批判性推理入门Critical-Reasoning-for-beginners全笔记.doc

Critical Reasoning for beginners
by Marianne Talbot Oxford

Lesson 1 How to recognize arguments and What is the nature of arguments

Arguments are a set of sentences such that one of them (the conclusion) is being said to be true, and the other(s) (the premises) are being offered as reasons for believing the truth of the one.

An argument isn't a set of contradictions.
Part of the point of an argument is to move us on from where we are to somewhere a bit further.
Arguments lead to deeper thoughts. (from where we are to where we want)

An Argument:
(one or more) Premises Conclusion (Function)
[to prove---reasons] [suppose true]
relationship among sentences

e.g. It's Friday.
Marianne always wears jeans on Friday.
Therefore Marianne will wear jeans today.

Play attention to suppressed premises（隐藏前提）.
context——all sentences may be argument.

implication（实质蕴涵）
entailment（逻辑蕴涵）

Distinguish arguments from
(a) sets of sentences not related as arguments
(1) aren't related at all
e.g. The sea is salt.
Sydney is in Australia.
(2) related but not an argument
e.g. Towards lunchtime clouds formed and the sky blackened. Then the storm broke.
(b) sentences (assertions) 'if...then...'
e.g. If it is snowing, the mail will be late.
(implication not entailment)

An argument is a set of sentences, one of which is being asserted.
An assertion is a single sentence (possibly complex) ,that is being expressed in assertive mode.

'because' may be causal or rational.

reason and cause
causal relations（因果关系） and rational relations（推理关系）
A and B entail C doesn't mean A and B cause C.
e.g. It's Friday. (A)
Marianne always wears jeans on Friday. (B)
Therefore Marianne will wear jeans today. (C)

explanation:
(1) causal explanation（因果性解释）:
e.g. Pawl fell down because he wanted to amuse children.
(2) rational explanation（推理性解释）:
e.g. Pawl fell down because Jelly pushed him.

Facts are what makes sentences true or false. They are not true or false, they just exist or don't exist.
Only beliefs or sentences that express beliefs are true or false.

Belief (e.g. concept)..............the concept 'chair'
Language..................................the language 'c-h-a-i-r'
Reality.......................................the object 'chair'

Arguments can only be good or bad ,they can only be valid or invalid ,they can't be true or false because the only thing that can be true or false is beliefs or the sentences that express beliefs.

A good argument is one in which:
(1)the conclusion must follow the premises
(2)the premises must all be true.
The conclusion must be true. (truth preserving)
逻辑学并不关心前提正确与否，而只关心前提与结论的关系。

Lesson 2 Different sorts of arguments

two basic types of arguments: deduction and induction

Deductive argument :
the truth of their premises guarantees the truth of their conclusion.
e.g. It's Friday.
Marianne always wears jeans on Friday.
Therefore Marianne will wear jeans today.
If the premises are true, the conclusion would be true.
'truth guaranteeing' 'truth preserving'

Deduction is an 'either or' thing:
a good deductive argument gives us conditional certainty.
a bad one tells us nothing.

Inductive arguments are such that the truth of their premises makes the conclusion more or less probable. (don't guarantee)
Inductive arguments can be either weak or strong.
[strong]:The sun has risen every day in the history of the universe. Therefore the sun will rise tomorrow.
[weak]:Every time I met Mary, she wore a necklace.
Therefore the next time I meet her, she will wear a necklace.

逻辑学是中立性的，逻辑的形式可以适用于任何的内容。
Logicians study deduction by studying valid arguments forms
Arguments that are valid is in virtue of their forms as opposed to their contents.

the forms of deduction:
1、Modus Ponens肯定前件取拒式
If P then Q, P, therefore Q. (P,Q sentences)

wrong: If P then Q, Q, therefore P.
(Affirming consequent肯定后件式)

2、Modus tollens否定后件式
If P then Q, not-Q, therefore not-P.

3、Disjunctive syllogism选言三段论
P or Q, not-P, therefore Q.
（P或Q成立，P不成立，因此Q成立）

4、Leibniz's Law 莱布尼兹律（相同者不可辨识）
a is F, a=b, therefore b is F.
e.g. Jane is(predication) tall.
Jane is(identity) the bank manager.
Therefore the bank manager is(predication) tall.

Note:
'is' can serve as a predication（论断） or identity（同等）.
The 'is's above serve as predications.
And the '=' above serves as identity.

5、Syllogism三段论
all Fs are G.
a is an F.
Therefore a is a G.

6、Deontic Logic道义逻辑
e.g. Lying is wrong.
Therefore we shouldn't lie.

