批判性推理入門CriticalReasoningforbeginners全筆記

1、Critical Reasoning for beginnersby Marianne Talbot OxfordLessonl How to recognize arguments and What is the n ature of argume ntsArguments 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 believin

2、g the truth of the one.An argume nt isnt a set of con tradicti ons.Part of the point of an argume nt is to move us on from where we are to somewhere a bit further.Argume nts lead to deeper thoughts. (from where we are to where we want)An Argume nt:(one or more) Premises iCon clusi on(Fun cti on)to p

3、rove-reas onssuppose truerelati on ship among sentencese.g. Its Friday.Maria nne always wears jea ns on Friday.Therefore Maria nne will wear jea ns today.Play atte nti on to suppressed premises (隱藏前提)contextall senten ces may be argume nt.implication (實質(zhì)蘊涵)entailment (邏輯蘊涵)Disti nguish argume nts fr

4、om(a) sets of senten ces not related as argume nts(1) arent related at alle.g. The sea is salt.Sydney is in Australia.(2) related but not an argume nte.g. Towards lun chtime clouds formed and the sky blacke ned. The n the storm broke.(b) senten ces (asserti ons)if.the n.e.g. If it is snowing, the ma

5、il will be late.(implicatio nnot en tailme nt)An argume nt is a set of senten ces, one of which is being asserted.An asserti on is a sin gle sentence (possibly complex) ,that is being expressed in assertive mode.because may be causal or rati on al.reas on and causecausal relations (因果關(guān)系)and rational

6、 relations (推理關(guān)系)A and B en tail C does nt mea n A and B cause C.e.g. Its Friday. (A)Maria nne always wears jea ns on Friday. (B)Therefore Maria nne will wear jea ns today. (C)expla natio n:(1) causal explanation (因果性解釋)：e.g. Pawl fell dow n because he wan ted to amuse childre n. rational explanatio

7、n (推理性解釋)：e.g. Pawl fell dow n because Jelly pushed him.Factsare what makes senten ces true or false. They are not true or false, they just exist or dont exist.Only beliefs or sentences that express beliefsire true or false.Belief (e.g. concept)the concept chairLanguagethe Ian guage c-h-a-i-rReality

8、the object chairArgume nts can only be good or bad ,they can only be valid or in valid ,they cant be true or false because the only thing that can be true or false is beliefs or the senten ces that express beliefs.A good argume nt is one in which:(1) the conclusion must follow the premises(2) the pr

9、emises must all be trueThe conclusion must be true. (truth preserving)邏輯學并不關(guān)心前提正確與否，而只關(guān)心前提與結(jié)論的關(guān)系。Lesson 2 Different sorts of argumentstwo basic types of argume nts: deducti on and in ducti onDeductive argume nt :the truth of their premises guara ntees the truth of their con clusi on.e.g. Its Friday.

10、Maria nne always wears jea ns on Friday.Therefore Maria nne will wear jea ns today.If the premises are true, the conclusion would be true.truth guara ntee ing truth preserv ingDeducti on is an either or thi ng:a good deductive argume nt gives us con diti onal certa in ty.a bad one tells us nothing.I

11、nductive arguments are such that the truth of their premises makes the conclusion more or less probable. (dont 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

12、, she wore a necklace.Therefore the next time I meet her, she will wear a necklace. 邏輯學是中立性的，邏輯的形式可以適用于任何的內(nèi)容。Logicians study deduction by studying valid arguments formsArguments 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 t

13、hen 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選言三段論P or Q, not-P, therefore Q.(P或Q成立，P不成立，因此Q成立)4、Leibnizs Law 萊布尼茲律(相同者不可辨識) a is F, a=b, therefore b is F.e.g. Ja

14、ne is(predication) tall.Jane is(identity) the bank manager.Therefore the bank manager is(predication) tall.Note:is can serve as a predication (論斷)or identity (同等).The iss above serve as predications.And the = above serves as identity.5、Syllogism三段論all Fs are G.a is an F.Therefore a is a G.6、Deontic

15、Logic道義邏輯e.g. Lying is wrong.Therefore we shouldnt lie.7、Modal Logic模態(tài)邏輯(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時序邏輯(時態(tài)邏輯)e.g. It is raining today.Therefore to

16、morrow it will have been raining yesterday.Inductive argumentsAll inductive arguments rely on the assumption of the uniformity of nature (the idea that the future will be like the past)哲學中的一個基本問題是， 我們對未來的假設， 會不會和過去的經(jīng)驗相一致？ Uniformity 一致性,uniformity of nature (David Hume)自然界是否具有一致性？Within the category

17、 of inductive arguments there are many different sub-types:1、arguments from analogy類比推理 a is like b, a is F, therefore b is F.(小寫字母： particular thing 特定的事物大寫字母：性質(zhì)或句子)2、arguments from authority 訴諸權(quán)威的論證e.g. Einstein is a brilliant physicist.Einstein says relativism is true.Therefore relativism is true

18、.Causal argume nts 因果論證Causal arguments can bedeductive 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.n ega

