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Backward Causation

Backward Causation - BACKWARD CAUSATION CAN WE CHANGE THE...

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Unformatted text preview: BACKWARD CAUSATION: CAN WE CHANGE THE PAST? What follows is a portion of a very famous article by Michael Dummett, in which he introduces his example of the chief of a tribe dancing to ensure the bravery of young men on a lion hunt. The various attempts to undermine the chief’s beliefs about the effect of his dancing are called “bilking arguments”. His arguments may be applied to any claim of backward causation, not just dancing chiefs. His article is basically an argument against the claim that the notion of backward causation is somehow incoherent, or logically inconsistent. That is, he is not trying to prove that there are instances of backward causation, only that the notion is not paradoxical. When we read Huw Price's book, we will see that he explicitly advocates a version of what he calls "retro-causation" in order to solve the interpretation difficulties confronting quantum mechanics. He maintains, roughly, that at the quantum level, there is no temporal asymmetry, or temporal arrow. Causal processes proceed in both temporal directions. Thus, for Price, at least, "backward" causation is a very real phenomenon. 124$ MICHAEL$ DUMMETT$ BRINGING$ ABOUT$ THE$ PAST 125$ make$ out$ that$ something$ is$ not$ meaningful$ than$ to$ make$ out$ that$ it$ is.)$ Thus,$ without$ more$ ado,$ I$ shall$ set$ aside$ the$ suggestion$ that$ the$ flaw$ in$ the$ fatalist$ argument$ lies$ in$ the$ very$ first$ step.$ The$ next$ two$ steps$ stand$ or$ fall$ together.$ They$ are:$ 'If$ you$ are$ going$ to$ be$ killed$ in$ this$ raid,$ you$ will$ be$ killed$ whatever$ precautions$ you$ take'$ and$ 'If$ you$ are$ not$ going$ to$ be$ killed$ in$ this$ raid,$ you$ will$ not$ be$ killed$ whatever$ precautions$ you$ neglect'.$ These$ are$ both$ of$ the$ form$ 'If$ p, then$ if$ q then$ p'; for$ example,$ `If$ you$ are going$ to$ be$ killed,$ then$ you$ will$ be$ killed$ even$ if$ you$ take$ precautions'.$ They$ are$ clearly$ correct$ on$ many$ interpretations$ of$ 'if;$ and$ I$ do$ not$ propose$ to$ waste$ time$ by$ enquiring$ whether$ they$ are$ correct$ on$ 'the'$ interpretation$ of$ 'if'$ proper$ to$ well-instructed$ users$ of$ the$ English$ language.$ The$ next$ two$ lines$ are$ as$ follows:$ 'Hence,$ if$ you$ are$ going$ to$ be$ killed$ in$ the$ raid,$ any$ precautions$ you$ take$ will$ be$ ineffective'$ and$ 'Hence,$ if$ you$ are$ not$ going$ to$ be$ killed$ in$ the$ raid,$ any$ precautions$ you$ take$ will$ have$ been$ superfluous'.$ The$ first$ of$ these$ is$ indisputable.$ The$ second$ gives$ an$ appearance$ of$ sophistry.