Introduction - What Church's thesis is and what it is not (relative to the principles of informal computability theory, especially those of Ebbinghaus)

4.1 Four related theses
Prologue and Preliminaries: Doublets, Dominoes, reductions, metamathematics as empirical theory and naturalism
4.1.1 Post's thesis (Did Post anticipate Church's thesis?)
4.1.2 Turing's definition/thesis
4.1.3 Gödel's thesis (Did Gödel anticipate Church's thesis?)
4.1.4 Gandy's thesis
Epilogue: Church's thesis and Artificial Intelligence

4.2 Church's definition /thesis and its epistemological status
4.2.1 Church's original formulation
4.2.2 The so-called evidence     Arguments for the thesis     The standard argument for the converse     The argument from Martin-Löf randomness
4.2.3 Definition, thesis, hypothesis, or…?     The early debate     Further comments on the epistemological status     Mathematical theses     Comparisons and analogies     Is the thesis unprovable? Is it refutable     A brief resumé

4.3         Arguments against the converse of Church's thesis
4.3.1 Algorithmicity versus constructivity     Péter's vicious circle argument and Heyting's counter-examples     Excentric counter-examples     Extensional recursiveness versus intensional computability
4.3.2 Algorithmicity versus primitive recursiveness
4.3.3 Algorithmicity versus feasibility
4.3.4 The argument from unknown computational complexity

4.4         Arguments against Church's thesis
Preliminaries: Relative computability, computability versus chance
4.4.1 Kalmár's so-called implausibility argument
4.4.2 Bowie's argument from random number generators
4.4.3 Thomas' argument
4.4.4 Bringsjord's "narrational case"
4.4.5 The argument from machine

Epilogue: Conway's Life