2JKNQUQRJ[ QH .CPIWCIG

Contents

1 Logic 1 6JG UVWF[ QH NQIKE

.QIKECN HQTO &GFWEVKXG CPF KPFWEVKXG TGCUQPKPI CPF CDFWEVKXG KPHGTGPEG %QPUKUVGPE[ XCNKFKV[ UQWPFPGUU CPF EQORNGVGPGUU 4KXCN EQPEGRVKQPU QH NQIKE

*KUVQT[ 6[RGU QH NQIKE

5[NNQIKUVKE NQIKE 2TQRQUKVKQPCN NQIKE UGPVGPVKCN NQIKE 2TGFKECVG NQIKE /QFCN NQIKE +PHQTOCN TGCUQPKPI /CVJGOCVKECN NQIKE 2JKNQUQRJKECN NQIKE %QORWVCVKQPCN NQIKE $KXCNGPEG CPF VJG NCY QH VJG GZENWFGF OKFFNG PQPENCUUKECN NQIKEU +U NQIKE GORKTKECN! +ORNKECVKQP UVTKEV QT OCVGTKCN! 6QNGTCVKPI VJG KORQUUKDNG 4GLGEVKQP QH NQIKECN VTWVJ

5GG CNUQ 0QVGU CPF TGHGTGPEGU $KDNKQITCRJ[ 'ZVGTPCN NKPMU

2 Sense and reference 16 /QVKXCVKQP HQT CPF FGXGNQROGPV QH VJG FKUVKPEVKQP 6GTOKPQNQI[

5GPUG CPF TGHGTGPEG 5KPP WPF $GFGWVWPI

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#P GZRTGUUKQPU TGNCVKQP VQ UGPUG QT TGHGTGPEG 5GPUG YKVJQWV TGHGTGPEG (TGIG CPF 4WUUGNN

2TQRQUKVKQPU CPF UGPUGU 5GPUGU CPF FGUETKRVKQPU

4GNCVKQP VQ EQPPQVCVKQP CPF FGPQVCVKQP 5GG CNUQ (QQVPQVGU 'ZVGTPCN NKPMU

3 On Denoting 22 6JG FGPQVKPI RJTCUG

4WUUGNNU EQPEGRV QH C FGPQVKPI RJTCUG 4GHGTGPEG VQ UQOGVJKPI VJCV FQGU PQV GZKUV 'RKUVGOQNQI[

6JG VJGQT[ QH FGUETKRVKQPU /CVJGOCVKECN FGUETKRVKQP +NNWUVTCVKQP

/GKPQPI 4GUQNXKPI VJG RTQDNGO QH PGICVKXG GZKUVGPVKCNU

5VCVGOGPVU CDQWV EQPEGRVU YJGTG VJG QDLGEV FQGUPV GZKUV #ODKIWKV[ (KEVKQPCN PCOGU

%TKVKEKUOU 4GHGTGPEGU 5QWTEGU 'ZVGTPCN NKPMU

4 Theory of descriptions 26 +PVTQFWEVKQP &GPKVG FGUETKRVKQPU +PFGPKVG FGUETKRVKQPU %TKVKEKUO QH 4WUUGNNU CPCN[UKU

2 ( 5VTCYUQP -GKVJ &QPPGNNCP 5CWN -TKRMG

5GG CNUQ 0QVGU 4GHGTGPEGU CPF HWTVJGT TGCFKPI

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'ZVGTPCN NKPMU 6GZV CPF KOCIG UQWTEGU EQPVTKDWVQTU CPF NKEGPUGU

6GZV +OCIGU %QPVGPV NKEGPUG

Chapter 1

Logic

6JKU CTVKENG KU CDQWV TGCUQPKPI CPF KVU UVWF[ (QT QVJGT WUGU UGG .QIKE FKUCODKIWCVKQP

Logic HTQO VJG #PEKGPV )TGGM MPHJLF=? KU VJG WUG CPF UVWF[ QH XCNKF TGCUQPKPI=?=? 6JG UVWF[ QH NQIKE HGCVWTGUOQUV RTQOKPGPVN[ KP VJG UWDLGEVU QH RJKNQUQRJ[ OCVJGOCVKEU CPF EQORWVGT UEKGPEG.QIKE YCU UVWFKGF KP UGXGTCN CPEKGPV EKXKNK\CVKQPU KPENWFKPI +PFKC=? %JKPC=? 2GTUKC CPF )TGGEG +P VJG 9GUV NQIKEYCU GUVCDNKUJGF CU C HQTOCN FKUEKRNKPG D[ #TKUVQVNG YJQ ICXG KV C HWPFCOGPVCN RNCEG KP RJKNQUQRJ[ 6JG UVWF[ QH NQIKEYCU RCTV QH VJG ENCUUKECN VTKXKWO YJKEJ CNUQ KPENWFGF ITCOOCT CPF TJGVQTKE .QIKE YCU HWTVJGT GZVGPFGF D[ #N(CTCDKYJQ ECVGIQTK\GF KV KPVQ VYQ UGRCTCVG ITQWRU KFGC CPF RTQQH .CVGT #XKEGPPC TGXKXGF VJG UVWF[ QH NQIKE CPF FGXGNQRGFTGNCVKQPUJKR DGVYGGP VGORQTCNKU CPF VJG KORNKECVKQP +P VJG 'CUV NQIKE YCU FGXGNQRGF D[ $WFFJKUVU CPF ,CKPU.QIKE KU QHVGP FKXKFGF KPVQ VJTGG RCTVU KPFWEVKXG TGCUQPKPI CDFWEVKXG TGCUQPKPI CPF FGFWEVKXG TGCUQPKPI

1.1 The study of logic

6JG EQPEGRV QH NQIKECN HQTO KU EGPVTCN VQ NQIKE KV DGKPI JGNF VJCV VJG XCNKFKV[ QH CP CTIWOGPV KU FGVGTOKPGF D[ KVU NQIKECNHQTO PQV D[ KVU EQPVGPV 6TCFKVKQPCN #TKUVQVGNKCP U[NNQIKUVKE NQIKE CPF OQFGTP U[ODQNKE NQIKE CTG GZCORNGU QH HQTOCNNQIKEU

Informal logic KU VJG UVWF[ QH PCVWTCN NCPIWCIG CTIWOGPVU 6JG UVWF[ QH HCNNCEKGU KU CP GURGEKCNN[ KORQTVCPV DTCPEJQH KPHQTOCN NQIKE 6JG FKCNQIWGU QH 2NCVQ=? CTG IQQF GZCORNGU QH KPHQTOCN NQIKE

Formal logic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

Symbolic logic KU VJG UVWF[ QH U[ODQNKE CDUVTCEVKQPU VJCV ECRVWTG VJG HQTOCN HGCVWTGU QH NQIKECN KPHGTGPEG=?=?5[ODQNKE NQIKE KU QHVGP FKXKFGF KPVQ VYQ DTCPEJGU RTQRQUKVKQPCN NQIKE CPF RTGFKECVG NQIKE

Mathematical logic KU CP GZVGPUKQP QH U[ODQNKE NQIKE KPVQ QVJGT CTGCU KP RCTVKEWNCT VQ VJG UVWF[ QH OQFGN VJGQT[RTQQH VJGQT[ UGV VJGQT[ CPF TGEWTUKQP VJGQT[

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1.1.1 Logical form

/CKP CTVKENG .QIKECN HQTO

.QIKE KU IGPGTCNN[ EQPUKFGTGF formal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

+P VJG VTCFKVKQPCN XKGY VJG HQTO QH VJG UGPVGPEG EQPUKUVU QH C UWDLGEV GI OCP RNWU C UKIP QH SWCPVKV[ CNNQT UQOG QT PQ VJG EQRWNC YJKEJ KU QH VJG HQTO KU QT KU PQV C RTGFKECVG GI OQTVCN 6JWU CNNOGP CTG OQTVCN 6JG NQIKECN EQPUVCPVU UWEJ CU CNN PQ CPF UQ QP RNWU UGPVGPVKCN EQPPGEVKXGU UWEJ CU CPF CPFQT YGTG ECNNGF U[PECVGIQTGOCVKE VGTOU HTQO VJG )TGGM LBUFHPSFJ VQ RTGFKECVG CPF TZO VQIGVJGT YKVJ 6JKUKU C ZGF UEJGOG YJGTG GCEJ LWFIOGPV JCU CP KFGPVKGF SWCPVKV[ CPF EQRWNC FGVGTOKPKPI VJG NQIKECN HQTO QH VJGUGPVGPEG

#EEQTFKPI VQ VJG OQFGTP XKGY VJG HWPFCOGPVCN HQTO QH C UKORNG UGPVGPEG KU IKXGP D[ C TGEWTUKXG UEJGOC KPXQNXKPINQIKECN EQPPGEVKXGU UWEJ CU C SWCPVKGT YKVJ KVU DQWPF XCTKCDNG YJKEJ CTG LQKPGF D[ LWZVCRQUKVKQP VQ QVJGT UGPVGPEGUYJKEJ KP VWTP OC[ JCXG NQIKECN UVTWEVWTG

6JG OQFGTP XKGY KU OQTG EQORNGZ UKPEG C UKPING LWFIGOGPV QH #TKUVQVNGU U[UVGO KPXQNXGU VYQ QT OQTG NQIKECNEQPPGEVKXGU (QT GZCORNG VJG UGPVGPEG #NN OGP CTG OQTVCN KPXQNXGU KP VGTO NQIKE VYQ PQPNQIKECN VGTOU KU COCP JGTG . CPF KU OQTVCN JGTG % VJG UGPVGPEG KU IKXGP D[ VJG LWFIGOGPV #/& +P RTGFKECVG NQIKE VJGUGPVGPEG KPXQNXGU VJG UCOG VYQ PQPNQIKECN EQPEGRVU JGTG CPCN[\GF CU m(x) CPF d(x) CPF VJG UGPVGPEG KU IKXGPD[ x.(m(x) d(x)) KPXQNXKPI VJG NQIKECN EQPPGEVKXGU HQT WPKXGTUCN SWCPVKECVKQP CPF KORNKECVKQP

$WV GSWCNN[ VJG OQFGTP XKGY KU OQTG RQYGTHWN /GFKGXCN NQIKEKCPU TGEQIPK\GF VJG RTQDNGO QH OWNVKRNG IGPGTCNKV[YJGTG #TKUVQVGNKCP NQIKE KU WPCDNG VQ UCVKUHCEVQTKN[ TGPFGT UWEJ UGPVGPEGU CU 5QOG IW[U JCXG CNN VJG NWEM DGECWUGDQVJ SWCPVKVKGU CNN CPF UQOG OC[ DG TGNGXCPV KP CP KPHGTGPEG DWV VJG ZGF UEJGOG VJCV #TKUVQVNG WUGF CNNQYUQPN[ QPG VQ IQXGTP VJG KPHGTGPEG ,WUV CU NKPIWKUVU TGEQIPK\G TGEWTUKXG UVTWEVWTG KP PCVWTCN NCPIWCIGU KV CRRGCTU VJCVNQIKE PGGFU TGEWTUKXG UVTWEVWTG

1.1.2 Deductive and inductive reasoning, and abductive inference

&GFWEVKXG TGCUQPKPI EQPEGTPU YJCV HQNNQYU PGEGUUCTKN[ HTQO IKXGP RTGOKUGU KH B VJGP C *QYGXGT KPFWEVKXG TGCUQPKPIVJG RTQEGUU QH FGTKXKPI C TGNKCDNG IGPGTCNK\CVKQP HTQO QDUGTXCVKQPUJCU UQOGVKOGU DGGP KPENWFGF KP VJG UVWF[ QH NQIKE

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

QDUGTXCVKQP CPF UGGMU VQ GZRNCKP TGNGXCPV GXKFGPEG 6JG #OGTKECP RJKNQUQRJGT %JCTNGU 5CPFGTU 2GKTEG TUVKPVTQFWEGF VJG VGTO CU IWGUUKPI=? 2GKTEG UCKF VJCV VQ BCEVDF C J[RQVJGVKECN GZRNCPCVKQP a HTQO CP QDUGTXGF UWTRTKUKPIEKTEWOUVCPEG b KU VQ UWTOKUG VJCV a OC[ DG VTWG DGECWUG VJGP b YQWNF DG C OCVVGT QH EQWTUG=? 6JWU VQ CDFWEG a HTQO bKPXQNXGU FGVGTOKPKPI VJCV a KU UWEKGPV QT PGCTN[ UWEKGPV DWV PQV PGEGUUCT[ HQT b

1.1.3 Consistency, validity, soundness, and completeness

#OQPI VJG KORQTVCPV RTQRGTVKGU VJCV NQIKECN U[UVGOU ECP JCXG

Consistency YJKEJ OGCPU VJCV PQ VJGQTGO QH VJG U[UVGO EQPVTCFKEVU CPQVJGT=?

Validity YJKEJ OGCPU VJCV VJG U[UVGOU TWNGU QH RTQQH PGXGT CNNQY C HCNUG KPHGTGPEG HTQO VTWG RTGOKUGU # NQIKECNU[UVGO JCU VJG RTQRGTV[ QH UQWPFPGUU YJGP VJG NQIKECN U[UVGO JCU VJG RTQRGTV[ QH XCNKFKV[ CPF WUGU QPN[ RTGOKUGUVJCV RTQXG VTWG QT KP VJG ECUG QH CZKQOU CTG VTWG D[ FGPKVKQP=?

