Note: At 27:00, I had to make a cut because of my faulty internet connection. If it is not clear why an oracle for Pi^0_1 truth cannot be assumed at the beginning of the argument, that is because this assumption trivially implies the conclusion that one is arguing for (that the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any finite machine). This conversation is centred around two academic papers published by Professor Koellner in The Journal of Philosophy in 2018. They are: (a) On the Question of Whether the Mind Can Be Mechanized, I: From Gödel to Penrose (b) On the Question of Whether the Mind Can Be Mechanized II: Penrose's New Argument Make sure to check them out! Conversation outline: 00:00 What are the Incompleteness Theorems? 01:59 Why are Gödel’s results relevant for discussions concerning the mind? 03:28 Connections between Turing Machines and Formal Systems 04:20 When we talk about whether the mind can be mechanized or not, what do we mean? 06:56 Should Cognitive Scientists (or Philosophers of Mind) be interested in this discussion? 09:45 The First Generation of Arguments against The Prospects of Mechanizing the Mind 19:52 Three Versions of The Mechanistic Thesis 21:55 What makes Penrose’s New Argument harder to evaluate in theory EA+T? 22:56 Penrose’s Formulation of The Argument (Quote from his Book) 27:49 What are the explicit assumptions behind Penrose’s New Argument? 32:14 What are the indeterminate statements that Penrose uses in the argument? 36:10 Do you think we’ll ever have an adequate formal theory of type-free truth which settles Gödel’s First Disjunct (the one targeted by Penrose)? 37:18 Do you think your opponent would accept bringing the key notions of relative provability, absolute provability and truth in the setting of effectively formalized theories? 42:25 Why do you think Penrose does not abandon his New Argument, despite resistance from mathematical logicians? 44:35 Unlike Lucas or Penrose, some authors such as Hofstadter use Gödel’s results to illuminate the workings of the mind. Do you think the Incompleteness Theorems have anything worthwhile to say here? Enjoy!
There is an issue in the notion of the human mind as an 'idealized finite machine', as you can get a human to just output a random sequence of digits, and the sequence will eventually be different than that of any Turing machine. The proper system also has an idealized random-number source, which is a complexity source exceeding any Turing machine, because the complexity of a random sequence goes to infinity as the length goes to infinity.
What would your answear be to someone that would argue that the human mind is itself an idealized finite machine that is only complex enough to grasp the idea of infinity but, if it actually goes far enough it will not be able to practically go one step further, same as the argument against AI counciousness. Similarily, we can imagine a machine that could intuitively grasp infinity but it won't be able to go forever, it would appear to be like the human mind. I actually believe humans are councious and machines aren't, but it's useful to be skeptical so we don't just make unbased asumptions.
@@projecttheosis4539 You aren't aware of what these idealizations mean. The human mind can generate a RANDOM SEQUENCE of digits indefinitely far, you can do this by counting heartbeats with your eyes closed and recording whether the time the after-image fades is an even or odd number of heartbeats. Do this n times, you get n bits of entropy, which can only be generated by a Turing machine of length n, no shorter. You can do it indefinitely, so you get an infinite random sequence, so QED, you are "more" than a Turing machine. But so is a physical computer! A computer can look at random memory glitches, or some random input, to generate entropy. The random numbers cannot be generated by Turing machine. The proper computational model is therefore NOT Turing machines, but Turing machines PLUS a potentially infinite random number source. This is a stronger model than pure Turing machines. This is the proper model for natural computers, and for the human mind.
You may be aware that Penrose writes about TM+ Randomness his his book (Shadows). He argues about this several times over making the distinction between Randomness and Pseudo-randomness. He argues that neither possibility affects his argument, but he doesn't really analyse Randomness. So I am not convinced that this part of his discussion works with such little basis. However I have not seen others analyse this aspect either.
@@roys4244 Interesting. No, I didn't know Penrose makes this distinction. His arguments are nonsense, and I won't read the book, I already know them from skimming his other books. They are false, and obviously so, and it's pretty heartbreaking that someone that intelligent would have ideas that stupid.
