Comment author:[deleted]
24 May 2013 06:22:25AM
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We certainly can talk about the limit of a function whose codomain is a measure of probability being 1; the limit of the probability of a proposition as the amount of evidence in favor of it approaches infinity is 1. But that doesn't mean that 1 is a measure of probability. Infinity is valid as the limit of a function yielding real numbers, but infinity is not a real number.

As for your example with the amount of time it takes to run a particular distance, I can't be certain that we won't find a region of space with strange temporal effects that allow you to take a walk and arrive at your starting point before you left. This would allow you to run a hundred meters in negative time, in at least one sense of the word. Getting that sort of speed from the runner's point of view would be stranger, but the Dark Lords of the Matrix could probably make it happen.

## Comments (128)

OldWe certainly can talk about the limit of a function whose codomain is a measure of probability being 1; the limit of the probability of a proposition as the amount of evidence in favor of it approaches infinity is 1. But that doesn't mean that 1 is a measure of probability. Infinity is valid as the limit of a function yielding real numbers, but infinity is not a real number.

As for your example with the amount of time it takes to run a particular distance, I can't be certain that we won't find a region of space with strange temporal effects that allow you to take a walk and arrive at your starting point before you left. This would allow you to run a hundred meters in negative time, in at least one sense of the word. Getting that sort of speed from the runner's point of view would be stranger, but the Dark Lords of the Matrix could probably make it happen.