Completeness QH C NQIKECN U[UVGO YJKEJ OGCPU VJCV KH C HQTOWNC KU VTWG KV ECP DG RTQXGP KH KV KU VTWG KV KU CVJGQTGO QH VJG U[UVGO

Soundness VJG VGTO UQWPFPGUU JCU OWNVKRNG UGRCTCVG OGCPKPIU YJKEJ ETGCVGU C DKV QH EQPHWUKQP VJTQWIJQWV VJGNKVGTCVWTG /QUV EQOOQPN[ UQWPFPGUU TGHGTU VQ NQIKECN U[UVGOU YJKEJ OGCPU VJCV KH UQOG HQTOWNC ECP DG RTQXGPKP C U[UVGO VJGP KV KU VTWG KP VJG TGNGXCPV OQFGNUVTWEVWTG KH # KU C VJGQTGO KV KU VTWG 6JKU KU VJG EQPXGTUG QHEQORNGVGPGUU # FKUVKPEV RGTKRJGTCN WUG QH UQWPFPGUU TGHGTU VQ CTIWOGPVU YJKEJ OGCPU VJCV VJG RTGOKUGU QH C XCNKFCTIWOGPV CTG VTWG KP VJG CEVWCN YQTNF

5QOG NQIKECN U[UVGOU FQ PQV JCXG CNN HQWT RTQRGTVKGU #U CP GZCORNG -WTV )FGNU KPEQORNGVGPGUU VJGQTGOU UJQY VJCVUWEKGPVN[ EQORNGZ HQTOCN U[UVGOU QH CTKVJOGVKE ECPPQV DG EQPUKUVGPV CPF EQORNGVG=? JQYGXGT TUVQTFGT RTGFKECVGNQIKEU PQV GZVGPFGF D[ URGEKE CZKQOU VQ DG CTKVJOGVKE HQTOCN U[UVGOU YKVJ GSWCNKV[ ECP DG EQORNGVG CPF EQPUKUVGPV=?

1.1.4 Rival conceptions of logic

/CKP CTVKENG &GPKVKQPU QH NQIKE

.QIKE CTQUG UGG DGNQY HTQO C EQPEGTP YKVJ EQTTGEVPGUU QH CTIWOGPVCVKQP /QFGTP NQIKEKCPU WUWCNN[ YKUJ VQ GPUWTG VJCVNQIKE UVWFKGU LWUV VJQUG CTIWOGPVU VJCV CTKUG HTQO CRRTQRTKCVGN[ IGPGTCN HQTOU QH KPHGTGPEG (QT GZCORNG 6JQOCU *QHYGDGT YTKVGU KP VJG 5VCPHQTF 'PE[ENQRGFKC QH 2JKNQUQRJ[ VJCV NQIKE FQGU PQV JQYGXGT EQXGT IQQF TGCUQPKPI CU C YJQNG6JCV KU VJG LQD QH VJG VJGQT[ QH TCVKQPCNKV[ 4CVJGT KV FGCNU YKVJ KPHGTGPEGU YJQUG XCNKFKV[ ECP DG VTCEGF DCEM VQ VJG HQTOCNHGCVWTGU QH VJG TGRTGUGPVCVKQPU VJCV CTG KPXQNXGF KP VJCV KPHGTGPEG DG VJG[ NKPIWKUVKE OGPVCN QT QVJGT TGRTGUGPVCVKQPU=?

$[ EQPVTCUV +OOCPWGN -CPV CTIWGF VJCV NQIKE UJQWNF DG EQPEGKXGF CU VJG UEKGPEG QH LWFIGOGPV CP KFGC VCMGP WR KP)QVVNQD (TGIGU NQIKECN CPF RJKNQUQRJKECN YQTM $WV (TGIGU YQTM KU CODKIWQWU KP VJG UGPUG VJCV KV KU DQVJ EQPEGTPGF YKVJVJG NCYU QH VJQWIJV CU YGNN CU YKVJ VJG NCYU QH VTWVJ KG KV DQVJ VTGCVU NQIKE KP VJG EQPVGZV QH C VJGQT[ QH VJG OKPFCPF VTGCVU NQIKE CU VJG UVWF[ QH CDUVTCEV HQTOCN UVTWEVWTGU

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1.2 History

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

1.3 Types of logic

1.3.1 Syllogistic logic

/CKP CTVKENG #TKUVQVGNKCP NQIKE

6JG 0SHBOPO YCU #TKUVQVNGU DQF[ QH YQTM QP NQIKE YKVJ VJG 1SJPS "OBMZUJDT EQPUVKVWVKPI VJG TUV GZRNKEKV YQTM KP HQTOCNNQIKE KPVTQFWEKPI VJG U[NNQIKUVKE=? 6JG RCTVU QH U[NNQIKUVKE NQIKE CNUQ MPQYP D[ VJG PCOG VGTO NQIKE CTG VJG CPCN[UKU QHVJG LWFIGOGPVU KPVQ RTQRQUKVKQPU EQPUKUVKPI QH VYQ VGTOU VJCV CTG TGNCVGF D[ QPG QH C ZGF PWODGT QH TGNCVKQPU CPF VJGGZRTGUUKQP QH KPHGTGPEGU D[ OGCPU QH U[NNQIKUOU VJCV EQPUKUV QH VYQ RTQRQUKVKQPU UJCTKPI C EQOOQP VGTO CU RTGOKUG CPFC EQPENWUKQP VJCV KU C RTQRQUKVKQP KPXQNXKPI VJG VYQ WPTGNCVGF VGTOU HTQO VJG RTGOKUGU#TKUVQVNGU YQTM YCU TGICTFGF KP ENCUUKECN VKOGU CPF HTQOOGFKGXCN VKOGU KP 'WTQRG CPF VJG/KFFNG 'CUV CU VJG XGT[ RKEVWTGQH C HWNN[ YQTMGF QWV U[UVGO *QYGXGT KV YCU PQV CNQPG VJG 5VQKEU RTQRQUGF C U[UVGO QH RTQRQUKVKQPCN NQIKE VJCV YCUUVWFKGF D[ OGFKGXCN NQIKEKCPU #NUQ VJG RTQDNGO QH OWNVKRNG IGPGTCNKV[ YCU TGEQIPK\GF KP OGFKGXCN VKOGU 0QPGVJGNGUURTQDNGOU YKVJ U[NNQIKUVKE NQIKE YGTG PQV UGGP CU DGKPI KP PGGF QH TGXQNWVKQPCT[ UQNWVKQPU

5:1&4 0' -0(*$

"SJTUPUMF #$&

$)"15&3 -0(*$

6QFC[ UQOG CECFGOKEU ENCKO VJCV #TKUVQVNGU U[UVGO KU IGPGTCNN[ UGGP CU JCXKPI NKVVNG OQTG VJCP JKUVQTKECN XCNWG VJQWIJVJGTG KU UQOG EWTTGPV KPVGTGUV KP GZVGPFKPI VGTO NQIKEU TGICTFGF CU OCFG QDUQNGVG D[ VJG CFXGPV QH RTQRQUKVKQPCN NQIKE CPFVJG RTGFKECVG ECNEWNWU 1VJGTU WUG #TKUVQVNG KP CTIWOGPVCVKQP VJGQT[ VQ JGNR FGXGNQR CPF ETKVKECNN[ SWGUVKQP CTIWOGPVCVKQPUEJGOGU VJCV CTG WUGF KP CTVKEKCN KPVGNNKIGPEG CPF NGICN CTIWOGPVU

1.3.2 Propositional logic (sentential logic)

/CKP CTVKENG 2TQRQUKVKQPCN ECNEWNWU

# RTQRQUKVKQPCN ECNEWNWU QT NQIKE CNUQ C UGPVGPVKCN ECNEWNWU KU C HQTOCN U[UVGO KP YJKEJ HQTOWNCG TGRTGUGPVKPI RTQRQUKVKQPUECP DG HQTOGF D[ EQODKPKPI CVQOKE RTQRQUKVKQPU WUKPI NQIKECN EQPPGEVKXGU CPF KP YJKEJ C U[UVGO QH HQTOCN RTQQH TWNGUGUVCDNKUJGU EGTVCKP HQTOWNCG CU VJGQTGOU

1.3.3 Predicate logic

/CKP CTVKENG 2TGFKECVG NQIKE

2TGFKECVG NQIKE KU VJG IGPGTKE VGTO HQT U[ODQNKE HQTOCN U[UVGOU UWEJ CU TUVQTFGT NQIKE UGEQPFQTFGT NQIKE OCP[UQTVGFNQIKE CPF KPPKVCT[ NQIKE2TGFKECVG NQIKE RTQXKFGU CP CEEQWPV QH SWCPVKGTU IGPGTCN GPQWIJ VQ GZRTGUU C YKFG UGV QH CTIWOGPVU QEEWTTKPI KP PCVWTCNNCPIWCIG #TKUVQVGNKCP U[NNQIKUVKE NQIKE URGEKGU C UOCNN PWODGT QH HQTOU VJCV VJG TGNGXCPV RCTV QH VJG KPXQNXGF LWFIGOGPVUOC[ VCMG 2TGFKECVG NQIKE CNNQYU UGPVGPEGU VQ DG CPCN[UGF KPVQ UWDLGEV CPF CTIWOGPV KP UGXGTCN CFFKVKQPCN YC[UCNNQYKPIRTGFKECVG NQIKE VQ UQNXG VJG RTQDNGO QH OWNVKRNG IGPGTCNKV[ VJCV JCF RGTRNGZGF OGFKGXCN NQIKEKCPU6JG FGXGNQROGPV QH RTGFKECVG NQIKE KU WUWCNN[ CVVTKDWVGF VQ )QVVNQD (TGIG YJQ KU CNUQ ETGFKVGF CU QPG QH VJG HQWPFGTU QHCPCN[VKECN RJKNQUQRJ[ DWV VJG HQTOWNCVKQP QH RTGFKECVG NQIKE OQUV QHVGP WUGF VQFC[ KU VJG TUVQTFGT NQIKE RTGUGPVGF KP2TKPEKRNGU QH /CVJGOCVKECN .QIKE D[ &CXKF *KNDGTV CPF 9KNJGNO #EMGTOCPP KP 6JG CPCN[VKECN IGPGTCNKV[ QH RTGFKECVG NQIKE CNNQYGF VJG HQTOCNK\CVKQP QH OCVJGOCVKEU FTQXG VJG KPXGUVKICVKQP QH UGV VJGQT[ CPF CNNQYGF VJG FGXGNQROGPVQH #NHTGF 6CTUMKU CRRTQCEJ VQ OQFGN VJGQT[ +V RTQXKFGU VJG HQWPFCVKQP QH OQFGTP OCVJGOCVKECN NQIKE(TGIGU QTKIKPCN U[UVGO QH RTGFKECVG NQIKE YCU UGEQPFQTFGT TCVJGT VJCP TUVQTFGT 5GEQPFQTFGT NQIKE KUOQUV RTQOKPGPVN[FGHGPFGF CICKPUV VJG ETKVKEKUO QH 9KNNCTF 8CP 1TOCP 3WKPG CPF QVJGTU D[ )GQTIG $QQNQU CPF 5VGYCTV 5JCRKTQ

1.3.4 Modal logic

/CKP CTVKENG /QFCN NQIKE

+P NCPIWCIGU OQFCNKV[ FGCNU YKVJ VJG RJGPQOGPQP VJCV UWDRCTVU QH C UGPVGPEG OC[ JCXG VJGKT UGOCPVKEU OQFKGF D[URGEKCN XGTDU QT OQFCN RCTVKENGU (QT GZCORNG 8F HP UP UIF HBNFT ECP DG OQFKGF VQ IKXG 8F TIPVME HP UP UIF HBNFTCPF 8F DBO HP UP UIF HBNFT CPF RGTJCRU 8F XJMM HP UP UIF HBNFT /QTG CDUVTCEVN[ YG OKIJV UC[ VJCV OQFCNKV[ CGEVUVJG EKTEWOUVCPEGU KP YJKEJ YG VCMG CP CUUGTVKQP VQ DG UCVKUGF#TKUVQVNGU NQIKE KU KP NCTIG RCTVU EQPEGTPGF YKVJ VJG VJGQT[ QH PQPOQFCNK\GF NQIKE #NVJQWIJ VJGTG CTG RCUUCIGU KP JKUYQTM UWEJ CU VJG HCOQWU UGCDCVVNG CTIWOGPV KP %F *OUFSQSFUBUJPOF h VJCV CTG PQY UGGP CU CPVKEKRCVKQPU QH OQFCN NQIKECPF KVU EQPPGEVKQP YKVJ RQVGPVKCNKV[ CPF VKOG VJG GCTNKGUV HQTOCN U[UVGO QH OQFCN NQIKE YCU FGXGNQRGF D[ #XKEGPPC YJQOWNVKOCVGN[ FGXGNQRGF C VJGQT[ QH VGORQTCNN[ OQFCNK\GF U[NNQIKUVKE=?

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

5:1&4 0' -0(*$

YKVJ TKXCNU JKU VJGQT[ QH HTCOG UGOCPVKEU YJKEJ TGXQNWVKQPK\GF VJG HQTOCN VGEJPQNQI[ CXCKNCDNG VQ OQFCN NQIKEKCPU CPFICXG C PGY ITCRJVJGQTGVKE YC[ QH NQQMKPI CV OQFCNKV[ VJCV JCU FTKXGP OCP[ CRRNKECVKQPU KP EQORWVCVKQPCN NKPIWKUVKEU CPFEQORWVGT UEKGPEG UWEJ CU F[PCOKE NQIKE

1.3.5 Informal reasoning

/CKP CTVKENG +PHQTOCN NQIKE

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

1.3.6 Mathematical logic

/CKP CTVKENG /CVJGOCVKECN NQIKE

/CVJGOCVKECN NQIKE TGCNN[ TGHGTU VQ VYQ FKUVKPEV CTGCU QH TGUGCTEJ VJG TUV KU VJG CRRNKECVKQP QH VJG VGEJPKSWGU QH HQTOCNNQIKE VQ OCVJGOCVKEU CPF OCVJGOCVKECN TGCUQPKPI CPF VJG UGEQPF KP VJG QVJGT FKTGEVKQP VJG CRRNKECVKQP QH OCVJGOCVKECNVGEJPKSWGU VQ VJG TGRTGUGPVCVKQP CPF CPCN[UKU QH HQTOCN NQIKE=?

6JG GCTNKGUV WUG QH OCVJGOCVKEU CPF IGQOGVT[ KP TGNCVKQP VQ NQIKE CPF RJKNQUQRJ[ IQGU DCEM VQ VJG CPEKGPV )TGGMU UWEJ CU'WENKF 2NCVQ CPF #TKUVQVNG=? /CP[ QVJGT CPEKGPV CPF OGFKGXCN RJKNQUQRJGTU CRRNKGF OCVJGOCVKECN KFGCU CPF OGVJQFUVQ VJGKT RJKNQUQRJKECN ENCKOU=?