19、tive existe ntial否定存在判斷句e.g. 飛馬不存在。We can know thatarguments that are deductively validin virtue of their formsin virtue of their contente.g. Deontic Logic ,Temporal Logic arguments that are inductively valid the uniformity of natureLesson 3 logic-book-style 邏輯書the point:(a) it en ables us to add su

20、ppressed premise隱含前提(b) it enables us to eliminate cross references, irrelevancies and inconsistent term排除交叉弓丨用、無關(guān)和不一致詞語(c) it makes it easier to evaluate argume nts.A set of steps for analyzing arguments:1. identify the conclusion of the argumentLook for the argume nt in dicators (so, therefore, th

21、e n, if.the n., accord in gly, hen ce, sin ce, for, because, from which we see that, it follows that, which establishes that.)2. ide ntify each of the premises3. add suppressed premises4. remove irreleva ncies5. remove incon siste nt terms6. remove cross-refere ncesExample 1:Socialism did not provid

22、e the incen tives n eed for a prosperous economy. Therefore socialism was doomed to failure.Premise 1: Incen tives are n eeded for a prosperous economy.Premise 2: Socialism did n ot provide incen tives.Conclusion: Socialism was doomed to failure.Premises and con clusi on must be senten ces.P uni ess

23、 Q.If Q, the n R. PBut not R.Example 2:Si nee many n ewly emerg ing n ati ons do not have the capital resources n ecessary for susta ined growth, they will con ti nue to n eed help from in dustrial n ati ons.Premise 1: Many newly emerging nations do not have capital resourcesPremise 2: Capital resou

24、rces are n ecessary for susta ined growth.Premise 3: If a newly emerging nation is to sustain its growth, and it does not have capital resources, it will n eed help from in dustrial n ati ons.Con clusi on: Many n ewly emerg ing n ati ons will n eed help from in dustrial n atio ns.Example 3:Well perh

25、aps she did nt want you to tickle her tummy, or she did nt realize that was what you were going to do. If she did nt realize , the n you obviously went about it in the wrong way. In that case you deserved to get scratched uni ess you ready thought she was such a perceptive cat that shed understand w

26、oof-woof meant roll over . If you thought that youre an idiot.But youre not an idiot youre just twisted. So if the poor thing did want you to tickle her tummy you deserve to get scratched.1 Identify premises and conclusionPremisel: Well perhaps she did nt want you to tickle her tummy, or she did nt

27、realize that was what you were going to doPremise2: If she did nt realize , the n you obviously went about it in the wrong way.Premise3: In that case you deserved to get scratched uni ess you ready thought she was such a perceptive cat that shed un dersta nd woof-woof mean t roll over .Premise4: If

28、you thought that , youre an idiot. But youre not an idiot youre just twisted. Conclusion: So if the poor thing did want you to tickle her tummy you deserve to get scratched.2 Add suppressed premises(No ne)3 Remove irrelevanciesdraft:Premise1:Well perhaps she did nt want you to tickle her tummy, or s

29、he did nt realize that was what you were going to doPremise2: If she did nt realize , the n youobviously went about it in the wrong way.Premise3: In that case you deserved to get scratched! nl ess you ready thought she was such a perceptive cat that shed understand woof-woof meant roll over .Premise

30、4: If you thought that , youre an idiot. But youre not an idiot youre just twisted.Conclusion: So if the poor thing did want you to tickle her tummy you deserve to get scratched.Premisel: She did nt want you to tickle her, or she did nt realize that was what you were going to doPremise2: If she did

31、nt realize , the n you went about it in the wro ng way.Premise3: In that case you deserved to get scratched.Con clusi on: So if the poor thi ng did want you to tickle her you deserve to get scratched.4 Remove inconsistent terms and cross references (simplify)Premisel: She did nt want you to tickle h

32、er, or she did nt realize/ou were going to tickle her Premise2: If she did nt realize you were going to tickle her , the n 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 ifhe did want you to tickle

33、 her, you deserve to get scratched.To show you how easy it is to reveal the structure of this argume nt , lets formalize it.Premisel: She did nt want you to tickle her, or she did nt realize you were going to tickle her Premise2: If she did nt realize you were going to tickle her , the n you were go

34、ing 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.in terpreter:she didnt want you to tickle her is P. she didnt realize you were going to tickle

35、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 say

36、ing 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 oneAll inductive arguments rely on the pr

37、inciple 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 歸納性的概括 causal gen eralizatio ns 偶然的概括 arguments from analogy 從類推得到的論點 arguments from authority 從權(quán)威得到的論點Inductive ge

38、neralizations：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 generalizations1.Is the premises true?2. How large is the sample?3. How representative is the sample?4. Beware inf

39、ormal heuristics 當心非正式的啟發(fā)式方法 a way of making a decision5s there a coun terexample 反例?Causal generalization：sThe premise identifies a correlation between two types of event, the conclusion states that the events of the first type cause events of second type.Evaluati ng causal gen eralizati on因果歸纟納1.I

