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Logos01 comments on Practicing what you preach - Less Wrong Discussion

2 Post author: TwistingFingers 23 October 2011 06:12PM

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Comment author: Logos01 26 October 2011 08:42:45AM -2 points [-]

I don't think you understand what P(X)=1 means. [...]

Ergo, for P(X)=1 to be revised requires the person making that assertion be wrong, or for there to be a fundamental shift in reality.

Comment author: dbaupp 26 October 2011 09:13:31AM *  1 point [-]

Yeah, the person making the assertion can be wrong.

for there to be a fundamental shift in reality.

Huh? Did you read what I wrote:

It doesn't just mean X is going to happen if the laws of the universe remain the same [...] It means that X happens in every possible version of our universe from this point onward

Every. Possible. Universe. This accounts for "fundamental shift[s] in reality".

Comment author: Logos01 26 October 2011 09:17:38AM -2 points [-]

Huh? Did you read what I wrote:

Yup, I most assuredly did.

Every. Possible. Universe. This accounts for "fundamental shift[s] in reality".

Saving for those in which the principle you related is altered. Don't try to wrap your head around it. It's a paradox.

Comment author: dbaupp 26 October 2011 09:39:59AM *  0 points [-]

Which principle?

Comment author: Logos01 26 October 2011 09:42:15AM 0 points [-]

Which principle?

"[P(X)=1] doesn't just mean X is going to happen if the laws of the universe remain the same, it doesn't just mean X going to happen if 3^^^3 coins are flipped and at least one lands on heads.

It means that X happens in every possible version of our universe from this point onward. Including ones where the universe is a simulation that explicitly disallows X."

Comment author: dbaupp 26 October 2011 09:47:13AM 2 points [-]

There is no paradox. Mathematics is independent of the physics of the universe in which it is being discussed, e.g. "The integers" satisfy the same properties as they do for us, even if there are 20 spatial dimensions and 20 temporal ones.

Sure, you can change the axioms you start with, but then you are talking about different objects.

Comment author: Logos01 26 October 2011 10:03:17AM 0 points [-]

Mathematics is independent of the physics of the universe in which it is being discussed, e.g.

The principles by which mathematics operates, certainly. Two things here:

1) I did not say a fundamental shift in the physics of reality.

2) The mathematics of probability describe real-world scenarios. Descriptions are subject to change.

Sure, you can change the axioms you start with, but then you are talking about different objects.

In this, you have my total agreement.

Comment author: dbaupp 26 October 2011 10:46:08AM 0 points [-]

I did not say a fundamental shift in the physics of reality.

How could one get a "fundamental" shift by any other method?

The mathematics of probability describe real-world scenarios. Descriptions are subject to change.

Yes, but the axioms of probability theory aren't (yes, it has axioms). So something like "to determine the probability of X you have to average the occurrences of X in every possible situation" won't change.

Comment author: Logos01 26 October 2011 11:39:54AM -2 points [-]

How could one get a "fundamental" shift by any other method?

Reality is not necessarily constrained by that which is physical. The Laws of Physics themselves; the Laws of Logic, several other such wholly immaterial and non-contingent elements are all considered real despite not existing. (Numbers for example.)

It is possible to postulate a counterfactual where any of these could be altered.

Yes, but the axioms of probability theory aren't (yes, it has axioms).

Enter the paradox I spoke of. The fact that certain things aren't subject to change itself can be subject to change.

Comment author: dbaupp 26 October 2011 12:12:13PM *  0 points [-]

Reality is not necessarily constrained by that which is physical. The Laws of Physics themselves; the Laws of Logic, several other such wholly immaterial and non-contingent elements are all considered real despite not existing. (Numbers for example.)

Any shift to the "Laws of Logic" is equivalent to a change in axioms, so we wouldn't be talking about our probability. And also, all this accounted for by the whole "average across all outcomes" bit (this is a bit hand-wavy, since one has to weight the average by the Kolmogorov complexity (or some such) of the various outcomes).

It is possible to postulate a counterfactual where any of these could be altered.

Nope. Here are the natural numbers {0,1,2,...} (source):

  • There is a natural number 0.
  • Every natural number a has a natural number successor, denoted by S(a).
  • There is no natural number whose successor is 0.
  • S is injective, i.e. if a ≠ b, then S(a) ≠ S(b).
  • If a property is possessed by 0 and also by the successor of every natural number which possesses it, then it is possessed by all natural numbers.

This has uniquely identified the natural numbers. There isn't a counterfactual where those 5 axioms don't identify the naturals.

Enter the paradox I spoke of. The fact that certain things aren't subject to change itself can be subject to change.

But you said:

Sure, you can change the axioms you start with, but then you are talking about different objects.

In this, you have my total agreement.

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