lOMoARcPSD|50811939 Final Analytical Skills Notes Analytical Skills (Singapore Management University) Scan to open on Studocu Studocu is not sponsored or endorsed by any college or university Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Concepts of reasoning : Statements : - Sentences that are either true or false To test whether something is a statement o “it is true that _____” if its sounds grammatically correct , it is a statement Rhetorical questions do express statements implicit assumption and implicit statement made if it is clear from the context of the question what the speaker’s answer is, the speaker is committed to the implicit statement Arguments - - - Giving reasons for conclusions Collection of statements, of which the truth of the conclusion that it is trying to prove, is based on the strength of the statements Reason o Statements that arguer offers in support of the conclusion Conclusion o STATEMENT that arguer wants to persuade his audience to accept Inference o PROCESS of drawing the conclusion from the reasons An inference is not a statement , it is a process , it does not have a true or false element in it Inference indicators umbrella terms that includes both conclusion and premise indicators Conclusion indicators o Therefore o So o Hence o Thus o Consequently o Which shows that o Which proves that o Which means that Premise indicators o Because of o As o Since o For o As indicated by the fact o Given that o Being that “if …. Then” statements o Conditional statements and disjunctions o Do not contain two claims , only contain one o ‘if’ is never an inference indicator 1 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - Principle of Charity o Requires us to interpret an argument in a way that makes it the best argument so long as it does not distort the intention of the arguer o Important not to put unintended works into an author’s mouth o Use when unclear whether the argument is given or not o When conclusions and premises are not explicitly stated o “would the arguer agree with the premise” Argument structure - After deciding whether the passage contains reasoning or not , split the conclusion from the premises Linked reasoning A two- premise argument Convergent reasoning Two one-premise argument 2 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Linked and convergent reasoning When more than one reason is given for a particular conclusion Linked reasoning works when - several reasons WORK TOGETHER in support of the conclusion Reasons need each other to support the conclusion Conditional statements “if … then” treated as one statement in diagramming If humpty dumpty was pushed , then someone was trying to kill him. Humpty dumpty was pushed , so someone was trying to kill him. Reason 1 needs reason 2 to give conclusion Convergent reasoning - Several reasons working INDEPENDENTLY in supporting a conclusion When each reason, can , by itself, support the conclusion on its own Reason is independent of other reasons in support of the conclusion when the support of the conclusion is INSENSITIVE to the truth or falsity of other reasons o Even if other reasons are wrong, the support of your own reason for the conclusion is not affected by any means Serial Reasoning - - Intermediate conclusion in between Drawing a conclusion from a basic premise but this conclusion may in turn stand as a reason for a further conclusion ( the intermediate conclusion is also a reason in support of the final conclusion) Intermediate conclusion functions both as a reason and a conlusion Divergent Reasoning One premise giving you TWO conclusions - Single reason used to support multiple conclusions Conclusions are separate 3 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Good argument - All of its basic premises to be true Inferences made to be acceptable Acceptable inference – if you were to assume for the sake of the argument that the premises are true , then it would guarantee the truth of the conclusion WHETHER OR NOT ARGUMENT HAS A TRUE OR FALSE PREMISE IS INDEPENDENT FROM WHETHER IT IS AN ACCEPTABLE OR UNACCEPTABLE INFERENCE VALID ARGUMENTS - - - If the premises are true , then the conclusion MUST be true TEST OF VALIDITY : if the premises are true , MUST the conclusion be true ? A valid inference : any argument with a valid inference is a valid argument o Truth of the premise provides a logical guarantee to the conclusion o The