This is good, but I feel like we'd better represent human psychology if we said:

Most people don't make a distinction between the concepts of "x has probability <0.1%" and "x is impossible".

I say this because I think there's an important difference between the times when people have a precise meaning in mind, which they've expressed poorly, and the times when people's actual concepts are vague and fuzzy. (Often, people don't realise how fuzzy their concepts are).

Comment author:Thomas
16 December 2010 06:45:46PM
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Probability zero and impossibility are not exactly the same thing. A possible event can have the probability 0. But an impossible event has the probability 0.

Comment author:benelliott
16 December 2010 06:51:58PM
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You are referring to the mathematical definition of impossibility, and I am well aware of the fact that it is different from probability zero (flipping a coin forever without getting tails has probability zero but is not mathematically impossible). My point is that neither of those is actually what most people (as opposed to mathematicians and philosophers) mean by impossible.

## Comments (179)

BestThe colloquial meaning of "x is impossible" is probably closer to "x has probability <0.1%" than "x has probability 0"

This is good, but I feel like we'd better represent human psychology if we said:

Most people don't make a distinction between the concepts of "x has probability <0.1%" and "x is impossible".

I say this because I think there's an important difference between the times when people have a precise meaning in mind, which they've expressed poorly, and the times when people's actual concepts are vague and fuzzy. (Often, people don't realise how fuzzy their concepts are).

Probability zero and impossibility are not exactly the same thing. A possible event can have the probability 0. But an impossible event has the probability 0.

*6 points [-]You are referring to the mathematical definition of impossibility, and I am well aware of the fact that it is different from probability zero (flipping a coin forever without getting tails has probability zero but is not mathematically impossible). My point is that neither of those is actually what most people (as opposed to mathematicians and philosophers) mean by impossible.