Re:Computing the Uncomputable
by daralthus on Wednesday April 06, 2016 @08:25AM
(#11438270)
This:
Perhaps it is fair to say that “finite” does not mean what we have always thought it to mean. What have we always thought it to mean? I used to think that I knew what I had always thought it to mean, but I no longer think so.
If we go down this road, Hamkins’ result takes on a different significance. It says that any subjectivity in the notion of ‘natural number’ may also infect what it means for a Turing machine to halt, and what function a Turing machine computes when it does halt.
Is beautiful. It seems like another proof for a leaky abstraction and incomepleteness.
We have to forget finite or admit that it has bounds on what we can explore with it, as it already defines our model.
Perhaps it is fair to say that “finite” does not mean what we have always thought it to mean. What have we always thought it to mean? I used to think that I knew what I had always thought it to mean, but I no longer think so.
If we go down this road, Hamkins’ result takes on a different significance. It says that any subjectivity in the notion of ‘natural number’ may also infect what it means for a Turing machine to halt, and what function a Turing machine computes when it does halt.
Is beautiful. It seems like another proof for a leaky abstraction and incomepleteness.
We have to forget finite or admit that it has bounds on what we can explore with it, as it already defines our model.