逻辑问题 (The Problem of Logic)

(Ke Ping [Ed.], 2002-2021)

1.   Logical Reasoning. 2

1.1   Deduction and Induction. 2

1.2   Data, Warrant, Claim.. 3

2.   Logical Fallacies. 3

2.1   Formal Logical Fallacies. 3

2.1.1  Syllogism.. 3

2.1.1.1 Hypothetical syllogism (假言三段论) 4

2.1.1.2 Disjunctive syllogism (选言三段论) 4

2.1.1.3 Categorical syllogism (直言三段论) 4

2.1.2  Fallacy of the consequent (后件推断谬误) 4

2.1.2.1 Denial of the antecedent (否定前件) 5

2.1.2.2 Affirmation of the consequent (肯定后件) 5

2.1.3  Fallacy of illicit major (or minor) premise (推理前提非法错误) 5

2.1.3.1 The formation of a categorical syllogism.. 5

2.1.3.2 Five basic rules governing the validity of categorical syllogisms. 6

2.1.3.3 Distribution of terms (周延) 6

2.1.4  Extended discussion on correct forms of or rules for syllogistic reasoning. 7

2.1.4.1 Distinction between a valid deduction (推断) and a valid argument (论断) 7

2.1.4.2 Verification (证实) vs falsification (证伪) 7

2.2   Informal Logical Fallacies. 9

2.2.1  Fallacies of relevance. 9

(1) Non sequitur (< Latin: “it does not follow” 推不出) 10

(2) Oversimplification (过份简单化) 10

(3) Hasty generalization (以偏概全;妄下定论) 11

(4) Argument from dubious authority (诉诸可疑权威) 11

(5) Begging the question (以假定作为论据来辩论;未经讨论就认为某一有待证明的论点或主张正确;武断;also called “Circular Argument” 循环论证) 12

(6) Argument ad hominem (< Latin, “against the man” 人身攻击) 12

(7) Argument from ignorance (因缺乏反证而得出结论) 12

(8) Post hoc ergo propter hoc (< Latin, “after this, therefore because of this” 发生于其后者必然是其结果) 12

(9) Stereotypes (定型观念;定式思维) 13

(10) Card-stacking (洗牌作弊;片面举证) 13

(11) Arguing by analogy (比喻式论证) 13

2.2.2  Fallacies of ambiguity (verbal fallacies) 13

2.3   Mixed Logical Fallacies. 13

 


 

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        意大利传教士Matteo Ricci (1552-1610)(利玛窦,明代万历年间来到中国并居住近30年,第一位阅读中国文学并对中国典籍进行钻研的西方学者,和京城的很多王公贵族和知名学者都有交往,对中国人的思维特点相当了解)用意大利文写的日记《利玛窦中国札记》:

 

        中国所熟悉的惟一较高深的哲理科学就是道德哲学,但在这方面他们由于引入了错误,似乎非但没有把事情弄明白,反倒弄糊涂了。他们没有逻辑规则的概念,因而处理伦理学的某些教诫时毫不考虑这一课题各个分支相互的内在联系。在他们那里,伦理学这门科学只是他们在理性之光的指引下所达到的一系列混乱的格言和推论。

中文里一些耳熟能详,但其中前提与结论风马牛不相及,没有内在逻辑关系的格言和俗语:

 

        耳朵发烧,有人念叨

        舍不得孩子套不住狼

        各人自扫门前雪,莫管他人瓦上霜

        金钱如粪土,朋友值千金

        远亲不如近邻

        善有善报、恶有恶报

        中国现代哲学和逻辑学开山祖师金岳霖早在中学时代,按照逻辑推理出中国俗语“金钱如粪土,朋友值千金”有问题。他发现,如果把这两句话作为前提,得出逻辑结论应该是“朋友如粪土”。

       In translating the following sentence from Chinese into English in the 1999 National Grade 8 Test for English Majors (TEM-8):

 

        温哥华的辉煌是温哥华人的智慧和勤奋的结晶,其中包括多民族的贡献。

        Vancouver's prosperity results from Vancouver people's wisdom and diligence and the contributions of many nationalities.

        or

        The splendor of Vancouver is the outcome of the intelligence and diligence of its citizens, involving the contributions of many ethnic groups.

 

many examinees failed to identify the logical subject of the predicate verb of the second clause 其中包括 (which should be 温哥华的辉煌), and turned out such Chinese translations with confused structure as:

 

        *The splendor of Vancouver is the outcome of the intelligence and diligence of its people, which includes the contributions of many peoples.