1PG QH VJG DQNFGUV CVVGORVU VQ CRRN[ NQIKE VQ OCVJGOCVKEU YCU WPFQWDVGFN[ VJG NQIKEKUO RKQPGGTGF D[ RJKNQUQRJGTNQIKEKCPU UWEJ CU )QVVNQD (TGIG CPF $GTVTCPF 4WUUGNN VJG KFGC YCU VJCV OCVJGOCVKECN VJGQTKGU YGTG NQIKECN VCWVQNQIKGUCPF VJG RTQITCOOG YCU VQ UJQY VJKU D[ OGCPU VQ C TGFWEVKQP QH OCVJGOCVKEU VQ NQIKE=? 6JG XCTKQWU CVVGORVU VQ ECTT[VJKU QWV OGV YKVJ C UGTKGU QH HCKNWTGU HTQO VJG ETKRRNKPI QH (TGIGU RTQLGEV KP JKU (SVOEHFTFU[F D[ 4WUUGNNU RCTCFQZ VQ VJGFGHGCV QH *KNDGTVU RTQITCO D[ )FGNU KPEQORNGVGPGUU VJGQTGOU$QVJ VJG UVCVGOGPV QH *KNDGTVU RTQITCO CPF KVU TGHWVCVKQP D[ )FGN FGRGPFGF WRQP VJGKT YQTM GUVCDNKUJKPI VJG UGEQPFCTGC QH OCVJGOCVKECN NQIKE VJG CRRNKECVKQP QH OCVJGOCVKEU VQ NQIKE KP VJG HQTO QH RTQQH VJGQT[=? &GURKVG VJG PGICVKXGPCVWTG QH VJG KPEQORNGVGPGUU VJGQTGOU )FGNU EQORNGVGPGUU VJGQTGO C TGUWNV KP OQFGN VJGQT[ CPF CPQVJGT CRRNKECVKQPQH OCVJGOCVKEU VQ NQIKE ECP DG WPFGTUVQQF CU UJQYKPI JQY ENQUG NQIKEKUO ECOG VQ DGKPI VTWG GXGT[ TKIQTQWUN[ FGPGFOCVJGOCVKECN VJGQT[ ECP DG GZCEVN[ ECRVWTGF D[ C TUVQTFGT NQIKECN VJGQT[ (TGIGU RTQQH ECNEWNWU KU GPQWIJ VQ EFTDSJCFVJG YJQNG QH OCVJGOCVKEU VJQWIJ PQV FRVJWBMFOU VQ KV+H RTQQH VJGQT[ CPF OQFGN VJGQT[ JCXG DGGP VJG HQWPFCVKQP QH OCVJGOCVKECN NQIKE VJG[ JCXG DGGP DWV VYQ QH VJG HQWTRKNNCTU QH VJG UWDLGEV 5GV VJGQT[ QTKIKPCVGF KP VJG UVWF[ QH VJG KPPKVG D[ )GQTI %CPVQT CPF KV JCU DGGP VJG UQWTEG QHOCP[ QH VJG OQUV EJCNNGPIKPI CPF KORQTVCPV KUUWGU KP OCVJGOCVKECN NQIKE HTQO %CPVQTU VJGQTGO VJTQWIJ VJG UVCVWU QHVJG #ZKQO QH %JQKEG CPF VJG SWGUVKQP QH VJG KPFGRGPFGPEG QH VJG EQPVKPWWO J[RQVJGUKU VQ VJG OQFGTP FGDCVG QP NCTIGECTFKPCN CZKQOU4GEWTUKQP VJGQT[ ECRVWTGU VJG KFGC QH EQORWVCVKQP KP NQIKECN CPF CTKVJOGVKE VGTOU KVU OQUV ENCUUKECN CEJKGXGOGPVU CTG VJGWPFGEKFCDKNKV[ QH VJG 'PVUEJGKFWPIURTQDNGO D[ #NCP 6WTKPI CPF JKU RTGUGPVCVKQP QH VJG %JWTEJ6WTKPI VJGUKU=? 6QFC[TGEWTUKQP VJGQT[ KU OQUVN[ EQPEGTPGF YKVJ VJG OQTG TGPGF RTQDNGO QH EQORNGZKV[ ENCUUGUYJGP KU C RTQDNGO GEKGPVN[UQNXCDNG!CPF VJG ENCUUKECVKQP QH FGITGGU QH WPUQNXCDKNKV[=?

$)"15&3 -0(*$

1.3.7 Philosophical logic

/CKP CTVKENG 2JKNQUQRJKECN NQIKE

2JKNQUQRJKECN NQIKE FGCNU YKVJ HQTOCN FGUETKRVKQPU QH QTFKPCT[ PQPURGEKCNKUV PCVWTCN NCPIWCIG /QUV RJKNQUQRJGTUCUUWOG VJCV VJG DWNM QH GXGT[FC[ TGCUQPKPI ECP DG ECRVWTGF KP NQIKE KH C OGVJQF QT OGVJQFU VQ VTCPUNCVG QTFKPCT[ NCPIWCIGKPVQ VJCV NQIKE ECP DG HQWPF 2JKNQUQRJKECN NQIKE KU GUUGPVKCNN[ C EQPVKPWCVKQP QH VJG VTCFKVKQPCN FKUEKRNKPG ECNNGF NQIKEDGHQTG VJG KPXGPVKQP QH OCVJGOCVKECN NQIKE 2JKNQUQRJKECN NQIKE JCU C OWEJ ITGCVGT EQPEGTP YKVJ VJG EQPPGEVKQP DGVYGGPPCVWTCN NCPIWCIG CPF NQIKE #U C TGUWNV RJKNQUQRJKECN NQIKEKCPU JCXG EQPVTKDWVGF C ITGCV FGCN VQ VJG FGXGNQROGPV QH PQPUVCPFCTF NQIKEU GI HTGG NQIKEU VGPUG NQIKEU CU YGNN CU XCTKQWU GZVGPUKQPU QH ENCUUKECN NQIKE GI OQFCN NQIKEU CPFPQPUVCPFCTF UGOCPVKEU HQT UWEJ NQIKEU GI -TKRMGU UWRGTXCNWCVKQPKUO KP VJG UGOCPVKEU QH NQIKE.QIKE CPF VJG RJKNQUQRJ[ QH NCPIWCIG CTG ENQUGN[ TGNCVGF 2JKNQUQRJ[ QH NCPIWCIG JCU VQ FQ YKVJ VJG UVWF[ QH JQY QWTNCPIWCIG GPICIGU CPF KPVGTCEVU YKVJ QWT VJKPMKPI .QIKE JCU CP KOOGFKCVG KORCEV QP QVJGT CTGCU QH UVWF[ 5VWF[KPI NQIKECPF VJG TGNCVKQPUJKR DGVYGGP NQIKE CPF QTFKPCT[ URGGEJ ECP JGNR C RGTUQP DGVVGT UVTWEVWTG JKU QYP CTIWOGPVU CPF ETKVKSWGVJG CTIWOGPVU QH QVJGTU /CP[ RQRWNCT CTIWOGPVU CTG NNGF YKVJ GTTQTU DGECWUG UQ OCP[ RGQRNG CTG WPVTCKPGF KP NQIKECPF WPCYCTG QH JQY VQ HQTOWNCVG CP CTIWOGPV EQTTGEVN[=?=?

1.3.8 Computational logic

/CKP CTVKENG .QIKE KP EQORWVGT UEKGPEG

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

5GEVKQP ( QP .QIKEU CPF OGCPKPIU QH RTQITCOU CPF ( QP /CVJGOCVKECN NQIKE CPF HQTOCN NCPIWCIGU CU RCTV QHVJG VJGQT[ QH EQORWVGT UEKGPEG VJKU YQTM EQXGTU HQTOCN UGOCPVKEU QH RTQITCOOKPI NCPIWCIGU CU YGNN CU YQTM QHHQTOCN OGVJQFU UWEJ CU *QCTG NQIKE

$QQNGCP NQIKE CU HWPFCOGPVCN VQ EQORWVGT JCTFYCTG RCTVKEWNCTN[ VJG U[UVGOU UGEVKQP $ QP #TKVJOGVKE CPF NQIKEUVTWEVWTGU TGNCVKPI VQ QRGTCVKXGU #0& 016 CPF 14

/CP[ HWPFCOGPVCN NQIKECN HQTOCNKUOU CTG GUUGPVKCN VQ UGEVKQP + QP CTVKEKCN KPVGNNKIGPEG HQT GZCORNG OQFCN NQIKECPF FGHCWNV NQIKE KP -PQYNGFIG TGRTGUGPVCVKQP HQTOCNKUOU CPF OGVJQFU *QTP ENCWUGU KP NQIKE RTQITCOOKPI CPFFGUETKRVKQP NQIKE

(WTVJGTOQTG EQORWVGTU ECP DG WUGF CU VQQNU HQT NQIKEKCPU (QT GZCORNG KP U[ODQNKE NQIKE CPF OCVJGOCVKECN NQIKE RTQQHUD[ JWOCPU ECP DG EQORWVGTCUUKUVGF 7UKPI CWVQOCVGF VJGQTGO RTQXKPI VJG OCEJKPGU ECP PF CPF EJGEM RTQQHU CU YGNNCU YQTM YKVJ RTQQHU VQQ NGPIVJ[ VQ YTKVG QWV D[ JCPF

1.3.9 Bivalence and the law of the excluded middle; non-classical logics

/CKP CTVKENG 2TKPEKRNG QH DKXCNGPEG

5:1&4 0' -0(*$

6JG NQIKEU FKUEWUUGF CDQXG CTG CNN DKXCNGPV QT VYQXCNWGF VJCV KU VJG[ CTG OQUV PCVWTCNN[ WPFGTUVQQF CU FKXKFKPIRTQRQUKVKQPU KPVQ VTWG CPF HCNUG RTQRQUKVKQPU 0QPENCUUKECN NQIKEU CTG VJQUG U[UVGOU VJCV TGLGEV DKXCNGPEG*GIGN FGXGNQRGF JKU QYP FKCNGEVKE NQIKE VJCV GZVGPFGF -CPVU VTCPUEGPFGPVCN NQIKE DWV CNUQ DTQWIJV KV DCEM VQ ITQWPFD[ CUUWTKPI WU VJCV PGKVJGT KP JGCXGP PQT KP GCTVJ PGKVJGT KP VJG YQTNF QH OKPF PQT QH PCVWTG KU VJGTG CP[YJGTG UWEJCP CDUVTCEV GKVJGTQT CU VJG WPFGTUVCPFKPI OCKPVCKPU 9JCVGXGT GZKUVU KU EQPETGVG YKVJ FKGTGPEG CPF QRRQUKVKQP KPKVUGNH=?

+P 0KEQNCK # 8CUKNKGX GZVGPFGF VJG NCY QH GZENWFGF OKFFNG CPF VJG NCY QH EQPVTCFKEVKQP CPF RTQRQUGF VJG NCY QHGZENWFGF HQWTVJ CPF NQIKE VQNGTCPV VQ EQPVTCFKEVKQP=? +P VJG GCTN[ VJ EGPVWT[ ,CP WMCUKGYKE\ KPXGUVKICVGF VJG GZVGPUKQPQH VJG VTCFKVKQPCN VTWGHCNUG XCNWGU VQ KPENWFG C VJKTF XCNWG RQUUKDNG UQ KPXGPVKPI VGTPCT[ NQIKE VJG TUV OWNVKXCNWGFNQIKE=?

.QIKEU UWEJ CU HW\\[ NQIKE JCXG UKPEG DGGP FGXKUGF YKVJ CP KPPKVG PWODGT QH FGITGGU QH VTWVJ TGRTGUGPVGF D[ C TGCNPWODGT DGVYGGP CPF =?

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

1.3.10 Is logic empirical?"

/CKP CTVKENG +U NQIKE GORKTKECN!

9JCV KU VJG GRKUVGOQNQIKECN UVCVWU QH VJG NCYU QH NQIKE! 9JCV UQTV QH CTIWOGPV KU CRRTQRTKCVG HQT ETKVKEK\KPI RWTRQTVGFRTKPEKRNGU QH NQIKE! +P CP KPWGPVKCN RCRGT GPVKVNGF +U NQIKE GORKTKECN!=? *KNCT[ 2WVPCO DWKNFKPI QP C UWIIGUVKQP QH9 8 3WKPG CTIWGF VJCV KP IGPGTCN VJG HCEVU QH RTQRQUKVKQPCN NQIKE JCXG C UKOKNCT GRKUVGOQNQIKECN UVCVWU CU HCEVU CDQWVVJG RJ[UKECN WPKXGTUG HQT GZCORNG CU VJG NCYU QH OGEJCPKEU QT QH IGPGTCN TGNCVKXKV[ CPF KP RCTVKEWNCT VJCV YJCV RJ[UKEKUVUJCXG NGCTPGF CDQWV SWCPVWO OGEJCPKEU RTQXKFGU C EQORGNNKPI ECUG HQT CDCPFQPKPI EGTVCKP HCOKNKCT RTKPEKRNGU QH ENCUUKECNNQIKE KH YG YCPV VQ DG TGCNKUVU CDQWV VJG RJ[UKECN RJGPQOGPC FGUETKDGF D[ SWCPVWO VJGQT[ VJGP YG UJQWNF CDCPFQP VJGRTKPEKRNG QH FKUVTKDWVKXKV[ UWDUVKVWVKPI HQT ENCUUKECN NQIKE VJG SWCPVWO NQIKE RTQRQUGF D[ )CTTGVV $KTMJQ CPF ,QJP XQP0GWOCPP=?