inference drawn from the truth of the premise guarantees truth of the conclusion Invalid : even when the premises are true , the conclusion need not be true o May have true premise and true conclusion o Just that even if the premises are true , conclusion is not GUARANTEED o Can have (TP,TC) , (TP, FC) (FP, TC) (FP , FC) Adding extra information will never turn a valid argument into and invalid argument Can have (FP , FC) , (FP, TC) , but will never have true premise and false conclusion Counterexample - - Showing that an argument is invalid Assuming the argument has an identifiable form Construct a new argument that has o Exactly the same form o Premises that are definitely true and with a conclusion that is definitely false NO COUNTEREXAMPLES TO VALID ARGUMENTS o Powerless in showing if arguments are valid Premises are either true or false Inferences have acceptability that comes in degrees 4 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 DEDUCTIVE INFERENCES - Premises are SUPPOSED to logically guarantee the conclusion The arguer is trying to give a VALID inference When arguer INTENDS for his argument to be valid Arguer is going for certainty Sound argument - A DEDUCTIVE argument All premises are true With a valid inference ALL SOUND ARGUMENTS HAVE A TRUE CONCLUSION Sound arguments cannot be attacked Unsound argument - A deductive argument Either the premises are not true , or the inference is invalid May have a true conclusion ( not guaranteed) VALID ARGUMENTS MAY HAVE FALSE PREMISES INVALID ARGUMENTS MAY HAVE TRUE PREMISES SOUND ARGUMENTS MUST BE VALID SOUND ARGUMENTS MUST HAVE TRUE PREMISES SOUND ARGUMENTS MUST HAVE A TRUE CONCLUSION UNSOUND ARGUMENTS MAY HAVE A TRUE CONCLUSION 5 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 INDUCTIVE - Premises are SUPPOSED to make the conclusion highly probable Arguer is trying to give a strong inference Arguer is NOT trying to give a VALID argument Arguer is going for probability from the premises , not certainty Whether or not inference is strong or weak , depends on the degree of strength Supposing premises are true , how probable will the conclusion be Strong conclusion most likely to be true Moderately strong conclusion more likely than not to be true Weak conclusion less likely than not to be true No link no in inference at all Induction indicators – it is a good bet that , it is highly probable that , so it is likely that *AGAIN , THE QUESTION OF WHETHER THE PREMISES ARE TRUE IS ENTIRELY INDEPENDENT MATTER FROM WHETHER THE INFERENCE IS STRONG OR NOT* Reliability and cogency - - - True premises (1) At least moderately strong argument (2) (1) and (2) are NEEDED for a good inductive argument But not enough for an inductive argument to be good Reliable (3) o Premises of the argument do not leave out extra information that would weaken the likelihood that the conclusion is true Cogent arguments o (1) all of its premises are true o (2) it is at least moderately strong o (3) it is reliable information does not leave out any information that you know that would reduce the likelihood of the truth of the conclusion o All three conditions are independent of each other o Satisfying one does not mean satisfying the others o All cogent arguments have conclusions that are PROBABLY TRUE Uncogent arguments o At least one or more of conditions are not met RULES (I COUNT THEM) STRONG ARGUMENTS MAY HAVE FALSE PREMISES WEAK ARGUMENTS MAY HAVE TRUE PREMISES COGENT ARGUMENTS MUST BE STRONG COGENT ARGUMENTS MUST HAVE TRUE PREMISES 6 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 COGENT ARGUMENTS MUST BE RELIABLE COGENT ARGUMENTS MAY HAVE FALSE CONCLUSION UNCOGENT ARGUMENTS MAY HAVE TRUE CONCLUSIONS Whether inference is good or bad, depends on whether the arguer is engaging in deductive or inductive reasoning Good deduction require inference to be VALID - Good deductive argument must have TRUE PREMISES and a VALID INFERENCE Good induction only require inference to be STRONG - Good inductive argument must have TRUE PREMISES and a strong inference LABELLING - Arguments are either invalid or valid Are either sound of unsound Are either cogent of uncogent Premises and conclusion are either TRUE OR FALSE Deductive arguments are either valid or invalid Inductive arguments are either cogent or uncogent Inductive arguments and their strengths depend on the strength of inferences Arguments against : When argument is