$ The$ fatalist$ argues$ from$ 'If$ you$ are$ not$ going$ to$ be$ killed,$ then$ you$ won't$ be$ killed$ even$ if$ you$ have$ taken$ no$ precautions'$ to$ 'If$ you$ are$ not$ going$ to$ be$ killed,$ then$ any$ precautions$ you$ take$ will$ have$ been$ superfluous';$ that$ is,$ granted$ the$ truth$ of$ the$ statement$ 'You$ will$ not$ be$ killed$ even$ if$ you$ take$ no$ precautions',$ you$ will$ have$ no$ motive$ to$ take$ precautions;$ or,$ to$ put$ it$ another$ way,$ if$ you$ would$ not$ be$ killed$ even$ if$ you$ took$ no$ precautions,$ then$ any$ precautions$ you$ take$ cannot$ be$ considered$ as$ being$ effective$ in$ bringing$ about$ your$ survival—that$ is,$ as$ effecting$ it.$ This$ employs$ a$ well-known$ principle.$ St$ Thomas,$ for$ instance,$ says$ it$ is$ a$ condition$ of$ ignorance$ to$ be$ an$ excuse$ for$ having$ done$ wrong$ that,$ if$ the$ person$ had$ not$ suffered$ from$ the$ ignorance,$ he$ would$ not$ have$ committed$ the$ wrongful$ act$ in$ question.$ But$ we$ want$ to$ object$ that$ it$ may$ be$ just$ the$ precautions$ that$ I$ am$ going$ to$ take$ which$ save$ me$ from$ being$ killed;$ so$ it$ cannot$ follow$ from$ the$ mere$ fact that$ I$ am$ not$ going$ to$ be$ killed$ that$ I$ should$ not$ have$ been$ going$ to$ be$ killed$ even$ if$ I$ had$ not$ been$ going$ to$ take$ precautions.$ Here$ it$ really$ does$ seem$ to$ be$ a$ matter$ of$ the$ way$ in$ which$ 'if'$ is$ understood;$ but,$ as$ I$ have$ said.$ I$ do$ not$ wish$ to$ call$ into$ question$ the$ legitimacy$ of$ a$ use$ of$ 'if'$ according$ to$ which$ '(Even)$ if$ you$ do$ not$ take$ precautions,$ you$ will$ not$ be$ killed'$ follows$ from$ 'You$ will$ not$ be$ killed'.$ It$ is,$ however,$ clear$ that,$ on$ any$ use$ of$ 'if'$ on$ which$ this$ inference$ is$ valid,$ it$ is$ possible$ that$ both$ of$ the$ statements$ 'If$ you$ do$ not$ take$ precautions,$ you$ will$ be$ killed'$ and$ 'If$ you$ do$ not$ take$ precautions,$ you$ will$ not$ be$ killed'$ should$ be$ true.$ It$ indeed$ follows$ from$ the$ truth$ of'$ these$ two$ statements$ together$ that$ their$ common$ antecedent$ is$ false;$ that$ is,$ that$ I$ am$ in$ fact$ going$ to$ take$ precautions.$ (It$ may$ be$ held$ that$ on$ a,$ or$ even$ the,$ use$ of$ 'if'$ in$ English,$ these$ two$ statements$ cannot$ both$ be$ true;$ or$ again,$ it$ may$ be$ held$ $ that$ they$ can$ both$ be$ true$ only$ when$ a$ stronger$ consequence$ follows,$ namely,$ that$ not$ only$ am$ I$ as$ a$ matter$ of$ fact$ going$ to$ take$ precautions,$ but$ that$ I$ could$ not$ fail$ to$ take$ them,$ that$ it$ was$ not$ in$ my$ power$ to$ refrain$ from$ taking$ them.$ But,$ as$ I$ have$ said,$ it$ is$ not$ my$ purpose$ here$ to$ enquire$ whether$ there$ are$ such$ uses$ of$ 'if'$ or$ whether,$ if$ so,$ they$ are$ important$ or$ typical$ uses.)$ Now$ let$ us$ say$ that$ it$ is$ correct$ to$ say$ of$ certain$ precautions$ that$ they$ are$ capable$ of$ being$ effective$ in$ preventing$ my$ death$ in$ the$ raid$ if$ the$ two$ conditional$ statements$ are$ true$ that,$ if$ I$ take$ them,$ I$ shall$ not$ be$ killed$ in$ the$ raid,$ and$ that,$ if$ I$ do$ not$ take$ them,$ I$ shall$ be$ killed$ in$ the$ raid.