#PQVJGT RCRGT QH VJG UCOG PCOG D[ 5KT /KEJCGN &WOOGVV CTIWGU VJCV 2WVPCOU FGUKTG HQT TGCNKUO OCPFCVGU VJG NCY QHFKUVTKDWVKXKV[=? &KUVTKDWVKXKV[ QH NQIKE KU GUUGPVKCN HQT VJG TGCNKUVU WPFGTUVCPFKPI QH JQY RTQRQUKVKQPU CTG VTWG QH VJG YQTNFKP LWUV VJG UCOG YC[ CU JG JCU CTIWGF VJG RTKPEKRNG QH DKXCNGPEG KU +P VJKU YC[ VJG SWGUVKQP +U NQIKE GORKTKECN! ECP DGUGGP VQ NGCF PCVWTCNN[ KPVQ VJG HWPFCOGPVCN EQPVTQXGTU[ KP OGVCRJ[UKEU QP TGCNKUO XGTUWU CPVKTGCNKUO

1.3.11 Implication: strict or material?

/CKP CTVKENG 2CTCFQZ QH GPVCKNOGPV

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

$)"15&3 -0(*$

VJG CPVGEGFGPV VJWU KH VJCV OCP IGVU GNGEVGF ITCPP[ YKNN FKG KU OCVGTKCNN[ VTWG UKPEG ITCPP[ KU OQTVCN TGICTFNGUU QHVJG OCPU GNGEVKQP RTQURGEVU 5WEJ UGPVGPEGU XKQNCVG VJG )TKEGCP OCZKO QH TGNGXCPEG CPF ECP DG OQFGNNGF D[ NQIKEU VJCVTGLGEV VJG RTKPEKRNG QH OQPQVQPKEKV[ QH GPVCKNOGPV UWEJ CU TGNGXCPEG NQIKE

1.3.12 Tolerating the impossible

/CKP CTVKENG 2CTCEQPUKUVGPV NQIKE

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

1.3.13 Rejection of logical truth

6JG RJKNQUQRJKECN XGKP QH XCTKQWU MKPFU QH UMGRVKEKUO EQPVCKPU OCP[ MKPFU QH FQWDV CPF TGLGEVKQP QH VJG XCTKQWU DCUGU QPYJKEJ NQIKE TGUVU UWEJ CU VJG KFGC QH NQIKECN HQTO EQTTGEV KPHGTGPEG QT OGCPKPI V[RKECNN[ NGCFKPI VQ VJG EQPENWUKQP VJCVVJGTG CTG PQ NQIKECN VTWVJU 1DUGTXG VJCV VJKU KU QRRQUKVG VQ VJG WUWCN XKGYU KP RJKNQUQRJKECN UMGRVKEKUO YJGTG NQIKE FKTGEVUUMGRVKECN GPSWKT[ VQ FQWDV TGEGKXGF YKUFQOU CU KP VJG YQTM QH 5GZVWU 'ORKTKEWU(TKGFTKEJ 0KGV\UEJG RTQXKFGU C UVTQPI GZCORNG QH VJG TGLGEVKQP QH VJG WUWCN DCUKU QH NQIKE JKU TCFKECN TGLGEVKQP QH KFGCNK\CVKQP NGF JKO VQ TGLGEV VTWVJ CU C OQDKNG CTO[ QH OGVCRJQTU OGVQP[OU CPF CPVJTQRQOQTRJKUOUKP UJQTV OGVCRJQTU YJKEJ CTG YQTP QWV CPF YKVJQWV UGPUWQWU RQYGT EQKPU YJKEJ JCXG NQUV VJGKT RKEVWTGU CPF PQY OCVVGT QPN[CU OGVCN PQ NQPIGT CU EQKPU=? *KU TGLGEVKQP QH VTWVJ FKF PQV NGCF JKO VQ TGLGEV VJG KFGC QH GKVJGT KPHGTGPEG QT NQIKEEQORNGVGN[ DWV TCVJGT UWIIGUVGF VJCV NQIKE =ECOG? KPVQ GZKUVGPEG KP OCPU JGCF =QWV? QH KNNQIKE YJQUG TGCNO QTKIKPCNN[OWUV JCXG DGGP KOOGPUG +PPWOGTCDNG DGKPIU YJQ OCFG KPHGTGPEGU KP C YC[ FKGTGPV HTQO QWTU RGTKUJGF=? 6JWUVJGTG KU VJG KFGC VJCV NQIKECN KPHGTGPEG JCU C WUG CU C VQQN HQT JWOCP UWTXKXCN DWV VJCV KVU GZKUVGPEG FQGU PQV UWRRQTV VJGGZKUVGPEG QH VTWVJ PQT FQGU KV JCXG C TGCNKV[ DG[QPF VJG KPUVTWOGPVCN .QIKE VQQ CNUQ TGUVU QP CUUWORVKQPU VJCV FQ PQVEQTTGURQPF VQ CP[VJKPI KP VJG TGCN YQTNF=?

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

1.4 See also

&KIKVCN GNGEVTQPKEU CNUQ MPQYP CU EJHJUBM MPHJD QT NQIKE ICVGU

/05&4 "/% 3&'&3&/$&4

(CNNCEKGU .KUV QH NQIKEKCPU .KUV QH NQIKE LQWTPCNU .QIKE RW\\NG .QIKE U[ODQNU /CVJGOCVKEU

.KUV QH OCVJGOCVKEU CTVKENGU 1WVNKPG QH OCVJGOCVKEU

/GVCNQIKE 1WVNKPG QH NQIKE 2JKNQUQRJ[

.KUV QH RJKNQUQRJ[ VQRKEU 1WVNKPG QH RJKNQUQRJ[

4GCUQP 4USBJHIU BOE $SPPLFE 5IJOLJOH DQQM 6CDNG QH NQIKE U[ODQNU 6TWVJ 8GEVQT NQIKE

1.5 Notes and references

=? RQUUGUUGF QH TGCUQP KPVGNNGEVWCN FKCNGEVKECN CTIWOGPVCVKXG CNUQ TGNCVGF VQ MPHPT YQTF VJQWIJV KFGC CTIWOGPVCEEQWPV TGCUQP QT RTKPEKRNG .KFFGNN 5EQVV 1PNKPG 'V[OQNQI[ &KEVKQPCT[

=? 4KEJCTF *GPT[ 2QRMKP #XTWO 5VTQNN ,WN[ 1IJMPTPQIZ .BEF 4JNQMF 4CPFQO *QWUG &KIKVCN +PE R +5$0 4GVTKGXGF /CTEJ

=? ,CESWGVVG & " $PNQBOJPO UP 1IJMPTPQIJDBM -PHJD 9KNG[ 1PNKPG .KDTCT[ R

=? (QT GZCORNG 0[C[C U[NNQIKUVKE TGEWTUKQP FCVGU DCEM [GCTU

=? /QJKUVU CPF VJG UEJQQN QH 0COGU FCVG DCEM CV [GCTU

=? 2NCVQ $WEJCPCP 5EQVV GF 5IF 1PSUBCMF 1MBUP 2GPIWKP +5$0

=? #TKUVQVNG 2QUVGTKQT #PCN[VKEU +P /EMGQP 4KEJCTF 5IF #BTJD 8PSLT /QFGTP .KDTCT[ +5$0

=? 9JKVGJGCF #NHTGF 0QTVJ 4WUUGNN $GTVTCPF 1SJODJQJB .BUIFNBUJDB UP %CODTKFIG 7PKXGTUKV[ 2TGUU +5$0

=? (QT C OQTG OQFGTP VTGCVOGPV UGG *COKNVQP # ) -PHJD GPS .BUIFNBUJDJBOT %CODTKFIG 7PKXGTUKV[ 2TGUU +5$0

=? WMCUKGYKE\ ,CP "SJTUPUMFT TZMMPHJTUJD GSPN UIF TUBOEQPJOU PG NPEFSO GPSNBM MPHJD PF GF 1ZHQTF 7PKXGTUKV[ 2TGUUR +5$0

$)"15&3 -0(*$

=? /CIPCPK . #DFWEVKQP 4GCUQP CPF 5EKGPEG 2TQEGUUGU QH &KUEQXGT[ CPF 'ZRNCPCVKQP ,MVXFS "DBEFNJD 1MFOVN1VCMJTIFST /FX :PSL ZXKK RCIGU *CTF EQXGT +5$0

4 ,QUGRJUQP , ) ,QUGRJUQP 5 #DFWEVKXG +PHGTGPEG %QORWVCVKQP 2JKNQUQRJ[ 6GEJPQNQI[ $BNCSJEHF 6OJWFSTJUZ1SFTT /FX :PSL $BNCSJEHF 6, XKKK RCIGU *CTF EQXGT +5$0 2CRGTDCEM +5$0

$WPV * $NCEM 9 #DFWEVKQP $GNKGH CPF %QPVGZV KP &KCNQIWG 5VWFKGU KP %QORWVCVKQPCN 2TCIOCVKEU /BUVSBM-BOHVBHF 1SPDFTTJOH +PIO #FOKBNJOT "NTUFSEBN 1IJMBEFMQIJB XK RCIGU *CTF EQXGT +5$0 'WTQRG

75

=? 2GKTEG % 5

1P VJG .QIKE QH FTCYKPI *KUVQT[ HTQO #PEKGPV &QEWOGPVU GURGEKCNN[ HTQO 6GUVKOQPKGU $PMMFDUFE 1BQFST X RCTCITCRJ

2#2 =2TQNGIQOGPC VQ CP#RQNQI[ HQT 2TCIOCVKUO? /5 E /FX&MFNFOUT PG.BUIFNBUJDT X RR # .GVVGT VQ ( # 9QQFU $PMMFDUFE 1BQFST X RCTCITCRJU

5GG WPFGT #DFWEVKQP CPF 4GVTQFWEVKQP CV $PNNFOT %JDUJPOBSZ PG 1FJSDFT 5FSNT

=? 2GKTEG % 5 *CTXCTF NGEVWTGU QP RTCIOCVKUO $PMMFDUFE 1BQFST X RCTCITCRJU

=? $GTIOCPP /GTTKG /QQT ,COGU 0GNUQP ,CEM 5IF -PHJD #PPL (KHVJ GF 0GY ;QTM 0; /E)TCY*KNN +5$0

=? /GPFGNUQP 'NNKQVV 3WCPVKECVKQP 6JGQT[ %QORNGVGPGUU 6JGQTGOU *OUSPEVDUJPO UP .BUIFNBUJDBM -PHJD 8CP 0QUVTCPF +5$0

=? *QHYGDGT 6 .QIKE CPF 1PVQNQI[ +P

#*#-*0(3"1):

=? $CTPGU ,QPCVJCP 5IF $BNCSJEHF $PNQBOJPO UP "SJTUPUMF %CODTKFIG 7PKXGTUKV[ 2TGUU R +5$0

=? #TKUVQVNG 1SJPS "OBMZUJDT *CEMGVV 2WDNKUJKPI %Q R +5$0

=? /GPFGNUQP 'NNKQVV (QTOCN 0WODGT 6JGQT[ )FGNU +PEQORNGVGPGUU 6JGQTGO *OUSPEVDUJPO UP .BUIFNBUJDBM -PHJD/QPVGTG[ %CNKH 9CFUYQTVJ $TQQMU%QNG #FXCPEGF $QQMU 5QHVYCTG 1%.%

=? $TQQMUJGCT , )NGPP %QORWVCDKNKV[ (QWPFCVKQPU QH 4GEWTUKXG (WPEVKQP 6JGQT[ 5IFPSZ PG DPNQVUBUJPO GPSNBMMBOHVBHFT BVUPNBUB BOE DPNQMFYJUZ 4GFYQQF %KV[ %CNKH $GPLCOKP%WOOKPIU 2WD %Q +5$0

=? $TQQMUJGCT , )NGPP %QORNGZKV[ 5IFPSZ PG DPNQVUBUJPO GPSNBM MBOHVBHFT BVUPNBUB BOE DPNQMFYJUZ 4GFYQQF%KV[ %CNKH $GPLCOKP%WOOKPIU 2WD %Q +5$0

=? )QNFOCP #NXKP + &QJTUFNPMPHZ BOE $PHOJUJPO *CTXCTF 7PKXGTUKV[ 2TGUU R +5$0 WPVTCKPGFUWDLGEVU CTG RTQPG VQ EQOOKV XCTKQWU UQTVU QH HCNNCEKGU CPF OKUVCMGU

=? &GOGVTKQW # 'HMNKFGU # GFU *OUFMMJHFODF .JOE BOE 3FBTPOJOH 4USVDUVSF BOE %FWFMPQNFOU #FXCPEGU KP 2U[EJQNQI[ 106 'NUGXKGT R +5$0

=? *GIGN ) 9 ( =? 1IJMPTPQIZ PG .JOE 'PE[ENQRGFKC QH VJG 2JKNQUQRJKECN 5EKGPEGU VTCPU 9KNNKCO 9CNNCEG1ZHQTF %NCTGPFQP 2TGUU R +5$0

=? ,QUGRJ ' $TGPPGT #WIWUV -PHJD JO 3FBMJUZ 5RTKPIGT RR +5$0 4GVTKGXGF #RTKN

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%QJGP 45 CPF 9CTVQHUM[ /9 -PHJDBM BOE &QJTUFNPMPHJDBM 4UVEJFT JO $POUFNQPSBSZ 1IZTJDT $QUVQP5VWFKGU KP VJG 2JKNQUQRJ[ QH 5EKGPEG & 4GKFGN 2WDNKUJKPI %QORCP[ &QTFTGEJV 0GVJGTNCPFU +5$0

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*KNDGTV & CPF #EMGTOCPP 9 (SVOE[HF EFS UIFPSFUJTDIFO -PHJL 1SJODJQMFT PG .BUIFNBUJDBM -PHJD5RTKPIGT8GTNCI 1%.%

5WUCP *CCEM %FWJBOU -PHJD 'V[[Z -PHJD #FZPOE UIF 'PSNBMJTN 7PKXGTUKV[ QH %JKECIQ 2TGUU *QFIGU 9 -PHJD "O JOUSPEVDUJPO UP &MFNFOUBSZ -PHJD 2GPIWKP $QQMU *QHYGDGT 6 .QIKE CPF 1PVQNQI[ 4UBOGPSE &ODZDMPQFEJB PG 1IJMPTPQIZ 'FYCTF 0