 

Another example:

 

        领导班子年轻化

        *make the leadership members younger

 

       One (except, perhaps, a beauty parlor) cannot really make any person younger in the literal sense of the word. What is meant here in the Chinese original is:

 

        to bring younger people into the leading group

        or

        to reduce the average age of leading officials

        爱因斯坦对逻辑方法在西方科学发展中所起的作用有如下精辟的论述:

 

        Development of Western Science is based on two great achievements—the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion, one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all. (* Quoted in Cleopatra's Nose, Essays on the Unexpected, Daniel J Boorstin [1995], New York: Vintage Books, p. 3. Retrieved May 29, 2005, from Wikiquote: http://en.wikiquote.org/wiki/Albert_Einstein).

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       Logic is no guarantee that we will not make mistakes in argument. But it will help us to avoid making obvious or absurd mistakes because some ways of reasoning are evidently more fallible than others.

 

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0.     传统逻辑基本规律 (Fundamental Laws of Traditional Logic or “Classic Laws of Thought”)

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1.  Logical Reasoning

1.1 Deduction and Induction

In Aristotle’s formal logic, two ways of reasoning are distinguished, i.e. deductive reasoning or deduction, and inductive reasoning or induction.

       A classic form of deductive reasoning is One traditional method of deductive reasoning may be stated in a syllogism, that is, (a reasoned argument in which there are two statements which must lead to a third statement). A typical syllogism is a three-step form like this:

 

              All trees have roots. (Major premise)

                A plane is a tree. (Minor premise)

                Therefore, a plane has roots. (Conclusion)

 

       Few writers arrange their statements in this strict form, favored by Aristotle in his Rhetoric, a classical guide to argument so brilliant that it remains useful today. And yet all of us still employ, at times, the same method of reasoning found in a syllogism: deductive reasoning. This kind of reasoning begins with a statement of general truth (“All trees have roots”) and moves to a statement about an individual (“A plane oak has roots”). Deductive reasoning is commonly applied to college writing. If, for an economics paper, you remark that all liberal senators favor a federally funded program of medical care for all citizens, then identify Edward M. Kennedy as a liberal senator, and conclude that he may be expected to favor the program, you reason deductively.

       But you might argue the other way around. If instead of starting with a general statement (“All trees have roots.”), you were to study a score of different trees, find them all having roots, and then conclude that trees have roots, you would follow the opposite method: inductive reasoning. Inductive reasoning is (sometimes called “scientific method.”) Scientists commonly work in this way: by observing particulars and then drawing general conclusions. In this way new knowledge is acquired about nature. Either method of reasoning is only as trustworthy as the observations on which it is based.

       Either method of reasoning is only as trustworthy as the observations on which it is based.

 

Case: Anselmus’ ontological proof of the existence of God

11世纪修道士安瑟伦 [Anselmus1033-1109,欧洲中世纪经院哲学家、神学家,唯实论的主要代表之一,被称为“最后一名教父和第一个经院哲学家”。出生于意大利皮埃蒙特奥斯塔城一贵族家庭。少时在法国毕尔冈底就学。1060年入本笃会。后入该会在法国诺曼底的柏克隐修院,不久升为副院长。1078年任院长,并教授神学。1093年任英国坎特伯雷大主教;因拥护教皇权益与英王发生争执,并为争夺主教叙任 [investiture: mass noun the action of formally investing a person with honours or rank 授权,授职 (NOECD)] 权两次被迫出走。1107年教皇与英王达成协议,安瑟伦遂被召回英国继任大主教。安瑟伦继承了柏拉图和奥古斯丁的思想,认为信仰高于理性,理性应当服从信仰。但他又主张必须从信仰出发,运用形式逻辑,以论证基督教正统教义。(安瑟伦.《中国大百科全书·宗教卷》)] 对上帝存在作了本体论论证 {对上帝存在的其他论证还有意大利神学家圣托马斯·阿奎那 (St. Thomas Aquinas, 1225-1274) 的宇宙学论证(万事皆有因,上帝是第一因)、英国哲学家佩里 (Wiiliam Perry, 1743-1805) 的设计论证(世上万事万物都有自己的位置和目的,显然是经过了上帝的设计)以及德国哲学家、启蒙运动最重要的思想家康德 (Kant Immanuel, 1724-1804) 的道德论证(见下)等。}

        1.     我们只能把上帝设想成一个无限的、最完美的东西。

        2.     一个具有除“存在”以外的所有完美性(公正、全知、全能等)的东西不能算是“最完美的”。

        3.     因此,最完美的东西 {上帝} 必然存在。

        此论证意味着仅仅通过逻辑就可以从我们关于上帝的观念中推出上帝必然存在的结论。果真如此的话,信仰上帝就成了一种严格建立在逻辑基础上的理性信仰。

        不用说,许多哲学家都对这种逻辑提出了质疑(即使他们本人也许对其结论深信不疑)。这其中最著名的要算是伊曼努尔·康德了。

 

Test yourself: If you were Kant, how would you challenge Anselmus’ ontological proof of God’s existence and what might be your way of proving the existence of God?

