• 1. The Nature of Arguments
  • 1.1 Definition of Argument
  • 1.2 Example
  • 1.3 The Structure of an Argument
  • 1.4 Sets of sentences that are not arguments
    • 1.4.1. have no relation between them
    • 1.4.2. have between them a relation other than that characterizing an argument
  • 1.5 How to make an argument
  • 1.6 Argument and Assertion 断言
  • 1.7 True or False
  • 1.8 Three separate levels
    • 1.8.1 Language
    • 1.8.2 Thought
    • 1.8.3 Reality
  • 1.9 Good argument
• 2. Different Types of Arguments 不同种类的论证
  • 2.1 Two basic type
  • 2.2 Deductive arguments
    • 2.2.1 Definition
    • 2.2.2 Example
  • 2.3 Inductive Argument
    • 2.3.1 Definition
    • 2.3.2 Example
      • Strong
      • Weak
  • 2.4 Form of deduction 演绎的形式
    • 2.4.1 相同形式的演绎
    • 2.4.2 不同的演绎形式
    • 2.4.3 道德逻辑
    • 2.4.4 模态论证 Modal logic
    • 2.4.5 时态逻辑 Temporal Logic
  • 2.5 Form of Induction 归纳的形式
    • 2.5.1 归纳的不同形式
      • Analog arguments 相似论证
      • Cause arguments 因果论证
• 3. Setting out arguments logic-book-style 将逻辑组织称逻辑书样式
  • 3.1 一个例子
  • 3.2 The point of setting out arguments logic-book-style 组织逻辑书样式的意义
  • 3.3 Steps for analyzing arguments
    • 3.3.1 Identifying premises and conclusions

1. The Nature of Arguments

1.1 Definition of Argument

a set of sentences such that one of them is being said to be true the others are being offered as reasons for believing the truth of the one

1.2 Example

It is Friday. Mary always wears jeans on Friday. So Mary will be wearing jeans today.

1. It is Friday.
2. Mary always wears jeans on Friday.
3. So Mary will be wearing jeans today.

1.3 The Structure of an Argument

1. Conclusion: the sentence being said to be true. (e.g. So Mary will be wearing jeans today.)
2. Premises: the sentences(s) being offered as reason(s) for believing the one. (e.g. It is Friday. Mary always wears jeans on Friday.)

Conclusion 和 Premises 在 Argument 中扮演了不通的功能 (Function)。辨识出一个句子的功能，是我们判断这个句子是属于 Conclusion 还是 Premises 的唯一方法。

1.4 Sets of sentences that are not arguments

1.4.1. have no relation between them

The sea is salt. Melbourne is in Australia. → not argument

The sea is salt. Therefore Melbourne is in Australia. → argument

The premeses of an argument do not cause the conclusion to be true!

Therefore 可能没有暗示因果关系

1.4.2. have between them a relation other than that characterizing an argument

1.5 How to make an argument

• Any sentence can be part of an argument
• We claim one sentence to be true
• We offer other sentences to believe that
• It is VERY EASY to make an argument

1. 只通过句子的内容，我们不能判断这些句子是否形成 Argument
2. 我们要通过句子之间的「关系」来判断其是否形成 Argument

1.6 Argument and Assertion 断言

• Argument: a set of sentences, one of which is being asserted
• Assertion: a single sentence (possibly complex) that is being expressed in assertoric mode

If it is snowing the mail will be late 这个是 assertion，我们断言的是「如果下雪邮件会晚到」这个假设

It is snowing so the mail will be late 这个是 argument

1.7 True or False

• Only believes or sentences that express believes can be true or not.
• Facts make sentences true or false. Facts can not be true or false. Facts are just facts.
• Arguments can not be true of false, arguments can only be good (正当) or bad (不正当).

如果前提是真，结论是真的话，argument 是保持真实的（truth-preserving），但不能说 argument 是真实的。

1.8 Three separate levels

1.8.1 Language

“Red” “红” 这个字

1.8.2 Thought

Red 红色的概念，同样的概念在不通的语言里有不同的表示方法

1.8.3 Reality

Redness 物质的红色的属性

我们可以思考（Thought 层面）和谈论（Language 层面）事实（Reality 层面）

1.9 Good argument

Good argument must have at least two characteristics:

1. The conclusion must follow from the premises
2. The premises must all be true (not considered by logicians)

2. Different Types of Arguments 不同种类的论证

2.1 Two basic type

1. deductive argument 演绎论证
2. inductive argument 归纳论证

演绎论证是确定的，归纳论证不是。归纳论证有的时候不是很管用。科学上常用归纳论证。

2.2 Deductive arguments

2.2.1 Definition

The truth of their premises guarantees the truth of their conclusion 如果前提为真，结论必为真

对于一个 Argument，它要么是合理演绎的（deductively valid），要么不是

2.2.2 Example

• It is Friday. (观察)
• Marianne always wears jeans on a Friday. (假设)
• Therefore Marianne is wearing jeans. (结论)

如果 Marianne 没有穿牛仔裤：今天不是周五（观察错误）；或者她不是每个周五都穿牛仔裤（假设错误）；或者观察与假设都出错。

2.3 Inductive Argument

2.3.1 Definition

The truth of their premises makes the conclusion more or less probable. 「归纳论证的前提为真」这个事实使得结论更有（或者没有）可能为真

归纳论证可以是弱（weak）的，也可能是强（strong）的。

2.3.2 Example

Strong

The sun has risen every day in the history of the universe. Therefore the sun will rise tomorrow.