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5[ODQNKE .QIKE CPF 6JG )COG QH .QIKE .GYKU %CTTQNN /CVJ .QIKE 6JG JKUVQT[ QH HQTOCN OCVJGOCVKECN NQIKECN NKPIWKUVKE CPF OGVJQFQNQIKECN KFGCU +P 5IF%JDUJPOBSZ PG UIF )JTUPSZ PG *EFBT

1PNKPG 6QQNU +PVGTCEVKXG 5[NNQIKUVKE /CEJKPG # YGD DCUGF U[NNQIKUVKE OCEJKPG HQT GZRNQTKPI HCNNCEKGU IWTGU VGTOU CPFOQFGU QH U[NNQIKUOU

4GHGTGPEG OCVGTKCN 6TCPUNCVKQP 6KRU D[ 2GVGT 5WDGT HQT VTCPUNCVKPI HTQO 'PINKUJ KPVQ NQIKECN PQVCVKQP 1PVQNQI[ CPF *KUVQT[ QH .QIKE #P +PVTQFWEVKQP YKVJ CP CPPQVCVGF DKDNKQITCRJ[

4GCFKPI NKUVU 6JG .QPFQP 2JKNQUQRJ[ 5VWF[ )WKFG QGTU OCP[ UWIIGUVKQPU QP YJCV VQ TGCF FGRGPFKPI QP VJG UVWFGPVUHCOKNKCTKV[ YKVJ VJG UWDLGEV .QIKE /GVCRJ[UKEU 5GV 6JGQT[ CPF (WTVJGT .QIKE /CVJGOCVKECN .QIKE

Chapter 2

Sense and reference

5KPP TGFKTGEVU JGTG (QT QVJGT WUGU UGG 5KPP FKUCODKIWCVKQP4JOO CPF #FEFVUVOH CTG WUWCNN[ VTCPUNCVGF TGURGEVKXGN[ CU TFOTF CPF SFGFSFODF 6YQ FKGTGPV CURGEVU QH UQOG VGTOUOGCPKPIU C VGTOU reference KU VJG PCKFDU VQ YJKEJ VJG VGTO TGHGTU YJKNG VJG VGTOU sense KU VJG XBZ VJCV VJG VGTO TGHGTUVQ VJCV QDLGEV4JOO CPF #FEFVUVOH YGTG KPVTQFWEGF D[ )GTOCP RJKNQUQRJGT CPF OCVJGOCVKEKCP )QVVNQD (TGIG KP JKU RCRGT DGT5KPP WPF $GFGWVWPI 1P UGPUG CPF TGHGTGPEG (TGIG CRRNKGF #FEFVUVOH OCKPN[ VQ RTQRGT PCOGU CPF KP NGUUGT GZVGPVVQ UGPVGPEGU6JQWIJ VJG FKUVKPEVKQP TGUKFGU KP RJKNQUQRJ[ QH NCPIWCIG KV GPVGTU RJKNQUQRJ[U QVJGT CTGCU KPENWFKPI RJKNQUQRJ[ QH OKPFOGVCRJ[UKEU CPF OGVCGVJKEU

2.1 Motivation for and development of the distinction

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

5&3.*/0-0(:

6JG SFGFSFODF KU VJG QDLGEV VJCV VJG GZRTGUUKQP TGHGTU VQ (QT KPUVCPEG VJG PCOG.BSL 5XBJO TGHGTU VQ /CTM 6YCKPKG 5COWGN %NGOGPU VJG OCP YJQ NKXGF KP VJG 75 CPF YTQVG UCVKTGU 6JG PCOG 4BNVFM $MFNFOT CNUQ TGHGTU VQVJCV OCP *GPEG VJG VYQ JCXG VJG UCOG TGHGTGPEG

6JG TFOTF KU VJG EQIPKVKXG UKIPKECPEG QT OQFG QH RTGUGPVCVKQP QH VJG TGHGTGPV .KPIWKUVKE 'ZRTGUUKQPU YKVJ VJG UCOG TGHGTGPEG OC[ JCXG FKGTGPV UGPUGU

(TGIG WUGU VJG HQNNQYKPI GZCORNG VQ KNNWUVTCVG VJKU XKGY .GV C D CPF E DG VJTGG NKPGU GCEJ QH YJKEJ LQKPU QPG XGTVGZ QHC VTKCPING VQ VJG OKFRQKPV QH VJG QRRQUKVG UKFG GCEJ QH C D CPF E KU VJWU C OGFKCP 6JGP KV KU C VJGQTGO VJCV

=V?JG RQKPV QH KPVGTUGEVKQP QH C CPF D KU VJGP VJG UCOG CU VJG RQKPV QH KPVGTUGEVKQP QH D CPF E 5Q YGJCXG FKGTGPV FGUKIPCVKQPU HQT VJG UCOG RQKPV CPF VJGUG PCOGU RQKPV QH KPVGTUGEVKQP QH C CPF D RQKPV QHKPVGTUGEVKQP QH D CPF E NKMGYKUG KPFKECVG VJG OQFG QH RTGUGPVCVKQP CPF JGPEG VJG UVCVGOGPV EQPVCKPU CEVWCNMPQYNGFIG )QVVNQD (TGIG CFS 4JOO VOE #FEFVUVOH

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

2.2 Terminology

2.2.1 Sense and reference (Sinn und Bedeutung)

$TQCFN[ URGCMKPI VJG reference QT referent QH C RTQRGT PCOG KU VJG QDLGEV KV FGPQVGU QT KPFKECVGU 6JG sense QH C RTQRGTPCOG KU YJCVGXGT OGCPKPI KV JCU YJGP VJGTG KU PQ QDLGEV VQ DG KPFKECVGF9JCV VJKU CTVKENG JCU ECNNGF TFOTF CPF SFGFSFODF CTG YJCV (TGIG ECNNU 4JOO CPF #FEFVUVOH TGURGEVKXGN[ KP VJG QTKIKPCN)GTOCP 5QOGVKOGU VJG RCKT QH VGTOU KU VTCPUNCVGF CU TFOTF CPFNFBOJOH QT CU TFOTF CPF OPNJOBUVN 6JG RTGEKUG OGCPKPIQH VJGUG VGTOU ECP XCT[ SWKVG UKIPKECPVN[ HTQO YTKVGT VQ YTKVGT UQ UQOG ECWVKQP KU FWG(QT 4JOO YTKVGTU JCXG WUGF VJG VGTOU TFOTF NFBOJOH JOUFOTJPO DPOOPUBUJPO DBTF CPF DPOUFOU(QT #FEFVUVOH YTKVGTU JCXG WUGF VJG VGTOU SFGFSFODF SFGFSFOU NFBOJOH FYUFOTJPO EFOPUBUJPO OPNJOBUVN CPF EFTJHOBUVN0QVG VJCV EQPHWUKPIN[ FBDI GZRTGUUKQP JCU DGGP VTCPUNCVGF CU NFBOJOH D[ UQOGQPG

2.2.2 An expressions relation to sense or reference

6GTOKPQNQI[ JCU CNUQ DGGP CRRNKGF VQ ECRVWTG VJG TGNCVKQP DGVYGGP

CP GZRTGUUKQP CPF KVU UGPUG

CP GZRTGUUKQP CPF KVU TGHGTGPEG

(TGIG KU V[RKECNN[ VTCPUNCVGF CU UC[KPI VJCV CP GZRTGUUKQP FYQSFTTFT KVU UGPUG CPF TUBOET GPS QT EFTJHOBUFT KVU TGHGTGPEG;GV GCTNKGT KP VJG GUUC[ JG QGTU CPQVJGT XGTD SFGFST YTKVKPI QH VJCV VQ YJKEJ VJG UKIP SFGFST YJKEJ OC[ DG ECNNGF VJGTGHGTGPEG QH VJG UKIP 5KPEG VJGP YTKVGTU JCXG XCTKQWUN[ UCKF VJCV CP GZRTGUUKQP TUBOET GPS EFTJHOBUFT SFGFST UP QT EFOPUFTKVU TGHGTGPEG 9G ECP CNUQ UC[ VJCV CP GZRTGUUKQP QJDLT PVU KVU TGHGTGPEG QT CNVGTPCVKXGN[ VJCV VJG UGPUG QH CP GZRTGUUKQPKU YJCV RKEMU QWV KVU TGHGTGPEG

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2.3 Sense without reference

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

2.4 Frege and Russell

2.4.1 Propositions and senses

$GTVTCPF 4WUUGNN HCOQWUN[ TGLGEVGF (TGIGU UGPUGTGHGTGPEG FKUVKPEVKQP VJQWIJ VJGTG KU UQOG RQUUKDKNKV[ VJCV VJG VYQ YGTGOKUKPVGTRTGVKPI CPF CTIWKPI RCUV QPG CPQVJGT (TGIG VCNMU CDQWV HQT GZCORNG UGPVGPEGU YJKEJ JCXG DQVJ C UGPUG CRTQRQUKVKQP CPF C TGHGTGPEG C VTWVJ XCNWG 4WUUGNN QP VJG QVJGT JCPF FGCNU FKTGEVN[ YKVJ RTQRQUKVKQPU DWV EQPUVTWGU VJGUGPQV CU CDUVTCEV RCTCNKPIWKUVKE KVGOU DWV CU VWRNGU QT UGVU QH QDLGEVU CPF EQPEGRVU(QT 4WUUGNN UGPUG KU YJQNN[ UGOCPVKE 4GHGTGPEG D[ EQPVTCUV KU KPVKOCVGN[ EQPPGEVGF YKVJ VJG PCOGF QDLGEV /QPV $NCPEKU VJG TGHGTGPV QH VJG PCOG /QPV $NCPE (TGIG CTIWGU VJCV VJG VJQWIJV /QPV $NCPE YKVJ KVU UPQYGNFU ECPPQV DG CDPNQPOFOU QH VJG VJQWIJV VJCV /QPV $NCPE KU OQTG VJCP OGVGTU JKIJ=? +H VJG UCOG GZRTGUUKQP /QPV $NCPE KUKP DQVJ UGPVGPEGU VJGP VJGTG KU UQOGVJKPI EQOOQP VQ GCEJ VJQWIJV CPF VJGTGHQTG TPNFUIJOH EQTTGURQPFKPI VQ VJG PCOG/QPV $NCPE 6JKU EQOOQP GNGOGPV YJKEJ ECPPQV DG VJG TGHGTGPV OWUV DG VJG OGCPKPI QT UGPUG

2.4.2 Senses and descriptions

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

3&-"5*0/ 50 $0//05"5*0/ "/% %&/05"5*0/

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

2.5 Relation to connotation and denotation

6JG UGPUGTGHGTGPEG FKUVKPEVKQP KU EQOOQPN[ EQPHWUGF YKVJ VJCV DGVYGGP EQPPQVCVKQP CPF FGPQVCVKQP YJKEJ RTGFCVGU(TGIG CPF KU HCOQWUN[ KPVGTRTGVGF D[ /KNN 6JKU FKUVKPEVKQP KU CRRNKGF OCKPN[ VQ YQTFU RCTVKEWNCTN[ RTGFKECVGU GZRTGUUKPIRTQRGTVKGU GI SFE EPH CBDIFMPS TCVJGT VJCP PCOKPI KPFKXKFWCNU UQ VJG FKGTGPEG DGVYGGP VJG VYQ FKUVKPEVKQPU ECP DGJCTF VQ UGG 6JG EQPPQVCVKQP QH C RTGFKECVG KU VJG EQPEGRV KV GZRTGUUGU QT OQTG QHVGP VJG UGV QH RTQRGTVKGU VJCV FGVGTOKPGYJGVJGT CP KPFKXKFWCN HCNNU WPFGT KV 6JG FGPQVCVKQP QH C EQPEGRV KU VJG CEVWCN EQNNGEVKQP QH GPVKVKGU VJCV EP HCNN WPFGT KV6JWU VJG EQPPQVCVKQP QH CBDIFMPS KU RGTJCRU WPOCTTKGF CFWNV OCNG JWOCP CPF KVU FGPQVCVKQP KU CNN VJG DCEJGNQTU KP VJGYQTNF7PFGT C FGUETKRVKXKUV TGCFKPI QH (TGIG UGPUG CPF TGHGTGPEG CTG RTQDCDN[ VJG UCOG CU EQPPQVCVKQP CPF FGPQVCVKQP7PFGT C PQPFGUETKRVKXKUV TGCFKPI VJG[ CTG RTQDCDN[ PQV +V KU CNYC[U RQUUKDNG VQ JCXG C EQPPQVCVKQP YKVJQWV C FGPQVCVKQPYJKEJ OC[ PQV DG VJG ECUG YKVJ UGPUG CPF TGHGTGPEG # IKXGP UGPUG CNYC[U FGVGTOKPGU VJG UCOG TGHGTGPEG YJKEJ OKIJV PQVDG VJG ECUG YKVJ EQPPQVCVKQP CPF FGPQVCVKQP /QUV ENGCTN[ C UKPING EQPEGRVYJKEJ D[ FGPKVKQP JCU QPN[ QPG EQPPQVCVKQPCPF FGPQVCVKQP CV C VKOG OKIJV DG GZRTGUUGF D[ VGTOU JCXKPI FKGTGPV UGPUGU (QT GZCORNG DBU CPF GFMJOF JCXG RTGEKUGN[VJG UCOG EQPPQVCVKQP OGODGT QH VJG (GNKFCG HCOKN[ QH ECTPKXQTQWU OCOOCNU CPF QDXKQWUN[ VJG UCOG FGPQVCVKQP CNNVJG ECVU VJCV KU CNN VJG HGNKPGU DWV KV KU RGTHGEVN[ KPVGNNKIKDNG VJCV UQOGQPG UJQWNF HCKN VQ TGCNK\G VJCV DBU CPF GFMJOF OGCPVJG UCOGRGTJCRU VJG[ JCXG QPN[ JGCTF QPG YQTF CRRNKGF VQ JQWUGECVU VJG QVJGT VQ VKIGTU CPF NKQPU +P VJCV ECUG VJGYQTFU JCXG FKGTGPV UGPUGU

