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logica interferente

Date post: 21-Apr-2015
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$’(9 5ø,9$/,’,7$7( 1.1,QIHUHQ œLUD LRQDPHQW Într-R DFFHS LXQH SRSXODU SH FkW GH IDFLO œL GH VXJHVWLY SH DWkWGHSX LQULJXURDV –, logica este FDUDFWHUL]DW GUHSWœWLLQ DJkQGLULL corecte, presupunându-VH F SULQFLSDOD GDF QX VLQJXUD HL XWLOLWDWH FRQVW vQ IDSWXO F QH vQYD FXP V JkQGLP IHULQGX-ne de erori. Ce-i GUHSW VWXGLXO ORJLFLL DU SXWHD œL DU WUHEXL V QH RIHUH EHQHILFLXO XQHL gândiri mai riguroase, cevQDLQWHD] PDLVLJXUVSUHDIODUHDXQRUDGHY UXUL ELQHvQWHPHLDWHHYLWkQGFXVSRULW FLUFXPVSHF LHFDSFDQHOHœLDSDUHQ HOH vQœHO WRDUH’DUIRORDVHOHHYHQWXDOHSHFDUHOHSRDWHDGXFHVWXGLXOORJLFLL VSRULQG DELOLWDWHD œL SURIXQ]LPHD JkQGLULL FXLYD QX UHSUH]LQW FkWXœL GH SX LQWU V WXULGHILQLWRULLDOHDFHVWXLGRPHQLXWHRUHWLFDœDFXPIDSWXOF QHDMXW V QHLOXPLQ PvQF SHULOHRULV DVFXOW PPX]LF ODFDVHWRIRQQX VXQWWU V WXULGHILQLWRULLDOHFXUHQWXOXLHOHFWULF ÌQ HOHJHUHD ORJLFLL FD œWLLQ D gândirii corecte induce presu- SR]L LD JUHœLW F DGHY UXULOH ORJLFLL V-DU ED]D FXPYD SH FRQVHQVXO œL SH X]DQ HOHPRGXOXLHIHFWLY vQFDUHRDPHQLLvœLvQO Q XLHLGHLOHœLFXYLQWHOH îndemnându-QH SDUF V DVRFLHP œWLLQ D ORJLFLL FX JUDPDWLFD 1XPDL F aceast DSDUHQW vQUXGLUH HVWH LQH[LVWHQW 5HJXOLOH GH PRUIRORJLH œL VLQWD[ SHFDUHOHHQXQ JUDPDWLFDVXQWYDODELOHvQWUXFkWFODULILF œLVLV- WHPDWL]HD] R SHUIRUPDQ OLQJYLVWLF X]XDO vQWU-un anumit stadiu de HYROX LHDXQHL OLPELHIHFWLYYRUELWH $VSXQHF µ(LYRUEHœWH prea mult’ VDXF µ9RLWUHEXL LV PDLvQY D L¶F µ7XHœWLmai superior¶RULF µ1X VH PHULW V PHUJL OD PDUH¶ HWF VXQW FRQVWUXF LL JUDPDWLFDO HURQDWH în OLPEDURPkQ SHQWUXF QXDœDVHYRUEHœWHFRUHFWURPkQHœWHFKLDUGDF
Transcript
Page 1: logica interferente

�$'(9 5�ù,�9$/,',7$7( 1.1�,QIHUHQ �úL�UD LRQDPHQW

Într-R�DFFHS LXQH�SRSXODU �–�SH�FkW�GH� IDFLO � úL�GH�VXJHVWLY ��SH�

DWkW�GH�SX LQ�ULJXURDV �–, logica este FDUDFWHUL]DW �GUHSW�úWLLQ D�JkQGLULL�

corecte, presupunându-VH� F � SULQFLSDOD� �GDF � QX� VLQJXUD�� HL� XWLOLWDWH�FRQVW � vQ� IDSWXO� F � QH� vQYD � FXP� V � JkQGLP�� IHULQGX-ne de erori. Ce-i GUHSW�� VWXGLXO� ORJLFLL� DU� SXWHD� úL� DU� WUHEXL� V � QH� RIHUH� EHQHILFLXO� XQHL�gândiri mai riguroase, ce�vQDLQWHD] �PDL�VLJXU�VSUH�DIODUHD�XQRU�DGHY UXUL�ELQH�vQWHPHLDWH��HYLWkQG�FX�VSRULW �FLUFXPVSHF LH�FDSFDQHOH�úL�DSDUHQ HOH�vQúHO WRDUH��'DU�IRORDVHOH�HYHQWXDOH�SH�FDUH�OH�SRDWH�DGXFH�VWXGLXO�ORJLFLL��VSRULQG�DELOLWDWHD�úL�SURIXQ]LPHD�JkQGLULL�FXLYD��QX� UHSUH]LQW �FkWXúL�GH�SX LQ�WU V WXUL�GHILQLWRULL�DOH�DFHVWXL�GRPHQLX�WHRUHWLF�–�DúD�FXP�IDSWXO�F �QH�DMXW �V �QH�LOXPLQ P�vQF SHULOH�RUL�V �DVFXOW P�PX]LF �OD�FDVHWRIRQ�QX�VXQW�WU V WXUL�GHILQLWRULL�DOH�FXUHQWXOXL�HOHFWULF��

ÌQ HOHJHUHD� ORJLFLL� FD� úWLLQ � D� gândirii corecte induce presu-SR]L LD�JUHúLW �F �DGHY UXULOH� ORJLFLL�V-DU�ED]D�FXPYD�SH�FRQVHQVXO�úL�SH�X]DQ HOH�PRGXOXL�HIHFWLY�vQ�FDUH�RDPHQLL�vúL�vQO Q XLH�LGHLOH�úL�FXYLQWHOH��îndemnându-QH�SDUF � V � DVRFLHP�úWLLQ D� ORJLFLL� FX�JUDPDWLFD� 1XPDL�F �aceast � DSDUHQW � vQUXGLUH� HVWH� LQH[LVWHQW �� 5HJXOLOH� GH� PRUIRORJLH� úL�VLQWD[ �SH�FDUH�OH�HQXQ �JUDPDWLFD�VXQW�YDODELOH�vQWUXFkW�FODULILF �úL�VLV-WHPDWL]HD] � R� SHUIRUPDQ � OLQJYLVWLF � X]XDO � vQWU-un anumit stadiu de HYROX LH�D�XQHL�OLPEL�HIHFWLY�YRUELWH��$�VSXQH�F �µ(L�YRUEHúWH prea mult’ VDX�F �µ9RL�WUHEXL L�V �PDL�vQY D L¶��F �µ7X�HúWL�mai superior¶�RUL�F �µ1X�VH� PHULW � V � PHUJL� OD�PDUH¶� HWF�� VXQW� FRQVWUXF LL� JUDPDWLFDO� HURQDWH� în OLPED�URPkQ �SHQWUX�F �QX�DúD�VH�YRUEHúWH�FRUHFW�URPkQHúWH�–�FKLDU�GDF �

Page 2: logica interferente

ideile exprimate într-R� IRUP � JUDPDWLFDO � HURQDW � SRW� IL� SHUWLQHQWH��3ULQFLSLXO�ORJLF�DO�LGHQWLW LL��SURSULHW LOH�LPSOLFD LHL�PDWHULDOH�VDX�OHJLOH�VLORJLVPXOXL�� GH� SLOG �� VXQW� vQV � YDODELOH� QX� SHQWUX� F � PDMRULWDWHD�RDPHQLORU� OH� FXQRVF� úL� OH� DSOLF � HIHFWLY� vQ� PRGul lor de gândire, ci vQWUXFkW� VH� VXV LQ� SULQ� GHPRQVWUD LL� ULJXURDVH�� FDUH� LQ� H[FOXVLY� GH�FRQVWUXF LD� XQRU� VLVWHPH� GH� HQWLW L� úL� UHOD LL� SXU� LGHDOH� –� WRW� DúD� FXP�teoremele lui Thales, Pitagora VDX�)HUPDWV �VSXQHP��ELQRPXO�OXL�1HZWRQ sau geometriile neeucOLGLHQH� QX� VH� vQWHPHLD] � SH� FXQRDúWHUHD� úL�VXV LQHUHD� ORU� GH� F WUH�PDMRULWDWHD� LQGLYL]LORU�� FL� QXPDL� SH� DUJXPHQWHOH�JkQGLULL� PDWHPDWLFH�� FDUH� HVWH� XQLYHUVDO � úL� DWHPSRUDO �� Ä1X� SXWHP�H[SOLFD� UD LXQHD� SULQWU-R� GHVFULHUH� QDWXUDOLVW � D� SUDFWLFLORU� OLPEDMXOXL�– DILUP � 7KRPDV� 1DJHO�� >���@� ÌQ� P VXUD� vQ� FDUH� SUDFWLFLOH� OLQJYLVWLFH� QH�GH]Y OXLH�SULQFLSLLOH�JkQGLULL��VDX�QH�LQGLF ��GH�SLOG ��FHYD�GHVSUH�QDWXUD�SURSR]L LLORU� DULWPHWLFH�� DFHVW� OXFUX� QX� VH� GDWRUHD] � IDSWXOXL� F � ORJLFD�HVWH�R�JUDPDWLF ��FL�IDSWXOXL�F �Jramatica se supune logicii. Un ‘limbaj’ în care modus ponens�QX�DU�IL�R�LQIHUHQ �YDOLG �VDX�vQ�FDUH�LGHQWLWDWHD�QX�DU�IL�WUDQ]LWLY �Q-ar putea fi folosit pentru a exprima nici un fel de idei.“1