7、Modal Logic模态逻辑
（a logic about necessity and possibility)
e.g. It is necessarily the case that there are no square circles.
Therefore it is not possible that there are square circles.

8、Temporal Logic时序逻辑（时态逻辑）
e.g. It is raining today.
Therefore tomorrow it will have been raining yesterday.

Inductive arguments
All inductive arguments rely on the assumption of the uniformity of nature (the idea that the future will be like the past)
哲学中的一个基本问题是，我们对未来的假设，会不会和过去的经验相一致？ Uniformity 一致性 ，uniformity of nature (David Hume)自然界是否具有一致性？

Within the category of inductive arguments there are many different sub-types:
1、arguments from analogy类比推理
a is like b, a is F, therefore b is F.
（小写字母：particular thing特定的事物
大写字母：性质或句子）

2、arguments from authority诉诸权威的论证
e.g. Einstein is a brilliant physicist.
Einstein says relativism is true.
Therefore relativism is true.

Causal arguments因果论证
Causal arguments can be deductive or inductive, depending on whether we are arguing from a causal claim or to a causal claim.

deductive: As cause Bs.
There was an A.
Therefore there will have been a B.

inductive: Every observed A has been followed by a B.
Therefore As cause Bs.

negative existential否定存在判断句
e.g. 飞马不存在。

We can know that
arguments that are deductively valid
——in virtue of their forms
——in virtue of their content
e.g. Deontic Logic ,Temporal Logic
arguments that are inductively valid
——the uniformity of nature

Lesson 3 'logic-book-style'逻辑书

the point:
(a)it enables us to add suppressed premises隐含前提
(b)it enables us to eliminate cross references, irrelevancies and inconsistent terms排除交叉引用、无关和不一致词语
(c)it makes it easier to evaluate arguments.

A set of steps for analyzing arguments:
1. identify the conclusion of the argument
Look for the argument indicators (so, therefore, then, if...then..., accordingly, hence, since, for, because, from which we see that, it follows that, which establishes that...)
2. identify each of the premises
3. add suppressed premises
4. remove irrelevancies
5. remove inconsistent terms
6. remove cross-references

Example 1:
Socialism did not provide the incentives need for a prosperous economy. Therefore socialism was doomed to failure.

Premise 1: Incentives are needed for a prosperous economy.
Premise 2: Socialism did not provide incentives.
Conclusion: Socialism was doomed to failure.

Premises and conclusion must be sentences.

P, unless Q.
If Q, then R. P
But not R.

Example 2:
Since many newly emerging nations do not have the capital resources necessary for sustained growth, they will continue to need help from industrial nations.

Premise 1: Many newly emerging nations do not have capital resources
Premise 2: Capital resources are necessary for sustained growth.
Premise 3: If a newly emerging nation is to sustain its growth, and it does not have capital resources, it will need help from industrial nations.
Conclusion: Many newly emerging nations will need help from industrial nations.

Example 3:
Well perhaps she didn't want you to tickle her tummy, or she didn't realize that was what you were going to do. If she didn't realize , then you obviously went about it in the wrong way. In that case you deserved to get scratched unless you ready thought she was such a perceptive cat that she'd understand 'woof-woof' meant 'roll over '. If you thought that you're an idiot. But you're not an idiot you're just twisted. So if the poor thing did want you to tickle her tummy you deserve to get scratched.

1 Identify premises and conclusion
Premise1: Well perhaps she didn't want you to tickle her tummy, or she didn't realize that was what you were going to do
Premise2: If she didn't realize , then you obviously went about it in the wrong way.
Premise3: In that case you deserved to get scratched unless you ready thought she was such a perceptive cat that she'd understand 'woof-woof' meant 'roll over '.
Premise4: If you thought that , you're an idiot. But you're not an idiot you're just twisted.
Conclusion: So if the poor thing did want you to tickle her tummy you deserve to get scratched.

2 Add suppressed premises
(None)

3 Remove irrelevancies

draft:
Premise1: Well perhaps she didn't want you to tickle her tummy, or she didn't realize that was what you were going to do
Premise2: If she didn't realize , then you obviously went about it in the wrong way.
Premise3: In that case you deserved to get scratched unless you ready thought she was such a perceptive cat that she'd understand 'woof-woof' meant 'roll over '.
Premise4: If you thought that , you're an idiot. But you're not an idiot you're just twisted.
Conclusion: So if the poor thing did want you to tickle her tummy you deserve to get scratched.

