6 ms·

I don't understand your claims that these statements are are meaningless. They are commonly uttered and understood.

lottin 6y ago
I can understand expressions such as "pretty sure" or "completely sure". I do not understand the expression "to be X% sure". If someone says they're "37% sure" tomorrow will rain, what does that mean exactly?
- dinosaurdynasty 6y ago
  37% of the time that someone says they are 37% sure of a statement X the statement X is true (assuming they're calibrated correctly/etc).
- kgwgk 6y ago
  Can you understand expressions like "more sure of A than B" or "as sure of A as of B"? Then, they are as sure that tomorrow will rain as they are sure that throwing three dice the sum will be 9 or less (37.5%).
  - lottin 6y ago
    It's clear that 37.5% sure is 0.5% more sure than 37% sure. The problem remains how to interpret these numbers.
    - kgwgk 6y ago
      You're asking about the interpretation of a statement such as "I assign the same probability to events A and B"? That would mean that both are equally likely as far as that person knows.
      - lottin 6y ago
        No, I'm not asking that.
        kgwgk 6y ago
        > If someone says they're "37% sure" tomorrow will rain, what does that mean exactly? When someone says they're "37% sure" tomorrow will rain they mean that they assign the same probability to "tomorrow will rain" that they do to "if you throw three dice you'll get 9 or less" or "when you threw three dice you got 9 or less". In the second case the event is either true or false already and there is no uncertainty for you, their probability assignment is their best guess with the information they have.
        lottin 6y ago
        The question is what is probability according to the subjective interpretation of probability? The answer usually given is that probability is a degree of belief. Thus, a probability of 37% means that you're 37% sure that some event will take place. What I'm saying is this definition is meaningless unless you define what it means to be X% sure about something, but the definition of "being X% sure" must not rely on the notion of probability because "probability" is what we are trying to define in the first place!
        kgwgk 6y ago
        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 happens to correspond to the notion of probability, but it has not been defined using a pre-existing notion of probability: https://en.wikipedia.org/wiki/Cox%27s_theorem https://en.wikipedia.org/wiki/Cox%27s_theorem
        lottin 6y ago

I can understand expressions such as "pretty sure" or "completely sure". I do not understand the expression "to be X% sure". If someone says they're "37% sure" tomorrow will rain, what does that mean exactly?

dinosaurdynasty 6y ago
37% of the time that someone says they are 37% sure of a statement X the statement X is true (assuming they're calibrated correctly/etc).
kgwgk 6y ago
Can you understand expressions like "more sure of A than B" or "as sure of A as of B"? Then, they are as sure that tomorrow will rain as they are sure that throwing three dice the sum will be 9 or less (37.5%).
- lottin 6y ago
  It's clear that 37.5% sure is 0.5% more sure than 37% sure. The problem remains how to interpret these numbers.
  - kgwgk 6y ago
    You're asking about the interpretation of a statement such as "I assign the same probability to events A and B"? That would mean that both are equally likely as far as that person knows.
    - lottin 6y ago
      No, I'm not asking that.
      - kgwgk 6y ago
        > If someone says they're "37% sure" tomorrow will rain, what does that mean exactly? When someone says they're "37% sure" tomorrow will rain they mean that they assign the same probability to "tomorrow will rain" that they do to "if you throw three dice you'll get 9 or less" or "when you threw three dice you got 9 or less". In the second case the event is either true or false already and there is no uncertainty for you, their probability assignment is their best guess with the information they have.
        lottin 6y ago
        The question is what is probability according to the subjective interpretation of probability? The answer usually given is that probability is a degree of belief. Thus, a probability of 37% means that you're 37% sure that some event will take place. What I'm saying is this definition is meaningless unless you define what it means to be X% sure about something, but the definition of "being X% sure" must not rely on the notion of probability because "probability" is what we are trying to define in the first place!
        kgwgk 6y ago
        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 happens to correspond to the notion of probability, but it has not been defined using a pre-existing notion of probability: https://en.wikipedia.org/wiki/Cox%27s_theorem https://en.wikipedia.org/wiki/Cox%27s_theorem
        lottin 6y ago