/RJLFLHQLL� GH� DVW ]L� UHVSLQJ� vQ HOHJHUHD� ORJLFLL� FD� úWLLQ � D JkQGLULL�FRUHFWH�úL�SHQWUX�F �gândirea� HVWH�R�DFWLYLWDWH�SVLKLF ��GHRVHELW�GH� FRPSOH[ �� FDUH� VH�GHVI úRDU � vQ�PLQ LOH�RDPHQLORU�� DYkQG�GH� ILHFDUH�GDW �R� LQDOLHQDELO �QRW � VXELHFWLY ��SULQ�FDUH� LQGLYL]LL� VH�GHRVHEHVF�PDL�PXOW�VDX�PDL�SX LQ�XQXO�GH�DOWXO��*ândirea este un obiect de studiu pentru psihologie, úWLLQ � H[SHULPHQWDO � FDUH� XUP UHúWH� V � GHWHUPLQH� SULQ�REVHUYD LH�� P VXUDUH�� FRPSDUDUH�� VLPXODUH�� PRGHODUH� HWF�� FHHD� FH�� de UHJXO sau vQ� PRG� RELúQXLW� GHFXUJH� vQ� PRG� µQRUPDO¶� vQ� PLQ LOH�oamenilor, sinteti]kQG� úL� LQIRUPD LLOH� H[WUHP�GH�GLYHUVLILFDWH� SH� FDUH� OH�IXUQL]HD] � GLVFLSOLQH� SUHFXP� FLEHUQHWLFD�� WHRULD� LQIRUPD LHL�� QHXUR-IL]LRORJLD�úL�DOWHOH�

ÌQUXGLW �PXOW�PDL�vQGHDSURDSH�FX�PDWHPDWLFD decât cu psihologia sau gramatica, logica QX�HVWH�R�úWLLQ �H[SHULPHQWDO , F FL�HD�QX�GHVFULH�úL�QX� H[SOLF �PRGXO� FRQFUHW� vQ� FDUH� RDPHQLL� GH� WRW� IHOXO� JkQGHVF� HIHFWLY��îndrumându-L�FX�VIDWXUL�úL�UHFRPDQG UL�SH�FDUH�HL�VXQW�OLEHUL�V �OH�XUPH]H�sau nu, cu rezultate ierarhizabile pe diferite VFDOH� GH� SHUIRUPDQ ��NeinteresaW �GH�FRQ LQXWXO�DFWHORU�GH�JkQGLUH��LQGLIHUHQW �ID �GH�VHQVXO�úL�YDORDUHD� LQIRUPD LRQDO � D� ©LGHLORUª�� ORJLFD� VWXGLD] � VWUXFWXUL� GH� UHOD LL�

Page 3: logica interferente

QHFHVDUH� vQWUH� HQWLW L� LGHDOH�� DEVWUDFWH� –� VWUXFWXUL� GH� SURJUHVLY �generalitate, izomorfe nu numai cu actele cogniWLYH��FL�úL�FX�QHQXP UDWH�VLVWHPH�QDWXUDOH�VDX�DUWLILFLDOH�GLQ�OXPHD�IHQRPHQDO �

,DW �GH�FH�� O VkQG�JkQGLUHD�vQ�VHDPD�SVLKRORJLORU�úL�YRUELUHD�FRUHFW vQ� VHDPD� ILORORJLORU��YRP�VSXQH�F � ORJLFD�VWXGLD] �GLQ�SXQFW�GH�YHGHUH�

IRUPDO� LQIHUHQ HOH� YDOLGH. ÌQ HOHJem prin LQIHUHQ orice extragere sau derivare dintr-una sau mai multe�SURSR]L LL�GDWH��QXPLWH�SUHPLVH��D�XQHL noi SURSR]L LL�� QXPLW � concluzie. Cu alte cuvinte, fiind reunite n premise, printr-R� LQIHUHQ � FRUHFW � GLQ� SXQFW� GH� YHGHUH� ORJLF� HVWH� SRVLELO � VDu QHFHVDU �DILUPDUHD�XQHL�DQXPLWH�FRQFOX]LL��FDUH�VH�GHVSULQGH�VDX�UH]XOW �GLQ�SUHPLVHOH�GDWH�úL�DFFHSWDWH�–�LQGLIHUHQW�FkW�GH�PXO L�VDX�FkW�GH�SX LQL�DU�IL�LQGLYL]LL�FDSDELOL�V �HIHFWXH]H�PLQWDO�GHVSULQGHUHD�FRQFOX]LHL�FRUHFWH�úL� LQGLIHUHQW� FkW� GH� PDUH� VDu de mic ar fi efortul intelectual necesar SHQWUX� vQ HOHJHUHD� PHFDQLVPXOXL� ORJLF� SULQ� FDUH� FRQFOX]LD� GHULY � GLQ�SUHPLVHOH�VDOH��6SXQH�3HLUFH��Ä1X�VH�SXQH�FkWXúL�GH�SX LQ�SUREOHPD�GDF ��DWXQFL� FkQG� PLQWHD� QRDVWU � DFFHSW � SUHPLVHOH�� VLP LP� LPEROGXO� V �accept P� úL� FRQFOX]LD�� (VWH� DGHY UDW� F � GLQ� ILUH� UD LRQ P� vQ� JHQHUDO�FRUHFW�� $FHVWD� HVWH� vQV � XQ� DFFLGHQW�� FRQFOX]LD� DGHY UDW � DU� U PkQH�DGHY UDW �úL�GDF �QX�DP�VLP L�QLFL�XQ�LPEROG�GH�D�R�DFFHSWD��LDU�FHD�IDOV �DU�U PkQH�IDOV �FKLDU�GDF �QX�DP�SXWHD�UH]LVWD�SRUnirii de a crede în ea.“2

,DW �FkWHYD�H[HPSOH�GH�LQIHUHQ H�HOHPHQWDUH� �����'DW �ILLQG�SUHPLVD�µ�x = 10’, putem infera concluzia ‘x = 5’. (2) Din premisa ‘x2� ���¶�UH]XOW �SULQ�LQIHUHQ �µx = 4 sau

x = (–4)’. (3) )LLQG� GDWH� GUHSWHOH� �D��� �E�� úL� �F��� SUHFXP� úL� UHOD LD� GH�

SDUDOHOLVP�� GLQ� SUHPLVHOH� µ�D�� __� �E�¶� úL� µ�E�� __� �F�¶� UH]XOW �concluzia: ‘(a) || (c)’.

(4) Date fiind premisele: µ7RDWH�SDWUXODWHUHOH�VXQW�SROLJRDQH¶�úL� ‘Toate romburile sunt patrulatere’, se poate infera concluzia: ‘Toate romburile sunt poligoane’.

(5) 'DF �DP�UHPDUFDW�XQ�LQV�QHFXQRVFXW��FX�FDUH�QX�DP�GLVFXWDW�QLPLF��GDU�FDUH�DYHD�WHQXO�JDOEHQ��RFKL�REOLFL��HUD�VFXQG�úL�SXUWD�RFKHODUL��

Page 4: logica interferente

SXWHP�LQIHUD�F �UHVSHFWLYXO�LQGLYLG�WUHEXLH�V �ILH�XQ�DVLDWLF�GLQ�([WUHPXO�Orient.

(6) Intrând într-R� FDPHU �� DS V� SH� FRPXWDWRU� úL� QX� VH� DSULQGH�OXPLQD�� IDSWXO� FD� DWDUH�� FRURERUDW� FX� QR LXQLOH� SH� FDUH� OH� SRVHG� GHVSUH�LQVWDOD LLOH�HOHFWULFH��P �IDF�V �SUHVXSXQ�F �IHQRPHQXO�VH�GDWRUHD] �XQHLD�GLQWUH� XUP WRDUHOH� FDX]H� SRVLELOH�� QX� HVWH� FXUHQW� vQ� UH HD�� V-a ars filamentul becului; s-a defectat comutatorul etc.

ÌQO Q XLUHD� ORJLF �GLQWUH�SUHPLVH�úL�FRQFOX]LH�VH�PDL�QXPHúWH�úL�argument –� WHUPHQ� SUHIHUDW� GH� F WUH� XQLL� ORJLFLHQL� vQ� ORFXO� FHOXL� GH�LQIHUHQ ��vQWUXFkW�HVWH��VDX��FHO�SX LQ��SDUH��PDL�IDPLOLDU��7RWXúL, cei doi termeni nu sunt, credem noi, pe deplin sinonimi. A argumenta sau a FRQVWUXL� XQ� DUJXPHQW� vQVHDPQ �� FkWHRGDW �� D�GHULYD�GLQ�SUHPLVH�GDWH� úL�DFFHSWDWH�R�DQXPLW �FRQFOX]LH�– cu alte cuvinte, a infera; în multe cazuri, vQV �� D� DUJXPHQWD� vQVHDPQ � D� VXV LQH� FX� DQXPLWH� WHPHLXUL� R� SURSR]L LH�GDW �� DO� F UHL� DGHY U� QX� HVWH� FHUW��$OWIHO� VSXV�� D� FRQVWUXL� XQ� DUJXPHQW�SRDWH� V � vQVHPQH� D� GHVFRSHUL� DQXPLWH� SUHPLVH�� GLQ� FDUH� SURSR]L LD� GH�VXV LQXW� GHULY � ORJLF� GUHSW� FRQFOX]LD� ORU�� ,DW � FkWHYD� H[HPSOH� GH�argumente de acest tip:

����$ILUPD LD�F �DULD�XQXL�FHUF�QX�SRDWH�IL�vQ�QLFL�XQ�FD]�HJDO �FX�DULD� XQXL� S WUDW� �IDLPRDVD� SUREOHP � FXQRVFXW � vQ� LVWRULD� PDWHPDWLFLL�GUHSW� µFYDGUDWXUD� FHUFXOXL¶�� QX�HVWH� FkWXúL� GH�SX LQ�GH� OD� VLQH�HYLGHQW ��'H� FH� úL� FXP� V � QH� FRQYLQJHP� GH� DGHY UXO� HL"� $YHP� QHYRLH� GH� XQ�DUJXPHQW��$FHVWD� D� IRVW� IRUPXODW� vQ� DQXO� �����GH�F WUH�PDWHPDWLFLDQXO�Ferdinand Lindemann (1852 -�������GXS �FXP�XUPHD] ��DULD�S WUDWXOXL�VH�FDOFXOHD] �GXS �IRUPXOD�l2 – latura l�DYkQG�vQ�RULFH�VLWXD LH�R�OXQJLPH�(valoare numHULF � vQ� VLVWHPXO� PHWULF�� ILQLW �� DVWIHO� vQFkW� úL� VXSUDID D�S WUDWXOXL� HVWH� FX� QHFHVLWDWH� ILQLW �� DULD� FHUFXOXL� VH� FDOFXOHD] � GXS �formula π r2��QXP UXO�π�ILLQG�LUD LRQDO��FX�XQ�QXP U�LQILQLW�GH�]HFLPDOH��astfel încât aria nici unui cerc nu poate avea o vaORDUH�QXPHULF � ILQLW ��'H�DLFL�UH]XOW �FX�FHUWLWXGLQH�H[DFW�SURSR]L LD�LQL LDO ��GH�FDUH�DFXP�VXQWHP FRQYLQúL�SULQWU-R�DUJXPHQWDUH�ULJXURDV �

(8) 2DPHQLL�GH�GHPXOW�DX�IRVW�H[WUHP�GH�FRQWUDULD L�DWXQFL�FkQG�XQLL� µvQ HOHS L¶�– filosofi, matematicieni, astronomi din Antichitate – au VXV LQXW�F �S PkQWXO�QX�HVWH�SODW��FL�VIHULF�VDX�µURWXQG¶��DILUPD LH�DIODW �într-XQ�YLROHQW�FRQIOLFW�FX�HYLGHQ HOH�SHUFHSWLYH��,DW �FH�IHO�GH�DUJXPHQWH�

Page 5: logica interferente

DGXFH�� GH� SLOG �� $ULVWRWHO vQ� VSULMLQXO� DFHVWHL� DILUPD LL�� DWXQFL� FkQG� R�corabie dispare în larg, la limita orizontului, se pierde din vedere mai vQWkL�FRFD�VDX�FRUSXO�QDYHL��úL�DELD�SH�XUP �GLVSDUH�úL�FDWDUJXO��FD�úL�FXP�corabia s-ar scufunda în mare –�úL�LQYHUV��DWXQFL�FkQG�R�FRUDELH�VH�LYHúWH�din larg mai întâL�L�VH�] UHúWH�FDWDUJXO�úL�DELD�SH�XUP �DSDUH�GLQ�YDOXUL�úL�FRFD� QDYHL�� FD� úL� FXP� FRUDELD� V-ar ridica din mare; umbra pe care o SURLHFWHD] �S PkQWXO�SH�VXSUDID D�OXQLL�vQ�WLPSXO�HFOLSVHORU�GH�OXQ �HVWH�întotGHDXQD�FLUFXODU �–�QLFLRGDW �HOLSWLF �VDX�OLQLDU ��DúD�FXP�DU�WUHEXL�V �VH� vQWkPSOH� P FDU� GLQ� FkQG� vQ� FkQG� GDF � S PkQWXO� DU� IL�� DúD� FXP� V-a FUH]XW�PXOW�WLPS��XQ�GLVF�SODW��vQ�VIkUúLW��FX�FkW�QH�ULGLF P�OD�R�ODWLWXGLQH�PDL� vQGHS UWDW �GH�(FXDWRU��FX�DWkW�XQJKLXO�VXE�FDUH�VH�vQDO �VRDUHOH� OD�zenit este mai mic. Toate aceste fapte nu se pot explica altcumva decât GDF �QH�UHSUH]HQW P�S PkQWXO�FD�SH�XQ�FRUS�FHUHVF�GH�PDUL�GLPHQVLXQL�úL�GH� IRUP � VIHULF � �DELD� PDL� WkU]LX� V-D� DIODW� FX� FHUWLWXGLQH� F � SODQHWD�QRDVWU � HVWH� XQ� JHRLG� GH� URWD LH�� DGLF � R� VIHU � WXUWLW � OD� SROL� GLQ� FDX]D�IRU HL�FHQWULIXJH�SH�FDUH�R�GH]YROW �PLúFDUHD�GH� URWD LH�D�S PkQWXOXL� vQ�jurul axei sale).

����8Q�FRSLO�SRDWH�IL�FRQWUDULDW�DWXQFL�FkQG�vL�VSXQHP�F �GHOILQLL�QX�VXQW�SHúWL��FL�PDPLIHUH��FD�úL�QRL��RDPHQLL�–�GHúL�SULQ�PHGLXO� ORU�GH�YLD �� SULQ� IRUP � úL� PRG� GH� ORFRPR LH� VH� DVHDP Q � L]ELWRU� FX� SHúWLL��'UHSW�DUJXPHQWH�YRP�IRORVL�GHILQL LLOH�QR LXQLORU�GH�SHúWH�úL�GH�PDPLIHU��SUHFXP� úL� R� VHULH� GH� REVHUYD LL� FDUH� DWHVW � F � GHOILQLL� QX� VXQW� SHúWL� – întrucât nu au ‘sânge rece’, nu se înPXO HVF�SULQ� LFUH�úL�QX� UHVSLU �SULQ�branhii, ci sunt mamifere, deoarece au ‘sânge cald’, nasc pui vii, pe care vL�KU QHVF�FX� ODSWH�úL� UHVSLU �SULQ�SO PkQL��DYkQG�GH�DFHHD�QHYRLH�V �VH�ULGLFH�GLQ�FkQG�vQ�FkQG�OD�VXSUDID D�DSHL�SHQWUX�D�QX�VH�VXIRFD�

6 �UHPDUF P�IDSWXO�F �vQ�H[HPSOHOH�����úL�����FRQFOX]LD�GHFXUJH�nemijlocit dintr-R�VLQJXU �SUHPLV �–�DúD�FXP�VH�vQWkPSO �úL�vQ�LQIHUHQ H�de genul:

(10) ùWLLQG�F � µ1LFL�R�SDV UH�QX�HVWH�SDWUXSHG¶��UH]XOW �F �µ1LFL�XQ�SDWUXSHG�QX�HVWH�SDV UH¶�

(11) 'DF �DU�IL�DGHY UDW�F �µ7R L�PDJLVWUD LL�VXQW�LQWHJUL¶��I FkQG�DEVWUDF LH�GH�IDSWXO�UHJUHWDELO�F ��vQ�UHDOLWDWH��OXFUXULOH�QX�VWDX�FKLDU�DúD���s-DU� SXWHD� LQIHUD� GH� DLFL� F � µ1LFL� XQ� RP� OLSVLW� GH� LQWHJULWDWH� QX� HVWH�magistrat’.

Page 6: logica interferente

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Page 10: logica interferente

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$GHY UXULOH� GH� UD LRQDPHQW� VXQW� QHFHVDUH� úL� RSXVXO� ORU� H� LPSRVLELO�� LDU�cele de fapt� VXQW�FRQWLQJHQWH�úL�RSXVXO� ORU�HVWH�SRVLELO��&kQG�XQ�DGHY U�HVWH� QHFHVDU�� vL� SXWHP� J VL� WHPHLXO� SULQ� DQDOL] �� UH]ROvându-O� vQ� LGHL� úL�DGHY UXUL�PDL�VLPSOH��SkQ �FkQG�DMXQJHP�OD�FHOH�SULPitive“.12

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7RW�.DQW�RSHUHD] �úL�GLVWLQF LD�GLQWUH�MXGHF L�analitice – în toate FD]XULOH� úL� a priori�� GHRDUHFH� vQWUH� VXELHFWXO� úL� SUHGLFDWXO� SURSR]L LHL�H[LVW �R�UHOD LH�ORJLF�QHFHVDU ��DVWIHO�vQFkW�FRQFHSHUHD�VXELHFWXOXL�SUHVX-pune asocierea lui cu predicatul ce-i este, oarecum, inerent –�úL�MXGHF L�sintetice, numite astfel deoarece se construiesc prin asocierea unor

