Definition of causality.docx
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Definitionofcausality
Definitionofcausality
ZhangNanlun
nanlunzhang@
Thisdefinitionwaspublishedaschapter6inthebook，“TheNewControlPrinciple”,NationalDefenseIndustryPress,China,2005.
1.1Definitionofnecessaryandsufficientsymptoms
Inagivencausalseries,xandyaretwoevents（phenomena）,
（1）whenxoccursatthekmoment,ywilloccuratthekmomenttoo,
（2）whenxdoesnotoccuratthekmoment,ywouldnotoccuratthekmomenteither;and,（3）whenyoccursatthekmoment,xwilloccuratthekmomenttoo,（4）whenydoesnotoccuratthekmoment,xwouldnotoccuratthekmomenteither.
Thejointtruthtableisdefinedasfollows:
x
y
”ifxtheny”
y
x
”ifythenx”
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
Table1:
definitionofnecessaryandsufficientsymptoms
Thatistosay:
（1）Ifeventxoccurs（eventxtrue）andeventyoccurs（eventytrue）thenthiscausalstatementistrue;
（2）Ifeventxoccurs（eventxtrue）andeventydoesnotoccur（eventyfalse）thenthiscausalstatementisfalse;
（3）Ifeventxdoesnotoccur（eventxfalse）andeventyoccurs（eventytrue）thenthiscausalstatementisfalse;
（4）Ifeventxdoesnotoccur（eventxfalse）andeventydoesnotoccur（eventyfalse）thenthiscausalstatementistrue;
（5）Ifeventyoccurs（eventytrue）andeventxoccurs（eventxtrue）thenthiscausalstatementistrue;
（6）Ifeventyoccurs（eventytrue）andeventxdoesnotoccur（eventxfalse）thenthiscausalstatementisfalse;
（7）Ifeventydoesnotoccur（eventyfalse）andeventxoccurs（eventxtrue）thenthiscausalstatementisfalse;
（8）Ifeventydoesnotoccur（eventyfalse）andeventxdoesnotoccur（eventxfalse）thenthiscausalstatementistrue.
Conclusion:
thereisacausalitybetween“eventxoccurs”and“eventyoccurs”.Ifeventxoccurstheneventywilloccurandifeventyoccurstheneventxmustoccur.
Clearly,underthiscondition“eventxoccurs”isanecessaryandsufficientsymptomof“eventyoccurs”;“eventyoccurs”isalsoanecessaryandsufficientsymptomof“eventxoccurs”.
1.2Examples
Theexamplesbelowarelistedinordertoshowthisdefinition.
Example`1.21
Causalityanalysisof“thereisaforce=x”and“thereisacounterforce=y”.
Inthisgivencausalseries,xandyaretwoevents（phenomena）,
（1）whenxoccursatthekmoment,ywilloccuratthekmomenttoo,
（2）whenxdoesnotoccuratthekmoment,ywouldnotoccuratthekmomenteither;and,（3）whenyoccursatthekmoment,xwilloccuratthekmomenttoo,（4）whenydoesnotoccuratthekmoment,xwouldnotoccuratthekmomenteither.
Thejointtruthtableisasfollows:
x
y
”ifxtheny”
y
x
”ifythenx”
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
Table2:
Causalityanalysisofexample1.21
Thatistosay:
（1）Ifthereisaforce（eventxtrue）andthereisacounterforce（eventytrue）thenthiscausalstatementistrue;
（2）Ifthereisaforce（eventxtrue）andthereisnocounterforce（eventyfalse）thenthiscausalstatementisfalse;
（3）Ifthereisnoforce（eventxfalse）andthereisacounterforce（eventytrue）thenthiscausalstatementisfalse;
（4）Ifthereisnoforce（eventxfalse）andthereisnocounterforce（eventyfalse）thenthiscausalstatementistrue;
（5）Ifthereisacounterforce（eventytrue）andthereisaforce（eventxtrue）thenthiscausalstatementistrue;
（6）Ifthereisacounterforce（eventytrue）andthereisnoforce（eventxfalse）thenthiscausalstatementisfalse;
（7）Ifthereisnocounterforce（eventyfalse）andthereisaforce（eventxtrue）thenthiscausalstatementisfalse;
（8）Ifthereisnocounterforce（eventyfalse）andthereisnoforce（eventxfalse）thenthiscausalstatementistrue.
Conclusion:
thereisacausalitybetween“thereisaforce”and“thereisacounterforce”.Ifthereisaforcethentherewillbeacounterforceandifthereisacounterforcethentheremustbeaforce.
Clearly,undercertaincondition“thereisaforce”isanecessaryandsufficientsymptomof“thereisacounterforce”;“thereisacounterforce”isalsoanecessaryandsufficientsymptomof“thereisaforce”.
Example`1.22
Causalityanalysisof“thelightbulbisemittinglight=x”,and“thelightbulbisemittingheat=y”.
Inthisgivencausalseries,xandyaretwoevents（phenomena）,
（1）whenxoccursatthekmoment,ywilloccuratthekmomenttoo,
（2）whenxdoesnotoccuratthekmoment,ywouldnotoccuratthekmomenteither;and,（3）whenyoccursatthekmoment,xwilloccuratthekmomenttoo,（4）whenydoesnotoccuratthekmoment,xwouldnotoccuratthekmomenteither.