Answer:

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(Solomon, Robert C., & Higgins, Kathleen M. (所罗门、希金斯). (2014).《大问题. 简明哲学导论》[张卜天 ] [第四版]. 桂林:广西师范大学出版社. 541 . [原著出版于2014 ]. 122-129 )

 

       In Zen and the Art of Motorcycle Maintenance, Robert M. Pirsig gives memorable short illustrations of the two kinds of reasoning:

 

        If the cycle goes over a bump [a patch of raised road] and the engine misfires [fail to go off or start or function properly], and then goes over another bump and the engine misfires, and then goes over another bump and the engine misfires, and then goes over a long smooth stretch of road and there is no misfiring, and then goes over a fourth bump and the engine misfires again, one can logically conclude that the misfiring is caused by the bumps. That is induction: reasoning from particular experiences to general truths.

        Deductive inferences do the reverse. They start with general knowledge and predict a specific observation. For example if, from reading the hierarchy of facts about the machine, the mechanic knows the horn of the cycle is powered exclusively by electricity from the battery, then he can logically infer that if the battery is dead the horn will not work. That is deduction.

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1.2 Data, Warrant, Claim

In modern times, a simple, practical method of reasoning has been devised by the British philosopher Stephen Toulmin in The Uses of Argument (Cambridge University Press, 1969). Helpfully, Toulmin has divided a typical argument into three parts:

 

1.             The data, or evidence to prove something

2.             The claim, what you are proving with the data

3.             The warrant, the thinking that leads from data to claim

 

       Any clear, explicit argument has to have all three parts. Toulmin’s own example of such an argument is this:

 

Tommy was born in Bermuda ————————— Tommy is a British subject.

                (Data)                                       |                                (Claim)

                                                                 |      

Since Bermuda is a British colony in NW Atlantic and a man born there is by birth a British subject.

                                                         (Warrant)

(Toulmin, 1969. [The Uses of Argument]. Cambridge University Press)

 

2.  Logical Fallacies

In arguments we hear or read, we often detect logical fallacies, i.e. common mistakes in thinking or reasoning, or more precisely, a mistake made in the process of moving from the premises of an argument to the conclusion. When we argue by ourselves, we may also inadvertently commit logical fallacies from time to time. As a result of the fallacy, the premises do not justify the conclusion. (Kennedy, X.J. & Dorothy M. Kennedy, 1987, p. 280. [The Bedford Guide for College Writers. NY: St Martin’s Press.])

       In the following we list some most frequently committed logical fallacies with a view to helping you to recognize them when you read or hear them and to guard against them when you make arguments in your own speech and writing. (Some arguments can exhibit more than one fallacy at once.)

       Basically, there are three types of logical fallacy:

 

1.             Formal Logical Fallacies (推断形式上的错误)

2.             Informal Logical Fallacies (推断内容上的错误)

3.             Mixed Logical Fallacies

 

2.1 Formal Logical Fallacies

Formal logical fallacies are mistakes in which the argument violates a rule of the logical system of which that argument is a part. They are classified into:

 

1.             Fallacy of the consequent

                a      Denial of the antecedent

                b      Affirmation of the consequent

2.             Fallacy of illicit major (or minor) premise

 
2.1.1      Syllogism

Formal logical fallacies occur when an inference maker violates any rule governing the validity of a syllogism, so before characterizing formal logical fallacies, we need to take a closer look at syllogism.

       Syllogism is a mode of argument that forms the core of the body of Western logical thought. Aristotle defined syllogistic logic, and his formulations were thought to be the final word in logic; they underwent only minor revisions in the subsequent 2,200 years. Every syllogism is a sequence of three propositions such that the first two imply [(of a fact or occurrence) suggest (something) as a logical consequence: The forecasted traffic increase implied more roads and more air pollution.  (NOECD) 必然包含; 暗示……为必然结果] the third, the conclusion.

       There are three basic types of syllogism: hypothetical, disjunctive, and categorical.

 
2.1.1.1     Hypothetical syllogism (假言三段论)

       The hypothetical syllogism (modus ponens) has as its first premise a conditional hypothesis:

 

If p then q; it continues: p, therefore q, e.g.

 

              If there is life on Mars [p], then Mars has an atmosphere [q].

                It is the case that there is life on Mars [p].

                Therefore, it is the case that Mars has an atmosphere [q].

 

       It should be noted that in the conditional hypothesis, term p presupposes [To require or involve necessarily as an antecedent condition (AHD4)] term q. Only when this condition is met, can the syllogism be true in both its positive form and negative form. The negative form and its example are displayed in the following:

 

If p, then q; it is not the case that q; therefore, it is not the case that p, e.g.

