This is a real classic. I’ve requested the book, but for now here are some excerpts from part 1.
Till then I propose to retain the time-honoured technical term
‘proof’ for a thought-experiment or quasi-experiment which suggests
a decomposition of the original conjecture into subconjectures or lemmas, thus embedding it in a possibly quite distant body of knowledge. p. 10
TEACHER: ‘Plausible’ or even ‘trivially true’ propositions are
usually soon refuted: sophisticated, implausible conjectures, matured in
criticism, might hit on the truth.p. 14
If, for the time being, you agree to my earlierp roposalt o use the word ‘proof’ for a ‘thought-experiment which leads to decompositiono f the originalc onjecturei nto subconjecture’s, insteado f usingi t in the senseo f a ‘ guaranteoe f certain truth’, you need not draw this conclusion. My proof certainly provedE uler’sc onjecturein the firsts ense,b ut not necessariliyn the second. You arei nterestedo nly in proofsw hich ‘prove’ what they have set out to prove. I am interestedin proofse ven if they do not
accomplishth eiri ntendedt ask. p. 15
It turned out that the extension of the concept wasn’t at all obvious: definitionas re
frequentlyp roposeda nd argueda bout when counterexamplesm erge. p. 18
ALPHA: You are a real old-fashionedT ory! You blame the
wickednesso f anarchistfso r the spoilingo f your ‘order’ and ‘harmony’,
andy ou ‘solve’ the difficultiebsy verbalr ecommendations. p. 22
Excuse the strange letter order, I’m pasting from a pdf and lack the time to fix it.