prase comments on 5 Axioms of Decision Making - Less Wrong

35 Post author: Vaniver 01 December 2011 10:22PM

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Comment author: taw 02 December 2011 12:17:00PM 1 point [-]

I am equally willing to put p = 0.1 to the statement "last decimal digit of 1543! is 7", although in fact this is quite easy to check. Just I don't want to spend time checking.

What probabilities are are you willing to assign to statements:

  • 1543! = 1540 * (1543 * 1542 * 1541 * 1539!)
  • The last digit of "1540 * (1543 * 1542 * 1541 * 1539!)" is 0 and not 7

Bayesian probabilities don't give you any anchoring to reality, they only give you consistency.

If you're willing to abandon consistency as well, they give you precisely nothing whatsoever.

Probabilities are a tool for talking about uncertainty, they are not uncertainty, to think otherwise is a ridiculous map-territory confusion.

sounds frequentistish.

As ad hominem attacks go, that's an interesting one.

If there's one possible universe where Collatz conjecture is true/false, it is true/false is all other possible universes as well. There are no frequencies there, it's just pure fact of logic.

Comment author: prase 02 December 2011 01:06:35PM *  5 points [-]

The last digit of "1540 * (1543 * 1542 * 1541 * 1539!)" is 0 and not 7

Updated. (Didn't occur to me it would be so easy.)

Bayesian probabilities don't give you any anchoring to reality, they only give you consistency. If you're willing to abandon consistency as well, they give you precisely nothing whatsoever.

It is unnecessarily black-and-white point of view on consistency. I can improve my consistency a lot without becoming completely consistent. In practice we all compartmentalise.

Probabilities are a tool for talking about uncertainty, they are not uncertainty.

I did certainly not dispute that (if I understand correctly what you mean, which I am not much sure about).

As ad hominem attacks go, that's an interesting one.

The point was, subjective probability is a degree of belief in the proposition; saying "it must be either 0 or 1 by laws of mathematics" rather implies that it is an objective property of the proposition. This seems to signal that you use a non-subjectivist (not necessarily frequentist, my fault) interpretation of probability. We may be then talking about different things. Sorry for ad hominem impression.

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