inductive we may attack the reliability of inference When argument is deductive try to attack the validity of the inference Attacks upon the truth of the premises - Whether the truth of the attacking reason makes the attacked reason less likely to be true Can attack ONLY the PREMISE of a deductively valid inference Attacks on the basis of the conclusion - Remaining agnostic to the truth of the reasons given for the conclusion We don’t attack the truth of the reason in order to attack the truth of the conclusion Attack upon the inference - Neither attack the truth of the premise or the conclusion Even if we were to assume for the sake of the argument that the reasons are true, we wish to show that the conclusion is not firmly established Attacks upon inference usually involve only inductive arguments One can successfully attack a deductively invalid inference (counterexample) ONE CAN NEVER SUCCESSFULLY ATTACK A DEDUCTIVELY VALID INFERENCE 7 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Assume that the basic premise is true, decide for ourselves how well the conclusion is supported. Then assume that the attacking reason is true and add the information with the basic premise. Ask whether the support for the eventual conclusion was weaker than before or not. If yes – successful attack Lesson 5 – FORMS OF DEDUCTIVE ARGUMENT PROPOSITIONAL LOGIC Conditional reasoning - Modus ponens Modus tollens Fallacy of denying the antecedent Fallacy of affirming the consequent Transposition Hypothetical syllogism Disjunctive syllogism - False dichotomy Disjunctive syllogism Dilemma Conjunctive reasoning - Simplification Addition Conditional reasoning - Antecedent comes just after the ‘If” “If P then Q” = “ Q if P” P is the antecedent 8 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 MODUS PONENS IF P THEN Q IF HE LIVES IN BANGKOK THEN HE LIVES IN THAILAND P HE LIVES IN BANKOK THEREFORE Q THEREFORE HE LIVES IN THAILAND VALID : if the antecedent is true, then conclusion must be true MODUS TOLLENS IF HE LIVES IN BANGKOK THEN HE LIVES IN THAILAND IF P THEN Q NOT Q HE DOES NOT LIVE IN THAILAND THEREFORE NOT P THEREFORE HE DOES NOT LIVES IN BANGKOK VALID : if the consequent is not true, then the antecedent cannot be true FALLACY OF DENYING THE ANTECEDENT IF P THEN Q NOT P IF HE LIVES IN BANGKOK THEN HE LIVES IN THAILAND THEREFORE NOT Q HE DOES NOT LIVE IN BANGKOK THEREFORE HE DOES NOT LIVE IN THAILAND ( BUT LIVES IN HATYAI!!) INVALID : just because he doesn’t live in doesn’t mean he doesn’t live in Thailand Bangkok Just because the antecedent isn’t true doesn’t mean that the consequent is false FALLACY OF AFFIRMING THE CONSEQUENT IF P THEN Q Q IF HE LIVES IN BANGKOK THEREFORE HE LIVES IN THAILAND THEREFORE P HE LIVES IN THAILAND, THEREFORE HE MUST LIVE IN BANGKOK ( HE LIVES IN PHUKET THO) 9 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 INVALID : the truth of the consequent does not guarantee the truth of the antecedent as well HYPOTHETICAL SYLLOGISM IF P THEN Q IF Q THEN R IF IT IS RAINING THEN THE STREETS ARE WET THEREFORE IF P THEN R IF THE STREETS ARE WET, THEN THE STREETS WILL BE SLIPPERY THEREFORE IF IT IS RAINING THEN THE STREETS WILL BE SLIPPERY VALID TRANSPOSITION IF P THEN Q THEREFORE IF NOT Q THEN NOT P VALID CONDITIONAL STATEMENTS IF P THEN Q, P Q IF P THEN Q, NOT Q P IF P THEN Q, Q P VALID VALID INVALID IF P THEN Q, NOT P NOT Q INVALID IF P THEN Q IF NOT Q THEN NOT P IF P THEN Q, Q THEN R IF P THEN R VALID MODUS PONENS MODUS TOLLENS FALLACY OF AFFIRMING THE CONSEQUENT FALLACY OF DENYING THE ANTECEDENT TRANSPOSITION VALID HYPOTHETICAL SYLLOGISM 10 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 DISJUNCTIVE REASONING EITHER P OR Q P THEREFORE NOT Q VALID ONLY IF DISJUCTION IS EXCLUSIVE EXCLUSIVE DISJUNCTION: EITHER P OR Q AND NOT BOTH you can either go to Thailand or China INCLUSIVE DISJUNCTION: EITHER P OR Q and POSSIBLY BOTH either you miss class if youre sick or it is your birthday False Dichotomies only valid if the disjunction is exclusive - If unclear, always assume that the disjunction is inclusive DISJUNCTIVE SYLLOGISM EITHER P OR Q NOT P THEREFORE Q VALID REGARDLESS OF WHETHER DISJUNCTION IS INCLUSIVE OR EXCLUSIVE DILEMMA CONSTRUCTIVE DILEMMA IF IT RAINS THEN THEN THE MATCH WILL BE CANCELLED IF P THEN Q IF IT SNOWS THE MATCH WILL BE POSTPONED IF R THEN S IT IS GOING TO SNOW P/R THEREFORE THE MATCH WILL BE POSTPONED THERFORE Q / S 