keynes_notation - Keynesian Logical and Probabilistic...

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Keynesian Logical and Probabilistic Notation 09/14/07 Branden Fitelson Keynes uses notation for logical and probabilistic expressions that will be foreign to most modern read- ers. The following table contains some expressions from Keynes’s text, along with our modern equivalent: Keynesian Notation Modern Meaning and Notation φ(x) , f(x) Open monadic predicate-logical atoms. We’ll use Fx , Gx , etc. , instead. φ(a 1 ) , f(a 2 ) Closed monadic predicate-logical atoms. We’ll use Fa , Gb , etc. , instead. g(φ,f) Simple monadic universal claim. We’ll use ( x)(Fx Gx) , etc. , instead. g(φ 1 φ 2 ,f) Universal claim with conjunctive antecedent. ( x)[(F 1 x F 2 x) Gx] . g(φ,f 1 f 2 ) Universal claim with conjunctive consequent. ( x)[Fx (G 1 x G 2 x)] . A a 1 ,...,a n (φ) Conjunction of n closed monadic atoms. We’ll use Fa 1 ··· Fa n , instead. A a 1 ,...,a n (φ) Assertion that, among n objects, at least one of them has F and at least one of them lacks
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