$ Then,$ since,$ as$ we$ have$ seen,$ the$ truth$ of$ these$ two$ statements$ is$ quite$ compatible$ with$ the$ truth$ of$ the$ statement$ that,$ if$ I$ do$ not$ take$ precautions,$ I$ shall$ not$ be$ killed,$ the$ truth$ of$ this$ latter$ statement$ cannot$ be$ a$ ground$ for$ saying$ that$ my$ taking$ precautions$ will$ not$ be$ effective$ in$ preventing$ my$ death.$ Thus,$ briefly,$ my$ method$ of$ rebutting$ the$ fatalist$ is$ to$ allow$ him$ to$ infer$ from$ 'You$ will$ not$ be$ killed'$ to$ 'If$ you$ do$ not$ take$ precautions,$ you$ will$ not$ be$ killed';$ but$ to$ point$ out$ that,$ on$ any$ sense$ of$ 'if'$ on$ which$ this$ inference$ is$ valid,$ it$ is$ impermissible$ to$ pass$ from$ 'If$ you$ do$ not$ take$ precautions,$ you$ will$ not$ be$ killed'$ to$ 'Your$ taking$ precautions$ will$ not$ be$ effective$ in$ preventing$ your$ death'.$ For$ this$ to$ be$ permissible,$ the$ truth$ of$ 'If$ you$ do$ not$ take$ precautions,$ you$ will$ not$ be$ killed'$ would$ have$ to$ be$ incompatible$ with$ that$ of$ 'If$ you$ do$ not$ take$ precautions,$ you$ will$ be$ killed';$ but,$ on$ the$ sense$ of$ 'if$ on$ which$ the$ first$ step$ was$ justified,$ these$ would$ not$ be$ incompatible.$ I$ prefer$ to$ put$ the$ matter$ this$ way$ than$ to$ make$ out$ that$ there$ is$ a$ sense$ of$ 'if'$ on$ which$ these$ two$ are$ indeed$ incompatible,$ but$ on$ which$ the$ first$ step$ is$ unjustified,$ because$ it$ is$ notoriously$ difficult$ to$ elucidate$ such$ a$ sense$ of$ 'if$ .$ Having$ arrived$ at$ a$ formulation$ of$ the$ fallacy$ of$ the$ fatalist$ argument,$ let$ us$ now$ consider$ whether$ the$ parallel$ argument$ to$ demonstrate$ the$ absurdity$ of$ attempting$ to$ bring$ about$ the$ past$ is$ fallacious$ in$ the$ same$ way.$ I$ will$ abandon$ the$ theological$ example$ in$ favour$ of$ a$ magical$ one.$ Suppose$ we$ come$ across$ a$ tribe$ who$ have$ the$ following$ custom.$ Every$ second$ year$ the$ young$ men$ of$ the$ tribe$ are$ sent,$ as$ part$ of$ their$ initiation$ ritual,$ on$ a$ lion$ hunt:$ they$ have$ to$ prove$ their$ manhood.$ They$ travel$ for$ two$ days,$ hunt$ lions$ for$ two$ days,$ and$ spend$ two$ days$ on$ the$ return$ journey;$ observers$ go$ with$ them,$ and$ report$ to$ the$ chief$ upon$ their$ return$ whether$ the$ young$ men$ acquitted$ themselves$ with$ bravery$ or$ not.$ The$ people$ of$ the$ tribe$ believe$ that$ various$ ceremonies,$ carried$ out$ by$ the$ chief,$ influence$ the$ weather,$ the$ crops,$ and$ so$ forth.$ I$ do$ not$ want$ these$ ceremonies$ to$ be$ thought$ of$ as$ religious$ rites,$ intended$ to$ dispose$ the$ gods$ favourably$ towards$ them,$ but$ simply$ as$ performed$ on$ the$ basis$ of$ a$ wholly$ mistaken$ system$ of$ causal$ beliefs.