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1
1
φ φ
P P, Q Q, …
φ φ T2 φ
φ φ
T
T 3
T T
T 4
東京大学哲学研究室『論集』35号(2016年度)pp.77-90
2
5
T6
T
2
3
4
7
PA 8
3
9
LPA PA LPA+ PA
Tr φ LPA φ #φ
φ LPA LPA Tr( φ )←→φ
PA LPA LPA+
IND+ φ(0)& x(φ(x)→φ(x+1))→ xφ(x) φ LPA+
TB PA
LPA IND φ(0)& x(φ(x)→φ(x+1))→ xφ(x) φ
LPA TB− TB− TB
Tr( 0=1&5+7=12 )←→(Tr ( 0=1 )&Tr ( 5+7=12 )) TB−
~(T( 0=1 ) & T( ~0=1 ))
TB TB− TB10 TB
x(Sent(x&y) (Tr(x&y)←→Tr(x)&Tr(y)))
Sent(x)
x PA TB
TB TB− CT CT− CT LPA+
IND+ CT1–4 PA CT− PA
CT1–4 LPA IND
s t PA s t11 ~ &
x(t/v) x v t
PA
78 東京大学哲学研究室『論集』35号(2016年度)
2
5
T6
T
2
3
4
7
PA 8
3
9
LPA PA LPA+ PA
Tr φ LPA φ #φ
φ LPA LPA Tr( φ )←→φ
PA LPA LPA+
IND+ φ(0)& x(φ(x)→φ(x+1))→ xφ(x) φ LPA+
TB PA
LPA IND φ(0)& x(φ(x)→φ(x+1))→ xφ(x) φ
LPA TB− TB− TB
Tr( 0=1&5+7=12 )←→(Tr ( 0=1 )&Tr ( 5+7=12 )) TB−
~(T( 0=1 ) & T( ~0=1 ))
TB TB− TB10 TB
x(Sent(x&y) (Tr(x&y)←→Tr(x)&Tr(y)))
Sent(x)
x PA TB
TB TB− CT CT− CT LPA+
IND+ CT1–4 PA CT− PA
CT1–4 LPA IND
s t PA s t11 ~ &
x(t/v) x v t
PA
79保存性解釈に基づいた真理のデフレ主義批判について
4
CT1 s t(Tr( s=t )←→s =t )
CT2 x(Sent(~x)→(Tr(~x)←→~Tr(x)))
CT3 x y(Sent(x&y)→(Tr(x&y)←→Tr(x)&Tr(y))
CT4 v x(Sent( vx)→(Tr( vx)←→ tTr(x(t/v)))
CT1 CT2 CT3
CT412
CT CT−
CT CT− TB TB−
x(Sent(x&y) (T(x&y)←→T(x)&T(y)))
TB TB−
CT CT−
CT CT−
CT− IND LPA
CT IND+
CT− PA CT PA
T S T S S T
LS φ φ T T|–φ S S|–φ
CT− PA
LPA CT− PA13 CT− CT
Reflection Principle RP
CT
global reflection principle GRP 14
x(Sent(x)&ProvPA(x) Tr(x))
ProvPA(x) PA PA GRP PA
GRP 0=1 CT1
Sent( 0=1 ) PA ProvPA( 0=1 ) 0=1 PA
0 1 ~ProvPA( 0=1 ) PA
5
CT ~ProvPA( 0=1 ) LPA
~ProvPA( 0=1 ) PA CT
PA local
reflection principle LRP CT PA
ProvPA( 0=1 ) 0=1 15
ProvPA( φ ) φ
TB CT
TB CT Tr( Tr( 0=0 ) )
5+7=12
5+7=12 Tr( 0=1 )
Tr( 5+7=12 Tr( 0=1 ) )
16
CT
Friedman–Sheard FS 17 FS
FS1–4 NECCONEC PA IND+
Sent+(x) x LPA+ Sent(x)
Sent+(x)
FS1 s t(Tr( s=t )←→s =t )
FS2 x(Sent+ (~x)→(Tr(~x)←→~Tr(x)))
