[lottin]

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?

[kgwgk]

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]

It's clear that 37.5% sure is 0.5% more sure than 37% sure. The problem remains how to interpret these numbers.

[kgwgk]

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]

No, I'm not asking that.

[kgwgk]

> 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]

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!

[dinosaurdynasty]

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).