2.6 See also

#NKCUKPI EQORWVKPI CP GZCORNG QH UGPUG CPF TGHGTGPEG KP EQORWVGT RTQITCOOKPI YJGTG VYQ QT OQTG RQKPVGTUQT TGHGTGPEGU RQKPV VQ VJG UCOG OGOQT[ NQECVKQP QT QDLGEV

&KJ[FTQIGPOQPQZKFG JQCZ VJCV GZRNQKVU VJG KIPQTCPEG QHOCP[ RGQRNG VJCV VJG VYQ UGPUGU FKJ[FTQIGPOQPQZKFGCPF YCVGT TGHGT VQ VJG UCOG EJGOKECN UWDUVCPEG *21 UKOKNCTN[ VQ (TGIGU GZCORNG QH *GURGTWU KU 2JQURJQTWU

)QVVNQD (TGIG /GFKCVGF TGHGTGPEG VJGQT[ 1P &GPQVKPI YJKEJ QWVNKPGF $GTVTCPF 4WUUGNNU 2JKNQUQRJ[ QH .CPIWCIG

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3WKFFKV[ CPF *CGEEGKV[ UKOKNCT EQPEGRVU HTQO /GFKGXCN RJKNQUQRJ[ 4WUUGNNU 2CTCFQZ C RW\\NGEQPKEV DGVYGGP 4WUUGNN CPF (TGIG 5KIP UGOKQVKEU 6JGQT[ QH FGUETKRVKQPU

2.7 Footnotes

=? (TGIGU GZCORNG KU VJG NGCUV TCRKFN[ EQPXGTIGPV UGTKGU CPF VJGTG KU CNYC[U VJG RTGUGPV -KPI QH (TCPEG

=? 5GG 5GOCPVKE EQORQUKVKQP

=? 6JKU GZCORNG KU HTQO C NGVVGT VQ 4WUUGNN

=? 'XCPU )CTGVJ ,QJP /E&QYGNN GF 5IF 7BSJFUJFT PG 3FGFSFODF 1ZHQTF 1ZHQTF 7PKXGTUKV[ 2TGUU

=? /E&QYGNN ,QJP #RTKN 1P VJG 5GPUG CPF 4GHGTGPEG QH C 2TQRGT 0COG .JOE 0GY 5GTKGU 86

2.8 External links

)QVVNQD (TGIG DGT 5KPP WPF $GFGWVWPI )QVVNQD (TGIG 1P 5GPUG CPF 4GHGTGPEG 'PINKUJ VTCPUNCVKQP D[ /CZ $NCEM +PVGTPGV 'PE[ENQRGFKC QH 2JKNQUQRJ[ (TGIG CPF .CPIWCIG (TGIGU %QPVTKDWVKQP VQ VJG 2JKNQUQRJ[ QH .CPIWCIG D[ 4KEJCTF ) *GEM CPF 4QDGTV /C[ RWDNKUJGF KP VJG 1ZHQTF*CPFDQQM VQ VJG 2JKNQUQRJ[ QH .CPIWCIG

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CFS 4JOO VOE #FEFVUVOH DMJDL UP SFBE

Chapter 3

On Denoting

On Denoting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

3.1 The denoting phrase

3.1.1 Russells concept of a denoting phrase

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

3.1.2 Reference to something that does not exist

*QYGXGT CV VJG XGT[ DGIKPPKPI QH VJG CTVKENG 4WUUGNN FKUVKPIWKUJGU DGVYGGP ECUGU YJGTG C RJTCUG OC[ DG FGPQVKPI CPF[GV PQV FGPQVG CP[VJKPI GI VJG RTGUGPV -KPI QH (TCPEG CPF ECUGU YJGTG VJG[ OC[ FGPQVG QPG FGPKVG QDLGEV UWEJ CUVJG RTGUGPV -KPI QH 'PINCPF +H VJKU RCUUCIG KU KPVGTRTGVGF CU UC[KPI VJCV FGUETKRVKQPU OC[ TGHGT VQ QPG FGPKVG QDLGEVVJGP KV EQWNF DG VJCV 4WUUGNN CEVWCNN[ TGEQIPKUGF VJG VYQ FKUVKPEV WUGU QH FGPKVG FGUETKRVKQPU CVVTKDWVKXG CPF TGHGTGPVKCN

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VJCV &QPPGNNCP NCVGT RTQRQUGF

3.1.3 Epistemology

+P CP[ ECUG CHVGT ENCTKH[KPI VJG UGPUG QH VJG VGTO FGPQVKPI RJTCUG CPF RTQXKFKPI UGXGTCN GZCORNGU VQ KNNWUVTCVG VJG KFGC4WUUGNN GZRNCKPU VJG GRKUVGOQNQIKECN OQVKXCVKQPU HQT JKU VJGQT[ 4WUUGNN DGNKGXGU CV VJKU RQKPV VJCV VJGTG CTG GUUGPVKCNN[VYQ OQFGU QH MPQYKPI MPQYNGFIG D[ FGUETKRVKQP CPF MPQYNGFIG D[ FKTGEV CESWCKPVCPEG -PQYNGFIG D[ CESWCKPVCPEGKU NKOKVGF VQ VJG UGPUG FCVC QH VJG RJGPQOGPCN YQTNF CPF VQ QPGU QYP RTKXCVG KPPGT GZRGTKGPEGU YJKNG MPQYNGFIG QHGXGT[VJKPI GNUG QVJGT OKPFU RJ[UKECN QDLGEVU CPF UQ QP ECP QPN[ DG MPQYP D[ YC[ QH IGPGTCN FGUETKRVKQPU

3.2 The theory of descriptions

3.2.1 Mathematical description

4WUUGNN UVCTVU QWV D[ FGPKPI VJG HWPFCOGPVCN PQVKQP QH C QSPQPTJUJPOBM GVODUJPO 6JKU KU DCUKECNN[ C OQFKGF XGTUKQP QH(TGIGU KFGC QH VOTBUVSBUFE DPODFQUT *GPEG %Z UVCPFU HQT C RTQRQUKVKQP KP YJKEJ Z KU C EQPUVKVWGPV CPF YJGTG Z VJGXCTKCDNG KU GUUGPVKCNN[ CPF YJQNN[ WPFGVGTOKPGF 6JG PQVKQPU QH FWFSZUIJOH OPUIJOH CPF TPNFUIJOH VJG OQUV RTKOKVKXGQH FGPQVKPI RJTCUGU ECP VJGP DG FGPGF CU HQNNQYU

C(E) xC(x)

C(N) xC(x)C(S) xC(x)YJGTG & UVCPFU HQT GXGT[VJKPI / UVCPFU HQT PQVJKPI CPF 4 UVCPFU HQT UQOGVJKPI "MM KU VCMGP CU RTKOKVKXG CPF KPFGPCDNGCPF VJG QVJGTU CTG FGPGF KP VGTOU QH KV 4WUUGNN GORJCUKUGU VJCV VJGUG PQVKQPU ECP JCXG PQ OGCPKPI CRCTV HTQO VJCV YJKEJKU CUUKIPGF VQ VJGO YKVJKP VJG RTQRQUKVKQPU KP YJKEJ VJG[ QEEWT CNN QH YJKEJ CTG OGCPKPIHWN 6JKU KU VJG HQWPFCVKQP QH4WUUGNNU VJGQT[ QH FGUETKRVKQPU CU JG RTQEGGFU VQ KNNWUVTCVG

3.2.2 Illustration

6JG RJTCUG VJG HCVJGT QH %JCTNGU ++ ( YCU GZGEWVGF ' KU KPVGTRTGVGF CU VJG HQNNQYKPI SWCPVKECVKQPCN CUUGTVKQP

x ((F (x) y (F (y) x = y)) E (x))

+P QVJGT YQTFU VJGTG KU QPG CPF QPN[ QPG VJKPI Z UWEJ VJCV Z KU VJG HCVJGT QH %JCTNGU ++ CPF Z YCU GZGEWVGF5Q KH % TGRTGUGPVU CP[ UVCVGOGPV CV CNN CDQWV VJG HCVJGT QH %JCTNGU ++ VJG UVCVGOGPV % VJG HCVJGT QH %JCTNGU ++ CNYC[UKORNKGU

x (F (x) y (F (y) x = y))

+V HQNNQYU VJCV KH VJGTG KU PQV QPG CPF QPN[ QPG GPVKV[ VJCV UCVKUGU VJG CDQXG VJGP GXGT[ RTQRQUKVKQP VJCV EQPVCKPU VJGFGUETKRVKQPU KU HCNUG +H VJG OQVJGT QH %JCTNGU ++ YCU WPHCKVJHWN VJG UVCVGOGPV OC[ DG HCNUG +P VJKU YC[ 4WUUGNN RQKPVUQWV KV YKNN VWTP QWV VJCV CNN UVCVGOGPVU EQPVCKPKPI PQPTGHGTTKPI FGUETKRVKQPU GI 6JG RTGUGPV MKPI QH 5COQVJTCEG KU CITGCV YTKVGT CTG HCNUG 4WUUGNNU VJGQT[ TGFWEGU CNN RTQRQUKVKQPU VJCV EQPVCKP FGPKVG FGUETKRVKQPU KPVQ HQTOU VJCV FQ PQV

$)"15&3 0/ %&/05*/(

3.3 Meinong

*G VJGP ETKVKEKUGU/GKPQPIU VJGQT[ QH QDLGEVU YJKEJ CEEQTFKPI VQ 4WUUGNN KU QPVQNQIKECNN[ RTQOKUEWQWU CPF UGNHEQPVTCFKEVQT[$QVJ QH VJGUG ETKVKEKUOU UVGO HTQO /GKPQPIU VJGQT[ VJCV VJGTG KU CP QDLGEV YJGVJGT KV GZKUVU QT UWDUKUVU HQT GXGT[ UGVQH RTQRGTVKGU 6JGTGHQTG VJGTG KU CP QDLGEV VJCV KU DQVJ TQWPF CPF PQV TQWPF QT TQWPF CPF USWCTG 4WUUGNN CTIWGU VJCV/GKPQPIU VJGQT[ GPVCKNU EQPENWUKQPU UWEJ CU VJG RTGUGPV -KPI QH (TCPEG DQVJ GZKUVU CPF FQGU PQV GZKUV *QYGXGT/GKPQPI FQGU PQV CVVTKDWVG GZKUVGPEG QT CP[ QVJGT UQTV QH DGKPI VQ OPOFYJTUFOU PCKFDUT 4WUUGNN CNUQ CEEWUGU /GKPQPI QHXKQNCVKPI VJG NCY QH PQPEQPVTCFKEVKQP D[ CUUGTVKPI VJCV VJG TQWPF USWCTG KU DQVJ TQWPF CPF PQV TQWPF /GKPQPI QP VJGQVJGT JCPF OCKPVCKPU VJCV VJG NCYU QH NQIKE FQ PQV CRRN[ VQ UWEJ RJGPQOGPC CU KORQUUKDNG QDLGEVU VJCV JCXG PQ DGKPI=?

3.4 Resolving the problem of negative existentials

1PG QH VJG HWPFCOGPVCN RW\\NGU VJCV 4WUUGNN JQRGU VQ TGUQNXG YKVJ VJG VJGQT[ QH FGUETKRVKQPU KU VJG RTQDNGO QH PQPTGHGTTKPI GZRTGUUKQPU QT CU VJG[ CTG PQY ECNNGF PGICVKXG GZKUVGPVKCNU *G PCNN[ GZRNCKPU JQY JKU VJGQT[ TGUQNXGU VJKURTQDNGO CHVGT KPXQMKPI C FKUVKPEVKQP DGVYGGP YJCV JG ECNNU QSJNBSZ CPF TFDPOEBSZ QEEWTTGPEGU QH FGPQVKPI RJTCUGU

3.4.1 Statements about concepts where the object doesnt exist

5KPEG FGPKVG FGUETKRVKQPU CTG LWUV SWCPVKECVKQPCN FGXKEGU QP 4WUUGNNU XKGY VJG[ ECP GPVGT KPVQ UEQRG TGNCVKQPU YKVJ QVJGTNQIKECN QRGTCVQTU +P VJG ECUG QH PGICVKXG GZKUVGPVKCNU VJGTG KU CP CODKIWKV[ DGVYGGP VYQ FKGTGPV RTKOCT[ CPF UGEQPFCT[TGCFKPIU QH VJG SWCPVKECVKQPCN CUUGTVKQP (QT GZCORNG 4WUUGNN WUGU VJG ECUG QH VJG RTGUGPV -KPI QH (TCPEG KU PQV DCNF*GTG VJG VYQ RQUUKDNG TGCFKPIU CTG

x(K(x) y(K(y) y = x)) B(x))x(K(x) y(K(y) y = x)) B(x))+P VJG TUV ECUG VJG UVCVGOGPV KU HCNUG DGECWUG KV SWCPVKGU QXGT PQPGZKUVGPV GPVKVKGU +P VJG UGEQPF ECUG VJG UVCVGOGPVKU VTWG DGECWUG KV KU PQV VJG ECUG VJCV VJGTG KU C RTGUGPV -KPI QH (TCPEG 6JWU CNN RTQRQUKVKQPU KP YJKEJ VJG -KPI QH(TCPEG JCU C RTKOCT[ QEEWTTGPEG CTG HCNUG VJG FGPKCNU QH UWEJ RTQRQUKVKQPU CTG VTWG DWV KP VJGO VJG -KPI QH (TCPEG JCUC UGEQPFCT[ QEEWTTGPEG %QPVGORQTCTKN[ KV KU EWUVQOCT[ VQ FKUEWUU 4WUUGNNU RTKOCT[UGEQPFCT[ FKUVKPEVKQP KP VJG OQTGNQIKECNN[ GZCEV VGTOU QH YKFG CPF PCTTQY UEQRG 6JG UEQRG FKUVKPEVKQP TGICTFU VJG QRGTCVQT VJCV QP QPG TGCFKPI OQFKGUPOMZ VJG UWDLGEV CPF QP VJG QVJGT OQFKGU VJG GPVKTG UGPVGPEG

