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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 predicatelogical atoms. We’ll use
Fx
,
Gx
,
etc.
, instead.
φ(a
1
)
,
f(a
2
)
Closed monadic predicatelogical 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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 Fall '06
 FITELSON

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