Premise1: She didn't want you to tickle her, or she didn't realize that was what you were going to do
Premise2: If she didn't realize , then you went about it in the wrong way.
Premise3: In that case you deserved to get scratched.
Conclusion: So if the poor thing did want you to tickle her you deserve to get scratched.

4 Remove inconsistent terms and cross references (simplify)

Premise1: She didn't want you to tickle her, or she didn't realize you were going to tickle her
Premise2: If she didn't realize you were going to tickle her , then you were going to tickle her in the wrong way.
Premise3: If you were going to tickle her in the wrong way, you deserved to get scratched.
Conclusion: So if she did want you to tickle her, you deserve to get scratched.

To show you how easy it is to reveal the structure of this argument , let's formalize it.

Premise1: She didn't want you to tickle her, or she didn't realize you were going to tickle her
Premise2: If she didn't realize you were going to tickle her , then you were going to tickle her in the wrong way.
Premise3: If you were going to tickle her in the wrong way, you deserved to get scratched.
Conclusion: So if she did want you to tickle her, you deserve to get scratched.

interpreter:
'she didn't want you to tickle her' is P.
' she didn't realize you were going to tickle her' is Q.
' you were going to tickle her in the wrong way' is R.
' you deserved to get scratched' is S.

Premise1: P or Q.
Premise2: if Q then R.
Premise3: if R then S.
Conclusion: if not-P then S.

Note: you can apply this methodology to your own argument, this will help you understand exactly what you are saying and why you are saying it.

We saw that although we need to paraphrase arguments in order to complete these steps, we should not change the meaning of any of the premises or the conclusion.

Lesson 4 How to evaluate whether an argument is a good one or a bad one

All inductive arguments rely on the principle of the uniformity of nature and the only arguments for the principle of the uniformity of nature are themselves inductive.

Types of inductive argument:
inductive generalizations归纳性的概括
causal generalizations偶然的概括
arguments from analogy从类推得到的论点
arguments from authority从权威得到的论点

Inductive generalizations：
The premises identifies a characteristic of a sample of a population and the conclusion extrapolates that characteristic to the rest of the population.

Evaluating inductive generalizations
1.Is the premises true?
2.How large is the sample?
3.How representative is the sample?
4.Beware 'informal' heuristics当心非正式的启发式方法------a way of making a decision
5.Is there a counterexample反例?

Causal generalizations：
The premise identifies a correlation between two types of event, the conclusion states that the events of the first type cause events of second type.

Evaluating causal generalizations因果归纳
1.Is the premise true?
All we ever see is correlation（相互关系）. We never see the causal relationship itself.
2.How strong is the correlation?(sample......)
3.Does the causal relation make sense（有意义） or could it be accidental?
4.What cause what?
5.Is there a counterexample反例?

休谟认为，All we see are correlation, we never see and get to the causal relationship itself 更进一步认为因果关系实际上根本不存在，只是人的习惯性思维。

Arguments from analogy
Arguments from analogy take just one example of something and extrapolate from a character of that example to the character of something similar to that thing.

Evaluating arguments from analogy
1.Are the two things similar?
2.Are they similar in respect of（关于、涉及） something relevant?
3.Can we find a Disanalogy （不相似点---相似并非等同?）

Arguments from authority
Arguments from authority take one person or group of persons who are, or are assumed to be ,right about something and extrapolate to the claim they are right about other thing.

Evaluating arguments from authority
1.What exactly is the source of information?
2.Is this source qualified in the appropriate area?
3.Is this source impartial（公平公正的） in respect of this claim?
4.Do other experts make other claim?

Lesson 5 Validity vs. Truth (deductive argument)
A good deductive argument is SOUND（可靠的） if and only if it:
(a) is valid
(b) has true premises
Sound = valid argument + True premises

There are many ways in which we determine the truth or falsehood of premises and these ways do not fall into the scope of a class on critical reasoning.

Validity, on the other hand is very much of interest to logicians because validity preserves truth.

We often don't know the truth of our premises and we often test the truth of our premises by constructing valid arguments and testing the truth of the conclusion.
If we can show that the conclusion of a valid argument is false what do we thereby discover? At least one premise is false.

Hypothesis: Smoking causes cancer.
Prediction: If smoking causes cancer, then every smoker will get cancer.
Test: Each smoker gets cancer.[valid argument]
Test(conclusion) is false.——Prediction or Hypothesis(premise) is false.
Testing of scientific hypothesis:
Here is the best theory that philosophers and mathematicians can come up with: arguments is valid if and only if there is no possible situation in which all its premises are true and its conclusion false.

An argument is valid if and only if （当且仅当） there is no possible situation in which all its premises are true and its conclusion i