[FOM] Counterfactuals in relative computability theory

[joeshipman at aol.com]

It could be false if someone can describe an effective procedure taking a natural number as input, that you agree that a human could indeed carry out, which always terminates in principle, and which gives a result that, interpreted as a function, has a Turing degree other than 0, and is always the same function (up to errors whose probability can be effectively bounded below any pre-specified epsilon). 

The procedure will not be an algorithm, but rather a set of instructions, written in English, that presupposes that you have an abundance of raw materials and time, but which requires you only to be able to follow the instructions, and does not require any kind of intuition or insight or contingency in how you carry the instructions out.

-- JS


-----Original Message-----
From: W.Taylor <W.Taylor at math.canterbury.ac.nz>
To: fom <fom at cs.nyu.edu>
Sent: Fri, Aug 12, 2016 3:15 pm
Subject: Re: [FOM] Counterfactuals in relative computability theory

Suddenly I am at sea.

> you only mean them to be denials  of the
> Church-Turing thesis or things implying that denial.

Obviously the above presupposes that CTT is something that is
either true or false.   I had assumed it was merely a convention
or definition of "computable" (natural-domained-)function.

Can someone please enlighten us as to how it could be false?

-- Bill Taylor


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