$ While$ the$ young$ men$ are$ away$ from$ the$ village$ the$ chief$ performs$ ceremonies---$ 126$ MICHAEL$ DUMMETT$ BRINGING ABOUT THE PAST$ 127$ dances,$ let$ us$ say—intended$ to$ cause$ the$ young$ men$ to$ act$ bravely.$ We$ notice$ that$ he$ continues$ to$ perform$ these$ dances$ for$ the$ whole$ six$ days$ that$ the$ party$ is$ away,$ that$ is$ to$ say,$ for$ two$ days$ during$ which$ the$ events$ that$ the$ dancing$ is$ supposed$ to$ influence$ have$ already$ taken$ place.$ Now$ there$ is$ generally$ thought$ to$ be$ a special absurdity$ in$ the$ idea$ of$ affecting$ the$ past,$ much$ greater$ than$ the$ absurdity$ of$ believing$ that$ the$ performance$ of$ a$ dance$ can$ influence$ the$ behaviour$ of$ a$ man$ two$ days'$ journey$ away;$ so$ we$ ought$ to$ be$ able$ to$ persuade$ the$ chief$ of$ the$ absurdity$ of$ his$ continuing$ to$ dance$ after$ the$ first$ four$ days$ without$ qsestioning$ his$ general$ system$ of$ causal$ beliefs.$ How$ are$ we$ going$ to$ do$ it?$ Since$ the$ absurdity$ in$ question$ is$ alleged$ to$ be$ a$ logical absurdity,$ it$ must$ be$ capable$ of$ being$ seen$ to$ be$ absurd$ however$ things$ turn$ out;$ so$ I$ am$ entitled$ to$ suppose$ that$ things$ go$ as$ badly$ for$ us,$ who$ are$ trying$ to$ persuade$ the$ chief$ of$ this$ absurdity,$ as$ they$ can$ do;$ we$ ought$ still$ to$ be$ able$ to$ persuade$ him.$ We$ first$ point$ out$ to$ him$ that$ he$ would$ not$ think$ of$ continuing$ to$ perform$ the$ dances$ after$ the$ hunting$ party$ has$ returned;$ he$ agrees$ to$ that,$ but$ replies$ that$ that$ is$ because$ at$ that$ time$ he$ knows whether$ the$ young$ men$ have$ been$ brave$ or$ not,$ so$ there$ is$ no$ longer$ any$ point$ in$ trying$ to$ bring$ it$ about$ that$ they$ have$ been.$ It$ is$ irrelevant,$ he$ says,$ that$ during$ the$ last$ two$ days$ of$ the$ dancing$ they$ have$ already$ either$ been$ brave$ or$ cowardly:$ there$ is$ still$ a$ point$ in$ his$ trying$ to$ make$ them$ have$ been$ brave,$ because$ he$ does$ not$ yet$ know$ which$ they$ have$ been.$ We$ then$ say$ that$ it$ can$ be$ only$ the$ first$ four$ days$ of$ the$ dancing$ which$ could$ possibly$ affect$ the$ young$ men's$ performance;$ but$ he$ replies$ that$ experience$ is$ against$ that.$ There$ was$ for$ several$ years$ a$ chief$ who$ thought$ as$ we$ did,$ and$ danced$ for$ the$ first$ four$ days$ only;$ the$ results$ were$ disastrous.$ On$ two$ other$ occasions,$ he$ himself$ fell$ ill$ after$ four$ days$ of$ dancing$ and$ was$ unable$ to$ continue,$ and$ again,$ when$ the$ hunting$ party$ returned,$ it$ proved$ that$ the$ young$ men$ had$ behaved$ ignobly.$ The$ brief$ digression$ into$ fatalism$ was$ occasioned$ by$ our$ noticing$ that$ the$ standard$ argument$ against$ attempting$ to$ affect$ the$ past$ was$ a$ precise$ analogue$ of$ the$ standard$ fatalist$ argument$ against$ attempting$ to$ affect$ the$ future.