使用者:Hillgentleman/logic

理則(或曰邏輯)者，思辯之道也。西文Logic一詞源古希臘語λόγος(logos，意為言辭)，夫理則學者，演正論與謬論，使人能辨正曲論也。

古理則本為哲論，為語法、今所謂理則、與修辭之統稱，自十九世紀中，疇人亦之究，而近世電腦科學亦研之，電腦晶片亦多謂之「邏輯閘」也。

理則為形式科學，而查與類敘述論證，是行皆基於推斷之形式系統，及自然語言之論證研究。故理則所研者廣，由謬誤與悖論之主惑，及至法於概率之特殊推理分析及因果律所系者。而理則今亦用於論證結構理論矣。

理則本性

研理則，用形式法固可；惟於理則本性，爭議尚深。本文始述根基概念形式(form)，再概述學派、史、他學（格致）之繫，終以理則之要念。

非形式、形式與符號理則

形式概念乃論理則本性之關鍵。惟「形式理則」(formal logic)之「形式」(formal) 一辭多義，須慎辯之。符號理則實為一類形式理則。彼異於亞里士多德傳統三段論、範疇命題(en:categorical propositions)之理則。本文各定義如下：

非形式理則者，自然語言論證之研。謬論研究者，非形式理則至要之一。書如柏拉圖之語者，^[一]非形式理則之例矣。
形式理則者，推斷(en:inference)以純粹形式之文，而其文示以顯。(若吾人可用純抽象之則（即超然於物與物性之則）書一推斷，則稱此推斷有純形式之內容。) 吾人所用形式理則之始數律，沿自亞里士多德。^[二] 多種理則定義中，君將見，理則推導(logical inference)與純形式內容推導（inference with purely formal content）實二而一也。惟非形式理則仍非虚義，蓋吾人欲究理則而不宥於任何分析形式(not committed to a particular formal analysis)。

符號理則(en:Symbolic logic)究理則推斷之符號抽象。^[三] ^[四]

惟慎之：上述符號理則亦常見稱「形式理則」，未嘗符號抽象之理則學則亦曰「非形式理則」； it is this sense of 'formal' that is parallel to the received usages coming from "形式語言(formal languages)" or 形式論(en:formal theory).

形式理則可溯回兩千年前, 符號理則大部則較新, and arises with the application of insights from mathematics to problems in logic. 一符號理則常表以形式系統(en:formal system), comprising a 形式語言 including rules for creating expressions in the language, 與一推導法則集。 The expressions will normally be intended to represent claims that we may be interested in, and likewise the rules of derivation represent inferences; such systems usually have an 「目的演譯」(intended interpretation). ^[五]

例：設有一形式系統，僅有 "天"、 "地"、"與"三符。其語法為：（一）「『天與地』及『地與天』皆表達式(expressions)」；（二）「任何表達式均可以『與』併成又一表達式」。其推導法則為(rule of derivation)「由任何形如『天與地』之式，吾人可推導『天』」。吾人可演譯(interpret)此中"天" 及 "地" 為任何語句(sentence)；「與」之演譯，吾人以可藉整句之真偽設定。理則系統多演譯「與」如下：含「與」之句為真，若且僅若「與」左右之句俱真。

一形式系統亦可具公理。凡於一系統，公理者，為恒真句於其系統內。如多系統有句曰：「若P則Q，且P為真，則Q亦真矣」，凡欲衍以公理之系統者，必有衍義之法，是謂之「易物之法」矣。此謂人可由公理衍似公理之句，except that other sentences have been substituted for the 'P' and the 'Q'. For example, 由上述公理，we can conclude the following:「若R且S可得T或U，且R且S為真，T或U亦真矣」 (此設「R且S」與「T或U」為此形式系統內之句也) Most 形式系統 have either a rich set of rules of derivation, but few or no axioms; or a rich set of axioms but only the derivation rule of substitution.

衍以系統公理與衍義之則之句者，謂之定理也

相容性、soundness與完備性

形式系統可具之理想性質：

重要邏形式系統體系/Important families of formal systems

各異之理則構思/Rival conceptions of logic

與格致

推導/演譯與歸納

史

縱多文化有複雜之數學與推理，理則，做為外顯推理分析法，僅於三地起源與發展：印度始於西元前六世紀；中國始於西元前五世紀，而希臘則始於西元前四世紀至西元前一世紀。

課題

推斷理則/Syllogistic logic

主文：Aristotelian logic

謂詞理則/predicate calculus

模態理則/Modal logic

推導與思辯/Deduction and reasoning

數理邏輯

主文：數理邏輯

哲學理則/Philosophical logic

理則與計算

論辯理論/Argumentation Theory

爭議

理則何為之餘，真理(logical truth)何為亦有爭。

雙值與排中律

涵蘊：形式與現實 / Implication: strict or material?

