# TheOtherDave comments on 5 Axioms of Decision Making - Less Wrong

32 01 December 2011 10:22PM

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Comment author: 02 December 2011 04:43:11PM 4 points [-]

"Most people here seem to be extremely unwilling to admit that probabilities and uncertainty are not the same thing."

I can't speak for anyone else, but for my part that's because I rarely if ever see the terms used consistently to describe different things. That may not be true of mathematicians, but very little of my language use is determined by mathematicians.

For example, given questions like:
1) When I say that the coin I'm about to flip has an equal chance of coming up heads or tails, am I making a statement about probability or uncertainty?
2) When I say that the coin I have just flipped, but haven't yet looked at, has an equal chance of having come up heads or tails, am I making a statement about probability or uncertainty?
3) When I say that the coin I have just looked at has a much higher chance of having come up heads rather than tails, but you haven't looked at the coin yet and you say at the same time that it has an equal chance of having come up heads or tails, are we both making a statement about the same thing, and if so which thing is it?

...I don't expect consistent answers from 100 people in my linguistic environment. Rather I expect some people will answer "uncertainty" in all three cases, other people will answer "probability", still others will give neither answer. Some might even say that I'm talking about "probability" in case 1, "uncertainty" in case 2, and that in case 3 I'm talking about uncertainty and you're talking about probability.

In that kind of linguistic environment, it's safest to treat the words as synonyms. If someone wants to talk to me about the difference between two kinds of systems in the world, the terms "probability" and "uncertainty" aren't going to be very useful for doing so unless they first provide two definitions.