 

              If there is life on Mars [p], then Mars has an atmosphere [q].

                It is not the case that Mars has an atmosphere [q].

                Therefore, it is not the case that there is life on Mars [p].

 
2.1.1.2     Disjunctive syllogism (选言三段论)

       The disjunctive syllogism (modus tollens) has as its first premise a statement of alternatives:

 

Either p or q; it continues: not q, therefore p.

 
2.1.1.3     Categorical syllogism (直言三段论)

       The categorical syllogism comprises three categorical propositions, which must be statements of the form

 

all S’s are P’s,

no S is P,

some S is P, or

some S is not P.

 (Based on Syllogism. [2004]. In Columbia Encyclopaedia [6th ed.])

 
2.1.2      Fallacy of the consequent (后件推断谬误)

This fallacy (also known as “Aristotle’s fallacy of the consequent”) occurs when the inference maker violates the rule for making a hypothetical syllogism (If p then q; it continues: p, therefore q). It has two forms:

 
2.1.2.1     Denial of the antecedent (否定前件)

       Mistakenly arguing from the premises “If p, then q” and “not p” (symbolized ~ p1) to the conclusion “not q”, e.g.

 

              *If George is a man of good faith, he can be entrusted with this office; but George is not a man of good faith; therefore, George cannot be entrusted with this office.

                       {Comment: “Not p, then not q” cannot be deduced from “If p, then q” because in the conditional hypothesis in a hypothetical syllogism, term p is one of the many possible conditions conducive to, instead of a necessary precondition for, term q. Cannot see what is wrong with that? Look at a more obvious example:

                       *如果我有电动车我就能去学校

                       可是我没有电动车

                       所以我不能去学校。}

 
2.1.2.2     Affirmation of the consequent (肯定后件)

       Mistakenly arguing from the premises “If p, then q” and “q” to the conclusion “p”, e.g.

 

              *If Amos was a prophet, then he had a social conscience;

                Amos he had a social conscience; hence, Amos was a prophet.

                       {Comment: “If q, then p” cannot be deduced from “If p, then q” because in the conditional hypothesis in a hypothetical syllogism, term p, as we noted above, is one of the many possible conditions conducive to, instead of a necessary precondition for, term q.}

 
2.1.3      Fallacy of illicit major (or minor) premise (推理前提非法错误)

This fallacy occurs when the inference maker violates any one of the five basic rules governing the validity of categorical syllogisms.

 
2.1.3.1     The formation of a categorical syllogism

       Traditional Aristotelian logic is concerned with syllogistic reasoning, a form of deductive argument. A syllogism is an argument made up of propositions [statements 命题] in one of four forms:

 

“Every S is P”.                 (universal affirmative);

“No S is P”.                      (universal negative);

“Some S is P”.                 (particular affirmative); or

“Some S is not P”.           (particular negative).

 

       The letters stand for common nouns, such as “dog”, “four-footed animal”, “living thing”, which are called the terms of the syllogism. “S” is called the subject term (S, [判断的] 主词/主项), and “P”, the predicate (P, [判断的] 谓词/谓项), of the syllogism.

       A categorical syllogism contains precisely three terms: the major term (大项), which is the predicate of the conclusion; the minor term (小项), the subject of the conclusion; and the middle term (中项), which appears in both premises but not in the conclusion. Thus:

 

              Aall men [middle term] are mortal [major term], [Major premise]

                aAll philosophers [minor term] are men [middle term]; therefore [Minor premise]

                all philosophers [minor term] are mortal [major term]. [Conclusion]

 

       The premises containing the major and minor terms are named the major and minor premises (大前提和小前提), respectively.

 
2.1.3.2     Five basic rules governing the validity of categorical syllogisms

       Aristotle discovered five basic rules governing the validity of categorical syllogisms:

 

(1)            The middle term must be distributed at least once (a term is said to be distributed [周延] when it refers to all members of the denoted class, as in “All S are P” and “No S is P”; see 2.1.3.3 in the following for a more detailed explanation).

(2)            A term distributed in the conclusion must be distributed in the premise in which it occurs.

(3)            Two negative premises imply no valid conclusion.

(4)            If one premise is negative, then the conclusion must be negative.

(5)            Two affirmatives imply an affirmative.

 (Based on Syllogism. [2004]. In Columbia Encyclopaedia [6th ed.])

 
2.1.3.3     Distribution of terms (周延)

       In syllogistics [三段论式], the application of a term of a proposition to the entire class that the term denotes. A term is said to be distributed when reference is made to all members of the class.