容許不可能

理則屬經驗乎？

註

↑ Plato, The Portable Plato, edited by Scott Buchanan, Penguin, 1976, ISBN 0-14-015040-4
↑ Aristotle, The Basic Works, Richard Mckeon, editor, Modern Library, 2001, ISBN 0-375-75799-6, see especially, Posterior Analytics.
↑ Whitehead & Russell, Principia Mathematica to *56, Cambridge, 1997, ISBN 0-521-62606-4
↑ For a more modern treatment, see A. G. Hamilton, Logic for Mathematicians, Cambridge, 1980, ISBN 0-521-29291-3
↑ Paul Halmos, Steven Givant, Logic as Algebra, The Mathematical Association of America, 1998, ISBN 0-88385-327-2

據

Cohen, R.S, and Wartofsky, M.W. (1974), Logical and Epistemological Studies in Contemporary Physics, Boston Studies in the Philosophy of Science, D. Reidel Publishing Company, Dordrecht, Netherlands. ISBN 90-277-0377-9.
Finkelstein, D. (1969), "Matter, Space, and Logic", in R.S. Cohen and M.W. Wartofsky (eds. 1974).
Gabbay, D.M., and Guenthner, F. (eds., 2001-2005), Handbook of Philosophical Logic, 13 vols., 2nd edition, Kluwer Publishers, Dordrecht.
Vincent F. Hendricks, Thought 2 Talk: A Crash Course in Reflection and Expression, New York: Automatic Press / VIP, 2005, ISBN 87-991013-7-8
Hilbert, D., and Ackermann, W. (1928), Grundzüge der theoretischen Logik (Principles of Theoretical Logic), Springer-Verlag.
Hodges, W. (2001), Logic. An introduction to Elementary Logic, Penguin Books.
Hofweber, T. (2004), "Logic and Ontology", Stanford Encyclopedia of Philosophy, Edward N. Zalta (ed.), Eprint.
Hughes, R.I.G. (ed., 1993), A Philosophical Companion to First-Order Logic, Hackett Publishing.
Kneale, William, and Kneale, Martha, (1962), The Development of Logic, Oxford University Press, London, UK.
Smith, B. (1989), "Logic and the Sachverhalt", The Monist 72(1), 52–69.
Witzany, G. (1995). "From the 'Logic of the Molecular Syntax' to Molecular Pragmatism. Explanatory deficits in Manfred Eigen's conecpt of language and communication.", Evolution and Cognition 1(2):148-148.

進

Carroll, Lewis
- "The Game of Logic", 1886. [一]
- "Symbolic Logic", 1896.
Samuel D. Guttenplan, Samuel D., Tamny, Martin, "Logic, a Comprehensive Introduction", Basic Books, 1971.
Scriven, Michael, "Reasoning", McGraw-Hill, 1976, ISBN 0-07-055882-5

參

外

模板:Sisterlinks

模板:Wikia
An Introduction to Philosophical Logic, by Paul Newall, aimed at beginners
forall x: an introduction to formal logic, by P.D. Magnus, covers sentential and quantified logic
Translation Tips, by Peter Suber, for translating from English into logical notation
Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas. In The Dictionary of the History of Ideas.
[二] Test your logic skills

Hillgentleman/logic一文似未成。宜善之。

[1] Plato, The Portable Plato, edited by Scott Buchanan, Penguin, 1976, ISBN 0-14-015040-4

[2] Aristotle, The Basic Works, Richard Mckeon, editor, Modern Library, 2001, ISBN 0-375-75799-6, see especially, Posterior Analytics.

[3] Whitehead & Russell, Principia Mathematica to *56, Cambridge, 1997, ISBN 0-521-62606-4

[4] For a more modern treatment, see A. G. Hamilton, Logic for Mathematicians, Cambridge, 1980, ISBN 0-521-29291-3

[5] Paul Halmos, Steven Givant, Logic as Algebra, The Mathematical Association of America, 1998, ISBN 0-88385-327-2

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