5 ms·

It could also be the case the human mind transcends computation, i.e. a transfinite, yet limited, halting oracle, and as such is logically impossible to reduce

by yters 6y ago

It could also be the case the human mind transcends computation, i.e. a transfinite, yet limited, halting oracle, and as such is logically impossible to reduce to a Turing machine. To insist this is not the case merely based on materialism is begging the question. It is a very simple and formally rigorous point, but gets obscure by high fallutin philosophical language like "reductionism".

Thiez 6y ago
Is there any reason to believe that the human mind has these amazing computation-transcending powers? What would be the mechanism behind it? Unless there is evidence for these suggested special powers of the human mind, it looks to me like another instance of Russell's teapot.
- yters 6y ago
  Programming is one of the most obvious. Mathematics is another. Human success in both is easiest to explain if we are halting oracles of some variety, albeit not perfect, but still transfinite.
  - Thiez 6y ago
    So you don't have any concrete examples, just broad topics that you have a vague feeling about? I guess I am not truly human because I can't solve the halting problem in the general case. I'm probably also subject to Gödel's incompleteness theorem.
    - yters 6y ago
      Programming is concrete. Programmers have to reliably determine if their code will halt or not to make functioning software. Mathematics is concrete and mathematicians have to reliably create new consistent axioms to expand our mathematical knowledge. Notice that the fact you too are subject to Gödel's theorem does not entail you are a Turing machine. There is an oracle hierarchy where each level has its own halting problem and a higher level oracle. This does not cause the hierarchy to collapse. So even though humans have their own halting problem does not entail they are reducible to Turing machines. It is a subtle point of logic, but one I see many people miss, even philosophers and computer scientists who attempt to refute oracle arguments.

by yters 6y ago

Thiez 6y ago

Is there any reason to believe that the human mind has these amazing computation-transcending powers? What would be the mechanism behind it? Unless there is evidence for these suggested special powers of the human mind, it looks to me like another instance of Russell's teapot.

yters 6y ago
Programming is one of the most obvious. Mathematics is another. Human success in both is easiest to explain if we are halting oracles of some variety, albeit not perfect, but still transfinite.
- Thiez 6y ago
  So you don't have any concrete examples, just broad topics that you have a vague feeling about? I guess I am not truly human because I can't solve the halting problem in the general case. I'm probably also subject to Gödel's incompleteness theorem.
  - yters 6y ago
    Programming is concrete. Programmers have to reliably determine if their code will halt or not to make functioning software. Mathematics is concrete and mathematicians have to reliably create new consistent axioms to expand our mathematical knowledge. Notice that the fact you too are subject to Gödel's theorem does not entail you are a Turing machine. There is an oracle hierarchy where each level has its own halting problem and a higher level oracle. This does not cause the hierarchy to collapse. So even though humans have their own halting problem does not entail they are reducible to Turing machines. It is a subtle point of logic, but one I see many people miss, even philosophers and computer scientists who attempt to refute oracle arguments.