Weak

Every time I have seen Marianne she has been wearing earrings. Therefore next time I see Marianne she will be wearing earrings.

2.4 Form of deduction 演绎的形式

• 逻辑学家通过研究合理论证的形式来研究演绎
• 对于大多数演绎，论证的「演绎合理（deductively valid）」取决于论证的形式，而不是内容。

2.4.1 相同形式的演绎

• All A is B. S is A. S is B.
• All men are mortal. Socrates is a man. Socrates is mortal.
• All actions that produce the GHGN are right. That action produced the GHGN. That action was right.

逻辑与内容无关。论证因为形式而合理。同样的论证形式对于不同的主题都是同样合理的。

2.4.2 不同的演绎形式

• If P then Q, P therefore Q. (modus ponens)
• If P then Q, not-Q therefore not-P. (modus tollens)
• P or Q, not-P therefore Q. (Disjunctive syllogism)
• a is F, a=b, therefore b is F. (Leibniz’s Law)
• all Fs are G, a is an F, therefore a is a G. (syllogism)

(小写字母表示具体事物，大写字母表示「性质」或者「句子」。本课程中，老师爱用 P, Q, R 来表示「句子」。)

2.4.3 道德逻辑

Lying is wrong. Therefore we should not lie.

这里，”wrong” 有很特殊的道德含义，不能被归结为抽象形式。这个论证是由于 wrong 这个特殊的词而成立的。

2.4.4 模态论证 Modal logic

模态论证是关于「必然性」和「可能性」的论证。

It is necessarily the case that there are no square circles.

Therefore it is not possible that there are square circles.

形式：If A is necessary, then not A is not possible.

2.4.5 时态逻辑 Temporal Logic

时态逻辑是时间运行的逻辑。

It is raining day.

Therefore tomorrow it will have been raining yesterday.

这个论证是由于 is raining, tomorrow, yesterday 等与时间有关的词而成立的。

2.5 Form of Induction 归纳的形式

All inductive arguments rely on the assumption of the uniformity of nature, the idea that the future will be like the past.

所有归纳论证依赖于对自然的「统一性」的假设。

要证明「未来和过去一样」，我们必须使用循环论证：因为我们现在的经验能够确定「过去和现在一样」，所以我们认为这个事实能够再未来重现。

2.5.1 归纳的不同形式

Analog arguments 相似论证

a is like b, a is F, therefore b is F.

(小写字母表示具体事物，大写字母表示「性质」或者「句子」。本课程中，老师爱用 P, Q, R 来表示「句子」。)

这个形式为什么是归纳？a 在某一方面与 b 相似，则在 F 方面也相似。这依赖于自然统一性假设衍生出的，相似性的「传递」。

不好的论证的例子：

• 爱因斯坦是杰出的物理学家
• 爱因斯坦认为相对主义是好的
• 相对主义是好的

这个例子的不好的地方在于，爱因斯坦是杰出的物理学家，但是不是杰出的政治学家。

Cause arguments 因果论证

Every time A occurs a B occurs, therefore As cause Bs.

实际上，Cause arguments 既可以是演绎的，也可以是归纳的：

• As cause Bs, there was an A, therefore there will have been a B (deductive).
• Every observed A has been followed by a B, therefore As cause Bs (inductive).

3. Setting out arguments logic-book-style 将逻辑组织称逻辑书样式

3.1 一个例子

Premise One (P1): It is Friday. Premise Two (P2): Marianne always wears jeans on Fridays. Conclusion (C): Marianne is wearing jeans.

3.2 The point of setting out arguments logic-book-style 组织逻辑书样式的意义

1. 让我们加入隐含的前提
2. 让我们排出「交叉引用 (cross references)」，「无关的东西 (irrelevancies)」和「不一致的辞语 (inconsistent terms)」
3. 让我们更容易评价 (evaluate) 论证过程

3.3 Steps for analyzing arguments

1. identify the conclusion of the argument 找到结论
2. identify each of the premises 找到每一个前提
3. add suppressed premises
4. remove irrelevancies
5. remove inconsistent terms
6. remove cross-references

3.3.1 Identifying premises and conclusions

• 结论是什么？要论证的东西 (the thing someone is arguing for)
• 前提是什么？支持证据 (evidence)，支持理由 (reasons)
• 寻找论证标志词 (argument indicators)
  • so
  • therefore
  • then
  • accordingly
  • hence
  • since
  • for
  • because
  • from which we see that …
  • it follows that …
  • which establishes that …