logika

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sylogismu v SUYQt ILJX H WHG\ PRG\ %DUEDUD &HODUHQW ’DULL D )HULR SURWR H MH SRYD RYDO ]D
~VXGN\ MHMLFK SODWQRVW MH EH]SURVW HGQ ] HMPi D QHY\ DGXMH WHG\ GDOªtFK G$ND]$ 9ªHFKQ\
ostatní platné mody jsou z W FKWR PRG$ RGYR]HQy s SRX LWtP REUDW$ ]iP Q\ SUHPLV QD
]iNODG ORJLFNpKR WYHUFH D SRGOH SULQFLSX VSRUX R NWHUŒFK X G tYH XNi]DO H WR MVRX SODWQp
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V\ORJLVP$ SUYQt ILJXU\ MH ]DUX HQD MHKR NRUHNWQRVW 3R]G ML $ULVWRWHOHV XNi]DO H GRNRQFH
VWD t MDNR D[LRP\ Y]tW MHQ SUYQt GYD PRG\ SUYQt ILJXU\ – %DUEDUD D &HODUHQW = W FKWR GYRX
PRG$ MH PR Qp QD ]iNODG XYHGHQŒFK SUDYLGHO RGYR]RYiQt ]tVNDW YªHFKQ\ ]EŒYDMtFt SODWQp
PRG\ RVWDWQtFK ILJXU NWHUp WtP MVRX X]QiQ\ ]D SUDYLGOD VSUiYQpKR XVX]RYiQt – VWHMQ VSUiYQi
jako jsou oba axiomy.
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GRSOQ Q R GDOªt GUREQRVWL MDN MH GRE H YLG W QD PQHPRWHFKQLFNŒFK SRP$FNiFK 3HWUD
+LVSiQVNpKR -PpQD SODWQŒFK PRG$ V\ORJLVPX WRWL QHMVRX Y\WYR HQD QiKRGQ .URP WRKR
H VDPRKOiVN\ tNDMt MDNp W\S\ VRXG$ Y Q P ILJXUXMt PDMt VY$M S HVQŒ YŒ]QDP L Q NWHUi GDOªt
StVPHQD 3UYQt StVPHQR tNi RG NWHUpKR PRGX SUYQt ILJXU\ WHQWR V\ORJLVPXV RGYR]XMH VYRMt
SODWQRVW YªHFKQ\ V\ORJLVP\ ]D tQDMtFt QD % O]H S HYpVW QD PRGXV %DUEDUD D SRGREQ
3tVPHQD V S P D F tNDMt SURVW HGQLFWYtP MDNŒFK ~SUDY MH WRWR S HYHGHQt PR Qp V R]QD XMH
SURVWΠREUDW S REUDW SR S tSDGHFK P ]iP QX SUHPLV D F G$ND] VSRUHP
Scholastika dovedla sylogistiku k GRNRQDORVWL NWHURX Mt DQL GQHV SR MHMtP S HNRQiQt
QHO]H XS tW 7HQWR V\VWpP Pi WRWL YODVWQRVWL NWHUp MVRX L GQHV X WHRULt SRYD RYiQ\ ]D S HGQRVW
a sice axiomatizovatelnost, rozhodnutelnost, bezespornost a úplnost.
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MHGQRGXFKp SRGRE VQDGQR GHPRQVWUXMt GRGQHV SODWQp ORJLFNp SULQFLS\ = GQHªQtKR KOHGLVND
MH DULVWRWHOVNi ORJLND X S HNRQDQRX ]iOH LWRVWt 1LNROLY SURWR H E\ VQDG E\OD ªSDWQ DOH
SURWR H GQHªQt ORJLND SURVW QDEt]t OHSªt D ~ HOQ Mªt SURVW HGN\ 3ULQFLS\ ]H NWHUŒFK
$ULVWRWHOHV S L MHMt WYRUE Y\ªHO MVRX YªDN SODWQp GRGQHV D PRGHUQt ORJLND MH Y VRE QHVH VWHMQ
jako aristotelská sylogistika.
