7. Pō͘-tiúⁿ sī sò͘-ha̍k-ka mā sī si-jîn
"Góa tùi hit-chióng thui-lí ê èng-iōng kap kè-ta̍t piáu-sī hoâi-gî, in-ūi he m̄-sī sûn-chhùi thiu-siōng ê logic /lo,chek/, he sī kō͘ te̍k-sû hêng-sek só͘ hoat-tián chhut-lâi ê. Góa iû-kî hoâi-gî, ùi sò͘-ha̍k gián-kiù só͘ hoat-tián ê thui-lí. Sò͘-ha̍k sī iú-koan hêng-sek kap sò͘-liōng ê kho-ha̍k; sò͘-ha̍k thui-lí put-kò sī kā logic èng-iōng tī hêng-sek kap sò͘-liōng. Siōng tōa ê chhò-gō͘ sī kā só͘-ūi sûn tāi-sò͘-ha̍k ê chin-lí tòng-chò thiu-siōng a̍h phó͘-phiàn ê chin-lí. Chit-ê chhò-gō͘ hiah tōa, soah siū-tio̍h hiah phó͘-phiàn ê chiap-siū, che hō͘ góa chin bē lí-kái. Sò͘-ha̍k ê kong-lí (axiom) m̄-sī phó͘-phiàn chin-lí ê kong-lí. Tī hêng-sek kap sò͘-liōng ê koan-hē sī chin, kí-lē lâi kóng, bô tāi-piáu tī tō-tek hong-bīn mā sī chin. Tī tō-tek lâi kóng, pō͘-hūn ê lúi-chek téng-î choân-pō͘ chit-chióng thui-lūn, thong-siông m̄-sī chin. Tī hòa-ha̍k, chit-ê kong-lí mā khiā bē-chāi. Tī khó-lī kàu tōng-ki hong-bīn, i tō khiā bē-chāi ah; in-ūi nn̄g-ê kok-iú kè-ta̍t ê tōng-ki ke chò-hóe ê kè-ta̍t, bô it-tēng sī kò-pia̍t kè-ta̍t ê chóng-sò͘. Iáu ū chē-chē sò͘-ha̍k chin-lí kan-ta tī sò͘-ha̍k koan-hē ê hoān-ûi lāi sī chin-lí. M̄-koh sò͘-ha̍k-ka tiu-tiu kā i he iú-hān ê chin-lí tòng-chò choa̍t-tùi phó͘-phiàn ê chin-lí teh lí-lūn -- sè-kan lâng mā sī án-ne teh kā chiap-siū. Bryant tī i hit-pún ha̍k-būn pá ê ‘Sîn-ōe-ha̍k’ (Mythology) lāi-bīn kóng tio̍h chi̍t-ê lūi-sū ê chhò-gō͘ lâi-goân: ‘sui-bóng lán bô siong-sìn Ī-kàu-tô͘ ê sîn-ōe, m̄-koh lán ka-tī tiu-tiu kā pàng bē-kì-tit, koh kō͘ he lâi thui-lūn hiān-si̍t ê koan-hē.’ Put-jî-kò, pún-sin tō sī Ī-kàu-tô͘ ê tāi-sò͘-ha̍k-ka, in siong-sìn ‘Ī-kàu-tô͘ sîn-ōe,’ in thàu-kòe kì-tî ê thui-lūn iáu bô thàu-kòe hô͘-tô͘ ê thâu-náu hiah chē. Kán-tan kóng, ùi kāng-khoán ê kin-goân, góa m̄-bat tú-tio̍h ē sìn-jīm-tit ê sò͘-ha̍k-ka, a̍h sī bē àm-tiong choa̍t-tùi koh bô tiâu-kiāⁿ siong-sìn x^2 + px = q. Lí ē-sái chò chi̍t-ê si̍t-giām, kā chi̍t-ê chit-chióng lâng kóng, lí siong-sìn, ū-sî x^2 + px = q bē sêng-li̍p, koh kái-soeh hō͘ i liáu-kái, liáu-āu, lí tio̍h kín-kín làng-káng, in-ūi i tiāⁿ-tio̍h ē piàⁿ-miā boeh kòng tó lí."