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QR LXQL� FDUH� QX� VH� SUHVXSXQ� XQD� SH� FHDODOW � úL� QX� VXQW� vQWRWGHDXQD�FRQFHSXWH�ODRODOW ��ÄÌQ�WRDWH�MXGHF LOH�vQ care este gândit raportul dintre un subiHFW� úL� XQ� SUHGLFDW�– spune Kant –� DFHVW� UDSRUW� HVWH� SRVLELO� vQ� GRX �feluri. Sau predicatul B� DSDU LQH� VXELHFWXOXL� A ca ceva ce e cuprins (implicit) în acest concept, sau B�VH�J VHúWH�FX�WRWXO�vQ�DIDUD�FRQFHSWXOXL�A��GHúL�VW �vQ�OHJ WXU �FX�HO��ÌQ�FD]XO�GLQtâi numesc judecata DQDOLWLF , în FHO ODOW�VLQWHWLF ��-XGHF LOH�DQDOLWLFH��DILUPDWLYH��VXQW�GHFL�DFHOHD�vQ�FDUH�OHJ WXUD�SUHGLFDWXOXL�FX�VXELHFWXO�HVWH�JkQGLW �SULQ� LGHQWLWDWH�� LDU�DFHOHD�vQ�FDUH�DFHDVW �OHJ WXU �HVWH�JkQGLW �I U �LGHQWLWDWH�WUHEXLH�V �ILe numite MXGHF L�VLQWHWLFH��3H�FHOH�GLQWkL�OH-DP�SXWHD�QXPL�úL�MXGHF L�H[SOLFDWLYH, pe cHOHODOWH� MXGHF L�H[WHQVLYH��ILLQGF �FHOH�GLQWkL� QX� DGDXJ �SULQ�SUHGLFDW�QLPLF� OD� FRQFHSWXO� VXELHFWXOXL�� FL� QXPDL� vO� GHVFRPSXQ� SULQ� DQDOL] � vQ�FRQFHSWHOH�OXL�SDU LDOH��FDUH�HUDX�GHMD�JkQGLWH�vQ�HO��GHúL�FRQIX]���SH�FkQG�FHOH�GLQ�XUP �DGDXJ �OD�FRQFHSWXO�VXELHFWXOXL�XQ�SUHGLFDW�FDUH�QX�HUD�GH�ORF�JkQGLW�vQ�HO�úL�QX�SXWHD�IL�VFRV�SULQ�GHVFRPSXQHUHD�OXL³�14 Epistemo-ORJLD� NDQWLDQ � vúL� SURSXQH� V � GHPRQVWUH]H� F �� SH� OkQJ � MXGHF LOH�sintetice a posteriori� �vQ� FDUH� H[SHULHQ D� QH� RIHU � VLQJXUXO� WHPHL� DO�DVRFLHULL� XQRU� QR LXQL��� PDL� H[LVW � úL� MXGHF L� VLQWHWLFH� a priori, IXQGDPHQWDOH� vQ� HODERUDUHD� IL]LFLL� WHRUHWLFH�� MXGHF L� vQ� FDUH� OHJ WXUD�GLQWUH�VXELHFWXO�úL�SUHGLFDWXO�SURSR]L LHL�HVWH�QHFHVDU ��GHúL�QX�VH�ED]HD] �SH� H[SHULHQ �� FL� SH� DQXPLWH� VFKHPH� VDX� IRUPH� a priori, constitutive RULF UXL�DFW�GH�JkQGLUH�DO�(X-lui transcendental.

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Cu toate aFHVWHD��vQ�OLPEDMXO�YLH LL�FRWLGLHQH��RDPHQLL�FRQWLQX �V �XWLOL]H]H�úL�DOWH�VHPQLILFD LL�DOH�WHUPHQXOXL�µDGHY U¶��OHJDWH�QX�QXPDL�GH�SURFHVHOH�VWULFW�FRJQLWLYH��FL�úL�GH�R�PDUH�YDULHWDWH�GH�FRQWH[WH�SUDFWLFH��vQ�FDUH�DGHY UXO�HVWH�DWULEXLW�XQRU�SURSR]L LL�FH�QX�H[SULP �FXQRúWLQ H�VDX�LQIRUPD LL�� FL� GRULQ H�� UXJ PLQ L�� DSUHFLHUL�� VROLFLW UL�� PLU UL� HWF�� 'LQ�FRQVLGHUDUHD� DFHVWRU� PRGDOLW L� QRQFRJQLWLYH� DOH� OLPEDMXOXL�� SULYLWH� FD�LQVWUXPHQWH�XWLOH�vQ�DGDSWDUHD�SUDFWLF �D�DJHQWXOXL�OD�VROLFLW ULOH�PHGLXOXL�social în care trebXLH� V � DF LRQH]H�� V-D� Q VFXW� WHRULD� SUDJPDWLVW a DGHY UXOXL� – utilitate,� LQL LDW � GH� DPHULFDQLL� &KDUOHV� 6DQGHUV� 3HLUFH�(1839 -� ������ úL� :LOOLDP� -DPHV� ������ -� ������� 3RWULYLW� FRQFHS LHL�pragmatiste,�R�LGHH�HVWH�DGHY UDW �GDF �úL�QXPDL�GDF �HVWH�XWLO ��FULWHULXO�XWLOLW LL�ILLQG�QXPDL�DFWLYLWDWHD�SUDFWLF ��5H]XPkQG�FRQFHS LD�OXL�3HLUFH��SH�FDUH�úL-R�vQVXúHúWH�úL�R�DPSOLILF ��:LOOLDP�-DPHV�VSXQH�XUP WRDUHOH��ÄvQ� JHQHUDO�� DGHY UXO� FUHGLQ HORU� QRDVWUH� FRQVW � vQ� IDSWXO� F � HOH� GDX�VDWLVIDF LH“.15 ÎQ�DOW �SDUWH��-DPHV�SUHFL]HD] ��ÄFUHGLQ HOH sunt reguli pentru DF LXQH��úL�vQWUHDJD�IXQF LH�D�JkQGLULL�QX�HVWH�GHFkW�XQ�SDV�vQ�SURGXFHUHD�RELFHLXULORU� DFWLYH�� >���@�3HQWUX�D�RE LQH�R�FODULWDWH�SHUIHFW � vQ�JkQGXULOH�QRDVWUH�GHVSUH�XQ�RELHFW�� WUHEXLH�GRDU�V �FKLE]XLP�FH�VHQ]D LL�� LPHGLDWH�VDX� vQWkU]LDWH�� SXWHP� DúWHSWD� GH� OD� HO�� úL� FH� FRQGXLW � WUHEXLH� V � QH�SUHJ WLP� vQ� FD]� F � DFHVWD� HVWH� DGHY UDW�� >���@� DGHY UDW� HVWH� FHHD� FH�IXQF LRQHD] �ELQH³�16

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VH� J VHVF� GRL� RDPHQL� GLIHUL L� FDUH� V � J VHDVF �� ILHFDUH� vQ� IHOXO� V X�� R�utilitate într-una sau alWD�GLQ�FHOH�GRX �SURSR]L LL�

1.3.2�$GHY UXO�FD�YDORDUH�ORJLF �D�SURSR]L LLORU

2GDW � FH� DP� FRQYHQLW� DVXSUD� IDSWXOXL� F � ORJLFD� �vQ� VHQV� VWULFW��HVWH� XQ� VWXGLX� IRUPDO� DO� LQIHUHQ HORU� GHGXFWLYH�� WUHEXLH� V � FODULILF P�URVWXO� úL� ILQDOLWDWHD� DFHVWRUD�� 2� GHGXF LH� ELQH� FRQVWUXLW �� FDUH� vúL�vQGHSOLQHúWH�PHQLUHD��HVWH�DFHHD�FDUH�QH�FRQGXFH�OD�R�FRQFOX]LH� vQ�PRG�FHUW� DGHY UDW �� ÌQF � GH� OD� vQFHSXWXULOH� HL�� ORJLFD� D� IRVW� FRQFHSXW � úL�UHDOL]DW � FD� XQ� LQVWUXPHQW� LQGLVSHQVDELO� SHQWUX� DIODUHD� úL� vQWHPHLHUHD�FXQRúWLQ HORU� DGHY UDWH� –� UHVSHFWLY� SHQWUX� GHSLVWDUHD� úL� HOLPLQDUHD�RSLQLLORU�IDOVH��& XWkQG�XQ�PD[LPXP�GH�FODULWDWH��ORJLFD� WUHEXLH�V �IDF �SH� FkW� SRVLELO� DEVWUDF LH� GH� FRPSOLFD LL� úL� VXEWLOLW L� PHWDIL]LFH�� GkQG�DGHY UXOXL�R�VHPQLILFD LH�µWHKQLF ¶�úL��FD�DWDUH��RSHUD LRQDO �

ÌQ�FHOH�FH�XUPHD] ��YRP�FRQVLGHUD�F �DGHY UXO�úL��vQ�RSR]L LH�FX�el, falsitatea sunt, din punct de vedere logic� úL� epistemologic (nu QHDS UDW� PHWDIL]LF� VDX� WHRORJLF�� QLúWH� SURSULHW L� VDX� vQVXúLUL� FDUH� QX�DSDU LQ� lucrurilor�VDX�HQWLW LORU� UHDOH, aIODWH�vQ�DIDUD�FRQúWLLQ HL�QRDVWUH� ci QXPDL�FXQRúWLQ HORU�VDX�LGHLORU�QRDVWUH�GHVSUH�OXFUXUL��LGHL�H[SULPDWH�vQ�SURSR]L LL�GHFODUDWLYH�VDX�DVHU LXQL��&X�DOWH�FXYLQWH��PDVD�SH�FDUH�VFULX��FDVD�vQ�FDUH�P �DIOX��F U LOH�FDUH�P �vQFRQMRDU �HWF��QX�VXQW�úL�QX�pot fi QLFLFXP�úL�QLFLRGDW �DGHY UDWH sau false din punct de vedere logic – chiar GDF ��vQ�DPELJXLWDWHD�SOLQ �GH�VXJHVWLL�úL�VXEvQ HOHVXUL�DOH�OLPELL�QDWXUDOH��SXWHP�YRUEL�FX�VHQV�GHVSUH�R�PDV ��R�FDV �RUL�R�FDUWH�µDGHY UDW ¶��DGLF �EXQ ��GHRVHELW ��DSUHFLDELO �HWF��6XE�DVSHFW�ORJLF�vQV ��OXFUXULOH�VXQW�VDX�nu sunt reale, H[LVW sau QX�H[LVW �vQ�PRG�HIHFWLY��$GHY UDWH�VDX�IDOVH�SRW�IL�QXPDL�DILUPD LLOH�VDX�QHJD LLOH��FRQVWUXLWH�vQWU-un anumit limbaj, despre lucruri –� FHHD� FH� DP�GHQXPLW� GUHSW�SURSR]L LL�GHFODUDWLYH�VDX�DVHU LXQL��'XS � FXP� DP� Y ]XW� vQ� SDUDJUDIXO� DQWHULRU�� QX� WRDWH� DVHU LXQLOH� SRW� IL�DGHY UDWH�VDX�IDOVH�vQ�DFHOHDúL�FRQGL LL�úL�FRQIRUP�DFHORUDúL�FULWHULL�

Vom numi analitice� SURSR]L LLOH� FDUH� VH� UHIHU � H[FOXVLY� OD�RELHFWH�LGHDOH�úL�OD�UDSRUWXULOH�GLQWUH�HOH��$GHY UXO�ORU�GHSLQGH�QXPDL�GH�FRUHFWLWXGLQHD�JkQGLULL�� ILLQG�LQGLIHUHQW�ID �GH�RULFH�IDSW�VDX�HYHQLPHQW�

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UHDO�� FXQRVFXW� vQ� H[SHULHQ �� ÌQ� WHUPLQRORJLD� NDQWLDQ �� SURSR]L LLOH�analitice sunt toate a priori��DGLF �SXU�FRQFHSWLELOH�vQDLQWH�úL�LQGHpendent GH�RULFH�FRQWDFW�HPSLULF�FX�UHDOLWDWHD��FX�OXPHD�µH[WHULRDU ¶�JkQGLULL��8U-P WRDUHOH�DVHU LXQL�VXQW�DQDOLWLFH�

(1) ‘Toate unghiurile cu laturile în prelungire sunt congruente.’ (2) ‘2ULFH�QXP U�QDWXUDO�HVWH�SDU�VDX�LPSDU�¶ (3) ‘'DF � GRX �P ULPL��$� úL� %�� VXQW� ILHFDUH� HJDO � FX� R� D� WUHLD�

P ULPH�&��DWXQFL�$� �%�¶ (4) ‘Toate mamiferele sunt vivipare.’ $GHY UXO� DFHVWRU� SURSR]L LL�� VWDELOLW� H[FOXVLY� SULQ� H[HUFL LXO�

gândirii,� HVWH� DQDOLWLF�GHRDUHFH�HO�GHFXUJH�QXPDL�GLQ�DQXPLWH�SURSULHW L�ale unor idei acceSWDWH� I U � GHPRQVWUD LH� FD� QHvQGRLHOQLFH� �ILH� GDWRULW �µHYLGHQ HL¶�ORU�LQWXLWLYH��ILH�SULQ�FRQYHQ LH�VDX�SULQ�GHILQL LH���3URSR]L LLOH�DQDOLWLFH� QX� QH� IXUQL]HD] � LQIRUPD LL� GHVSUH� OXPH� úL� QX� H[WLQG� FXQRú-WLQ HOH� QRDVWUH�� GHRDUHFH� HOH� H[WUDJ� QXPDL� úL� H[SOLFLWHD] � SURSULHW L� úL�UHOD LL�SH�FDUH�LGHLOH�µSULPLWLYH¶�VDX�µRULJLQDUH¶�OH�FRQ LQ�vQ�PRG�LPSOLFLW��'LQ� GHILQL LD� S WUDWXOXL�� GH� H[HPSOX�� FD� µURPE� FX� XQ� XQJKL� GUHSW¶��GHFXUJH� QXPDL� SULQ� DQDOL]D� FRQFHSWHORU� SURSR]L LD� µ7RDWH� XQJKLXULOH�S WUDWXOXL� VXQW� FRQJUXHQWH¶�� ÌQ� VFKLPE�� SURSR]L LD� µ7ULXQJKLXO� GUHSWXQ-JKLF�$%&�DUH�WRDWH�XQJKLXULOH�DVFX LWH¶�HVWH�DQDOLWLF�IDOV �GHRDUHFH��SULQ�GHILQL LH��WULXQJKLXO�GUHSWXQJKLF�DUH�XQ�XQJKL�GUHSW�

Vom numi sintetice� SURSR]L LLOH� FDUH� VH� UHIHU � OD� RELHFWH��SURSULHW L�� UHOD LL��HYHQLPHQWH� UHDOH��$VWIHO�GH�SURSR]L LL� VXQW�DGHY UDWH�GDF � UHOD LD� GLQWUH� FRPSRQHQWHOH� SURSR]L LHL� FRUHVSXQGH� XQHL� VW UL� GH�IDSW�� FRQWURODELO � úL� YHULILFDELO � vQ� H[SHULHQ �� 'LQ� DFHVW� PRWLY��SURSR]L LLOH� GH� DFHVW� JHQ� VH� PDL� QXPHVF� úL� factuale, având – în WHUPLQRORJLD� NDQWLDQ � – un caracter a posteriori, întrucât nu putem DILUPD�VDX�QHJD�FHYD�GHFkW�GXS �R�FRQVWDWDUH�HPSLULF ��FH�QH�IXUQL]HD] �DQXPLWH� LQIRUPD LL� GHVSUH� VW ULOH� GH� IDSW� GLQ� OXPH�� 6XQW� IDFWXDOH�SURSR]L LL�GH�JHQXO�

(5) ‘3ORX �¶��vQ�ORFXO�S�úi la momentul t) (6) ‘Aluminiul este inoxidabil.’ (7) ‘6WUDGD�&UkQJXOXL�P VRDU �����P�¶ (8) ‘Mercurul este mai greu decât aurul.’ (9) ‘Ion e fratele lui Mihai.’

Page 16: logica interferente

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(11) ‘Vacile nebuQH�DX�S U�SH�SLHSW�¶ 'LQ�DFHVWH�GRX �SURSR]L LL�SXWHP�LQIHUD�FRQFOX]LD� (12) ‘Vacile nebune iubesc manelele.’ 6H�SRDWH�RELHFWD�F �SUHPLVHOH�VXQW�DLXULWH��GDF �QX�GH-a dreptul

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SRDWH�RE LQH��vQ�PRG�accidental sau artificios��R�FRQFOX]LH�DGHY UDW ��6 �DSOLF P�DFHHDúL�VFKHP �LQIHUHQ LDO �FRUHFW �VDX�YDOLG �

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sau Toate numerele divizibile cu 3 sunt pare (fals) 14 este divizibil cu 3 (fals) 'HFL�����HVWH�QXP U�SDU �DGHY UDW�

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FRQVW �YLFLXO�GH�IRUP �DO�LQIHUHQ HL�GDU��LQWXLWLY��QH�SXWHP�GD�VHDPD�F �vQ�FDPHU � SRDWH� IL� OXPLQ � FKLDU� úL� FX� EHFXO� VWLQV�� SHQWUX� F � QH� DIO P� vQ�WLPSXO� ]LOHL�� 'LQ� DFHOHDúL� PRWLYH�� VHVL] P� F � úL� XUP WRUXO� UD LRQDPHQW�este incorect:

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Putem sesiza acum mai bine în ce sens logica este un instrument HVHQ LDO� SHQWUX� GHVFRSHULUHD� úL� GHPRQVWUDUHD� DGHY UXOXL�� QX� SULQ�YHULILFDUHD�HPSLULF �D�SURSR]L LLORU�IDFWXDOH��FL�SULQ�GHGXF LD�ULJXURDV �D�XQRU� SURSR]L LL� QHFXQRVFXWH� VDX� LQFHUWH� GLQ� SURSR]L LL� FXQRVFXWH� VDX�SUHVXSXVH�FD�DGHY UDWH��JDUDQ LD�GH�FHUWLWXGLQH�D�DGHY UXOXL�SURSR]L LLORU�GHULYDWH�ILLQG�YDOLGLWDWHD�IRUPDO �D�LQIHUHQ HORU�HIHFWXDWH�

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ÌQ� DIDU � GH� DFHVWH� SURSR]L LL� SULPitive, acceptate ca premise adeY UDWH�I U �V �IL�IRVW�DUJXPHQWDWH��GHPRQVWUD LD�vQV úL�VH�FRQVWUXLHúWH�pe baza câtorva ‘reguli primitive¶��D�F URU�DFFHSWDUH�HVWH�DEVROXW�QHFHVDU �pentru precizarea uQRU� FRQGL LL� VDX� FULWHULL� GH� YDOLGLWDWH� LQIHUHQ LDO �� ÌQ�ORJLFD� WUDGL LRQDO � VDX� FODVLF � DX� IRVW� FRQVDFUDWH� FkWHYD� UHJXOL�fundamentale ale gândirii corecte, numite cel mai adesea principii logice.