FS3 x y(Sent+ (x&y)→(Tr(x&y)←→Tr(x)&Tr(y))
FS4 v x(Sent+ ( vx)→(Tr( vx)←→ tTr(x(t/v)))
80 東京大学哲学研究室『論集』35号(2016年度)
4
CT1 s t(Tr( s=t )←→s =t )
CT2 x(Sent(~x)→(Tr(~x)←→~Tr(x)))
CT3 x y(Sent(x&y)→(Tr(x&y)←→Tr(x)&Tr(y))
CT4 v x(Sent( vx)→(Tr( vx)←→ tTr(x(t/v)))
CT1 CT2 CT3
CT412
CT CT−
CT CT− TB TB−
x(Sent(x&y) (T(x&y)←→T(x)&T(y)))
TB TB−
CT CT−
CT CT−
CT− IND LPA
CT IND+
CT− PA CT PA
T S T S S T
LS φ φ T T|–φ S S|–φ
CT− PA
LPA CT− PA13 CT− CT
Reflection Principle RP
CT
global reflection principle GRP 14
x(Sent(x)&ProvPA(x) Tr(x))
ProvPA(x) PA PA GRP PA
GRP 0=1 CT1
Sent( 0=1 ) PA ProvPA( 0=1 ) 0=1 PA
0 1 ~ProvPA( 0=1 ) PA
5
CT ~ProvPA( 0=1 ) LPA
~ProvPA( 0=1 ) PA CT
PA local
reflection principle LRP CT PA
ProvPA( 0=1 ) 0=1 15
ProvPA( φ ) φ
TB CT
TB CT Tr( Tr( 0=0 ) )
5+7=12
5+7=12 Tr( 0=1 )
Tr( 5+7=12 Tr( 0=1 ) )
16
CT
Friedman–Sheard FS 17 FS
FS1–4 NECCONEC PA IND+
Sent+(x) x LPA+ Sent(x)
Sent+(x)
FS1 s t(Tr( s=t )←→s =t )
FS2 x(Sent+ (~x)→(Tr(~x)←→~Tr(x)))
FS3 x y(Sent+ (x&y)→(Tr(x&y)←→Tr(x)&Tr(y))
FS4 v x(Sent+ ( vx)→(Tr( vx)←→ tTr(x(t/v)))
81保存性解釈に基づいた真理のデフレ主義批判について
6
NEC |–φ CONEC |– Tr( φ )
|–Tr( φ ) |–φ
FS1–4 LPA LPA+
18 NEC φ FS φ
φ CONEC φ
FS φ φ
φ φ
φ φ
NEC CONEC
FS CT FS NEC CONEC FS
FS1–4 LPA LPA+
19 FS
GRP+ 20
GRP+ x(Sent+(x)&ProvPA+(x) Tr(x))
GRP+ LPA+ PA+ PA IND+
GRP+ GRP PA+
FS ω 21 ω FS
PA NEC T
x(Sent+(~x)→(Tr(~x)→~Tr(x))) x y(Sent+(x&y)→(Tr(x&y)→Tr(x)&Tr(y)))
v x(Sent+ ( vx)→(Tr( vx)→ tTr(x(t/v)))) T ω 22
FS PA FS2–4 NEC
FS ω ω
FS 23
7
2 CT PA
24
25
CT
CT PA CT PA
CT
CT− CT PA CT−
IND+ IND
0
82 東京大学哲学研究室『論集』35号(2016年度)
6
NEC |–φ CONEC |– Tr( φ )
|–Tr( φ ) |–φ
FS1–4 LPA LPA+
18 NEC φ FS φ
φ CONEC φ
FS φ φ
φ φ
φ φ
NEC CONEC
FS CT FS NEC CONEC FS
FS1–4 LPA LPA+
19 FS
GRP+ 20
GRP+ x(Sent+(x)&ProvPA+(x) Tr(x))
GRP+ LPA+ PA+ PA IND+
GRP+ GRP PA+
FS ω 21 ω FS
PA NEC T
x(Sent+(~x)→(Tr(~x)→~Tr(x))) x y(Sent+(x&y)→(Tr(x&y)→Tr(x)&Tr(y)))