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> Empirical/physical science doesn't deal with conclusive proof from axioms, anyway: it deals mainly in probability and evidential falsification. Of course it

by lutusp 13y ago

> Empirical/physical science doesn't deal with conclusive proof from axioms, anyway: it deals mainly in probability and evidential falsification. Of course it does. Modern physics requires rigorous mathematics, the latter certainly are influenced by the incompleteness theorems. If I shape a theory about the universe in modern physics, if my theory doesn't have a mathematical form it won't be taken seriously for very good reasons. Therefore modern physics, the most scientific of sciences, requires a very high level of mathematical reasoning. Therefore the incompleteness theorems need to be taken into account. Even something as trivial as the Turing halting problem is known to be insoluble because of its connection to the incompleteness theorems. Link: http://en.wikipedia.org/wiki/Halting_problem http://en.wikipedia.org/wiki/Halting_problem Quote: "The concepts raised by Gödel's incompleteness theorems are very similar to those raised by the halting problem, and the proofs are quite similar. In fact, a weaker form of the First Incompleteness Theorem is an easy consequence of the undecidability of the halting problem." This is just one of many examples in which the incompleteness theorems affect the outcome of a pedestrian scientific issue. > ... since science isn't a proof system subject to the Theorem in the first place. This is false. Beyond the examples given above, many aspects of present scientific theories are influenced, directly or indirectly, by the incompleteness theorems.

DerpDerpDerp 13y ago
Your reversing of the relationship between the Halting Problem and the Incompleteness theorem (based on the quote you provided) makes me doubt the rest of your conclusions. It's not that the Incompleteness Theorem tells us about the Halting Problem, but rather, that the Halting Problem tells us about the Incompleteness theorem. Also, we have no reason to think that the universe satisfies some of the requirements of the Incompleteness Theorem (or even things like the Halting Problem). Both require some kind of unbounded or self-referential behavior, which we might not have in the universe.
- lutusp 13y ago
  > Your reversing of the relationship between the Halting Problem and the Incompleteness theorem ... Here's what I said: "Even something as trivial as the Turing halting problem is known to be insoluble because of its connection to the incompleteness theorems." That doesn't reverse the relationship between the two, it identifies that there is a relationship. That's not controversial. > It's not that the Incompleteness Theorem tells us about the Halting Problem, but rather, that the Halting Problem tells us about the Incompleteness theorem. The Turing halting problem and the incompleteness theorems are related. Without the GIT, we would not be aware that the Turing halting problem is insoluble, a statement that can be made about any number of similar issues. > Also, we have no reason to think that the universe satisfies some of the requirements of the Incompleteness Theorem (or even things like the Halting Problem). You mean, apart from the fact that the question is whether the universe is a vast computer simulation, by definition subject to the halting problem, which lacks a solution because of the GIT? > Both require some kind of unbounded or self-referential behavior, which we might not have in the universe. We're not discussing the universe's behavior, we're discussing the feasibility of establishing whether or not it is a simulation, and do this from within the universe. That is the very definition of self-referential.

by lutusp 13y ago

DerpDerpDerp 13y ago

Your reversing of the relationship between the Halting Problem and the Incompleteness theorem (based on the quote you provided) makes me doubt the rest of your conclusions. It's not that the Incompleteness Theorem tells us about the Halting Problem, but rather, that the Halting Problem tells us about the Incompleteness theorem. Also, we have no reason to think that the universe satisfies some of the requirements of the Incompleteness Theorem (or even things like the Halting Problem). Both require some kind of unbounded or self-referential behavior, which we might not have in the universe.

lutusp 13y ago
> Your reversing of the relationship between the Halting Problem and the Incompleteness theorem ... Here's what I said: "Even something as trivial as the Turing halting problem is known to be insoluble because of its connection to the incompleteness theorems." That doesn't reverse the relationship between the two, it identifies that there is a relationship. That's not controversial. > It's not that the Incompleteness Theorem tells us about the Halting Problem, but rather, that the Halting Problem tells us about the Incompleteness theorem. The Turing halting problem and the incompleteness theorems are related. Without the GIT, we would not be aware that the Turing halting problem is insoluble, a statement that can be made about any number of similar issues. > Also, we have no reason to think that the universe satisfies some of the requirements of the Incompleteness Theorem (or even things like the Halting Problem). You mean, apart from the fact that the question is whether the universe is a vast computer simulation, by definition subject to the halting problem, which lacks a solution because of the GIT? > Both require some kind of unbounded or self-referential behavior, which we might not have in the universe. We're not discussing the universe's behavior, we're discussing the feasibility of establishing whether or not it is a simulation, and do this from within the universe. That is the very definition of self-referential.