       Briefly, only universal propositions distribute their subject term (S, [判断的]主词), and only negative propositions distribute their predicate (P, [判断的] 谓词). {肯定一类事物必须能肯定其全体,而否认一类事物只要举出一个反例即可。}

       Naturally, singular terms [singular: Logic Of or relating to the specific as distinguished from the general; individual.【逻辑学】单称的 (AHD)] (including proper names used as singular terms) are always distributed, for they refer only to one object and cannot refer to fewer.

 

Test yourself: What terms are distributed and what are not?

What terms in the following forms of proposition are distributed and what are not?

        1)     Every S is P.

        2)     No S is P.

        3)     Some S is P.

        4)     Some S is not P.

        Discuss both the subject term (主词) and the predicate (谓词) in each proposition.

Answer:

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        1)        In a proposition of the form “Every S is P,” S is distributed, but P is not.

        2)        In “No S is P,” both the subject and the predicate are distributed.

        3)        In the form “Some S is P,” neither S nor P is distributed.

        4)        In “Some S is not P,” S is not distributed, but P is, e.g. in “Some crows are not friendly,” “friendly” is distributed, “crows” are not (reference is made to all friendly things but not to all crows).

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       The importance of distribution lies in its being a principle of formal inference (specifically, the second rule governing the well-formedness of a categorical syllogism) that no term may be distributed in the conclusion unless it was distributed in the premises. (Based on “Distribution. In BCD 2002)

       The illicit major (or minor) premise fallacy arises when a major (or minor) term that is undistributed in the premise is distributed in the conclusion, e.g.

 

              *All tubers are high-starch foods;

                no squashes are tubers;

                therefore, no squashes are high-starch foods.

 

Analysis:

              *All tubers are high-starch foods; [undistributed: reference is made to high-starch foods in terms of their quality of having much starch, not of their totality.] [Cf. Every S is P.]

                no squashes are tubers;

                therefore, no squashes are high-starch foods. [distributed: reference is made to any kind of high-starch food (no squash is high-starch food of whatever kind).] [Cf. No S is P.]

 

(Based on Distribution. In Blackburn, Simon 2000. [Oxford Dictionary of Philosophy. 上海上海外语教育. ix + 418 pp.]; Distribution. In BCD 2002, and MERL 2004.)

 

Test yourself: What is it that makes Twain’s “apology” funny?

Mark Twain once remarked to the press that “some American congressmen are bastards.” That, of course, made some congressmen mad. They pressured Twain to make a public apology. By way of apology, Twain said: “some American congressmen are not bastards.” What is it that makes Twain’s “apology” funny?

Analysis:

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Conclusion:

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Test yourself: What would have Twain said if he had sincerely wished to apologize?

What form of syllogistic reasoning would Twain have used if he had sincerely wished to apologize to the congressmen he had cursed earlier?

Answer:

        ?

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2.1.4      Extended discussion on correct forms of or rules for syllogistic reasoning
2.1.4.1     Distinction between a valid deduction (推断) and a valid argument (论断)

Deduction A

              All the planets in our solar system are equipped with an atmosphere.

                Pluto is a planet in our solar system.

                × Therefore, Pluto is equipped with an atmosphere. {Valid deduction, but wrong argument.}

 

       Whether an argument is a valid argument is determined by the truth or falsity of the content of its premises. Deduction A is invalid, but Argument A is false because its major premise is false. It is one of the informal logical fallacies (Fallacies of relevance―the claims made by the premises are wrong or irrelevant to the truth of the conclusion), which we will discuss later.

 

Deduction B ×

              *Some animals [middle term, undistributed; Cf. Some S is P.] are two-footed.

                All people are animals [middle term, undistributed; Cf. Every S is P.].

               Therefore, all people are two-footed. {Sound argument, but invalid deduction.}

 

       Whether an argument is a valid deduction is determined by its form. This deduction is invalid because it violated the first basic rule governing the validity of categorical syllogism, i.e.

 

(1)            The middle term must be distributed at least once.

In general, arguments that display the form “All p’s are q’s; t is p (or a p). Therefore, t is q (or a Q)” are valid, as are arguments that display the form “If p, then q; it is not the case that p; therefore, it is not the case that q.” The following example displays the latter form:

  If there is life on Pluto, then Pluto has an atmosphere.

  It is not the case that Pluto has an atmosphere.

  Therefore, it is not the case that there is life on Pluto.

 
2.1.4.2     Verification (证实) vs falsification (证伪)

       An experiment in scientific research (in principle) allows the researcher to check against the hypothesis and say “this hypothesis is right”. If so, the experiment supports (or verifies) the hypothesis and the researcher is justified in adding the idea behind the hypothesis to their theoretical base.

       If, on the other hand, the experiment says “this hypothesis is wrong”, this would be falsifying the hypothesis.

