https://plato.stanford.edu/archIves/win2016/entries/church-turing/
“The Church-Turing thesis concerns the notion of an effective or mechanical method in logic and mathematics. ‘Effective’ and its synonym ‘mechanical’ are terms of art in these disciplines: they do not carry their everyday meaning. A method, or procedure, M, for achieving some desired result is called ‘effective’ or ‘mechanical’ just in case
- M is set out in terms of a finite number of exact instructions (each instruction being expressed by means of a finite number of symbols);
- M will, if carried out without error, produce the desired result in a finite number of steps;
- M can (in practice or in principle) be carried out by a human being unaided by any machinery save paper and pencil;
- M demands no insight or ingenuity on the part of the human being carrying it out.
Church’s thesis: A function of positive integers is effectively calculable only if recursive. The reverse implication, that every recursive function of positive integers is effectively calculable, is commonly referred to as the converse of Church’s thesis…If attention is restricted to functions of positive integers then Church’s thesis and Turing’s thesis are equivalent, in view of the previously mentioned results by Church, Kleene and Turing.”
QSOL Application:
ON COMPUTABLE NUMBERS, WITH AN APPLICATION TO METRE MEASUREMENT VALUE: A CORRECTION.
SYSTEMS OF LOGIC BASED ON ORDINALS – NOT CARDINALS
- QSOL is set out in terms of a finite number of exact solar light stream realignment measurement instructions (each instruction being expressed by means of a finite number of symbols);
- QSOL will, if carried out without error, produce the desired realignment results in a finite number of steps;
- QSOL can (in practice or in principle) be carried out by a human being unaided by any machinery save paper and pencil;
- QSOL demands no insight or ingenuity on the part of the human being carrying it out. More information here: BP26.