$ Having$ diagnosed$ the$ fallacy$ in$ the$ fatalist$ argument,$ my$ announced$ intention$ was$ to$ discover$ whether$ there$ was$ not$ a$ similar$ fallacy$ in$ the$ standard$ argument$ against$ affecting$ the$ past. And$ it$ indeed$ appears$ to$ me$ that$ there$ is.$ We$ say$ to$ the$ chief,$ 'Why$ go$ on$ dancing$ now?$ Either$ the$ young$ men$ have$ already$ been$ brave,$ or$ they$ have$ already$ been$ cowardly.$ If$ they$ have$ been$ brave,$ then$ they$ have$ been$ brave$ whether$ you$ dance$ or$ not.$ If$ they$ have$ been$ cowardly,$ then$ they$ have$ been$ cowardly$ whether$ you$ dance$ or$ not.$ If$ they$ have$ been$ brave,$ then$ your$ dancing$ now$ will$ not$ be$ effective$ in$ making$ them$ have$ been$ brave,$ since$ they$ have$ been$ brave$ even$ if$ you$ do$ not$ dance.$ And$ if$ they$ have$ not$ been$ brave,$ then$ your$ dancing$ will$ certainly$ not$ be$ effective.$ Thus$ your$ continuing$ to$ dance$ will$ in$ the$ one$ case$ be$ superfluous,$ and$ in$ the$ other$ fruitless:$ in$ neither$ case$ is$ there$ any$ point$ in$ your$ continuing$ to$ dance.'$ The$ chief$ can$ reply$ in$ exactly$ the$ way$ in$ which$ we$ replied$ to$ the$ fatalist.$ He$ can$ say,$ 'If$ they$ have$ been$ brave,$ then$ indeed$ there$ is$ a$ sense$ in$ which$ it$ will$ be$ true$ to$ say$ that,$ even$ if$ I$ do$ not$ dance,$ they$ will$ have$ been$ brave:$ but$ this$ is$ not$ incompatible$ with$ its$ also$ being$ true$ to$ say$ that,$ if$ I$ do$ not$ dance,$ they$ will$ not$ have$ been$ brave.$ Now$ what$ saying$ that$ my$ continuing$ to$ dance$ is$ effective$ in$ causing$ them$ to$ have$ been$ brave$ amounts$ to$ is$ that$ it$ is$ true$ both$ that,$ if$ I$ go$ on$ dancing,$ they$ have$ been$ brave,$ and$ that,$ if$ I$ do$ not$ dance,$ they$ have$ not$ been$ brave.$ I$ have$ excellent$ empirical$ grounds$ for$ believing$ both$ these$ two$ statements$ to$ be$ true;$ and$ neither$ is$ incompatible$ with$ the$ truth$ of$ the$ statement$ that,$ if$ I$ do$ not$ dance,$ they$ have$ been$ brave.$ although,$ indeed,$ I$ have$ no$ reason$ for$ believing$ that statement.$ Hence,$ you$ have$ not$ shown$ that,$ from$ the$ mere$ hypothesis$ that$ they$ have$ been$ brave,$ it$ follows$ that$ the$ dancing$ I$ am$ going$ to$ do$ will$ not$ be$ effective$ in$ making$ them$ have$ been$ brave;$ on$ the$ contrary,$ it$ may$ well$ be$ that,$ although$ they$ have$ been$ brave,$ they$ have$ been$ brave$ just$ because I$ am$ going$ to$ go$ on$ dancing;$ that.$ if$ I$ were$ not$ going$ to$ go$ on$ dancing,$ they$ would$ not$ have$ been$ brave.'$ This$ reply$ sounds$ sophistical;$ but$ it$ cannot$ be$ sophistical$ if$ our$ answer$ to$ the$ fatalist$ was$ correct,$ because$ it$ is$ the$ exact$ analogue$ of$ that$ answer.$ We$ now$ try$ the$ following$ argument:$ 'Your$ knowledge of$ whether$ the$ young$ men$ have$ been$ brave$ or$ not$ may$ affect$ whether$ you$ think there$ is$ any$ point$ in$ performing$ the$ dances;$ but$ it$ cannot$ really$ make$ any$ difference$ to$ the$ effect the$ dances$ have$ on$ what$ has$ happened.