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, 21:28, 9 December 2008→Option 1 : Less General
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The umpire measure is defined at the level of truth functions, but can also be understood in terms of its implied judgments at the syntactic level. Interpreted this way, <math>\Upsilon_1\!</math> recognizes theorems of the propositional calculus over <math>[x, y],\!</math> giving a score of "1" to tautologies and a score of "0" to everything else, regarding all contingent statements as no better than falsehoods.
====Option 2 : More General====
====Option 2 : More General====