11 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 DESTRUCTIVE DILEMMA IF P THEN Q IF R THEN S NOT Q / NOT S THEFORE NOT P / NOT R EITHER P OR Q IF P THEN R IF Q THEN R THEREFORE R EITHER P OR Q IF P THEN R IF Q THEN S THEFORE EITHER R OR S EITHER P OR Q , P NOT Q EITHER P OR Q, Q NOT P EITHER P OR Q, NOT Q P EITHER P OR Q IF P THEN R IF Q THEN R R EITHER P OR Q IF P THEN R IF Q THEN S EITHER R OR S IF P THEN Q IF R THEN S P OR R Q OR S VALID ONLY IF DISJUNCTION IS EXCLUSIVE VALID ONLY IF DISJUNCTION IS EXCLUSIVE VALID FOR BOTH EXCLUSIVE AND INCLUSIVE VALID *exclusive – either you are at home or you are in school FALSE DICHOTOMY DISJUNCTIVE SYLLOGISM VALID VALID CONSTRUCTIVE DILEMMA 12 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 IF P THEN Q R THEN S NOT Q OR Q OR NOT S NOT P OR NOT R VALID DESTRUCTIVE DILEMMA CONJUNCTIVE REASONING P AND Q HE IS RICH AND HANDSOME THEREFORE P THEREFORE HE IS RICH VALID P HE IS HANDSOME EITHER P OR Q THEREFORE HE IS EITHER HANDSOME OR RICH VALID P AND Q VALID P P VALID EITHER P OR Q NECESSARY AND SUFFICIENT CONDITIONS SIMPLIFICATION ADDITION IF VS ONLY IF ONLY IF – NECESSARY CONDITION IF – SUFFICIENT CONDITION You’ll feel pain if you have a toothache You’ll feel pain only if you have a toothache XXX You’re a bachelor only if you’re a man You’re a bachelor if you’re a man XXX IF P THEN Q ( P BEING THE ANTECEDENT) P IS SUFFICIENT FOR Q Q IS NECESSARY FOR P IF THERE ARE CLOUDS IN THE SKY, IT IS RAINING P IF Q IF Q THEN P Q IS SUFFICIENT FOR P P ONLY IF Q IF NOT Q THEN NOT P 13 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Q IS NECESSARY FOR P IF P THEN Q EQUIVALENCES IF P THEN Q Q IF P P ONLY IF Q CHAPTER 8 – CATEGORICAL LOGIC Catergorical syllogisms – two premise arguments with a conclusion Categorical propositions - - - Categories or classes of things Categories described as quantifiers Quantifiers – all , none , some are Tell us how much of a class is being referred to Quantity o Universal all , none o Particular some = at least one Affirmative and negative (quality) o All are , some are o None are , some are not Subject and predicate o In the conclusion of a categorical syllogism o The term that comes first is the subject o The term that comes later is the predicate o The middle term does not appear in the conclusion but links the subject and he predicate A E I O ALL S ARE P NO S ARE P SOME S ARE P SOME S ARE NOT P UNIVERSALLY AFFIRMATIVE UNIVERSALLY NEGATIVE PARTICULAR AFFIRMATIVE PARTICULAR NEGATIVE Venn diagrams A = ALL S ARE P E = NO S ARE P I = SOME S ARE P O = SOME S ARE NOT P 14 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 SHADING BEFORE CROSSING, ALWAYS A = ALL S ARE P E = NO S ARE P I = SOME S ARE P O = SOME S ARE NOT P METHOD TO DRAW - Draw the template with the venn diagram Diagram only the premises , shading before crossing Can you see the conclusion clearly ? valid only if yes IF THE ARGUMENT IS NOT ALREADYY CLEARLY SHOWN o If the argument is not clearly valid o Conclusion is particular (I or O) o Make sure there is a cross in each circle (using the minimum number of crosses) o And try to avoid making the conclusion true 15 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 6 categorical syllogisms ALL S ARE M ALL M ARE P THEREFORE ALL S ARE P VALID, CONCLUSION ALREADY WITHIN THE INFORMATION BY PREMISES ALL S ARE M ALL P ARE M THEREFORE, ALL S ARE P INVALID : CONCLUSION IS NOT TRUE EVEN IF THE PREMISES ARE TRUE ALL M ARE P SOME M ARE S SOME S ARE P VALID : CONCLUSION EASILY SHOWN NO M ARE P SOME S ARE M SOME S ARE NOT P VALID ALL P ARE M SOME S ARE M SOME S ARE P INVALID : IT IS NOT A MUST FOR CONCLUSION TO BE TRUE SOME S ARE M SOME M ARE P SOME S ARE P 16 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 INVALID FULL SQUARE OF OPPOSITION To be compared using the same square, predicate terms and subject terms must be the same - Must belong to the same class Contradictory - Diagonally opposite Opposing truth values When one correct , the other one , must be false Contraries - Universal propositions that differ in quality Cannot both be true CAN SIMULATENEOUSLY BE FALSE ALL ZEBRAS ARE FEMALE AND ALL FEMALES ARE ZERBRAS BOTH FALSE Subcontraries - Can both be true , cannot both be false Cannot both be false because we are assuming that there is at least something in each S and P ( S and P exist) If O is false, I is true ‘ Some birds are not animals’ , ‘Some birds are animals’ 