������3ULQFLSLXO�LGHQWLW LL ÌQ�FHD�PDL�VLPSO �úL�LQWXLWLY �IRUPXODUH��SULQFLSLXO�LGHQWLW LL�FHUH�

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„IdeQWLF� vQ� VLQH� VH� ]LFH� GHVSUH� OXFUXULOH� D� F URU� PDWHULH� H� XQD�� ILH� FD�VSHFLH��ILH�FD�QXP U��FkW�úL�GHVSUH�DFHOHD�D�F URU�VXEVWDQ �H�XQD��'H�DLFL�UHLHVH�OLPSHGH�F �LGHQWLWDWHD�HVWH�XQ�IHO�GH�XQLWDWH��R�XQLWDWH�GH�H[LVWHQ �D� XQHL� SOXUDOLW L� VDX� DFHHD� FDUH� UH]XOW � GLQ� FRQVLGHUDUHD� PDL� PXOWRU�OXFUXUL�FD�XQXO��FD�DWXQFL�FkQG�VSXQHP�F �XQ�OXFUX�H�LGHQWLF�FX�VLQH��FD]�vQ�FDUH�DFHODúL�OXFUX�H�VRFRWLW�FD�GRX �OXFUXUL³�19

&HO� FDUH� D� IRUPXODW� FX� SUHFL]LH� SULQFLSLXO� LGHQWLW LL� D� IRVW�Leibniz. În Noi eseuri asupra intelectului omenesc, el spune: „Fiecare OXFUX�HVWH�FHHD�FH�HVWH��ùL�vQ�DWkWHD�H[HPSOH�FkWH�YUH L��$�HVWH�$��%�HVWH�%��9RL�IL�FHHD�FH�YRL�IL��$P�VFULV�FHHD�FH�DP�VFULV��ùL�QLPLF�vQ�YHUVXUL�FD�úL� vQ�SUR] �HVWH�QLPLF�VDX�SX LQ� OXFUX��'UHSWXQJKLXO�HFKLODWHUDO��DFHDVW �ILJXU � HVWH� XQ� GUHSWXQJKL���� 1RQ-A este non-$���� 'DF � $� HVWH� QRQ-B, XUPHD] �F �$�HVWH�QRQ-B...“20

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'LQFROR� GH� VHPQLILFD LD� µWHKQLF ¶� D� XQHL� UHJXOL� IRUPDOH�� FX�caracter tautologic, principiul ‘A este A’�SUHFL]HD] �F �$��FDUH�SRDWH�IL�XQ� RELHFW� UHDO�� R� QR LXQH� VDX� R� SURSR]L LH�� HVWH� HO� vQVXúL�� QHSXWkQG� IL�WRWRGDW � úL� DOWFHYD�� 3HWUH� %RWH]DWX� DUDW � F � ÄYHUEXO� µeste’ are în acest FRQWH[W� XQ� vQ HOHV� GHRVHELW�� QX� H[SULP � QLFL� SRVHVLD� XQHL� vQVXúLUL� �GH�exemplu, ‘omul este bun¶��� QLFL� DSDUWHQHQ D� OD� R� FODV � �GH� H[HPSOX��

Page 22: logica interferente

‘%XFXUHúWL�HVWH�R�PHWURSRO ’), nici incluziunea subclasei într-R�FODV ��GH�exemplu, ‘balenele sunt mamifere¶��� QLFL� SXU� úL� VLPSOX� H[LVWHQ D� �GH�exemplu, ‘este cald’) úL�QLFL�FKLDU�RSHUD LD�GH� LGHQWLILFDUH� �GH�H[HPSOX��‘%XFXUHúWL� HVWH� FDSLWDOD� 5RPkQLHL’). Pare paradoxal, dar principiul LGHQWLW LL� QX� VH� UHIHU � OD� VLPSOD� UHOD LH� GH� LGHQWLWDWH� GLQWUH� RELHFWH� VDX�QR LXQL��FL�HQXQ �FHYD�SURIXQG��SHUVLVWHQ D�VXEVWDQ HL��D�HVHQ HL�OXFUXOXL, GLQFROR� GH� YLFLVLWXGLQLOH� DFFLGHQWHORU�� 2PXO� HVWH� RP� úL� QX� DOWFHYD��obiectul indicat de termenul ‘om’ este omul�úL�QX�DOW �ILLQ �VDX�OXFUX³�21

1.4.2 Principiul non-FRQWUDGLF LHL ÌQ� OXPHD� IHQRPHQDO � GH� RELHFWH� úL� SURFHVH� SH� FDUH� OH� VHVL] P�

HPSLULF�� FRQWUDGLF LD� HVWH� DQWDJRQLVPXO� GLQWUH� DQXPLWH� HQWLW L�� IRU H��HQHUJLL� VDX� SURSULHW L� FDUH� VH� H[FOXG� vQWUH� HOH� RUL� WLQG� V � VH� DQLKLOH]H�UHFLSURF��/D�QLYHOXO�XQHL�IRORVLUL�HOHPHQWDUH�D�OLPEDMXOXL�úL�D�JkQGLULL�SDU�neînGRLHOQLFH�RSR]L LL�WUDQúDQWH��DEVROXWH��GH�JHQXO��GDF �µX este alb’ nu SRDWH�IL�WRWRGDW �úL�QHJUX��YHUGH��DOEDVWUX�HWF���GDF �µ%UDúRYXO�HVWH�OD�QRUG�GH�%XFXUHúWL¶��DWXQFL�QX�VH�SRDWH�DGPLWH��vQ�DFHODúL�WLPS��F �RUDúXO�GH�VXE�7kPSD�HVWH�úL�OD�VXG�GH�FDSLWDOD�5RPkQLHL�ú��D��P��G��

/D�R�SULYLUH�PDL�DWHQW ��VH�FRQVWDW �F �în realitate�HVWH�SRVLELO ��FKLDU�QHFHVDU �FkWHRGDW ��FRH[LVWHQ D�vQ�DFHHDúL�HQWLWDWH�D�XQRU�SURFHVH�úL�UHOD LL�FRQWUDGLFWRULL��RULFH�QXDQ �GH�JUL�HVWH�XQ�DPHVWHF�GH�DOE�úL�QHJUX��PHWDEROLVPXO� HVWH� RSR]L LD� GLQDPLF � GLQWUH� DVLPLOD LH� úL� GH]DVLPLOD LH��YLD D�SVLKLF �HVWH��SULQWUH�DOWHOH��R�HFKLOLEUDUH�SHUPDQHQW �vQWUH�H[FLWD LH�úL�LQKLEL LH��vQ�RULFH�PDJQHW�FRH[LVW �vQ�PRG�QHFHVDU�SROXO�QRUG�úL�SROXO�VXG�HWF�� ÌQ� ILORVRILH��JkQGLUHD�GLDOHFWLF �–� vQFHSXW �GH�+HUDFOLW��Socrate VDX�3ODWRQ�vQ�$QWLFKLWDWH�úL�vQFXQXQDW �GH�PRQXmentalul sistem hegelian –� IDFH�GLQ�QDWXUD�FRQWUDGLFWRULH�D�RULF UXL�OXFUX�VDX�SURFHV�XQ�SULQFLSLX�IXQGDPHQWDO�� SULQ� FDUH� VH� H[SOLF � SHUPDQHQWD� SUHIDFHUH� úL� GHYHQLUH� D�lumii reale.

În domeniul ideal SH�FDUH�vO�VWXGLD] �ORJLFD��FRQWUDGLF LD�HVWH�XQ�UDSRUW� vQWUH� GRX � SURSR]L LL�� GLQWUH� FDUH� XQD� DILUP � FHHD� FH� RSXVD� HL�FRQWUDGLFWRULH�QHDJ ��3URSR]L LD�µ2PXO�HVWH�R�ILLQ �UD LRQDO ¶�– din care DU� WUHEXL� V � IDFHP�XQ�SRVWXODW� DO� ORJLFLL�–� HVWH� FRQWUD]LV �GH�SURSR]L LD�

Page 23: logica interferente

FRQIRUP�F UHLD�µ2PXO�QX�HVWH�R�ILLQ �UD LRQDO ¶��FHHD�FH��GLQ�S FDWH��VH�DGHYHUHúWH�PXOW�PDL�GHV�GHFkW�QH�SODFH�V �R�UHFXQRDúWHP��

Principiul logic al non-FRQWUDGLF LHL� VDX� DO� FRQWUDGLF LHL� H[FOXVH�VH� ED]HD] � SH� SUHVXSR]L LD� F � R� SURSR]L LH� Rarecare nu poate fi decât DGHY UDW � VDX� IDOV � úL� VXV LQH� F � QX� SXWHP� DGPLWH� F � XQD� úL� DFHHDúL�SURSR]L LH� HVWH�� vQ� DFHODúL� WLPS� úL� SULYLW � vQ� DFHODúL� FRQWH[W�� WRWRGDW �DGHY UDW � úL� IDOV �� &X� DOWH� FXYLQWH�� R� DILUPD LH� úL� QHJD LD� HL� QX� SRW� IL�DGHY UDWH� vQ� DFHODúL� WLPS�� IRUPXOD� FDUH� H[SULP � DFHDVW � UHJXO �funGDPHQWDO �D�ORJLFLL�ILLQG��µ(VWH�H[FOXV�$�úL�QRQ-A’.