I siōng-bóe só͘ kóng ê hō͘ góa kan-ta teh ài-chhiò, Dupin sûi koh kè-sio̍k kóng:
"Góa ê ì-sù sī án-ne, jû-kó Pō͘--tiúⁿ kan-ta sī sò͘-ha̍k-ka, Kio̍k-tiúⁿ tō m̄-bián khui chi-phiò hō͘ góa. M̄-koh góa chai, i sī sò͘-ha̍k-ka mā sī si-jîn, góa iōng ê hong-hoat sī kin-kì i ê lêng-le̍k, koh chham-khó i ê chōng-hóng. Góa chai-iáⁿ i sī chi̍t-ê phô͘-sian, mā kāu kè-bô͘. Góa siūⁿ, chit-chióng lâng bô khó-lêng m̄-chai it-poaⁿ kéng-chhat ê hêng-ûi bô͘-sek. I bô khó-lêng bô liāu tio̍h -- sū-si̍t chèng-bêng i chá tō liāu tio̍h -- i ē pòaⁿ-lō͘ tú-tio̍h kong-kek. Góa koh siūⁿ, i mā liāu tio̍h in tau ē siū-tio̍h pì-bi̍t kiám-cha. I chhiâng-chāi kui-mê bô tńg chhù, Kio̍k-tiúⁿ hoaⁿ-hí án-ne hong-piān i ê tiâu-cha, góa sī kan-ta kā khòaⁿ chò kè-bô͘, thang hō͘ kéng-chhat chò thiat-té ê chhiau-chhōe, chin kín tō ē siong-sìn -- sū-si̍t G mā án-ne siong-sìn -- hit-tiuⁿ phoe bô khǹg tī chhù-lāi. Góa mā kám-kak, tī chia góa sin-sin khó͘-khó͘ kā lí kài-siāu, iú-koan kéng-chhat chhiau-chhōe mi̍h-kiāⁿ ê put-piàn goân-chek ê chiah-ê siūⁿ-hoat, góa siong-sìn Pō͘-tiúⁿ it-tēng mā lóng ū siūⁿ tio̍h. Án-ne, i tiāⁿ-tio̍h tō khòaⁿ bē-khí it-poaⁿ iōng-lâi am-chhàng ê khang-á-phāng. Góa siūⁿ, i bô khó-lêng hàm kah m̄-chai, in tau siōng ho̍k-cha̍p, siōng phian-phiah ê khang-phāng, tō ná chhiūⁿ pho͘-thong piah-tû kāng-khoán, lóng siám bē-kòe Kio̍k-tiúⁿ ê ba̍k-chiu, thàm-chiam, chǹg-á, a̍h hàm-kiàⁿ. Góa khòaⁿ kah chin chheng-chhó, nā m̄-sī thiau kò͘-ì ê chú-tōng soán-te̍k, i mā tio̍h put-tek-í kā tāi-chì kán-tan-hòa. Hoān-sè lí iáu ē-kì-tit, tī téng-pái ê thó-lūn tiong-kan, góa kiàn-gī kóng, sī-m̄-sī in-ūi siuⁿ bêng-hián, chit-ê pì-bi̍t chiah ē hō͘ i hiah-nī khùn-jiáu, i thiaⁿ tio̍h soah chhiò kah tòng bē tiām."
"Sī ah," góa kóng, "góa ē-kì-tit i ê tōa chhiò siaⁿ, góa siūⁿ-kóng i sī-m̄-sī chhiò kah boeh kiù-kin ah."
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7. 部長是數學家 mā 是詩人
"我對彼種推理 ê 應用 kap 價值表示懷疑, 因為彼毋是純粹抽象 ê logic /lo.chek/, 彼是 kō͘ 特殊形式所發展出來 ê. 我尤其懷疑, ùi 數學研究所發展 ê 推理. 數學是有關形式 kap 數量 ê 科學; 數學推理不過是 kā logic 應用 tī 形式 kap 數量. 上大 ê 錯誤是 kā 所謂純代數學 ê 真理當做抽象 a̍h 普遍 ê 真理. 這个錯誤 hiah 大, 煞受著 hiah 普遍 ê 接受, 這予我真袂理解. 數學 ê 公理 (axiom) 毋是普遍真理 ê 公理. Tī 形式 kap 數量 ê 關係是真, 舉例來講, 無代表 tī 道德方面 mā 是真. Tī 道德來講, 部份 ê 累積等於全部, 這種推論通常毋是真. Tī 化學, 這个公理 mā 徛袂在. Tī 考慮到動機方面, 伊 tō 徛袂在 ah; 因為兩个各有價值 ê 動機加做伙 ê 價值, 無一定是個別價值 ê 總數. 猶有濟濟數學真理干焦 tī 數學關係 ê 範圍內是真理. M̄-koh 數學家 tiu-tiu kā 伊 he 有限 ê 真理當做絕對普遍 ê 真理 teh 理論 -- 世間人 mā 是 án-ne teh kā 接受. Bryant tī 伊彼本學問飽 ê ‘神話學’ (Mythology) 內面講著一个類似 ê 錯誤來源: ‘雖罔咱無相信異教徒 ê 神話, m̄-koh 咱 ka-tī tiu-tiu kā 放袂記得, koh kō͘ he 來推論現實 ê 關係.’ 不而過, 本身 tō 是異教徒 ê 代數學家, in 相信 ‘異教徒神話,’ in 透過記持 ê 推論猶無透過糊塗 ê 頭腦 hiah 濟. 簡單講, ùi 仝款 ê 根源, 我 m̄-bat 拄著會信任得 ê 數學家, a̍h 是袂暗中絕對 koh 無條件相信 x^2 + px = q. 你會使做一个實驗, kā 一个這種人講, 你相信, 有時 x^2 + px = q 袂成立, koh 解說予伊了解, 了後, 你著緊緊閬港, 因為伊定著會拚命欲摃倒你."
