a discourse on method-第4节

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consideration　of　figures；　that　it　can　exercise　the　understanding　only　on　condition　of　greatly　fatiguing　the　imagination；　and；　in　the　latter；　there　is　so　complete　a　subjection　to　certain　rules　and　formulas；　that　there　results　an　art　full　of　confusion　and　obscurity　calculated　to　embarrass；　instead　of　a　science　fitted　to　cultivate　the　mind。　　By　these　considerations　I　was　induced　to　seek　some　other　method　which　would　comprise　the　advantages　of　the　three　and　be　exempt　from　their　defects。　　And　as　a　multitude　of　laws　often　only　hampers　justice；　so　that　a　state　is　best　governed　when；　with　few　laws；　these　are　rigidly　administered；　in　like　manner；　instead　of　the　great　number　of　precepts　of　which　logic　is　composed；　I　believed　that　the　four　following　would　prove　perfectly　sufficient　for　me；　provided　I　took　the　firm　and　unwavering　resolution　never　in　a　single　instance　to　fail　in　observing　them。

The　first　was　never　to　accept　anything　for　true　which　I　did　not　clearly　know　to　be　such；　that　is　to　say；　carefully　to　avoid　precipitancy　and　prejudice；　and　to　comprise　nothing　more　in　my　judgement　than　what　was　presented　to　my　mind　so　clearly　and　distinctly　as　to　exclude　all　ground　of　doubt。

The　second；　to　divide　each　of　the　difficulties　under　examination　into　as　many　parts　as　possible；　and　as　might　be　necessary　for　its　adequate　solution。

The　third；　to　conduct　my　thoughts　in　such　order　that；　by　commencing　with　objects　the　simplest　and　easiest　to　know；　I　might　ascend　by　little　and　little；　and；　as　it　were；　step　by　step；　to　the　knowledge　of　the　more　complex；　assigning　in　thought　a　certain　order　even　to　those　objects　which　in　their　own　nature　do　not　stand　in　a　relation　of　antecedence　and　sequence。

And　the　last；　in　every　case　to　make　enumerations　so　complete；　and　reviews　so　general；　that　I　might　be　assured　that　nothing　was　omitted。

The　long　chains　of　simple　and　easy　reasonings　by　means　of　which　geometers　are　accustomed　to　reach　the　conclusions　of　their　most　difficult　demonstrations；　had　led　me　to　imagine　that　all　things；　to　the　knowledge　of　which　man　is　competent；　are　mutually　connected　in　the　same　way；　and　that　there　is　nothing　so　far　removed　from　us　as　to　be　beyond　our　reach；　or　so　hidden　that　we　cannot　discover　it；　provided　only　we　abstain　from　accepting　the　false　for　the　true；　and　always　preserve　in　our　thoughts　the　order　necessary　for　the　deduction　of　one　truth　from　another。　　And　I　had　little　difficulty　in　determining　the　objects　with　which　it　was　necessary　to　commence；　for　I　was　already　persuaded　that　it　must　be　with　the　simplest　and　easiest　to　know；　and；　considering　that　of　all　those　who　have　hitherto　sought　truth　in　the　sciences；　the　mathematicians　alone　have　been　able　to　find　any　demonstrations；　that　is；　any　certain　and　evident　reasons；　I　did　not　doubt　but　that　such　must　have　been　the　rule　of　their　investigations。　　I　resolved　to　commence；　therefore；　with　the　examination　of　the　simplest　objects；　not　anticipating；　however；　from　this　any　other　advantage　than　that　to　be　found　in　accustoming　my　mind　to　the　love　and　nourishment　of　truth；　and　to　a　distaste　for　all　such　reasonings　as　were　unsound。　　But　I　had　no　intention　on　that　account　of　attempting　to　master　all　the　particular　sciences　commonly　denominated　mathematics：　　but　observing　that；　however　different　their　objects；　they　all　agree　in　considering　only　the　various　relations　or　proportions　subsisting　among　those　objects；　I　thought　it　best　for　my　purpose　to　consider　these　proportions　in　the　most　general　form　possible；　without　referring　them　to　any　objects　in　particular；　except　such　as　would　most　facilitate　the　knowledge　of　them；　and　without　by　any　means　restricting　them　to　these；　that　afterwards　I　might　thus　be　the　better　able　to　apply　them　to　every　other　class　of　objects　to　which　they　are　legitimately　applicable。　　Perceiving　further；　that　in　order　to　understand　these　relations　I　should　sometimes　have　to　consider　them　one　by　one　and　sometimes　only　to　bear　them　in　mind；　or　embrace　them　in　the　aggregate；　I　thought　that；　in　order　the　better　to　consider　them　individually；　I　should　view　them　as　subsisting　between　straight　lines；　than　which　I　could　find　no　objects　more　simple；　or　capable　of　being　more　distinctly　represented　to　my　imagination　and　senses；　and　on　the　other　hand；　that　in　order　to　retain　them　in　the　memory　or　embrace　an　aggregate　of　many；　I　should　express　them　by　certain　characters　the　briefest　possible。　　In　this　way　I　believed　that　I　could　borrow　all　that　was　best　both　in　geometrical　analysis　and　in　algebra；　and　correct　all　the　defects　of　the　one　by　help　of　the　other。