 

Case: What is the logical basis of Popper’s famous argument that one can never totally verify a theory?

The importance that scientists have attached to falsification (as opposed to verification) goes back to the 1930s, when Karl Popper [1902-1994. Austrian-born British philosopher of science, known for his theory of scientific method and for his criticism of historical determinism] developed our current view of how theories are created and re-created.

        According to Popper, it is possible to overturn a theory, but it is impossible to make it absolutely correct. In Popper’s terms you can never totally verify (“prove”) a theory—but you can falsify it with one conflicting observation.

        What is the logical basis of Popper’s famous argument that one can never totally verify a theory?

(Based on Goodman, Albert. [School of Computing and Mathematics, Deakin University, Australia] [1996]. Introduction to Data Collection and Analysis.)

 

Test yourself: What is wrong with verification?

Analysis:

        ?

        ?/

 

Test yourself: How should we find out the scientific validity of the theory of translation universals?

The theory of translation universals developed by Mona Baker and others has concerned a number of scholars in the international translation community in the past decade or so. How should we find out the scientific validity of this theory?

Analysis:

        ?

        ?/

 

2.2 Informal Logical Fallacies

Informal logical fallacies are mistakes caused by wrong, irrelevant or ambiguous evidence. They are classified into:

 

1.             Fallacies of relevance

2.             Fallacies of ambiguity (verbal fallacies)

 
2.2.1      Fallacies of relevance

Fallacies of relevance are those arguments in which the truth of the conclusion does not depend on the claims made by the premises; in other words, the claims made by the premises are wrong or irrelevant to the truth of the conclusion. The following are some familiar fallacies of relevance:

 

              Non sequitur

              Oversimplification

              Hasty generalization

              Argument from dubious authority

              Begging the question

              Argument ad hominem

              Argument from ignorance

              Post hoc ergo propter hoc

              Stereotypes

              Card-stacking

              Arguing by analogy

 
(1)    Non sequitur (< Latin: “it does not follow” 推不出)

       Stating a claim that doesn’t follow from the (minor) premise (or the statement you begin with), because the major premise is false.

 

              Jergus will make an excellent husband for Marge. Why, in high school he got all A’s.

              In order to greet National Day, Beijing is carrying out various renovations. Many renovated buildings belong to the so-called "bean dregs” or shoddy project. Because of the limited time, those projects have to be finished in a hurry. So though the government calls on the builders to pay attention to quality, many new or renewed bean dregs projects still kept appearing “irresistibly.” (Students’ essay)

              The cover of a 1997 Beijing Youth Weekly has “Chinese Defeat Kasparov!” splashed across a picture of the downcast grand master. Two of the six members of the IBM research group that programmed “Deep Blue,” it turns out, were Chinese-Americans. “It was the genius of these two Chinese,” one article asserts, “that allowed ‘Deep Blue’ to defeat Mr. Kasparov.” (Peter Hays Gries. 2003. China's New Nationalism: Pride, Politics, and Diplomacy. A Philip E. Lilienthal Book in Asian Studies. The University of California Press. Retrieved December 22, 2004, from http://www.ucpress.edu/books/pages/9662/9662.intro.html)

 

      收到过坏人送的匾的人一定自己不是东西

        李敖攻击诗人余光中(就是那位著名的“乡愁”诗的作者),理由如下:“余光中70岁生日的时候,国民党主席、混蛋李登辉赠他一个匾‘连珠缀玉’。请大家去想好了,你不是个拍马屁,你不是个马屁精,为什么有李登辉这种货色的人送匾给你。可见你是什么东西啊!”

(Retrieved October 16, 2006, from http://blog.sina.com.cn/u/48670cb20100062a)

 

       A special kind of non-sequitur fallacy―reversing cause and effect or taking cause for effect [倒因为果]):

 

              Bob is well trained, therefore Bob is an astronaut.

              我们将英语翻译分为两类:汉译英和英译汉。其实,在中国英语学习者的思维角度上,语言在大脑的思维过程正是这两类的不断应用。由于我国的教育体制尚为应试教育,所以,这两类之间的运用更始根深蒂固,说白了,如果能灵活地运用汉译英和英译汉,语言水平将会有质的飞跃! (机械工业出版社时代金科编辑室约稿函)

 
(2)    Oversimplification (过份简单化)

       Supplying neat and easy explanations for large and complicated phenomena (Cf. Albert Einstein’s famous quote—paying special attention to the second half of this quote: “everything should be made as simple as possible, but not one bit simpler.”).

 

              We have a lot of unemployment now in this country because people are too lazy to work.

              If we want to do away with drug abuse, let’s get tough: let’s sentence every drug user to death.

