The Myth of Hypercomputation

[FOM] The Myth of Hypercomputation

One argument against hypercomputation
is that even if someone hands me a hypercomputer (that solves the halting
problem, say), I cannot verify that it really works as advertised from a
finite set of finite measurements. Without the ability to make a finite
verification, I can never really "know" that the hypercomputer is "really
solving" the halting problem.

This is good stuff. I'll have to look at it later.



Also:

Héctor Zenil & Francisco Hernández-Quiroz - How might the human mind be computationally more powerful than Turing machines?

Finally, there are several arguments by Bringsjord.

I get the impression that all these arguments for hypercomputing minds are made in order to justify "romantic intuitions", i.e. they are not exploratory discoveries, which is what you would expect from unbiased scientists. I confess that I suffer from the symmetrical problem: always trying to justify my computationalist intuitions. (never mind that I may actually be a dualist in philosophy of mind)

reasoning about approximations in symbolic AI

Frank van Harmelen seems like an interesting person

"Groot, Ten Heije, van Harmelen - Towards a Structured Analysis of Approximate Problem Solving: a Case Study in Classification

The use of approximation as a method for dealing with complex problems is a fundamental research issue in Knowledge Representation. Using approximation in symbolic AI is not straightforward. Since many systems use some form of logic as representation, there is no obvious metric that tells us `how far' an approximate solution is from the correct solution.

This is an issue in the philosophy of science, in particular the issue of how reliable simulations are: how much will errors spread? In terms of inference, I think of a simulation as a large chunk full of deductions with a few (false) auxiliary assumptions thrown in. Ideally, we would use the false assumptions as little as possible, but the reason we make those assumptions in the first place is because analytical solutions are intractable.