邏輯推論的類型 - pugec.org

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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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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)。
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)
Analytica Priora(68b 15-29)
 完全歸納法
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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))
Analytica Priora(68b41-69a11)
 類比推論
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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
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)

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?

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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
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)

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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.

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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