Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version of the Church–Turing Thesis is...

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version of the Church–Turing Thesis is unaffected by SAD computation.

SAD Computability 1.1

The basic idea of SAD computation

Avoiding supertasks

Davies's model of SAD computation

Hogarth's model of SAD computation

Generalizing SAD computers

Physical Computability 2.1

The Physical Church–Turing Thesis

Deterministic barriers to physical computation

Probabilistic barriers to physical computation

Effective Computability 3.1

The Effective Church–Turing Thesis

Hogarth's challenge to the Effective Church–Turing Thesis

Arguing from SAD computability is a non-sequitur

SAD computability is built from finitary computability

Concluding Remarks