伊上尾所講 ê 予我干焦 teh 愛笑, Dupin 隨 koh 繼續講:
"我 ê 意思是 án-ne, 如果部長干焦是數學家, 局長 tō 毋免開支票予我. M̄-koh 我知, 伊是數學家 mā 是詩人, 我用 ê 方法是根據伊 ê 能力, koh 參考伊 ê 狀況. 我知影伊是一个扶仙, mā 厚計謀. 我想, 這種人無可能毋知一般警察 ê 行為模式. 伊無可能無料著 -- 事實證明伊早 tō 料著 -- 伊會半路拄著攻擊. 我 koh 想, 伊 mā 料著 in 兜會受著祕密檢查. 伊常在規暝無轉厝, 局長歡喜 án-ne 方便伊 ê 調查, 我是干焦 kā 看做計謀, 通予警察做徹底 ê 搜揣, 真緊 tō 會相信 -- 事實 G mā án-ne 相信 -- 彼張批無囥 tī 厝內. 我 mā 感覺, tī chia 我辛辛苦苦 kā 你介紹, 有關警察搜揣物件 ê 不變原則 ê chiah-ê 想法, 我相信部長一定 mā lóng 有想著. Án-ne, 伊定著 tō 看袂起一般用來掩藏 ê 空仔縫. 我想, 伊無可能譀 kah 毋知, in 兜上複雜, 上偏僻 ê 空縫, tō ná 像普通壁櫥仝款, lóng 閃袂過局長 ê 目睭, 探針, 鑽仔, a̍h 譀鏡. 我看 kah 真清楚, 若毋是 thiau 故意 ê 主動選擇, 伊 mā 著不得已 kā 代誌簡單化. 凡勢你猶會記得, tī 頂擺 ê 討論中間, 我建議講, 是毋是因為 siuⁿ 明顯, 這个祕密才會予伊 hiah-nī 困擾, 伊聽著煞笑 kah 擋袂恬."
"是 ah," 我講, "我會記得伊 ê 大笑聲, 我想講伊是毋是笑 kah 欲糾筋 ah."
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7.
"I dispute the availability, and thus the value, of that reason which is cultivated in any especial form other than the abstractly logical. I dispute, in particular, the reason educed by mathematical study. The mathematics are the science of form and quantity; mathematical reasoning is merely logic applied to observation upon form and quantity. The great error lies in supposing that even the truths of what is called pure algebra, are abstract or general truths. And this error is so egregious that I am confounded at the universality with which it has been received. Mathematical axioms are not axioms of general truth. What is true of relation --of form and quantity --is often grossly false in regard to morals, for example. In this latter science it is very usually untrue that the aggregated parts are equal to the whole. In chemistry also the axiom falls. In the consideration of motive it falls; for two motives, each of a given value, have not, necessarily, a value when united, equal to the sum of their values apart. There are numerous other mathematical truths which are only truths within the limits of relation. But the mathematician argues, from his finite truths, through habit, as if they were of an absolutely general applicability --as the world indeed imagines them to be. Bryant, in his very learned 'Mythology,' mentions an analogous source of error, when he says that 'although the Pagan fables are not believed, yet we forget ourselves continually, and make inferences from them as existing realities.' With the algebraists, however, who are Pagans themselves, the 'Pagan fables' are believed, and the inferences are made, not so much through lapse of memory, as through an unaccountable addling of the brains. In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith that x squared + px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x squared + px is not altogether equal to q, and, having made him understand what you mean, get out of his reach as speedily as convenient, for, beyond doubt, he will endeavor to knock you down."
"I mean to say," continued Dupin, while I merely laughed at his last observations, "that if the Minister had been no more than a mathematician, the Prefect would have been under no necessity of giving me this check. I knew him, however, as both mathematician and poet, and my measures were adapted to his capacity, with reference to the circumstances by which he was surrounded. I knew him as a courtier, too, and as a bold intriguant. Such a man, I considered, could not fall to be aware of the ordinary policial modes of action. He could not have failed to anticipate --and events have proved that he did not fail to anticipate --the waylayings to which he was subjected. He must have foreseen, I reflected, the secret investigations of his premises. His frequent absences from home at night, which were hailed by the Prefect as certain aids to his success, I regarded only as ruses, to afford opportunity for thorough search to the police, and thus the sooner to impress them with the conviction to which G--, in fact, did finally arrive --the conviction that the letter was not upon the premises. I felt, also, that the whole train of thought, which I was at some pains in detailing to you just now, concerning the invariable principle of policial action in searches for articles concealed --I felt that this whole train of thought would necessarily pass through the mind of the Minister. It would imperatively lead him to despise all the ordinary nooks of concealment. He could not, I reflected, be so weak as not to see that the most intricate and remote recess of his hotel would be as open as his commonest closets to the eyes, to the probes, to the gimlets, and to the microscopes of the Prefect. I saw, in fine, that he would be driven, as a matter of course, to simplicity, if not deliberately induced to it as a matter of choice. You will remember, perhaps, how desperately the Prefect laughed when I suggested, upon our first interview, that it was just possible this mystery troubled him so much on account of its being so very self-evident."
"Yes," said I, "I remember his merriment well. I really thought he would have fallen into convulsions."
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