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
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
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
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?
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)
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。