3.4.2 Ambiguity

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

(FPSHF *7 XPOEFSFE XIFUIFS UIF Y UIBU JT JEFOUJDBM UP UIF Z UIBU

YJGTG UVCPFU HQT UQOG FGPKVG FGUETKRVKQP UWEJ CU VJG ENGXGT HGNNQY YJQ YTQVG +XCPJQG CPF UVCPFU HQT UQOGVJKPINKMG VJG GNGICPV IGPVNGOCP UGCVGF PGZV VQ VJG 2TKPEGUU +P VJG EF SF ECUG VJG CDQXG UGPVGPEG ECP DG KPVGTRTGVGF CU HQNNQYUKPUVGCF

UIF Y UIBU JT TVDI UIBU ,JOH (FPSHF XPOEFSFE XIFUIFS Y JT JEFOUJDBM UP UIF Z UIBU

$3*5*$*4.4

3.4.3 Fictional names

(KPCNN[ 4WUUGNN UWIIGUVU VJCV EVKQPCN PCOGU UWEJ CU #RQNNQ ECP DG VTGCVGF CU CDDTGXKCVGF FGPKVG FGUETKRVKQPU VJCVTGHGT VQ PQVJKPI #NN RTQRQUKVKQPU VJCV EQPVCKP PCOGU QH UWEJ EVKQPCN GPVKVKGU CTG VQ DG VTGCVGF KP VJG UCOG OCPPGT CU VJGPGICVKXG GZKUVGPVKCNU FGUETKDGF CDQXG

3.5 Criticisms

+P JKU GUUC[ 1P 4GHGTTKPI 2 ( 5VTCYUQP ETKVKEKUGF 4WUUGNNU EJCTCEVGTKUCVKQP QH UVCVGOGPVU YJGTG VJG QDLGEV FQGUPVGZKUV UWEJ CU VJG RTGUGPV -KPI QH (TCPEG CU DGKPI HCNUG 5WEJ UVCVGOGPVU 5VTCYUQP JGNF CTG PGKVJGT VTWG PQT HCNUGDWV TCVJGT CDUWTF 5VTCYUQP DGNKGXGF VJCV EQPVTCT[ VQ 4WUUGNN WUG FQGU FGVGTOKPG VJG OGCPKPI QH C UGPVGPEG 6Q IKXGVJG OGCPKPI QH CP GZRTGUUKQP KU VQ IKXG IGPGTCN FKTGEVKQPU HQT KVU WUG=? $GECWUG QH VJKU 5VTCYUQP CTIWGF VJCV YGTGUQOGQPG VQ UC[ VJG -KPI QH (TCPEG YCU YKUG YG YQWNF PQV UC[ JGT UVCVGOGPV KU VTWG QT HCNUG DWV TCVJGT FGEKFG UJG OWUVDG WPFGT C OKUCRRTGJGPUKQP UKPEG PQTOCNN[ VJG SWGUVKQP YQWNF PQV CTKUG CU VJGTG KU PQ -KPI QH (TCPEG=?

5VTCYUQP CNUQ CTIWGF VJCV YG QHVGP PGGF VQ MPQY VJG WUG QH C YQTF VQ WPFGTUVCPF KVU OGCPKPI UWEJ CU KP UVCVGOGPVU QHVJG HQTO 6JG VCDNG KU EQXGTGF YKVJ DQQMU +P PQTOCN WUG VJG GZRTGUUKQP YQWNF DG TGHGTTKPI VQ QPG RCTVKEWNCT VCDNG +VKU HCNUG 5VTCYUQP DGNKGXGF VQ VJKPM CU 4WUUGNN VJCV VJG RJTCUG YKNN QPN[ JCXG OGCPKPI KPUQHCT CU VJGTG KU QPN[ QPG VCDNGCPF PQ OQTG 6JG RJTCUG JCU CRRNKECVKQP KP XKTVWG QH VJG HCEV VJCV QPG VCDNG CPF PQ OQTG KU YJCV KU DGKPI TGHGTTGF VQ CPFKV KU WPFGTUVQQF VJCV VJG VCDNG KU YJCV KU DGKPI TGHGTGPEGF=?

3.6 References

=? (TCPM 2NWORVQP 4COUG[ 4KEJCTF $GXCP $TCKVJYCKVG 4KEJCTF $GXCP $TCKVJYCKVG GF 5IF GPVOEBUJPOT PG NBUIFNBUJDTBOE PUIFS MPHJDBM FTTBZT 4QWVNGFIG R +5$0 TGVTKGXGF #WIWUV

=? # 9 5RCTMGU 5BMLJOH QIJMPTPQIZ B XPSECPPL 6C[NQT (TCPEKU R +5$0 TGVTKGXGF #WIWUV

=? .WFNQY 2GVGT &GUETKRVKQPU 5IF 4UBOGPSE &ODZDMPQFEJB PG 1IJMPTPQIZ 5WOOGT 'FKVKQP 'FYCTF 0

Chapter 4

Theory of descriptions

6JG theory of descriptions KU VJG RJKNQUQRJGT $GTVTCPF 4WUUGNNU OQUV UKIPKECPV EQPVTKDWVKQP VQ VJG RJKNQUQRJ[ QH NCPIWCIG +V KU CNUQ MPQYP CU Russells Theory of Descriptions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

4.1 Introduction

$GTVTCPF 4WUUGNNU VJGQT[ QH FGUETKRVKQPU YCU KPKVKCNN[ RWV HQTVJ KP JKU GUUC[ 1P &GPQVKPI RWDNKUJGF KP VJG LQWTPCNQH RJKNQUQRJ[ .JOE 4WUUGNNU VJGQT[ KU HQEWUGF QP VJG NQIKECN HQTO QH GZRTGUUKQPU KPXQNXKPI FGPQVKPI RJTCUGU YJKEJ JGFKXKFGU KPVQ VJTGG ITQWRU

&GPQVKPI RJTCUGU YJKEJ FQ PQV FGPQVG CP[VJKPI HQT GZCORNG VJG EWTTGPV 'ORGTQT QH -GPVWEM[

2JTCUGU YJKEJ FGPQVG QPG FGPKVG QDLGEV HQT GZCORNG VJG RTGUGPV 2TGUKFGPV QH VJG 75# 9G PGGF PQV MPQYYJKEJ QDLGEV VJG RJTCUG TGHGTU VQ HQT KV VQ DG WPCODKIWQWU HQT GZCORNG VJG EWVGUV MKVVGP KU C WPKSWG KPFKXKFWCNDWV JKU QT JGT CEVWCN KFGPVKV[ KU WPMPQYP

2JTCUGU YJKEJ FGPQVG CODKIWQWUN[ HQT GZCORNG CP #CTFXCTM

*OEFOJUF EFTDSJQUJPOT EQPUVKVWVG 4WUUGNNU VJKTF ITQWR &GUETKRVKQPU OQUV HTGSWGPVN[ CRRGCT KP VJG UVCPFCTF UWDLGEVRTGFKECVG HQTO4WUUGNN RWV HQTYCTF JKU VJGQT[ QH FGUETKRVKQPU VQ UQNXG C PWODGT QH RTQDNGOU KP VJG RJKNQUQRJ[ QH NCPIWCIG 6JG VYQOCLQT RTQDNGOU CTG EQTGHGTTKPI GZRTGUUKQPU CPF PQPTGHGTTKPI GZRTGUUKQPU6JG RTQDNGO QH EQTGHGTTKPI GZRTGUUKQPU QTKIKPCVGF RTKOCTKN[ YKVJ )QVVNQD (TGIG CU VJG RTQDNGO QH KPHQTOCVKXG KFGPVKVKGU(QT GZCORNG KH VJG OQTPKPI UVCT CPF VJG GXGPKPI UVCT CTG VJG UCOG RNCPGV KP VJG UM[ UGGP CV FKGTGPV VKOGU QH FC[ KPFGGFVJG[ CTG DQVJ VJG RNCPGV 8GPWU VJG OQTPKPI UVCT KU VJG RNCPGV 8GPWU UGGP KP VJG OQTPKPI UM[ CPF VJG GXGPKPI UVCT KU VJGRNCPGV 8GPWU UGGP KP VJG GXGPKPI UM[ JQY KU KV VJCV UQOGQPG ECP VJKPM VJCV VJG OQTPKPI UVCT TKUGU KP VJG OQTPKPI DWV

%&'*/*5& %&4$3*15*0/4

VJG GXGPKPI UVCT FQGU PQV! 6JKU KU CRRCTGPVN[ RTQDNGOCVKE DGECWUG CNVJQWIJ VJG VYQ GZRTGUUKQPU UGGO VQ FGPQVG VJG UCOGVJKPI QPG ECPPQV UWDUVKVWVG QPG HQT VJG QVJGT YJKEJ QPG QWIJV VQ DG CDNG VQ FQ YKVJ KFGPVKECN QT U[PQP[OQWU GZRTGUUKQPU6JG RTQDNGO QH PQPTGHGTTKPI GZRTGUUKQPU KU VJCV EGTVCKP GZRTGUUKQPU VJCV CTG OGCPKPIHWN FQ PQV VTWN[ TGHGT VQ CP[VJKPI(QT GZCORNG D[ CP[ FQI KU CPPQ[KPI KV KU PQV OGCPV VJCV VJGTG KU C RCTVKEWNCT KPFKXKFWCN FQI PCOGN[ BOZ EPH VJCV JCUVJG RTQRGTV[ QH DGKPI CPPQ[KPI UKOKNCT EQPUKFGTCVKQPU IQ HQT UQOG FQI GXGT[ FQI C FQI CPF UQ QP .KMGYKUG D[VJG EWTTGPV 'ORGTQT QH -GPVWEM[ KU ITC[ KV KU PQV OGCPV VJCV VJGTG KU UQOG KPFKXKFWCN PCOGN[ UIF DVSSFOU &NQFSPS PG,FOUVDLZ YJQ JCU VJG RTQRGTV[ QH DGKPI ITG[ -GPVWEM[ YCU PGXGT C OQPCTEJ[ UQ VJGTG KU EWTTGPVN[ PQ 'ORGTQT 6JWUYJCV 4WUUGNN YCPVU VQ CXQKF KU CFOKVVKPI O[UVGTKQWU PQPGZKUVGPV GPVKVKGU KPVQ JKU QPVQNQI[ (WTVJGTOQTG VJG NCY QH VJGGZENWFGF OKFFNG TGSWKTGU VJCV QPG QH VJG HQNNQYKPI RTQRQUKVKQPU HQT GZCORNG OWUV DG VTWG GKVJGT VJG EWTTGPV 'ORGTQTQH -GPVWEM[ KU ITC[ QT KV KU PQV VJG ECUG VJCV VJG EWTTGPV 'ORGTQT QH -GPVWEM[ KU ITC[ 0QTOCNN[ RTQRQUKVKQPU QHVJG UWDLGEVRTGFKECVG HQTO CTG UCKF VQ DG VTWG KH CPF QPN[ KH VJG UWDLGEV KU KP VJG GZVGPUKQP QH VJG RTGFKECVG $WV VJGTG KUEWTTGPVN[ PQ 'ORGTQT QH -GPVWEM[ 5Q UKPEG VJG UWDLGEV FQGU PQV GZKUV KV KU PQV KP VJG GZVGPUKQP QH GKVJGT RTGFKECVG KV KUPQV QP VJG NKUV QH ITG[ RGQRNG QT PQPITC[ RGQRNG 6JWU KV CRRGCTU VJCV VJKU KU C ECUG KP YJKEJ VJG NCY QH GZENWFGF OKFFNGKU XKQNCVGF YJKEJ KU CNUQ CP KPFKECVKQP VJCV UQOGVJKPI JCU IQPG YTQPI

4.2 Denite descriptions

5GG CNUQ &GPKVG FGUETKRVKQP

4WUUGNN CPCN[UGU FGPKVG FGUETKRVKQPU UKOKNCTN[ VQ KPFGPKVG FGUETKRVKQPU GZEGRV VJCV VJG KPFKXKFWCN KU PQY WPKSWGN[ URGEKGF 6CMG CU CP GZCORNG QH C FGPKVG FGUETKRVKQP VJG UGPVGPEG VJG EWTTGPV 'ORGTQT QH -GPVWEM[ KU ITC[ 4WUUGNNCPCN[UGU VJKU RJTCUG KPVQ VJG HQNNQYKPI EQORQPGPV RCTVU YKVJ Z CPF [ TGRTGUGPVKPI XCTKCDNGU

VJGTG KU CP Z UWEJ VJCV Z KU CP GORGTQT QH -GPVWEM[

HQT GXGT[ Z CPF GXGT[ [ KH DQVJ Z CPF [ CTG GORGTQTU QH -GPVWEM[ VJGP [ KU Z KG VJGTG KU CV OQUV QPG GORGTQT QH-GPVWEM[

CP[VJKPI VJCV KU CP GORGTQT QH -GPVWEM[ KU ITC[

6JWU C FGPKVG FGUETKRVKQP QH VJG IGPGTCN HQTO VJG ( KU ) DGEQOGU VJG HQNNQYKPI GZKUVGPVKCNN[ SWCPVKGF RJTCUG KPENCUUKE U[ODQNKE NQIKE YJGTG Z CPF [ CTG XCTKCDNGU CPF ( CPF ) CTG RTGFKECVGU KP VJG GZCORNG CDQXG ( YQWNF DGKU CP GORGTQT QH -GPVWEM[ CPF ) YQWNF DG KU ITC[

Z=(Z [([ Z[ )Z?