And；　in　point　of　fact；　the　accurate　observance　of　these　few　precepts　gave　me；　I　take　the　liberty　of　saying；　such　ease　in　unraveling　all　the　questions　embraced　in　these　two　sciences；　that　in　the　two　or　three　months　I　devoted　to　their　examination；　not　only　did　I　reach　solutions　of　questions　I　had　formerly　deemed　exceedingly　difficult　but　even　as　regards　questions　of　the　solution　of　which　I　continued　ignorant；　I　was　enabled；　as　it　appeared　to　me；　to　determine　the　means　whereby；　and　the　extent　to　which　a　solution　was　possible；　results　attributable　to　the　circumstance　that　I　commenced　with　the　simplest　and　most　general　truths；　and　that　thus　each　truth　discovered　was　a　rule　available　in　the　discovery　of　subsequent　ones　Nor　in　this　perhaps　shall　I　appear　too　vain；　if　it　be　considered　that；　as　the　truth　on　any　particular　point　is　one　whoever　apprehends　the　truth；　knows　all　that　on　that　　point　can　be　known。　　The　child；　for　example；　who　has　been　instructed　in　the　elements　of　arithmetic；　and　has　made　a　particular　addition；　according　to　rule；　may　be　assured　that　he　has　found；　with　respect　to　the　sum　of　the　numbers　before　him；　and　that　in　this　instance　is　within　the　reach　of　human　genius。　　Now；　in　conclusion；　the　method　which　teaches　adherence　to　the　true　order；　and　an　exact　enumeration　of　all　the　conditions　of　the　thing　。sought　includes　all　that　gives　certitude　to　the　rules　of　arithmetic。

But　the　chief　ground　of　my　satisfaction　with　thus　method；　was　the　assurance　I　had　of　thereby　exercising　my　reason　in　all　matters；　if　not　with　absolute　perfection；　at　least　with　the　greatest　attainable　by　me：　besides；　I　was　conscious　that　by　its　use　my　mind　was　becoming　gradually　habituated　to　clearer　and　more　distinct　conceptions　of　its　objects；　and　I　hoped　also；　from　not　having　restricted　this　method　to　any　particular　matter；　to　apply　it　to　the　difficulties　of　the　other　sciences；　with　not　less　success　than　to　those　of　algebra。　　I　should　not；　however；　on　this　account　have　ventured　at　once　on　the　examination　of　all　the　difficulties　of　the　sciences　which　presented　themselves　to　me；　for　this　would　have　been　contrary　to　the　order　prescribed　in　the　method；　but　observing　that　the　knowledge　of　such　is　dependent　on　principles　borrowed　from　philosophy；　in　which　I　found　nothing　certain；　I　thought　it　necessary　first　of　all　to　endeavor　to　establish　its　principles。　　。And　because　I　observed；　besides；　that　an　inquiry　of　this　kind　was　of　all　others　of　the　greatest　moment；　and　one　in　which　precipitancy　and　anticipation　in　judgment　were　most　to　be　dreaded；　I　thought　that　I　ought　not　to　approach　it　till　I　had　reached　a　more　mature　age　（being　at　that　time　but　twenty…three）；　and　had　first　of　all　employed　much　of　my　time　in　preparation　for　the　work；　as　well　by　eradicating　from　my　mind　all　the　erroneous　opinions　I　had　up　to　that　moment　accepted；　as　by　amassing　variety　of　experience　to　afford　materials　for　my　reasonings；　and　by　continually　exercising　myself　in　my　chosen　method　with　a　view　to　increased　skill　in　its　application。



PART　III

And　finally；　as　it　is　not　enough；　before　commencing　to　rebuild　the　house　in　which　we　live；　that　it　be　pulled　down；　and　materials　and　builders　provided；　or　that　we　engage　in　the　work　ourselves；　according　to　a　plan　which　we　have　beforehand　carefully　drawn　out；　but　as　it　is　likewise　necessary　that　we　be　furnished　with　some　other　house　in　which　we　may　live　commodiously　during　the　operations；　so　that　I　might　not　remain　irresolute　in　my　actions；　while　my　reason　compelled　me　to　suspend　my　judgement；　and　that　I　might　not　be　prevented　from　living　thenceforward　in　the　greatest　possible　felicity；　I　formed　a　provisory　code　of　morals；　composed　of　three　or　four　maxims；　with　which　I　am　desirous　to　make　you　acquainted。

The　first　was　to　obey　the　laws　and　customs　of　my　country；　adhering　firmly　to　the　faith　in　which；　by　the　grace　of　God；　I　had　been　educated　from　my　childhood　and　regulating　my　conduct　in　every　other　matter　according　to　the　most　moderate　opinions；　and　the　farthest　removed　from　extremes；　which　should　happen　to　be　adopted　in　practice　with　general　consent　of　the　most　judicious　of　those　among　whom　I　might　be　living。　　For　as　I　had　from　that　time　begun　to　hold　my　own　opinions　for　nought　because　I　wished　to　subject　them　all　to　examination；　I　was　convinced　that　I　could　not　do　better　than　follow　in　the　meantime　the　opinions　of　the　most　judicious；　and　although　there　are　some　perhaps　among　the　Persians　and　Chinese　as　judicious　as　among　ourselves；　expediency　seemed　to　dictate　that　I　should　regulate　my　practice　conformably　to　the　opinions　of　those　with　whom　I　should　have　to　live；　and　it　appeared　to　me　that；　in　order　to　ascertain　the　real　opini