40、s the premise true?All we ever see is correlatio n (相互關(guān)系).We n ever see the causal relati on ship itself.2. How strong is the correlation?(sample)3. Does the causal relati on make sens(有意義)or could it be accide ntal?4. What cause what?5s there a coun terexample 反例?休謨認為，All we see are correlatio n, w

41、e n ever see and get to the causal relati on ship itsel更 進一步認為因果關(guān)系實際上根本不存在，只是人的習慣性思維。Arguments from analogyArgume nts from an alogy take just one example of somethi ng and extrapolate from a character of that example to the character of something similar to that thing.Evaluat ing argume nts from an

42、alogy1. Are the two things similar?2. Are they similar in respect of (關(guān)于、涉及)someth ing releva nt?3. Can we find a Disanalogy (不相似點-相似并非等同？)Arguments from authorityArgume nts from authority take one pers on or group of pers ons who are, or are assumed to be ,right about someth ing and extrapolate to

43、the claim they are right about other thing.Evaluating arguments from authority1. What exactly is the source of in formatio n?2.Is this source qualified in the appropriate area?3s this source impartial (公平公正的) in respect of this claim?4. Do other experts make other claim?Less on 5 Validity vs. Truth

44、(deductive argume nt)A good deductive argume nt is SOUND(可靠的)if and only if it:(a) is valid(b) has true premisesSound = valid argume nt + True premisesThere 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 reasoni

45、ng.Validity, on the other hand is very much of interest to logicians because validity preserves truth.We often dont know the truth of our premises and we often test the truth of our premises by con structi ng_valid_argume nts an d testi ng_the_truth_of the_c on clusi on.If we can show that the con c

46、lusi on of a valid argume nt 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 can cer.valid argume ntTest(conclusion) is false.Prediction or Hypothesis(pr

47、emise) is false.Testi ng of scie ntific hypothesis:Here is the best theory that philosophers and mathematicia ns can come up with: argume nts is valid if and only if there is no possible situation in which all its premises are true and its con clusi on false.An argume nt is valid if and.only .if （當且

48、僅當）there is no possiblesituati on in which all itspremises are true and its conclusion is false.Possibilitynot Actualityvalidtruth preserv ing 2+2=5.Therefore grass is green. valid-based on definition（前提永假） Grass is gree n.Therefore 2+2=4. valid（結(jié)論永真）paradox （悖論）矛盾可以推出任何結(jié)論。True premisesFalse premise

49、sTrue con clusi onPossibly validin validFalse con clusi onPossibly validPossibly validVenn.diagrams （韋恩圖） to determine arguments validity. Possible truth values matterPremises actually true and conclusion actually trueValid argume ntInv alid argume ntAll cat meow. Po does not meow.All cat meow. Dogs

50、 are not cats.Po is n ot a cat.Dogs dont meow.Premises actually false and con clusi on actually trueValid argume ntInv alid argume ntAll fish have lungs Whales are fish.All fish have scales. Whales have scales.Whales have lun gs.Whales are not fish.Premises actually false and conclus on actually fal

51、seValid argume ntInv alid argume ntAll fish have win gs. Whales are fish.All fish have scales. Whales have scales.Whales have wings.Whales are fish.Another way to determine validity is to. create. a. counterexample. set. and. determine con siste ncyIf the coun terexample set is con siste nt the n th

52、e orig inal argume nt is in valid.如果反例集合可 能同時為真，則原論證為無效的。IIf the coun terexample set isn不可能同時為真，則原論證為有效的e.g.t con siste nt the n the orig inal argume nt 如果反例集合If it is snowing the mail will be late.The mail will be late.Therefore .it_is_not_the_case (并非)it is snowing.If it is snowing the mail will b

53、e late.It is snowing.Therefore .it_is_ no t_the_case the mail will be late.Less on 6 Comm on fallaciesA FALLACY is an argument that looks like a good argument but which is not a good argument.In particular we are going to look at fallacies of:.Fallacies of releva nee(關(guān)聯(lián))(a) cit ing in support of a c

54、on clusi on someth ing that is true but irreleva ntNon- Sequiture.g.Bill lives in a large buildi ng, therefore his apartme nt is large.Every year many people are supported through life by their religious beliefs, so their religious beliefs must be true.Reas on for worki ng:These arguments work becau

55、se people don notice the irrelevanee, and because they are overly:a) generous (they are reluctant to point out the irrelevanee);b) proud (they don t want to admit they can t see a connection)prin ciple of charity:Argui ng is life blood of cooperati ng and searchi ng the truth. If you want know the t

56、ruth, you cooperate with other rational animals. If you find the contradiction, don a ssume other person is wrong, the only rational thing to assume is one of you is wrong. Even that might be false.(b) Attack ing the pers on making the argume nt rather tha n the argume nt that is madee.g.Nick Griffi

57、n is leader of the BNptherefore his claim that some people worry about immigratio n is rubbish.Von Dan ikens books about ancient astronauts are worthless because he is a convicted forger and embezzler.Be careful to disti nguishad hominem attacks: attacks on some one s_right to saySomethi ng. -OKad hominem fallacies: attacks on the truth of what some onLSays - Not OKe.g.An ad hominem attack:Nick Griffin is