 

       A special kind of oversimplified thinking—Either/or reasoning [assuming that a reality may be divided into only two parts, that there are only two sides to a question, that all statements are either true or false, that all questions demand either a yes or a no answer.]:

 

              What are we going to do about acid rain? Either we shut down all the factories that cause it, or we just forget about acid rain and learn to live with it. We’ve got no choice, right?

 

      中山陵雨花台门票上涨成定局

        昨天,在南京市物价局组织的价格调整听证会上,21名来自社会各界的听证代表一致同意上调“两陵”价格。

        此次,中山陵景区申请把25元的门票上升到40元;雨花台申请从15元调至25元。

        南京市人大代表、中山大厦工会主席周敏华认为,据统计,“两陵”的游客95%是外地人,由于门票相对便宜,因此一到长假中山陵的游客骤增,最多一天达10万人次,远远超过了景区的承受能力,极不利于景区的品牌形象。因此,提高价格可以缓解人流量,有利于景区的可持续发展。

(《新华日报》200211291)

 
(3)    Hasty generalization (以偏概全;妄下定论)

       The assumption that what is true of a few cases is true in general.

Example 1.

 

              Bertrand Russell’s “cruel” example: the chicken’s hasty generalization that the farmwife’s coming means food.

 

Example 2.

 

              … “But that’s not my dog.”

 
(4)    Argument from dubious authority (诉诸可疑权威)

       The practice of defending a conclusion by appealing to force, pity, authority, or popular belief.

 

                     According to some of the most knowing scientists in America, smoking two packs a day is as harmless as eating a couple of oatmeal cookies.

                     According to some of the most famous scientists in China, eating our pills will help short men to grow taller within a few days.

                     腰酸背疼腿抽筋——请服巨能钙;买好钙——巨能钙;8位博士、48位科学家、{Who were they?} 100项科学实践、10年呕心沥血,终于研究出一种产品——那就是巨能钙。

    {Comment: 由农业部质检中心出具的检验报告显示,检测对象涵盖了从婴幼儿型到老年型口服片几乎所有的11种巨能钙产品,除了4种产品中过氧化氢含量为0之外,其余7种产品每千克的双氧水(H2O2)含量最低为1.04克,而最高值则达到了6.28克。巨能公司有关负责人在先前接受媒体采访时曾表示,企业内部制定的标准是每千克双氧水含量不超过500毫克,即使是按照这一数字,两个数据仍相去甚远。 (20041123 来源: 新京报; http://www.gmw.cn/content/2004-11/23/content_137052.htm)

    过氧化氢危害汇总:

    1)  过氧化氢可致人体遗传物质DNA损伤及基因突变,与各种病变的发生关系密切,长期食用危险性巨大。

    2)  过氧化氢可导致老鼠及家兔等动物致癌,从而可能对人类具有致癌的危险性。

    3)  过氧化氢可能加速人体的衰老进程。过氧化氢与老年痴呆,尤其是早老性痴呆的发生或发展关系密切。 (《河南商报》供稿 http://www.china.org.cn/chinese/difang/706405.htm)}

 

       Defending a conclusion by appealing to popular belief is known as “Bandwagon appeals,” i.e. using the desire to “go along with the crowd” as fact:

 

              Surveys show that a majority of the people want only “family oriented” programming on television. Therefore, this must be our goal.

 
(5)    Begging the question (以假定作为论据来辩论;未经讨论就认为某一有待证明的论点或主张正确;武断;also called “Circular Argument” 循环论证)

       Setting out to prove a statement that is already taken for granted (or, in other words, assuming in the premises what is to be proved).

       This fallacy sometimes takes the form of tautology or arguing in a circle (i.e. stating or believing a fact to be its own reason).

 

              He is a liar because he simply is not telling the truth.

              Most people like gardening because it is something they enjoy.

              It’s wet because it has water on it.

              I know because I know.

 
(6)    Argument ad hominem (< Latin, “against the man” 人身攻击)

       Attacking people’s opinions by attacking their character.

 

              Jack may argue that we need to save the whales, but Jack is the kind of person who always gets excited over nothing.

              Jack would have us spend millions to save whales, but I happen to know that he owns a yacht from which he selfishly enjoys watching whales.

              西方翻译理论家对于普遍性的诉求和具有的广阔的 [学术研究] 视野,“同时不也反映了他们与生俱来的种族优越感吗?”(《中国翻译》2002年第2期第5)

                                 {Comment: 此论还犯有常识性错误:当今国际翻译界有影响的理论家,很多原籍甚至现籍都并非欧美,人也并非“金发碧眼”的“优秀民族”的成员。}

 
(7)    Argument from ignorance (因缺乏反证而得出结论)

       Maintaining that, because a conclusion has not been disproved, it has to be accepted or, because a conclusion has not been proved, it should be rejected.