Aristotelská a moderní logika
Základní aristotelské logické principy platné v moderní logice
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SODWQp ORJLFNp SULQFLS\ QDMGHPH Y 2UJDQRQ ]IRUPXORYDQp 6WHMQ WDN WDP QDMGHPH Y SUYQt D
SR iWH Qt SRGRE Y WªLQX W FK SUREOpP$ VH NWHUŒPL VH PXVt VRX DVQi ORJLND Y\SR iGDW
3RNXG $ULVWRWHOHV QHQDEt]t S tPR Q MDNp MHMLFK HªHQt D" X ] GQHªQtKR KOHGLVND S LMDWHOQp L
QLNROLY MH VL DOHVSR Y GRP WRKR H WDNRYŒ SUREOpP WX MH D SRW HEXMH Y\ HªLW
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dvouhodnotovost.
Formálnost MDN X E\OR G tYH Y\OR HQR ]QDPHQi H QD ~VXGFtFK QiV ]DMtPi QLNROLY MHMLFK
obsah, ale pouze jejich forma. Oproti Aristotelovi je v dnešní logice tato formálnost jen
G$VOHGQ Mªt
Princip extenzionality ]MHGQRGXªHQ H HQR VWDQRYXMH H Y ORJLFH QiV Y S tSDG WYU]HQt
]DMtPi SRX]H MHKR SUDYGLYRVWQt KRGQRWD D QLNROLY YŒ]QDP 9\SOŒYi WR X ] $ULVWRWHORYD
SURJUDPX H ORJLND MH KOHGiQtP SUDYG\ 9H VYŒFK G$VOHGFtFK WR PLPR MLQp L ]QDPHQi H
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Dvouhodnotovost SDN ]QDPHQi H Y ORJLFH VH SUDFXMH SRX]H VH GY PD SUDYGLYRVWQtPL
hodnotami - pravdou a nepravdou. Princip dvouhodnotovosti je zakotven ve dvou základních
ORJLFNŒFK ]iNRQHFK YŒVORYQ ]IRUPXORYDQŒFK D $ULVWRWHOHP L NG\ MDNR SODWQp SULQFLS\ VH
SRX tYDO\ X G tYH QDS X VRILVW$ QHER 3DUPHQLGD -VRX WR ]iNRQ VSRUX D ]iNRQ Y\ORX HQpKR
W HWtKR Zákon sporu tNi ¯7RWp QHPc H WpPX Y WpP RKOHGX ]iURYHB QiOH HW L QHQiOH HW· (Aristoteles,
Metafyzika) 3UR ORJLNX WR ]QDPHQi H iGQp WYU]HQt QHP$ H EŒW ]iURYH SUDYGLYp L
nepravdivé. =iNRQ Y\ORX HQpKR W HWtKR tNi H ND Gp WYU]HQt MH EX SUDYGLYp QHER
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Pi SUiY MHGQX SUDYGLYRVWQt KRGQRWX D VLFH EX SUDYGD QHER QHSUDYGD 7RKRWR SULQFLSX
GYRXKRGQRWRYRVWL VH NODVLFNi ORJLND GU t GRGQHV =Gi VH YªDN H ]iNRQ VSRUX MH ]iVDGQ Mªt
QH ]iNRQ Y\ORX HQpKR W HWtKR SURWR H ]DWtPFR Q NWHUp V\VWpP\ QHNODVLFNŒFK ORJLN ]iNRQ
Y\ORX HQpKR W HWtKR RGPtWDMt D S LSRXªW Mt W HWt KRGQRWX QHER GRNRQFH L YtFH KRGQRW ]iNRQ
VSRUX QHRGPtWi iGQŒ
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MHGQRWOLYp SUREOpP\ D QHS HVQRVWL
3RMPRYp ]DOR HQt DULVWRWHOVNp ORJLN\ EUiQt G$VOHGQp IRUPDOL]DFL a omezuje odvozovací
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SURWR H VXEMHNW SUHGLNiW "tma" nijak nesouvisí (z formálního hlediska) s predikátem "bát se
tmy". Vezmeme-li ale predikát "bát se tmy" jako relaci, vztah mezi individui .D HQNRX a
tmou MH X RGYR]HQt PR Qp 3RGOH PRGHUQt ORJLN\ MH WRWL ORJLFNi IRUPD Y W\ UHOD Qt WM
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strukturou, od které se nedokázala osvobodit.
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D VORYD ]DVH ]QDNHP SRMP$
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3 HGSRNODG MHGQR]QD Qp NRUHVSRQGHQFH MD]\N P\ªOHQt VY W Y VRE ORJLND QHVH GRGQHV L
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