If we are a TM computation (which is the standard reductionist explanation), we are vulnerable to the halting problem (which he also argue we can solve), and if we are a formal system of some kind (also standard, although maybe not quite so commonly said), Godel etc applies.
(I was using Godelian in the broader sense, which includes Halting-esque problems.).
I would argue strenuously against the idea that we resemble a formal system at all. Our cells act like a network of noisy differential equations that with enough training can approximate some of its outputs to resemble those of mathematically defined systems—AKA, what you do once you have learned math.
We also aren’t turing machines. Not in the sense that we aren’t turing complete or capable of running the steps that a turing machine would do, but in the sense that we, again, are an electrochemical system that does a lot of things natively without resorting to much in the way of turing-style computation. A network grows that becomes able to do some task.
We are not stuck in the formal system or the computation, we are approximating it via learned behavior and when we hit a wall in the formal system or the computation we stop it and say ‘well that doesn’t work’. That deosn’t mean we transcend the issues, it means that we go do something else.
If we are a TM computation (which is the standard reductionist explanation), we are vulnerable to the halting problem (which he also argue we can solve), and if we are a formal system of some kind (also standard, although maybe not quite so commonly said), Godel etc applies.
(I was using Godelian in the broader sense, which includes Halting-esque problems.).
I would argue strenuously against the idea that we resemble a formal system at all. Our cells act like a network of noisy differential equations that with enough training can approximate some of its outputs to resemble those of mathematically defined systems—AKA, what you do once you have learned math.
We also aren’t turing machines. Not in the sense that we aren’t turing complete or capable of running the steps that a turing machine would do, but in the sense that we, again, are an electrochemical system that does a lot of things natively without resorting to much in the way of turing-style computation. A network grows that becomes able to do some task.
We are not stuck in the formal system or the computation, we are approximating it via learned behavior and when we hit a wall in the formal system or the computation we stop it and say ‘well that doesn’t work’. That deosn’t mean we transcend the issues, it means that we go do something else.