17 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Propositions that differ in quantity – subalternates - Truth flows down Falsity flows upwards Basic inferences IF E IS TRUE - I IS FALSE (CONTRADICTORIES) A IS FALSE (CONTRARIES) O IS TRUE (SUBALTERNATION) IF E IS FALSE - I IS TRUE CANNOT CONFIRM WHETHER A IS TRUE OR NOT IF I IS FALSE - E IS TRUE O IS TRUE A IS FALSE If A is false - O is true (contradictory) NO MORE OTHER INFO E AND I ARE UNDERMINED Immediate inferences - Single premise to a conclusion Propositions have same subject and predicate terms Using the rules of the square i.E A- All fish are aquatic creatures Therefore , E – Some fish are aquatic creatures By subalternate nature , the premise guarantees the conclusion – valid 18 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 TWIDDLING OPERATIONS CONVERSION Switching the subject and the predicate Only applies to E AND I E : NO S ARE P = NO P ARE S I : SOME S ARE NOT P = SOME P ARE NOT S DOES NOT APPLY TO A AND O NO S ARE P SOME S ARE P NO P ARE S SOME P ARE S OBVERSION Change the quality (affirmative to negative) Negate the predicate term , replacing with the complement A: ALL S ARE P E: NO S ARE P I: SOME S ARE P O: SOME S ARE NOT P NO S ARE NON-P ALL S ARE NON-P SOME S ARE NOT NON-P SOME S ARE NON-P OBVERSION ALWAYS WORKS CONTRAPOSITION ONLY WORKS FOR A AND O Step 1 Switch the Subject and Predicate terms Step 2 Negate both terms with their complements ALL S ARE P SOME S ARE NOT P ALL NON-P ARE NON-S SOME NON-P ARE NOT NON-S 19 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Equivalences ONLY S ARE P ALL P ARE S ALL S ARE NON-P ALL non-P are are non-S NO S ARE P ALL S are P Nothing that is not an S that is aP NO P ARE S Major and Minor Premise - Predicate term in conclusion is the major term , P All M are P = major premise Subject term in conclusion is the minor term , S All S are M = minor premise STATISTICAL SYLLOGISM n% of Fs are G 99% of the balls in the bag are white This is an F This is a ball from the bag THEREFORE It is white ( Principle of charity) This is a G *IF N =100% , THE STATEMENT IS A VALID DEDUCTION Statistical syllogisms are strong IF AND ONLY IF the candidate was selected at random AND than the sample is large enough INDUCTIVE GENERALIZATION In a sample of Fs, n% are Gs Roughly n% of ALL Fs are Gs 20 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 STRONG IF AND ONLY IF the sample is large enough and unbiased HOW LARGE IS LARGE For populations between 100-1000 10% is enough The bigger the population, the smaller the sample size The smaller the population , the bigger the sample size EXACT AND APPROXIMATION - Always harder to argue for EXACT figures like 60% because one shift in the statistic and your argument becomes very weak Always easier to argue for roughly and approximately FALLACY OF SMALL SAMPLE In a 1% of the Residents of London, 66% are car owners Thus , 66% of all residents of London are car owners SAMPLE IS TOO SMALL TO BE REPRESENTATIVE OF THE ENTIRE POPULATION ! FALLACY OF A BIASED SAMPLE In a sample of 20% of Londoners exiting the MRT station, 45% of them owned cars Thus, 45% of all Londoners own cars Sample is taken at an MRT at a specific time, cannot be reflective of the truth of the entire population ARGUMENT FROM ANALOGY x has properties of P,Q,R….. and Z y has properties of P,Q,R therefore, Y has property Z - Your car is Japanese, less than two years old, had fuel injection and a 1300cc engine. That is the same for my car. Your car is fuel efficient, so does mine too The greater the number of properties P,Q,R The more relevant the properties are to Z , the stronger the reference Presence of relevant DISANALOGIES weakens the inference 21 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Properties must be relevant! - - “your car is red, has tinted windows , nice stereo system and a box of Kleenex tissues in the car. That is the same for my car. Since you get good mileage per gallon of gas , I should do too” Obviously the properties are not relevant to fuel efficiency Presence of dianalogies - - “your car is Japanese , less than two years old, has a 1300CC engine ans that is the same for my car. Your car has good mileage per gas , so should mine” “ but ive modified my exhaust and gears” Presence of disanalogies weakens the argument ARGUMENT FROM AUTHORITY S SAID THAT IT IS TRUE THAT P S IS AN AUTHORITY OF THE SUBJECT IT IS TRUE