 

              Despite years of effort, no one has conclusively proved that ghosts don’t exist; therefore, we should expect to see them at any time.

              No one has ever shown that there is intelligent life on any other planet. Evidently the notion of visitors from other planets in the universe is unthinkable.

 
(8)    Post hoc ergo propter hoc (< Latin, “after this, therefore because of this” 发生于其后者必然是其结果)

       Confusing cause and effect.

 

              Because the new Premier of Russia sent a rose to every woman member of the Duma as a token of his gratitude for their support of the work of his government, he was soon dismissed from office by President Yeltzin.

              The devastating earthquake which struck Taiwan recently was a warning sent by Heaven to Li Denghui, since it occurred shortly after Li made another attempt to split China by claiming statehood for Taiwan.

 
(9)    Stereotypes (定型观念;定式思维)

       Both positive and negative ones should be avoided.

 

              Being a woman meant she was smaller than a man.

              Being a woman meant she was more compassionate than a man.

 
(10)  Card-stacking (洗牌作弊;片面举证)

       Ignoring an issue’s contrary evidence.

 

              A “pro-gun” paper that cites only people who have used guns to protect themselves from danger, or an “anti-gun” paper that cites only accidental deaths caused by guns.

 

(11)  Arguing by analogy (比喻式论证)

       Using a metaphor as though it were evidence.

       In logic, analogy is the name of an inductive form of argument which asserts that if two or more entities are similar in one or more respects, then a probability exists that they will be similar in other respects.

       An analogy explains a complicated idea in terms of something familiar: for instance, shooting a spacecraft to another planet is like placing a golf ball with uncanny accuracy into a hole half a mile away and a risky action is analogized to “盲人骑瞎马,夜半临深池” in Chinese.

 

              People were born as free as the birds. It’s wrong and cruel to expect them to work.

              [In 1633, Scipio Chiaramonti, professor of philosophy at the University of Pisa, argued against Galileo:] “Animals, which move, have limbs and muscles. The earth has no limbs and muscles, hence it does not move.”

              [江苏经济台保险全接触节目(平安保险公司赞助)广告]现代生活离不开保险,就像生命离不开水、阳光和空气。

              [街头广告]X,做真正的男人/女人!

 
2.2.2      Fallacies of ambiguity (verbal fallacies)

Fallacies of ambiguity (verbal fallacies) are erroneous conclusions based on the equivocal use of language.

 

              All laws are the product of legislative activity. Newton discovered several laws; therefore, Newton discovered several products of legislative activity.

              [CCTV-1 advertisement featuring 唐国强]

                Shot 1     唐国强:“买保险就是买平安”

                Shot 2     Slogan:中国平安(保险)

(Partly based on Kennedy, X.J. & Dorothy M. Kennedy [1987] [The Bedford Guide for College Writers. NY: St Martin’s Press.])

 

2.3 Mixed Logical Fallacies

Mixed logical fallacies refer to cases in which formal and informal fallacies co-exist in an inference.

 

Case: 工人都没看过的书农民也不会看

        2003年年底,安徽作家陈桂棣、吴春桃(南大中文系毕业生)夫妇历经三年创作的报告文学《中国农民调查》,在《当代》杂志第6期上发表了。由于作品深刻地揭示了当前“三农问题”面临的诸多难题和矛盾,真实地反映了农民的心声,因此在读者中引起了强烈共鸣。2004年元月,《中国农民调查》一书由人民文学出版社出版,在一个多月的时间内就发行了近十万册。2004年该书荣获尤里西斯国际报导文学奖。20041020日南大中文系请他们来做演讲。演讲结束后一个同学的提问是:我问一个在合肥市工厂里工作的朋友有没有看过你们的书。他都说没看过。请问还会有农民看你们的书吗?陈桂棣说:“这个问题没法回答。不但我们没法回答,就是统计局也没法回答。”

        What logical fallacies can you identify in the student’s bewildering question?

Analysis:

        ?

        ?/

 

Case: 不支持议会政治者不是思想家

        李敖认为鲁迅不是思想家,证明过程如下:

        在新文化运动的时候,五四时代,所谓提倡的德先生和赛先生,赛先生是科学,德先生是民主,可是鲁迅反对议会政治,请问反对议会政治的人,怎么能够提倡民主呢?如果民主没有议会,这叫什么民主呢?这表示说,鲁迅基本的社会科学常识,政治学的常识都不及格,而这种人怎么能够像毛泽东所说的是思想家呢?” (Retrieved October 16, 2006, from http://blog.sina.com.cn/u/48670cb20100062a)

        What logical fallacies can you identify in Li Ao’s argument?

Analysis:

        ?

        ?/

 

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