Thejointtruthtableisasfollows:
x
y
”ifxtheny”
y
x
”ifythenx”
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
Table3:
Causalityanalysisofexample1.22
Thatistosay:
（1）Ifthelightbulbisemittinglight（eventxtrue）andthelightbulbisemittingheat（eventytrue）thenthiscausalstatementistrue;
（2）Ifthelightbulbisemittinglight（eventxtrue）andthelightbulbisnotemittingheat（eventyfalse）thenthiscausalstatementisfalse;
（3）Ifthelightbulbisnotemittinglight（eventxfalse）andthelightbulbisemittingheat（eventytrue）thenthiscausalstatementisfalse;
（4）Ifthelightbulbisnotemittinglight（eventxfalse）andthelightbulbisnotemittingheat（eventyfalse）thenthiscausalstatementistrue;
（5）Ifthelightbulbisemittingheat（eventytrue）andthelightbulbisemittinglight（eventxtrue）thenthiscausalstatementistrue;
（6）Ifthelightbulbisemittingheat（eventytrue）andthelightbulbisnotemittinglight（eventxfalse）thenthiscausalstatementisfalse;
（7）Ifthelightbulbisnotemittingheat（eventyfalse）andthelightbulbisemittinglight（eventxtrue）thenthiscausalstatementisfalse;
（8）Ifthelightbulbisnotemittingheat（eventyfalse）andthelightbulbisnotemittinglight（eventxfalse）thenthiscausalstatementistrue.
Conclusion:
thereisacausalitybetween“thelightbulbisemittinglight”and“thelightbulbisemittingheat”.Ifthelightbulbisemittinglightthenthelightbulbwillbeemittingheatandifthelightbulbisemittingheatthenthelightbulbmustbeemittinglight.
Clearly,undercertaincondition“thelightbulbisemittinglight”isanecessaryandsufficientsymptomof“thelightbulbisemittingheat”;“thelightbulbisemittingheat”isalsoanecessaryandsufficientsymptomof“thelightbulbisemittinglight”.
Example`1.23
Causalityanalysisof“heismyopic=x”,and“theparallelraysarefocusedinfrontofhisretina=y”.
Inthisgivencausalseries,xandyaretwoevents（phenomena）,
（1）whenxoccursatthekmoment,ywilloccuratthekmomenttoo,
（2）whenxdoesnotoccuratthekmoment,ywouldnotoccuratthekmomenteither;and,（3）whenyoccursatthekmoment,xwilloccuratthekmomenttoo,（4）whenydoesnotoccuratthekmoment,xwouldnotoccuratthekmomenteither.
Thejointtruthtableisasfollows:
x
y
”ifxtheny”
y
x
”ifythenx”
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
Table4:
Causalityanalysisofexample1.23
Thatistosay:
（1）Ifheismyopic（eventxtrue）andtheparallelraysarefocusedinfrontofhisretina（eventytrue）thenthiscausalstatementistrue;
（2）Ifheismyopic（eventxtrue）andtheparallelraysarenotfocusedinfrontofhisretina（eventyfalse）thenthiscausalstatementisfalse;
（3）Ifheisnotmyopic（eventxfalse）andtheparallelraysarefocusedinfrontofhisretina（eventytrue）thenthiscausalstatementisfalse;
（4）Ifheisnotmyopic（eventxfalse）andtheparallelraysarenotfocusedinfrontofhisretina（eventyfalse）thenthiscausalstatementistrue;
（5）Iftheparallelraysarefocusedinfrontofhisretina（eventytrue）andheismyopic（eventxtrue）thenthiscausalstatementistrue;
（6）Iftheparallelraysarefocusedinfrontofhisretina（eventytrue）andheisnotmyopic（eventxfalse）thenthiscausalstatementisfalse;
（7）Iftheparallelraysarenotfocusedinfrontofhisretina（eventyfalse）andheismyopic（eventxtrue）thenthiscausalstatementisfalse;
（8）Iftheparallelraysarenotfocusedinfrontofhisretina（eventyfalse）andheisnotmyopic（eventxfalse）thenthiscausalstatementistrue.
Conclusion:
thereisacausalitybetween“heismyopic”and“theparallelraysarefocusedinfrontofhisretina”.Ifheismyopicthentheparallelrayswillbefocusedinfrontofhisretinaandiftheparallelraysarefocusedinfrontofhisretinathenhemustbemyopic.
Clearly,undercertaincondition“heismyopic”isanecessaryandsufficientsymptomof“theparallelraysarefocusedinfrontofhisretina”;“theparallelraysarefocusedinfrontofhisretina”isalsoanecessaryandsufficientsymptomof“heismyopic”.
Example`1.24
Causalityanalysisof“thebodyishere=x”,and“theshadowishere=y”
Inthisgivencausalseries,xandyaretwoevents（phenomena）,
（1）whenxoccursatthekmoment,ywilloccuratthekmomenttoo,
（2）whenxdoesnotoccuratthekmoment,ywouldnotoccuratthekmomenteither;and,（3）whenyoccursatthekmoment,xwilloccuratthekmomenttoo,（4）whenydoesnotoccuratthekmoment,xwouldnotoccuratthekmomenteither.
Thejointtruthtableisasfollows:
x
y
”ifxtheny”
y
x
”ifythenx”
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
Table5:
Causalityanalysisofexample1.24
Thati
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