THAT P Strong (IF AND ONLY IF) - Authorities by and large agree with each other Authority is relevant Authority has no reasons to give a biased answer 22 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 FALLACIES Mistakes in reasoning Formal fallacy – mistakes due to its structure Informal fallacy mistakes in reasoning that goes beyond the structure of the content that requires a closer inspection of the content Difference between formal and informal fallacy is a moveable boundary Fallacy a defective piece of reasoning no reasoning , no fallacy FALLACIES OF IRRELEVANCE Appeal to pity Appeal to popularity ( including appeal to tradition) Appeal against the person o Abusive o Circumstantial o You too Straw man Red herring Appeal to ignorance Rejecting the conclusion of a bad argument FALLACIES OF WEAK INDUCTION Suppressing information Hasty generalization o Biased sample o Small sample Exception proves the rule Appeal to unqualified authority After this , so because of this With this , so because of this Mistaking cause for effect and missing a common cause Causal slippery slope Weak analogy FALLACIES OF PRESUMPTION Begging the question o Omission of premise o Restatement o Circular chain Complex question False dichotomy o Overlooking alternatives o Overlapping alternatives 23 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 MISCELLANOUS FALLCIES Equivocation Missing comparative Composition Division Accident Semantic slippery slope FALLACIES OF IRRELEVANCE - Premises have no logical logical relevance to the conclusions Only a psychological conclusion at best , no logical conclusion Appeal to pity - - Arguer evokes pity to establish a logically unrelated conclusion o Your Honor, I admit I declared thirteen children as dependents on my tax return although I have only two. But if you find me guilty then my reputation will be ruined, I’ll lose my job and then my kids will starve. Surely I’m not guilty. o him losing his job and losing his reputation and negatively impacting the children has nothing to do with him being guilty or not o there is something pitiful about X’s situation o so something else about X is true also ( pity appealed to is not related to situation) pitiful circumstance might be relevant to the punishment ! Your Honor, I admit I’m guilty. I declared thirteen children as dependents on my tax return although I have only two. But if you send me to prison then my reputation will be ruined, I’ll lose my job and then my kids will starve. Surely I should be fined instead. o Not a fallacy conclusion he is trying to persuade the judge to believe is related to his arguments about him having children to support. (judge should accept the judgement if he feels that the degree of his punishment should be mitigated by the pitiful circumstances of his children) Appeal to popularity ( including appeal to tradition) - Something that is widely believed to be true by a lot of people(P) , therefore P is true Arguments of structure fail to support conclusion o Everybody believes that the earth is flat , therefore it is flat o Exception : No government should continue to implement a policy that most of its citizens believe to be wrong. Most Singaporeans believe that the death penalty is wrong. So the Singapore government should not continue to implement the death penalty. By merit of its first premise , this line of argument is correct 24 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - - Popular practice : Something that is widely practiced by people , most people do X , so it is acceptable to do X o Finding evidence of a particular practice that is commonly accepted only gives some sense of its moral acceptability Case of abortion , case of illegal downloading of music files o TRUE CONCLUSIONS WILL NOT PREVENT A FALLACY (process of arriving at the conclusion will prove the argument to be fallacious) Appeal to tradition : we have being doing this for the longest time , so we should continue to do it o Slavery in America has been going on for the past 100 years, we should therefore continue to legacy ! o Just because you have been doing something for the longest time just only means that it has been a tradition that is passed down , it goes nothing to show of the general normative value of it and how the entire world looks at it. Taking the example of imperial rule in china it has been going on for the longest time but it failed china ! Argument