Note: At 27:00, I had to make a cut because of my faulty internet connection. If it is not clear why an oracle for Pi^0_1 truth cannot be assumed at the beginning of the argument, that is because this assumption trivially implies the conclusion that one is arguing for (that the mathematical outputs of the idealized human mind do not coincide with the mathematical outputs of any finite machine).
This conversation is centred around two academic papers published by Professor Koellner in The Journal of Philosophy in 2018. They are:
(a) On the Question of Whether the Mind Can Be Mechanized, I: From Gödel to Penrose
(b) On the Question of Whether the Mind Can Be Mechanized II: Penrose's New Argument
Make sure to check them out!
Conversation outline:
00:00 What are the Incompleteness Theorems?
01:59 Why are Gödel’s results relevant for discussions concerning the mind?
03:28 Connections between Turing Machines and Formal Systems
04:20 When we talk about whether the mind can be mechanized or not, what do we mean?
06:56 Should Cognitive Scientists (or Philosophers of Mind) be interested in this discussion?
09:45 The First Generation of Arguments against The Prospects of Mechanizing the Mind
19:52 Three Versions of The Mechanistic Thesis
21:55 What makes Penrose’s New Argument harder to evaluate in theory EA+T?
22:56 Penrose’s Formulation of The Argument (Quote from his Book)
27:49 What are the explicit assumptions behind Penrose’s New Argument?
32:14 What are the indeterminate statements that Penrose uses in the argument?
36:10 Do you think we’ll ever have an adequate formal theory of type-free truth which settles Gödel’s First Disjunct (the one targeted by Penrose)?
37:18 Do you think your opponent would accept bringing the key notions of relative provability, absolute provability and truth in the setting of effectively formalized theories?
42:25 Why do you think Penrose does not abandon his New Argument, despite resistance from mathematical logicians?
44:35 Unlike Lucas or Penrose, some authors such as Hofstadter use Gödel’s results to illuminate the workings of the mind. Do you think the Incompleteness Theorems have anything worthwhile to say here?
Enjoy!
This was the best episode so far!
Super!!!
There is an issue in the notion of the human mind as an 'idealized finite machine', as you can get a human to just output a random sequence of digits, and the sequence will eventually be different than that of any Turing machine. The proper system also has an idealized random-number source, which is a complexity source exceeding any Turing machine, because the complexity of a random sequence goes to infinity as the length goes to infinity.
What would your answear be to someone that would argue that the human mind is itself an idealized finite machine that is only complex enough to grasp the idea of infinity but, if it actually goes far enough it will not be able to practically go one step further, same as the argument against AI counciousness. Similarily, we can imagine a machine that could intuitively grasp infinity but it won't be able to go forever, it would appear to be like the human mind. I actually believe humans are councious and machines aren't, but it's useful to be skeptical so we don't just make unbased asumptions.
@@projecttheosis4539 You aren't aware of what these idealizations mean. The human mind can generate a RANDOM SEQUENCE of digits indefinitely far, you can do this by counting heartbeats with your eyes closed and recording whether the time the after-image fades is an even or odd number of heartbeats. Do this n times, you get n bits of entropy, which can only be generated by a Turing machine of length n, no shorter. You can do it indefinitely, so you get an infinite random sequence, so QED, you are "more" than a Turing machine.
But so is a physical computer! A computer can look at random memory glitches, or some random input, to generate entropy. The random numbers cannot be generated by Turing machine.
The proper computational model is therefore NOT Turing machines, but Turing machines PLUS a potentially infinite random number source. This is a stronger model than pure Turing machines.
This is the proper model for natural computers, and for the human mind.
You may be aware that Penrose writes about TM+ Randomness his his book (Shadows). He argues about this several times over making the distinction between Randomness and Pseudo-randomness. He argues that neither possibility affects his argument, but he doesn't really analyse Randomness. So I am not convinced that this part of his discussion works with such little basis. However I have not seen others analyse this aspect either.
@@roys4244 Interesting. No, I didn't know Penrose makes this distinction. His arguments are nonsense, and I won't read the book, I already know them from skimming his other books. They are false, and obviously so, and it's pretty heartbreaking that someone that intelligent would have ideas that stupid.