 and 1) that you have that the coin on my desk is showing one face or the other, don't you agree that the right numbers that represent your indifference are 0.5 and 0.5? The quantity itself is not meaningless.

You say indifference, but indifference with regards to what? In economics, an individual is said to be indifferent between two alternatives if those alternatives result in the same level of utility for him or her, utility being an abstract concept representing well-being. But you don't say why this person is indifferent to the coin showing one face or the other. Because if it's because he or she thinks both options a…

(in reply to @kgwgk's comment https://news.ycombinator.com/item?id=25313531)

The argument is flawless, the problem is with the interpretation.

> p(A or B) = p(A) + p(B) - p(A and B)

How does one add degrees of belief and what sense do we make out of the result?

> p(H) = p(T) = 0.5

Sure, two equal quantities representing degrees of belief must mean the degrees of belief are of the same magnitude. But what about P(H) = 2P(T)? What does it mean for one degree of belief to be twice as large as the other?

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