against the person Argument against the person :Abusive - - There is something bad about so and so ( usually related to his character or something he did) Therefore , so and so’s argument is bad Something objectionable about his character , thus his argument , whatever it is , can be ignored To say an arguer is bad is not to say that his argument is bad o Tan is a criminal and a wife beater, so his argument about the legal system being corrupt is nonsense o Nobody knows what argument Tan has made about the legal system! Just because he is a criminal and a wife beater goes nothing to prove that his argument is faulty o The conclusion cannot be established from the premises No fallacy commited : o Character of the person is indeed relevant to the conclusion being drawn o Tan is child molester , so he should not be in charge of the kindergarten o Paul was drunk when he argued that the legal system was corrupt. When he gets drunk , he invariably talks nonsense. So his argument is nonsense Personal flaw is directly related to the conclusion Argument against the person :Circumstantial - Because of so and so’s circumstances , so and so has the motive for arguing in such and such way Therefore so and so’s argument is faulty ( has a false conclusion , or can be ignored) So and so must be arguing out of self interest , self motivated argument 25 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 o Salim has records that he claims shows that Malays are systematically discriminated against holding positions of power in the SAF. We can forget all that. What would you expect him to say? He’s a Malay! o We are in no position to comment about the wuality of the person’s argument when we have not even rationalized the argument yet. We are merely dismissed it on stereotypical grounds and his potential for giving and argument in a particular sense Argument against the person :You too - - So and so argues such and such is bad But so and so does such and such Therefore , so and so’s arguments are faulty ( or has a false conclusion) o Beng : you should give way to those exiting the mrt door cabin before boarding thr train o Lian : nonsense , you don’t even do it ! It at most only shows that the arguer does not practice what the aruger preaches , has nothing to do with the quality of his argument and the validity of it Straw man - - Misinterpreting the opponent’s argument Opponent says X Person 2 states X but rehashes it in a way that is a misrepresentation of the original intent and is easy to attack Attacks X and concludes that X is a bad argument Person 2 twisting the original meaning state by person 1 and subsequently goes on to attack it o Jack : forcing the children to study something tht they do not understand will only kill their passion for the subject ! o Jill : youre just saying that the kids should just go out to play! Then they will never be able to get an education In this way Person 2’s line of thought was never whats person actually meant. Taking person’s 1’s argument and inverting its meaning does not prove that person’s 1 argument is right or wrong, it wasn’t being given a proper evaluation even Red herring - Breaking of one’s commitment to argue about a certain topic by changing the subject Conclusion that was supposed to be supported comes at the beginning of the passage Arguer commits to argue for the original conclusion but goes on to argue for a different line of thought or rambles on about a separate subject Aruer distracts the audience so that they do not notice that what was supposed to be argued for was not argued. o There is a good deal of talk these days about the need to eliminate pesticides from our fruits and vegetables. But many of these foods are essential to our 26 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - - health. Carrots are excellent source of vitamin A, broccoli is rich in iron and oranges have lots of vitamin C o Conclusion that should have been argued = there is no need to eliminate pesticides from our fruits and vegetables. o Conclusion actually argued = Many fruits and vegetables are essential to our health Attention grabbing claim arguer commits to argue for conclusion C1 distracting claims presented , may or may not be related in getting conclusion C1 but goes on to argue forconclusion C2 in the end Require argument C1 is never established Rambling on : o Prof Lim claims that the study of IT is essential these