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The Treatment of Ordinary Quantification in English Proper

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(1)

2010-4.indd 150

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(2)

∀ x ( x )( . . . )

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(3)

<α β > <α β γ >

<α β > <α β γ >

X N

N

∀ x ( x ) . . . ∀ x ( x ) . . .

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(4)

< >

S →

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(5)

< >

S < >

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(6)

Q

x x

x

N N

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(7)

∀ x ( x )∃ y ( y ) ( x, y ) ∃ y ( y )∀ x ( x ) ( x, y )

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(8)

= ∅

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(9)

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(10)

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(11)

ζ ( s, o )

∀ x [∃ yζ ( x, y ) → ∃ zζ ( z, x )]

s

· x = y sx = sy

x + sy = s ( x + y ) x · sy = xy + x

αp

n

β ∈ L n > 4 , αp

n+1

β ∈ L

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