5 ms·

The actual scenario he presents with the physical boxes is not consistent, as the truth value of the label on the red box cannot be decided. i.e. Its value is t

The actual scenario he presents with the physical boxes is not consistent, as the truth value of the label on the red box cannot be decided. i.e. Its value is the opposite of its value. This is a troll question.

bottled_poe 11y ago
Honestly, on reading that entire post I'm convinced the writer doesn't know what he is talking about. He doesn't even mention the term paradox.
- chii 11y ago
  Because it's not a paradox.
  - bottled_poe 11y ago
    That is untrue.
phaemon 11y ago
Of course it's consistent: it actually exists. There is no paradox. It's clearly obvious that you can choose either box to put the treasure in. It's also clearly obvious that sticking labels on the boxes doesn't alter that, no matter what they say. You just got fooled by the puzzle. It's not a big deal.
- bottled_poe 11y ago
  Sorry for assuming the problem would adhere to standard expectations. By breaking the typical rules of a logic puzzle, the interesting aspects are replaced with groan-worthy ones.
  - TuringTest 11y ago
    That's true only if your interest is limited to the mechanical rules of logic derivation. For those of us interested in the relations between symbols and meaning, the puzzle is fascinating. > Sorry for assuming the problem would adhere to standard expectations. That was the solution to the puzzle - realizing that this was an invalid assumption, given the formulation.
TuringTest 11y ago
Actually, it's a very simple practical counterexample to the "law of excluded middle" logic axiom. [1] The situation described in the puzzle did physically exist when the photo was taken, yet the truth value of the first label is neither true nor false. It that's a troll, then trolls like this provide food for thought. [1] https://en.wikipedia.org/wiki/Law_of_excluded_middle https://en.wikipedia.org/wiki/Law_of_excluded_middle
- JadeNB 11y ago
  I think that this is not the correct interpretation of the law of the excluded middle. It says that `P or not-P`; that is, that P is true or not-P is true. That's different to saying that P is true or P is false; confusing "not-P is true" with "P is false" is exactly the distinction that logics, such as constructive logic, that avoid LEM try to avoid. (At least for me, it helps to think in terms of proveability, not of truth, which is, I think, almost what constructive logic does; there is a difference between saying that "P is not proveable" and "not-P is proveable".)
  - TuringTest 11y ago
    I keep telling myself that I should learn more about constructive logic, as my own intuitions tend to it. I get that in such logic you can't deduce "P is false" directly from "Not-P is true", and you have to build an explicit derivation for the former?
    - JadeNB 11y ago
      > I get that in such logic you can't deduce "P is false" directly from "Not-P is true" It's actually the other way around; if not-P is true, then P is false, but not conversely. (The computer-flavoured example that comes to mind is that it is not possible to decide equality of functions (so `P or not-P` fails), but any two functions either are (`P` is true) or are not (`P` is false) equal. Again, this confusion between truth and decideability is, I think, not quite rigorous, but it gets at the essential idea.) > I keep telling myself that I should learn more about constructive logic, as my own intuitions tend to it. Indeed, Brouwer's precursor of constructive logic was called "intuitionistic logic" precisely because he felt that it better captured an intuitive, rather than formalist, approach to reasoning. (I'm not sure I agree ….)

bottled_poe 11y ago

Honestly, on reading that entire post I'm convinced the writer doesn't know what he is talking about. He doesn't even mention the term paradox.

chii 11y ago
Because it's not a paradox.
- bottled_poe 11y ago
  That is untrue.

phaemon 11y ago

Of course it's consistent: it actually exists. There is no paradox. It's clearly obvious that you can choose either box to put the treasure in. It's also clearly obvious that sticking labels on the boxes doesn't alter that, no matter what they say. You just got fooled by the puzzle. It's not a big deal.

bottled_poe 11y ago
Sorry for assuming the problem would adhere to standard expectations. By breaking the typical rules of a logic puzzle, the interesting aspects are replaced with groan-worthy ones.
- TuringTest 11y ago
  That's true only if your interest is limited to the mechanical rules of logic derivation. For those of us interested in the relations between symbols and meaning, the puzzle is fascinating. > Sorry for assuming the problem would adhere to standard expectations. That was the solution to the puzzle - realizing that this was an invalid assumption, given the formulation.

TuringTest 11y ago

Actually, it's a very simple practical counterexample to the "law of excluded middle" logic axiom. [1] The situation described in the puzzle did physically exist when the photo was taken, yet the truth value of the first label is neither true nor false. It that's a troll, then trolls like this provide food for thought. [1] https://en.wikipedia.org/wiki/Law_of_excluded_middle https://en.wikipedia.org/wiki/Law_of_excluded_middle

JadeNB 11y ago
I think that this is not the correct interpretation of the law of the excluded middle. It says that `P or not-P`; that is, that P is true or not-P is true. That's different to saying that P is true or P is false; confusing "not-P is true" with "P is false" is exactly the distinction that logics, such as constructive logic, that avoid LEM try to avoid. (At least for me, it helps to think in terms of proveability, not of truth, which is, I think, almost what constructive logic does; there is a difference between saying that "P is not proveable" and "not-P is proveable".)
- TuringTest 11y ago
  I keep telling myself that I should learn more about constructive logic, as my own intuitions tend to it. I get that in such logic you can't deduce "P is false" directly from "Not-P is true", and you have to build an explicit derivation for the former?
  - JadeNB 11y ago
    > I get that in such logic you can't deduce "P is false" directly from "Not-P is true" It's actually the other way around; if not-P is true, then P is false, but not conversely. (The computer-flavoured example that comes to mind is that it is not possible to decide equality of functions (so `P or not-P` fails), but any two functions either are (`P` is true) or are not (`P` is false) equal. Again, this confusion between truth and decideability is, I think, not quite rigorous, but it gets at the essential idea.) > I keep telling myself that I should learn more about constructive logic, as my own intuitions tend to it. Indeed, Brouwer's precursor of constructive logic was called "intuitionistic logic" precisely because he felt that it better captured an intuitive, rather than formalist, approach to reasoning. (I'm not sure I agree ….)