+PHQTOCNN[ VJKU TGCFU CU HQNNQYU UQOGVJKPI GZKUVU YKVJ VJG RTQRGTV[ ( VJGTG KU QPN[ QPG UWEJ VJKPI CPF VJKU WPKSWG VJKPICNUQ JCU VJG RTQRGTV[ )6JKU CPCN[UKU CEEQTFKPI VQ 4WUUGNN UQNXGU VJG VYQ RTQDNGOU PQVGF CDQXG CU TGNCVGF VQ FGPKVG FGUETKRVKQPU

6JG OQTPKPI UVCT TKUGU KP VJG OQTPKPI PQ NQPIGT PGGFU VQ DG VJQWIJV QH CU JCXKPI VJG UWDLGEVRTGFKECVG HQTO +VKU KPUVGCF CPCN[UGF CU VJGTG KU QPG WPKSWG VJKPI UWEJ VJCV KV KU VJG OQTPKPI UVCT CPF KV TKUGU KP VJG OQTPKPI 6JWUUVTKEVN[ URGCMKPI VJG VYQ GZRTGUUKQPU VJG OQTPKPI UVCT CPF VJG GXGPKPI UVCT CTG PQV U[PQP[OQWU UQ KV OCMGUUGPUG VJCV VJG[ ECPPQV DG UWDUVKVWVGF VJG CPCN[UGF FGUETKRVKQP QH VJG GXGPKPI UVCT KU VJGTG KU QPG WPKSWG VJKPI UWEJVJCV KV KU VJG GXGPKPI UVCT CPF KV TKUGU KP VJG GXGPKPI 6JKU UQNXGU )QVVNQD (TGIGU RTQDNGO QH KPHQTOCVKXG KFGPVKVKGU

5KPEG VJG RJTCUG VJG EWTTGPV 'ORGTQT QH -GPVWEM[ KU ITC[ KU PQV C TGHGTTKPI GZRTGUUKQP CEEQTFKPI VQ 4WUUGNNUVJGQT[ KV PGGF PQV TGHGT VQ C O[UVGTKQWU PQPGZKUVGPV GPVKV[ 4WUUGNN UC[U VJCV KH VJGTG CTG PQ GPVKVKGU : YKVJ RTQRGTV[( VJG RTQRQUKVKQP : JCU RTQRGTV[ ) KU HCNUG HQT BMM XCNWGU QH :

4WUUGNN UC[U VJCV CNN RTQRQUKVKQPU KP YJKEJ VJG 'ORGTQT QH -GPVWEM[ JCU C RTKOCT[ QEEWTTGPEG CTG HCNUG 6JG FGPKCNU QHUWEJ RTQRQUKVKQPU CTG VTWG DWV KP VJGUG ECUGU VJG 'ORGTQT QH -GPVWEM[ JCU C UGEQPFCT[ QEEWTTGPEG VJG VTWVJ XCNWG QH VJGRTQRQUKVKQP KU PQV C HWPEVKQP QH VJG VTWVJ QH VJG GZKUVGPEG QH VJG 'ORGTQT QH -GPVWEM[

$)"15&3 5)&03: 0' %&4$3*15*0/4

4.3 Indenite descriptions

6CMG CU CP GZCORNG QH CP KPFGPKVG FGUETKRVKQP VJG UGPVGPEG UQOG FQI KU CPPQ[KPI 4WUUGNN CPCN[UGU VJKU RJTCUG KPVQVJG HQNNQYKPI EQORQPGPV RCTVU YKVJ Z CPF [ TGRTGUGPVKPI XCTKCDNGU

VJGTG KU CP Z UWEJ VJCV Z KU C FQI

Z KU DGKPI CPPQ[KPI

6JWU CP KPFGPKVG FGUETKRVKQP QH VJG IGPGTCN HQTO C & KU # DGEQOGU VJG HQNNQYKPI GZKUVGPVKCNN[ SWCPVKGF RJTCUG KPENCUUKE U[ODQNKE NQIKE YJGTG Z CPF [ CTG XCTKCDNGU CPF & CPF # CTG RTGFKECVGU

Z=&Z #Z?

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

4.4 Criticism of Russells analysis

4.4.1 P. F. Strawson

2 ( 5VTCYUQP CTIWGF VJCV 4WUUGNN JCF HCKNGF VQ EQTTGEVN[ TGRTGUGPV YJCV QPG OGCPU YJGP QPG UC[U C UGPVGPEG KP VJG HQTOQH VJG EWTTGPV 'ORGTQT QH -GPVWEM[ KU ITC[ #EEQTFKPI VQ 5VTCYUQP VJKU UGPVGPEG KU PQV EQPVTCFKEVGF D[ 0Q QPG KUVJG EWTTGPV 'ORGTQT QH -GPVWEM[ HQT VJG HQTOGT UGPVGPEG EQPVCKPU PQV CP GZKUVGPVKCN CUUGTVKQP DWV CVVGORVU VQ VTF VJGEWTTGPV 'ORGTQT QH -GPVWEM[ CU C TGHGTTKPI QT FGPQVKPI RJTCUG 5KPEG VJGTG KU PQ EWTTGPV 'ORGTQT QH -GPVWEM[ VJGRJTCUG HCKNU VQ TGHGT VQ CP[VJKPI CPF UQ VJG UGPVGPEG KU PGKVJGT VTWG PQT HCNUG#PQVJGT MKPF QH EQWPVGTGZCORNG VJCV 5VTCYUQP CPF RJKNQUQRJGTU UKPEG JCXG TCKUGF EQPEGTPU VJCV QH KPEQORNGVG FGPKVGFGUETKRVKQPU VJCV KU UGPVGPEGU YJKEJ JCXG VJG HQTO QH C FGPKVG FGUETKRVKQP DWV YJKEJ FQ PQV WPKSWGN[ FGPQVG CP QDLGEV5VTCYUQP IKXGU VJG GZCORNG VJG VCDNG KU EQXGTGF YKVJ DQQMU 7PFGT 4WUUGNNU VJGQT[ HQT UWEJ C UGPVGPEG VQ DG VTWG VJGTGYQWNF JCXG VQ DG QPN[ QPG VCDNG KP CNN QH GZKUVGPEG $WV D[ WVVGTKPI C RJTCUG UWEJ CU VJG VCDNG KU EQXGTGF YKVJ DQQMUVJG URGCMGT KU TGHGTTKPI VQ C RCTVKEWNCT VCDNG HQT KPUVCPEG QPG VJCV KU KP VJG XKEKPKV[ QH VJG URGCMGT 6YQ DTQCF TGURQPUGUJCXG DGGP EQPUVTWEVGF VQ VJKU HCKNWTG C UGOCPVKE CPF C RTCIOCVKE CRRTQCEJ 6JG UGOCPVKE CRRTQCEJ QH RJKNQUQRJGTUNKMG 5VGRJGP 0GCNG=? UWIIGUVU VJCV VJG UGPVGPEG FQGU KP HCEV JCXG VJG CRRTQRTKCVG OGCPKPI CU VQ OCMG KV VTWG 5WEJOGCPKPI KU CFFGF VQ VJG UGPVGPEG D[ VJG RCTVKEWNCT EQPVGZV QH VJG URGCMGTVJCV UC[ VJG EQPVGZV QH UVCPFKPI PGZV VQ CVCDNG EQORNGVGU VJG UGPVGPEG 'TPKG .GRQTG UWIIGUVU VJCV VJKU CRRTQCEJ VTGCVU FGPKVG FGUETKRVKQPU CU JCTDQTKPI JKFFGPKPFGZKECN GZRTGUUKQPU UQ VJCV YJCVGXGT FGUETKRVKXG OGCPKPI CNQPG NGCXGU WPPKUJGF KVU EQPVGZV QH WUG ECP EQORNGVG=?

2TCIOCVKUV TGURQPUGU FGP[ VJKU KPVWKVKQP CPF UC[ KPUVGCF VJCV VJG UGPVGPEG KVUGNH HQNNQYKPI 4WUUGNNU CPCN[UKU KU PQV VTWGDWV VJCV VJG CEV QH WVVGTKPI VJG HCNUG UGPVGPEG EQOOWPKECVGF VTWG KPHQTOCVKQP VQ VJG NKUVGPGT

4.4.2 Keith Donnellan

#EEQTFKPI VQ -GKVJ &QPPGNNCP VJGTG CTG VYQ FKUVKPEV YC[U YG OC[ WUG C FGPKVG FGUETKRVKQP UWEJ CU VJG EWTTGPV 'ORGTQTQH -GPVWEM[ KU ITC[ CPF VJWU OCMGU JKU FKUVKPEVKQP DGVYGGP VJG TGHGTGPVKCN CPF VJG CVVTKDWVKXG WUG QH C FGPKVG FGUETKRVKQP*G CTIWGU VJCV DQVJ 4WUUGNN CPF 5VTCYUQPOCMG VJGOKUVCMG QH CVVGORVKPI VQ CPCN[UG UGPVGPEGU TGOQXGF HTQO VJGKT EQPVGZV9G ECP OGCP FKGTGPV CPF FKUVKPEV VJKPIU YJKNG WUKPI VJG UCOG UGPVGPEG KP FKGTGPV UKVWCVKQPU

4&& "-40

(QT GZCORNG UWRRQUG 5OKVJ JCU DGGP DTWVCNN[ OWTFGTGF 9JGP VJG RGTUQP YJQ FKUEQXGTU 5OKVJU DQF[ UC[U 5OKVJUOWTFGTGT KU KPUCPG YG OC[ WPFGTUVCPF VJKU CU VJG CVVTKDWVKXG WUG QH VJG FGPKVG FGUETKRVKQP 5OKVJU OWTFGTGT CPFCPCN[UG VJG UGPVGPEG CEEQTFKPI VQ 4WUUGNN 6JKU KU DGECWUG VJG FKUEQXGTGT OKIJV GSWKXCNGPVN[ JCXG YQTFGF VJG CUUGTVKQP9JQGXGT MKNNGF 5OKVJ KU KPUCPG 0QY EQPUKFGT CPQVJGT URGCMGT UWRRQUG ,QPGU VJQWIJ KPPQEGPV JCU DGGP CTTGUVGFHQT VJG OWTFGT QH 5OKVJ CPF KU PQY QP VTKCN 9JGP C TGRQTVGT UGGU ,QPGU VCNMKPI VQ JKOUGNH QWVUKFG VJG EQWTVTQQO CPFFGUETKDGU YJCV UJG UGGU D[ UC[KPI 5OKVJU OWTFGTGT KU KPUCPG YG OC[ WPFGTUVCPF VJKU CU VJG TGHGTTKPI WUG QH VJG FGPKVGFGUETKRVKQP HQT YG OC[ GSWKXCNGPVN[ TGYQTF VJG TGRQTVGTU CUUGTVKQP VJWU 6JCV RGTUQP YJQ + UGG VCNMKPI VQ JKOUGNH CPFYJQ + DGNKGXG OWTFGTGF 5OKVJ KU KPUCPG +P VJKU ECUG YG UJQWNF PQV CEEGRV 4WUUGNNU CPCN[UKU CU EQTTGEVN[ TGRTGUGPVKPIVJG TGRQTVGTU CUUGTVKQP 1P 4WUUGNNU CPCN[UKU VJG UGPVGPEG KU VQ DG WPFGTUVQQF CU VJG EQPLWPEVKQP QH

VJGTG KU CP Z UWEJ VJCV Z OWTFGTGF 5OKVJ

VJGTG KU PQ [ [ PQV GSWCN Z UWEJ VJCV [ OWTFGTGF 5OKVJ CPF

Z KU KPUCPG

+H VJKU CPCN[UKU QH VJG TGRQTVGTU CUUGTVKQP YGTG EQTTGEV VJGP UKPEG ,QPGU KU KPPQEGPV YG UJQWNF VCMG JGT VQ OGCP YJCV VJGFKUEQXGTGT QH 5OKVJU DQF[ OGCPV VJCV YJQGXGT OWTFGTGF 5OKVJ KU KPUCPG 9G UJQWNF VJGP VCMG JGT QDUGTXCVKQP QH ,QPGUVCNMKPI VQ JKOUGNH VQ DG KTTGNGXCPV VQ VJG VTWVJ QH JGT CUUGTVKQP 6JKU ENGCTN[ OKUUGU JGT RQKPV6JWU VJG UCOG UGPVGPEG 5OKVJU OWTFGTGT KU KPUCPG ECP DG WUGF VQ OGCP SWKVG FKGTGPV VJKPIU KP FKGTGPV EQPVGZVU6JGTG CTG CEEQTFKPIN[ EQPVGZVU KP YJKEJ VJG EWTTGPV 'ORGTQT QH -GPVWEM[ KU PQV ITC[ KU HCNUG DGECWUG PQ QPG KU VJGEWTTGPV 'ORGTQT QH -GPVWEM[ CPF EQPVGZVU KP YJKEJ KV KU C UGPVGPEG TGHGTTKPI VQ C RGTUQP YJQO VJG URGCMGT VCMGU VQ DGVJG EWTTGPV 'ORGTQT QH -GPVWEM[ VTWG QT HCNUG CEEQTFKPI VQ VJG JCKT QH VJG RTGVGPFGT

4.4.3 Saul Kripke

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

4.5 See also

&GPKVG FGUETKRVKQP

5GPUG CPF TGHGTGPEG

2JKNQUQRJ[ QH NCPIWCIG

4.6 Notes

=? 0GCNG 5VGRJGP %FTDSJQUJPOT %CODTKFIG /CUU /+6 2TGUU +5$0

=? .GRQTG 'TPKG #DWUG QH %QPVGZV KP 5GOCPVKEU +P 4GKOGT /CTIC $G\WKFGPJQWV #PPG %FTDSJQUJPOT BOE #FZPOE1ZHQTF 7PKXGTUKV[ 2TGUU R +5$0 :

=? -TKRMGU WPRWDNKUJGF ,QJP .QEMG NGEVWTGU CV 1ZHQTF KP

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4.7 References and further reading

$GTVQNGV 4QF 6JGQT[ QH &GUETKRVKQPU 5IF $BNCSJEHF %JDUJPOBSZ PG 1IJMPTPQIZ UGEQPF GFKVKQP 0GY;QTM %CODTKFIG 7PKXGTUKV[ 2TGUU

&QPPGNNCP -GKVJ 4GHGTGPEG CPF &GPKVG &GUETKRVKQPU 1IJMPTPQIJDBM 3FWJFX RR -TKRMG 5CWN 5RGCMGTU 4GHGTGPEG CPF 5GOCPVKE 4GHGTGPEG .JEXFTU 4UVEJFT JO 1IJMPTPQIZ RR

.WFNQY 2GVGT &GUETKRVKQPU 5IF 4UBOGPSE &ODZDMPQFEJB PG 1IJMPTPQIZ '

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4.9 Text and image sources, contributors, and licenses

4.9.1 Text

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