Computationalism is the view that human minds are essentially computing machines. Stronger forms of the position claim that anything computable with the mind is possible with some equally powerful theoretical computer (typically idealized in the form of a Turing machine). In other words, for each human mind, there is a Turing machine isomorphic to that mind. The Church-Turing thesis is one such position, claiming that everything that is calculable is calculable with a Turing machine.
    Hypercomputationalism is the contrary position that humans are capable of computation beyond the capabilities of a Turing machine. For instance, a human mind may solve a problem in a finite period of time which would take a Turing machine an infinite amount of time.
    This is a PDF of an article arguing for hypercomputationalism.
    I'm particularly interested in discussing the merits and flaws of the argument articulated in this article, though I also welcome any general thoughts on the issue of computationalism vs. hypercomputationalism. The article isn't too long, but it's fairly dense and highly technical.

    With regard to the article's argument, I think the fatal flaw is in its third premise. I think it's unlikely that humans will always be able to find ∑(n + 1) when they solve ∑(n). At the very least, I have little reason to believe that is the case except for the optimistic claims of the researchers writing the article. Furthermore, I'm unconvinced that even if humans can employ a bootstrapping technique without limit that a sufficiently complex Turing machine couldn't be constructed to mimic such techniques. For those reasons, I find the argument unconvincing.
    I am inclined intuitively to accept the Church-Turing thesis. And since I have no real reason to suspect any physical or logical law-breaking properties of the human brain, I intuit that the human mind is probably just a very, very complex Turing machine (or isomorphic to one). I suppose Douglas Hoffstadter's Gödel, Escher, Bach and I Am a Strange Loop have had a significant influence on my formation of that opinion.

As far as solving a problem is concerned, you can always make a machine that is at the very least on-par with the human mind.

However, when it comes to stuff other than that, you cannot (at least not anytime soon) create a computer/machine that can do certain things that a human mind can do (such as rationalization, reasoning, etc.)

Well i can't open the article I just get an error that says "not a valid pdf. " I think it's because I'm on my phone though. Anyways I just read an article the other day about some researchers who made a breakthrough in quantum computing. We are still a ways away from ditching silicon completely buy we are getting closer. I do agree with the church-turing idea that any solvable function can be solved by a turing machine. However, I'm not sure that all functions can be solved in a reasonable amount of time. Ie: some would take centuries. With quantum computing, things like cracking RSA encryption, which is considered impossible to crack by today's computers, could be broken in a few seconds using a quantum computer effectively squashing the time problem.

    That's the very assertion under debate, and it's very controversial. Personally, I'm inclined to agree, but there are tasks solvable by humans for which no Turing machine is known to be able to solve as of yet.
    Quantum computers, if I recall correctly, are no more computationally powerful than Turing machines. They're just much faster at certain tasks. When we say that RSA encryption is impossible to crack, we aren't saying that the problem is uncomputable. We're merely saying that the problem is intractable.
    So the issue at hand is not tractability but solvability. I.e., can a computer or a human mind solve a given problem in any finite period of time, given finite power and resources?

What qualities would you put forward that a Turning Machine cannot do that a human mind can?

EDIT: Actually, you're not arguing for the hypercomputationalism premise. Good on you. Is anyone?

EDIT2: Step (2a) is actually where shit gets really difficult. How do you classify a chaotic automaton? The simple answer is you don't. You just run it. It's the halting problem defined.

I believe in computationalism.

If you want to know more, read Hofstadter's Gödel, Escher, Bach. Other than that, I don't know much of the arguments for or against yet.

GEB is pretty thick reading. It's kind of hard to respond to a post that just lists a book as its reasoning. Is there some specific reason within GEB that made you believe as you do, or is it just a general feeling? It seems kind of difficult to say you believe either one without knowing any arguments for or against them.

The human brain, on a large scale, is made of tissue, comprised of cells, which are a bunch of molecules interacting with each other, right? On the smallest scale, the brain is simply matter particles interacting and creating the illusion of reality. A sufficiently powerful Turing machine could simulate all these particles and their actions, effectively simulating a human brain. Now that you have a simulation of the brain, it will respond very much the same as a physical one to input assuming determinism.
So, to sum, a sufficiently powerful Turing machine can have the same capabilities as a brain.

I have not read GEB, this is just my perhaps flawed reasoning.

    That is an excellent argument, and I have found it compelling enough to take the side of computationalism. However, there is a flaw. Since as of yet physicists have been unable to derive and empirically confirm a computable theory of everything, we don't actually know that a Turing machine could simulate all the physical events in the brain.
    In other words, your argument rests on the computability of the universe, which could be a harder problem. The physics of the universe could itself be hypercomputational in nature, in which case there's no guarantee that human minds are computable through brain simulation. N.B. even if physics is uncomputable, the human mind may still be. It's conceivable that one wouldn't need to simulate the entire brain in order to solve the same problems a mind can.
    I can't speak from authority on either issue, but intuitively and based on reading, I tentatively suppose that both the universe and the mind are computable.

Here's an excellent link on an argument that will eventually emerge in this discussion sooner or later


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