$ULVWRWHO� HQXQ � SULQFLSLXO� QRQ-FRQWUDGLF LHL� DVWIHO�� ÄHVWH� SHVWH�SXWLQ �FD�XQXLD�úL�DFHOXLDúL�VXELHFW�V �L�VH�SRWULYHDVF �úL�WRWRGDW �V �QX�L�se potriYHDVF � VXE� DFHODúL� UDSRUW� XQXO� úL� DFHODúL� SUHGLFDW�� >���@� $FHVW�SULQFLSLX��PDL�VSXQH�$ULVWRWHO��H�FHO�PDL�VLJXU�GLQ� WRDWH��F FL� ����H�SHVWH�SXWLQ � FD� XQ� RP� V -úL� SRDW � vQFKLSXL� F � XQXO� úL� DFHODúL� OXFUX� HVWH� úL�WRWRGDW � QX� HVWH³�22� ) FkQG� GLQ� UHVSLQJHUea cRQWUDGLF LHL� SULQFLSLXO�funGDPHQWDO� DO� ORJLFLL�� $ULVWRWHO� vL� DFRUG � vQ� PRG� H[SOLFLW� R� HYLGHQ �axioPDWLF �� precizând F � OHJHD� QRQ-FRQWUDGLF LHL� QX� SRDWH� IL� GHGXV �dintr-R� DOW � OHJH� PDL� JHQHUDO �� &HO� PXOW�� DILUP � HO�� DFHVW� SULQFLSLX� VH�poate sus- LQH�SULQtr-R�GHPRQVWUD LH�LQGLUHFW �VDX�SULQ�PHWRGD�UHGXFHULL�OD�absurd.

/HLEQL]� SDUH� FkWHRGDW � V � DFRUGH� SULRULWDWH� LGHQWLW LL��FRQVLGHUkQG� F � SULQFLSLXO� QRQ-FRQWUDGLF LHL� HVWH� IRUPD� QHJDWLY � D�DFHVWXLD�� R� GDW � FH� XQ� OXFUX� HVWH� FHHD� FH� HVWH� úL� DúD� FXP� HVWH� �vQWU-o SURSR]L LH���HO�QX�SRDWH�IL� WRWRGDW �úL�FHHD�FH�QX�HVWH�úL�DOWIHO�GHFkW�HVWH�(cum s-DU�HQXQ D�vQ�QHJD LD�SULPHL�SURSR]L LL��

&HUW�HVWH�F �SULQFLSLXO�QRQ-FRQWUDGLF LHL�DUH�R�HYLGHQ �VSRQWDQ ��FKLDU� úL� OD� QLYHOXO� VLP XOXL� FRPXQ��1LPHQL� QX� DUH� QHYRLH� GH� Xn studiu sistematic al logicii teoretice pentru a-úL�GD�LQWXLWLY�VHDPD�GH�IDSWXO�F �R�GHPRQVWUD LH�VDX�XQ�GLVFXUV�vQ�FDUH�VH�VXV LQ�SURSR]L LL�FRQWUDGLFWRULL�VXQW�incorecte, iar concluziile lor inacceptabile. Cu atât mai mult în elaborarea unor sisteme formale, logico-matematice, excluderea contraGLF LHL� VH�LPSXQH� FD� R� SULP � úL� HOHPHQWDU � FHULQ �� F FL� D� GHPRQVWUD� VDX� D�DUJXPHQWD� FRUHFW� vQVHDPQ �� vQ� SULPXO� UkQG�� D� QX� WH� FRQWUD]LFH��5HVSHFWDUHD� FX� VWULFWH H� D� SULQFLSLXOXL� QRQ-FRQWUDGLF LHL� DVLJXU �consecveQ D�ORJLF �D�GHPRQVWUD LHL�

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1.����3ULQFLSLXO�WHU XOXL�H[FOXV�

3ULQFLSLXO� WHU XOXL�H[FOXV�QX�DUH�R�HYLGHQ �D[LRPDWLF ��DúD�FXP�

SDUH� V � ILH� FD]XO� QRQ-FRQWUDGLF LHL�� HO� HVWH�PDL� GHJUDE � XQ� SRVWXODW� �vQ�VHQVXO� FODVLF� HXFOLGLDQ��� FDUH� GHFUHWHD] � –� I U � GHPRQVWUD LH�� GHúL� QX� H�FkWXúL�GH�SX LQ�HYLGHQW�–�F �QX�H[LVW �GHFkW�GRX �YDORUL�ORJLFH��µDGHY UDW¶�úL�µIDOV¶��$OWIHO�VSXV��RULFH�SURSR]L LH�HVWH�VDX�DGHY UDW ��VDX�IDOV ��D�WUHLD�SRVLELOLWDWH�ILLQG�H[FOXV �– tertium non datur.

În vreme ce principiul non-contraGLF LHL�VXV LQH�F �SURSR]L LLOH�$�úL�QHJD LD�HL�QRQ-A nu pot fi��vQ�DFHODúL�WLPS�úL�VXE�DFHODúL�UDSRUW��ambele DGHY UDWH�� XQD� GLQ� HOH� WUHEXLQG� V � ILH� IDOV �–� SULQFLSLXO� WHU XOXL� H[FOXV�VXV LQH� F � GRX � SURSR]L LL� FRQWUDGLFWRULL�� $� úL� QRQ-A nu pot fi ambele false��XQD�GLQWUH�HOH��LQGLIHUHQW�FDUH��WUHEXLH�vQ�RULFH�FD]�V �ILH�DGHY UDW �

În Despre interpretare –�XQD�GLQWUH�OXFU ULOH�FH�LQWU �vQ�DOF WXLUHD�operei logice a lui Aristotel��LQWLWXODW �GH�FRQWLQXDWRULL�úL�FRPHQWDWRULL�V L�Organon – sH� VSXQH�� ÄRULFH� DILUPD LH� VDX� QHJD LH� HVWH� DGHY UDW � VDX�IDOV ³�23�$ULVWRWHO�QX�DFRUG � vQV � WHU XOXL�H[FOXV�YDORDUHD�XQXL�SULQFLSLX�ORJLF� OD� IHO�GH� VWULQJHQW�FD�úL�QRQ-FRQWUDGLF LD��FRQVLGHUkQG�F �DSOLFDUHD�regulii tertium non datur� HVWH� XWLO � QXPDL� vQ� GHPRQVWUD LD� LQGLUHFW ��Ä3ULQFLSLXO�F �XQ�SUHGLFDW� WUHEXLH�V �ILH�RUL�DILUPDW��RUL�QHJDW�GHVSUH�XQ�VXELHFW�HVWH�FHUXW�GH�GHPRQVWUD LD�FDUH�XWLOL]HD] �UHGXFHUHD�OD�LPSRsibil, GDU�úL�DWXQFL�QX�WRWGHDXQD�XQLYHUVDO���³24

/D� UkQGXO� V X�� /HLEQL]� FRQVLGHU � WHU XO� H[FOXV� PDL� GHJUDE � R�completare sau un corolar al non-FRQWUDGLF LHL�� DWXQFL� FkQG� VFULH��„Principiul non-FRQWUDGLF LHL��HVWH�DFHOD�F �� vQ�JHQHUDO��R�SURSR]L LH�HVWH�

VDX�DGHY UDW �VDX�IDOV ��FHHD�FH�FRQ LQH�GRX �HQXQ XUL�DGHY UDWH��XQXO��F �DGHY UXO�úL�IDOVXO�QX�VXQW�FRPSDWLELOH�vQ�DFHHDúL�SURSR]L LH��VDX�F �R�SURSR]L LH�QX�DU�SXWHD�V �ILH�DGHY UDW �úL�IDOV �vQ�DFHODúL�WLPS��FHO ODOW��F �RSXVXO�VDX�QHJD LD�DGHY UDWXOXL�úL�IDOVXOXL�QX�VXQW�FRPSDWLELOH��VDX�F �QX�H[LVW �PLMORFLX�vQWUH�DGHY UDW�úL�IDOV��VDX�F �nX�VH�SRDWH�FD�R�SURSR]L LH�V �

QX�ILH�QLFL�DGHY UDW �QLFL�IDOV “.25 3ULQFLSLXO� WHU XOXL� H[FOXV� HVWH� PDL� VODE� GHFkW� QRQ-FRQWUDGLF LD��

DYkQG� R� JHQHUDOLWDWH�PDL� UHVWUkQV �� 3ULQFLSLXO� QRQ-FRQWUDGLF LHL� FHUH� FD�SUHGLFDWHOH� V � VH� H[FOXG � XQXO� SH� DOWXO�� GDU� QX� OLPLWHD] � QXP UXO� ORU��

Page 25: logica interferente

'DF �XQ�FRUS�HVWH�DOE��DWXQFL�HO�QX�SRDWH�IL�YHUGH��JDOEHQ��URúX��DObastru HWF���GDF �XQ�PDPLIHU�HVWH�FDO��DWXQFL�HO�QX�SRDWH�IL�vQ�DFHODúL�WLPS�OXS��XUV��JLUDI ��F PLO �HWF��'LPSRWULY ��SULQFLSLXO�WHU XOXL�H[FOXV�LQWURGXFH�R�FRQGL LH� VXSOLPHQWDU �� vQWUXFkW� UHVWUkQJH� QXP UXO� SUHGLcatelor la numai GRX �– tertium non datur��µ8Q�QXP U�QDWXUDO�HVWH�SDU�VDX�LPSDU¶��µ3LHVHOH�MRFXOXL�GH�úDK�SRW�IL�DOEH�VDX�QHJUH¶�HWF�

