10 definitions
Atomic proposition (n.) turned out not to be independent, as the Tractatus assumed: a man 6 ft tall is therefore not 7 ft.
A Calculus (n.) is all right as long as one can play; contradiction appears only in prose stepping outside it.
A Consistency proof (n.) cannot lift the fog: if unclear about mathematics no proof helps, and if clear the question cannot arise.
Contradiction (n.) haunts mathematicians like a nightmare, though it is no worse than a tautology.
A Game (n.) can be defined by rules, but never the game; permission and prohibition fix only one game among many.
A Hidden contradiction (n.) is imagined like tuberculosis, unsuspected until it kills; but a contradiction is one only when it arises.
Identity (n.) written as 'a = a' is rubbish however often written; schoolmasters rightly teach 2 + 2 = 4, not 2 = 2.
Metamathematics (n.) as Hilbert pursued it is only mathematics, another calculus, not a metagame.
A Pawn (n.) is the sum of the rules for its moves, as rules define the logic of a word.
Syntax (n.) cannot be justified, and there is no justification for a game, unlike Newton's laws, which experiments verify.