**From:** Ashley Thomas (*Ashley.A.Thomas@dartmouth.edu*)

**Date:** Mon Sep 12 2005 - 14:55:48 MDT

**Next message:**Ben Goertzel: "RE: Non-black non-ravens etc."**Previous message:**Richard Loosemore: "Re: Complex computer programs"**In reply to:**Eliezer S. Yudkowsky: "Re: Hempel's Paradox"**Next in thread:**Eliezer S. Yudkowsky: "Re: Hempel's Paradox"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

If you test a hypothesis in a way which *could* falsify it, and *fail*

to falsify it, then your confidence in the hypothesis should increase.

The amount by which your confidence should increase should depend on

how likely it was that you would falsify your hypothesis.

Suppose we have a bag full of objects, which can be ravens or

not-ravens, and black or not-black. We can reach into the bag with

manipulators which can select an object based on whether it's a raven

or not, or whether it's black or not, but not both.

We hypothesize that all ravens in the bag are black. We can falsify

this hypothesis by finding a not-black raven. There are two possible

experiments we can perform: we can pull out a raven and see if it's

not-black, or we can pull out a not-black object and see if it's a

raven. Without knowing the relative numbers of ravens to not-black

objects, these two searches have an equal chance of finding a not-black

raven. Every time we fail to falsify our hypothesis, our confidence in

the hypothesis increases. If we find a black object when searching

through ravens, our confidence increases because we have failed to

falsify the hypothesis. If we find a not-raven when searching through

not-black objects, our confidence increases because we have failed to

falsify the hypothesis.

How much our confidence increases for either of the two searches

depends on how many of the objects we thought were ravens, and how many

of the objects we thought were not-black. If we think that there are

many fewer objects which are ravens than objects which are not-black,

then our confidence will increase faster by searching through the

ravens (alternate pov: the same number of searches gets us closer to an

exhaustive search faster checking the few ravens than checking the many

not-black objects), but our confidence will still increase a smaller

amount searching through the not-black objects. Even a single result of

a not-raven found when searching the not-black objects (even a purple

goose) increases our confidence, because we tested the hypothesis in a

way which could have falsified it, but got a result which didn't.

If the number of not-black objects in the bag goes to infinity while

the number of ravens in the bag stays finite, then the amount our

confidence in our hypothesis should increase goes to zero when

searching not-black objects for a raven, because it becomes

increasingly unlikely that we'll be able to falsify our hypothesis by

finding one of the finite number of ravens among the infinite number of

not-black objects.

Ashley "ASE" Thomas

**Next message:**Ben Goertzel: "RE: Non-black non-ravens etc."**Previous message:**Richard Loosemore: "Re: Complex computer programs"**In reply to:**Eliezer S. Yudkowsky: "Re: Hempel's Paradox"**Next in thread:**Eliezer S. Yudkowsky: "Re: Hempel's Paradox"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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