`Hal Ruhl wrote:`

To clarify - the All contains all information simultaneously [see the definition in the original post] - including ALL Truing machines with ALL possible output tapes - so it contains simultaneously both output tapes re your comment below.

But if there is a fact which is true in one "world" being simulated by a given Turing machine, but false in a different Turing machine simulation, that doesn't mean that "the All" is contradictory. After all, the statement "this planet contains life" is true of Earth but not true of Pluto, but that doesn't mean the solar system is contradictory, it just means that different facts are true of different planets.

This really misses my meaning. That is not how Somethings evolve in the All. The Somethings incorporate preexisting information such as states of universes in a random dynamic.

I am not asking about how "Somethings" evolve in your theory, I'm asking what's your justification for claiming that the All is inconsistent.

I am not asking about how "Somethings" evolve in your theory, I'm asking what's your justification for claiming that the All is inconsistent.

As long as you always describe the *context* of any statement, I don't see any reason why we should describe the All as inconsistent. So if you think the All is inconsistent somehow, you need to explain in more detail why you think this is.

I already have. Would you agree that Turing's result says that some subset of FAS are inconsistent?

You don't need Turing's results to show that, it is quite trivial to construct an axiomatic system with two contradictory axioms, or with different subsets of axioms that can be used to prove inconsistent theorems.

You don't need Turing's results to show that, it is quite trivial to construct an axiomatic system with two contradictory axioms, or with different subsets of axioms that can be used to prove inconsistent theorems.

`However, there is a distinction between saying an axiomatic system is inconsistent, and saying there is something inconsistent in the behavior of the Turing machine simulating that system. There will always be a single definite truth about what symbol the Turing machine prints out at what time--it is only when you try to interpret the *meaning* of different strings of symbols that it prints out that you will see an inconsistency. As an analogy, suppose I am running a complex simulation of a human being sitting at a writing desk, and he writes two sentences on a simulated piece of paper: "I have a beard" and "I do not have a beard". If we interpret these sentences in terms of their english meaning, obviously they represent inconsistent statements, but that doesn't mean the simulation itself is somehow "inconsistent", does it? One of the statements will be true and one will be false, so there's no problem.`

`Your argument would only show the All to be inconsistent if you believe that for every axiomatic system a Turing machine can simulate, there must be a corresponding "world" within the All where all the axioms and theorems represent simultaneously true statements about that world. But if you believe that, then you are saying the All must contain not only all possible worlds, but logically impossible worlds as well. Is that what you're saying?`

Also, you didn't answer my earlier question about whether your idea of the All only includes worlds that could be simulated on a Turing machine, or if it also includes worlds that could be simulated by a "hypercomputer" which is capable of performing uncomputable operations (like instantly deciding if a given Turing machine program will halt or not).

The All is all information without restriction. All the information is in there all the time. The boundaries of the Somethings wash across the inherent counterfactuals counterfactually.

I don't understand what these words are supposed to mean, or how they address my question above. Can you just answer "yes" or "no"?

I don't understand what these words are supposed to mean, or how they address my question above. Can you just answer "yes" or "no"?

Jesse