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邏輯推論的類型

邏輯推論的類型. Deduction( 演繹推論 ). A deduction is speech ( logos ) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. ( Prior Analytics I.2, 24b18-20) Aristotle(384-322 B.C.) Organon.

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邏輯推論的類型

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  1. 邏輯推論的類型

  2. Deduction(演繹推論) • A deduction is speech (logos) in which, certain things having been supposed, something different from those supposed results of necessity because of their being so. (Prior Analytics I.2, 24b18-20) • Aristotle(384-322 B.C.) • Organon

  3. Evaluation：由普遍性的律則出發，推出一個真命題(只要形式正確而前提全真，結論必然真)。Evaluation：由普遍性的律則出發，推出一個真命題(只要形式正確而前提全真，結論必然真)。

  4. Induction(歸納推論) • induction (epagôgê)：another specie of argument recognized by Aristotle. • “argument from the particular to the universal”(Organon, Cateroriae, 105a11-12). • E.g. 假設技藝精湛的領航員是最有效能的，技藝精湛的戰車駕駛員亦然，那麼，一般的說，技藝精湛的人都是各自在其工作中最有效能的人。(105a 13-15) • [(Ta∧Ea) ∧(Tb∧Eb)] x(Tx∧Ex)

  5. AnalyticaPriora(68b 15-29) • 完全歸納法 • 人是長壽的 馬是長壽的 騾是長壽的 人馬騾……等就是所有沒有膽汁的動物 所以，凡是沒有膽汁的動物都是長壽的 • [F(x1) ∧…∧F(xn) ∧y(G(y) y=x1∨…∨y=xn)]  y(G(y) F(y))

  6. AnalyticaPriora(68b41-69a11) • 類比推論 • 底比斯人進攻福申人的戰爭是對鄰國開戰 雅典人進攻底比斯人是對鄰國開戰 底比斯人進攻福申人的戰爭是罪惡的 所以，雅典人進攻底比斯人的戰爭是罪惡的

  7. Francis Bacon(1561-1626) • New Organon(1620) • 亞里斯多德以來建立的邏輯理論，並不能幫助我們建立新的科學，我們需要新的思維工具。(卷一，箴言11)

  8. David Hume(1711-1776) • Problem of Induction(歸納推論的合理性問題)：我們從經驗到的東西推到未曾經驗到的東西，從所考查對象的過去、現在如此推到它未來也將如此，究竟有甚麼根據?它的合理性何在?

  9. Evaluation：透過累積個案的觀察，獲得一個普遍性的律則。結論超出前提的範圍，是擴充性的推論，結論與前提的關係不是必然的。Evaluation：透過累積個案的觀察，獲得一個普遍性的律則。結論超出前提的範圍，是擴充性的推論，結論與前提的關係不是必然的。 • 增加歸納強度的方法： 1. 前提觀察個案越多越好 2. 個案間個體差異越大越好

  10. Abduction(回溯推論) • Inference to the Best Explanation. • this type of inference is frequently employed, in some form or other, both in everyday and in scientific reasoning. • C. S. Peirce(1839-1914)

  11. Deduction. • Rule: All the beans from this bag are white.Case: These beans are from this bag.Result: These beans are white. • Induction. • Case: These beans are [randomly selected] from this bag.Result: These beans are white.Rule: All the beans from this bag are white. • Hypothesis (Abduction). • Rule: All the beans from this bag are white.Result: These beans [oddly] are white.Case: These beans are from this bag.

  12. Evaluation：透過回溯性的尋求最佳可能的解釋，一個與人類實踐生活相關的困境(problem)被解決了。Evaluation：透過回溯性的尋求最佳可能的解釋，一個與人類實踐生活相關的困境(problem)被解決了。

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