$ If$ the$ dances$ are$ capable$ of$ bringing$ it$ about$ that$ the$ young$ men$ have$ acted$ bravely,$ then$ they$ ought$ to$ be$ able$ to$ do$ that$ even$ after$ you$ have$ learned$ that$ the$ young$ men$ have$ not acted$ bravely.$ But$ that$ is$ absurd,$ for$ that$ would$ mean$ that$ the$ dances$ can$ change$ the$ past.$ But$ if$ the$ dances$ cannot$ have$ any$ effect$ after$ you$ have$ learned$ whether$ the$ young$ men$ have$ been$ brave$ or$ not,$ they$ cannot$ have$ any$ effect$ before,$ either;$ for$ the$ mere$ state$ of$ your$ knowledge$ cannot$ make$ any$ difference$ to$ their$ efficacy.'$ Now$ since$ the$ causal$ beliefs$ of$ this$ tribe$ are$ so$ different$ from$ our$ own,$ I$ could$ imagine$ that$ the$ chief$ might$ simply$ deny$ this:$ he$ might$ say$ that$ what$ had$ an$ effect$ on$ the$ young$ men's$ behaviour$ was$ not$ merely$ the$ performance$ of$ the$ dances$ by$ the$ chief$ as$ such,$ but$ rather$ their$ performance$ by$ the$ chief$ when$ in$ a$ state$ of$ ignorance$ as$ to$ the$ outcome$ of$ the$ hunt.$ And$ if$ he$ says$ this,$ I$ think$ there$ is$ really$ no$ way$ of$ dissuading$ him,$ short$ of$ attacking$ his$ whole$ system$ of$ causal$ beliefs.$ But$ I$ will$ not$ allow$ him$ to$ say$ this,$ because$ it$ would$ make$ his$ causal$ beliefs$ so$ different$ in$ kind$ from$ ours$ that$ there$ would$ be$ no$ moral$ to$ draw$ for$ our$ own$ case.$ Before$ going$ on$ to$ consider$ his$ reaction$ to$ this$ argument,$ however,$ let$ us$ first$ pause$ to$ review$ the$ situation.$ 128$ MICHAEL$ DUMMETT$ BRINGING$ ABOUT$ THE$ PAST$ 129$ Suppose,$ then,$ that$ he$ agrees$ to$ our$ suggestion:$ agrees,$ that$ is,$ that$ it$ is$ his$ dancing$ as$ such$ that$ he$ wants$ to$ consider$ as$ bringing$ about$ the$ young$ men's$ bravery,$ and$ not$ his$ dancing$ in$ ignorance$ of$ whether$ they$ were$ brave.$ If$ this$ is$ his$ belief,$ then$ we$ may$ reasonably$ challenge$ him$ to$ try$ dancing$ on$ some$ occasion$ when$ the$ hunting$ party$ has$ returned$ and$ the$ observers$ have$ reported$ that$ the$ young$ men$ have$ not been$ brave.$ Here$ at$ last$ we$ appear$ to$ have$ hit$ on$ something$ which$ has$ no$ parallel$ in$ the$ case$ of$ affecting$ the$ future.$ If$ someone$ believes$ that$ a$ certain$ kind$ of$ action$ is$ effective$ in$ bringing$ about$ a$ subsequent$ event,$ I$ may$ challenge$ him$ to$ try$ it$ out$ in$ all$ possible$ circumstances:$ but$ I$ cannot$ demand$ that$ he$ try$ it$ out$ on$ some$ occasion$ when$ the$ event$ is$ not going$ to$ take$ place,$ since$ he$ cannot$ identify$ any$ such$ occasion$ independently$ of$ his$ intention$ to$ perform$ the$ action.$ Our$ knowledge$ of$ the$ future$ is$ of$ two$ kinds:$ prediction$ based$ on$ causal$ laws$ and$ knowledge$ in$ intention.