/RJLFD�WUDGL LRQDO �V-D�FRQVWUXLW�VSRQWDQ�SH�SULQFLSLXO�ELYDOHQ HL��potriviW�F UXLD�SURSR]L LLOH�QX�SRW�DYHD�GHFkW�XQD�VDX�DOWD�GLQWUH�GRX �úL�QXPDL�GRX �YDORUL�ORJLFH��µDGHY UDW¶�úL�µIDOV¶�–�FRQGL LH�FDUH�IDFH�SRVLELO �UHJXOD� WHU XOXL� H[FOXV��2U��GH�PXOWH�RUL�QH�DIO P� vQ� ID D�XQRU�SURSR]L LL�F URUD�QX�OH�SXWHP�DWULEXL�FX�FHUWLWXGLQH�QXPDL�XQD�GLQ�FHOH�GRX �YDORUL�ORJLFH��GLQ�YDULL�PRWLYH��SH�FDUH�QX�OH�GHWDOLHP�DLFL��µ$GDP�HUD�EUXQHW�úL�(YD�URúFDW ¶��µ5RúX�HVWH�R�FXORDUH�PDL�FDOG �GHFkW�SRUWRFDOLX¶��µÌQ�Fk LYD�ani, cel mult, se va produce un mare cutremur’; ‘Universul este infinit în VSD LX�úL�WLPS��QHFUHDW�úL�LQGHVWUXFWLELO¶�HWF��VXQW�GRDU�FkWHYD�H[HPSOH�GH�SURSR]L LL� F URUD� QX� OL� VH� SRDWH� DWULEXL� FX� FHUWLWXGLQH� YDORDUHD� ORJLF �µDGHY UDW¶�VDX�µIDOV¶��SXWHP�VSXQH�GHVSUH�HOH��FHO�PXOW��F �VXQW�SODX]LELOH��probabile, inteligibile,� FUHGLELOH� ú�� D�� P�� G�� /RJLFD� PRGHUQ � D� HODERUDW�sisteme polivalente, cu n�YDORUL� ORJLFH�� vQ�FDUH�SULQFLSLXO� WHU XOXL�H[FOXV�VH�DSOLF ��HYHQWXDO��vQ�IRUPH�JHQHUDOL]DWH�úL�QHLQWXLWLYH��GHPRQVWUDELOH�úL�inteligibile numai formal.

Marea utilitate a principiulXL� WHU XOXL� H[FOXV� FRQVW �� GXS � FXP�REVHUY �$ULVWRWHO��vQ�IDSWXO�F �IDFH�SRVLELO �GHPRQVWUD LD�SULQ�UHGXFHUH�OD�DEVXUG�� ÌQWUXFkW� GRX � SURSR]L LL� FRQWUDGLFWRULL� QX� SRW� IL� DPEHOH� IDOVH��UH]XOW �F �SUREkQG�IDOVLWDWHD�SURSR]L LHL�FDUH�QHDJ �WH]D�GH�GHPRQVWUDW�– úL� SH� FDUH� QX� R� SXWHP�DUJXPHQWD� GLUHFW�–� DP�GRYHGLW�� WRWRGDW � F � WH]D�HVWH�DGHY UDW �

������3ULQFLSLXO�UD LXQLL�VXILFLHQWH )RUPXODW�GH�F WUH�/HLEQL]��FD�SLDWU �XQJKLXODU �D�ILORVRILHL�VDOH��

SULQFLSLXO� UD LXQLL� VXILFLHQWH� QX� HVWH�� SURSULX-]LV�� R� UHJXO � IRUPDO � GH�FRQVWUXF LH� D� LQIHUHQ HORU� GHGXFWLYH� FRUHFWH�� FL� PDL� GHJUDE � R� UHJXO �PHWRGRORJLF ��GHILQLWRULH�SHQWUX�VSLULWXO�úWLLQ LILF�

Page 26: logica interferente

/HLEQL]�DUH�QHYRLH�GH�HQXQ DUHD�DFHVWXL�SULQFLSLX�GLQ�PRPHQWXO�în care a sesizat deosebirea –�PHQ LRQDW �DQWHULRU�– întrH�DGHY UXULOH�GH�UD LRQDPHQW� �DQDOLWLFH�� QHFHVDUH� úL� ULJXURV� GHPRQVWUDELOH� GHGXFWLY�� úL�DGHY UXULOH� GH� IDSW� �FRQWLQJHQWH� úL� vQWHPHLDWH� HPSLULF��� $GHY UXULOH�UD LRQDOH� VH� vQWHPHLD] � SH� FHOH� WUHL� SULQFipii anterioare, între care fundamental este principiul non-FRQWUDGLF LHL�� vQ� YUHPH� FH� DGHY UXULOH�IDFWXDOH�vúL�DX�WHPHLXO�vQ�DFHVW�DO�SDWUXOHD�SULQFLSLX��DO�UD LXQLL�VXILciente. Ä5D LRQDPHQWHOH�QRDVWUH��VSXQH�/HLEQL]�vQ�Monadologie, sunt întemeiate pe GRX � PDUL� SULQFLSLL�� SULQFLSLXO� FRQWUDGLF LHL, în virtutea F UXLD�socotim fals� WRW� FH� FXSULQGH� vQ� VLQH� R� FRQWUDGLF LH�� úL�DGHY UDW ceea ce HVWH� RSXV� IDOVXOXL�� DGLF � vQ� FRQWUDGLF LH� FX� DFHVWD�� úL�SULQFLSLXO� UD LXQLL�

suficiente�� vQ� YLUWXWHD� F UXLD� FRQVLGHU P� F � QLFL� XQ� IDSW� QX� SRDWH� IL�DGHY UDW� VDX� UHDO�� QLFL� R� SURSR]L LH� YHULGLF �� I U � V � H[LVWH� XQ� WHPHL�� R�UD LXQH� VXILFLHQW � SHQWUX� FDUH� OXFUXULOH� VXQW� DúD� úL� QX� DOWIHO�� GHúL�temeiurile acestea de cele mai multe ori nu ne pot fi cunoscute“.26

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Page 29: logica interferente

SHWUHFHUL�I U �*HOX�úL�QH-DP�GLVWUDW�IRDUWH�ELQH��RUL�GH�FkWH�RUL�HUD�úL�HO�GH�ID ��V-D�O VDW�FX�VFDQGDO��vQVHDPQ �F �*HOX�HVWH�XQ�VFDQGDODJLX��M��'DF �x2� ����� UH]XOW �F �x = 5 sau (- 5). k) Steaua a avut mereu probleme pe teren propriu cu PeWUROXO�� PLOLWDULL� DX� SUREDELO� XQ� FRPSOH[� vQ� ID D�SORLHúWHQLORU�� O�� 'H� FkWH� RUL� IXPH]� SHVWH� XQ� SDFKHW� GH� LJ UL� SH� ]L�� DP�LQVRPQLL�� H[LVW �� SUREDELO�� R� OHJ WXU � vQWUH� FDQWLWDWHD� GH� QLFRWLQ � úL�LQVRPQLH�� P�� 'DF � H� IDOV� F � µ7RDWH� WULXQJKLXULOH� VXQW� GUHSWunghice’ DWXQFL� H� IDOV� úL� F � µ1LFL� XQ� WULXQJKL�QX� HVWH� GUHSWXQJKLF¶�� Q��'DF �XQLL�DYRFD L�VXQW�ILODWHOLúWL��DWXQFL�XQLL�ILODWHOLúWL�VXQW�DYRFD L�

3.� &DUH� GLQWUH� XUP WRDUHOH� SURSR]L LL� VXQW� DQDOLWLFH� úL� FDUH� VXQW�sinteWLFH"�&DUH�VXQW�DGHY UDWH�úL�FDUH�VXQW�IDOVH"�$UJXPHQWD L�

a) Mamiferele sunt animale vivipare. b) Celibatarii sunt SHUVRDQHOH� QHF V WRULWH�� F�� )RUPHOH� GH� YLD � GH� SH�7HUUD� VH� ED]HD] � SH�FRPSXúL� DL� FDUERQXOXL�� G�� 0HUFXUXO� HVWH� PDL� JUHX� GHFkW� DXUXO�� e) Triunghiul dreptunghic ABC aUH�WRDWH�XQJKLXULOH�DVFX LWH��I��%DOHQHOH�VXQW� FHL� PDL� PDUL� SHúWL� GH� SH� 7HUUD�� J�� $GDP� HUD� EUXQHW� úL� (YD� HUD�URúFDW ��K��2PXO�HVWH�R� ILLQ � UD LRQDO �� L��2PXO�HVWH� LQIOXHQ DW�QHJDWLY��SVLKLF�úL�VRPDWLF��GH�H[SOR]LLOH�VRODUH�úL�GH�ID]HOH�/XQLL�� M��3 WUDWXO�este un romb cu un unghi drept. k) Trapezul are cinci laturi. l) Toate lebedele sunt albe. m) Homo homini lupus est �µ2PXO� HVWH� OXS� ID � GH� RP¶� – FHOHEUD�PD[LP �D�OXL�7KRPDV�+REEHV��GLQ�Leviathan). n) Anthropos zoon politikon (‘Omul este un animal social’ –�QX�PDL�SX LQ�FHOHEUD�PD[LP �din Politica lui ArisWRWHO���R��([LVW �ILLQ H�UD LRQDOH�H[WUDWHUHVWUH�

4.� ÌQ� ILHFDUH� GLQWUH� XUP WRDUHOH� DUJXPHQWH� FRQFOX]LD� HVWH� IDOV ��GHúL� DPEHOH� SUHPLVH� VXQW� FHUW� DGHY UDWH�� GLQ� FDX]D� QHUHVSHFW ULL� XQXLD�dintre principiilH� ORJLFH��6 �VH�DUDWH�GHVSUH�FH�SULQFLSLX logic este vorba, XQGH�DUH�ORF�vQF OFDUHD�OXL�úL�vQ�FH�DQXPH�FRQVW �HURDUHD�

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Page 30: logica interferente

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