$ If$ I$ think$ I$ can$ predict$ the$ non-occurrence$ of$ an$ event,$ then$ I$ cannot$ consistently$ also$ believe$ that$ I$ can$ do$ anything$ to$ bring$ it$ about;$ that$ is,$ I$ cannot$ have$ good$ grounds$ for$ believing,$ of$ any$ action,$ both$ that$ it$ is$ in$ my$ power$ to$ do$ it,$ and$ that$ it$ is$ a$ condition$ of$ the$ event's$ occurring.$ On$ the$ other$ hand,$ I$ cannot$ be$ asked$ to$ perform$ the$ action$ on$ some$ occasion$ when$ I$ believe$ that$ the$ event$ will$ not$ take$ place,$ when$ this$ knowledge$ lies$ in$ my$ intention$ to$ prevent$ it$ taking$ place;$ for$ as$ soon$ as$ I$ accede$ to$ the$ request,$ I$ thereby$ abandon$ my$ intention.$ It$ would,$ indeed,$ be$ different$ if$ we$ had$ foreknowledge:$ someone$ who$ thought,$ like$ Russell$ and$ Ayer,$ that$ it$ is$ a$ merely$ contingent$ fact$ that$ we$ have$ memory$ but$ not$ foreknowledge$ would$ conclude$ that$ the$ difference$ I$ have$ pointed$ to$ does$ not$ reveal$ a$ genuine$ asymmetry$ between$ past$ and$ future,$ but$ merely$ reflects$ this$ contingent$ fact.$ If$ the$ chief$ accepts$ the$ challenge,$ and$ dances$ when$ he$ knows$ that$ the$ young$ men$ have$ not$ been$ brave,$ it$ seems$ that$ he$ must$ concede$ that$ his$ dancing$ does$ not$ ensure their$ bravery.$ There$ is$ one$ other$ possibility$ favourable$ to$ us.$ Suppose$ that$ he$ accepts$ the$ challenge,$ but$ when$ he$ comes$ to$ try$ to$ dance,$ he$ unaccountably$ cannot$ do$ so:$ his$ limbs$ simply$ will$ not$ respond.$ Then$ we$ may$ say,$ 'It$ is$ not$ your$ dancing$ (after$ the$ event)$ which$ causes$ them$ to$ have$ been$ brave,$ but$ rather$ their$ bravery$ which$ makes$ possible$ your$ dancing:$ your$ dancing$ is$ not,$ as$ you$ thought,$ an$ action$ which$ it$ is$ in$ your$ power$ to$ do$ or$ not$ to$ do$ as$ you$ choose.$ So$ you$ ought$ not$ to$ say$ that$ you$ dance$ in$ the$ last$ two$ days$ in$ order$ to$ make$ them$ have$ been$ brave,$ but$ that$ you$ try$ to$ see$ whether$ you$ can$ dance,$ in$ order$ to$ find$ out$ whether$ they$ have$ been$ brave.'$ It$ may$ seem$ that$ this$ is$ conclusive;$ for$ are$ not$ these$ the$ only$ two$ possibilities?$ Either$ he$ does$ dance,$ in$ which$ case$ the$ dancing$ is$ proved$ not$ to$ be$ a$ sufficient$ condition$ of$ the$ previous$ bravery;$ or$ he$ does$ not,$ in$ which$ case$ $ vice$ versa.$ But$ in$ fact$ the$ situation$ is$ not$ quite$ so$ simple.$ For$ one$ thing,$ it$ is$ not$ justifiable$ to$ demand$ that$ the$ chief$ should$ either$ consider$ his$ dancing$ to$ be$ a$ sufficient$ condition$ of$ the$ young$ men's$ bravery,$ or$ regard$ it$ as$ wholly$ unconnected.$ It$ is$ enough,$ in$ order$ to$ provide$ him$ with$ a$ motive$ for$ performing$ the$ dances,$ that$ he$ should$ have$ grounds$ to$ believe$ that$ there$ is$ a$ significant$ positive$ correlation$ between$ his$ dancing$ and$ pr...
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