days because the world will become increasingly electronic. That’s nonsense. And I’ll tell you what else is nonsense. That’s his marriage. I saw him kissing his secretary today o After committing to initial argument, goes on to talk about a slew of unrelated topics and premises that possess little or no value in supporting C1 Appeal to ignorance - It has never been shown that not-P Therefore P o Ghost must exist since it has never been shown that they do not exist It has never been shown that P Therefore , not P o Ghost cant exist because nothing has been shown to prove that they do In our law courts a person is presumed innocent until proved guilty. The courts do not maintain that a lack of proof of guilt is a proof of innocence. They maintain only that until guilt is proven, innocence should be presumed Missing the point - - Drawing the wrong conclusion In the end , Q (a different conclusion that the premises do not support) o Crime and robbery have been increasing alarmingly, so obviously we should reinstate the death penalty. o What the premise supports: we should increase law-enforcement. o Conclusion drawn but unsupported: we should reinstate the death penalty Appeal to pity is one of the many forms of missing the point. There are many others Straw man, red herring and missing the point are easily confused Strawman a fallacy that involves two arguers In missing the point, unlike red herring, the conclusion actually drawn is always unsupported. The person guilty of red herring is often deceptive, but the person guilty of missing the point is often merely stupid Rejecting the conclusion of a bad argument 27 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 -o Rejecting the conclusion of the argument just because the reasons given by the arguer to support the conclusion are not logical o So-and-so’s reasons for concluding that such-and such are bad. o Mechanism is in between two parties , person one uses bad reason to support the argument ,person 2 rejects the conclusion just because of the badness of the reasons given o Therefore it is not the case that such-and-such o FALLACY IS STILL COMMITTED REGARDLESS OF THE FALSITY OF THE CONCLUSION MADE FALLACIES OF WEAK INDUCTION - Arguer attempts to give evidence that’s makes her conclusion likely to be true , but fails to do so Suppressing information - Ignoring extra information that is known to the arguer that will weaken the general argument Deliberately omitting information that will weaken the reliability of the arguer’s argument or strengthen the opponent’s argument Hasty generalization One third of 9,999 apples were sampled evenly from all parts of a barrel and exactly 12% of these were found to be rotten. So probably about 12% of all the apples are rotten. n% of a representative sample of members of class S are Fs > Probably about n% of all members of S are Fs *the less exact your conclusion is , the more likely to be true : bout 66% is more likely to be true than exactly 66% Hasty generalization- Biased sample - Biased sample where the sample taken is not representative of the entire population For example taking the apples only from the top of the crate to test quality isn’t very fair ?! Need to think about the relationship between the sampling methd and the thing that is being studied , biologically different characteristics have got nothing to do with their political beliefs o 20% of those who were interviewed at jurong east during the Monday morning rush hour (1000 of them) claimed that they owned cars , thus, 20% of the entire Singapore population of Singapore must own cars Hasty generalization - Small sample 28 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - - Sample fails to be representative of the entire population Choosing too small a sample factors out a lot of 3 apples , three possible outcomes hard to produce sensible results Population of 100- 1000 : 10% Very small population : 25% Large population : small percentage Sample size assessment need to consider if the population is homogenous or heterogenous mass produced battery packs usually homogenous. Ripeness of fruits need to have larger sample because ripeness can vary significantly from the next Drawing conclusions from our own limited experienced – anecdoctal evidence Modest conclusions usually better and more easily trustable ‘might improve my chances of losing some weight’ Exception proves the rule - - In an exceptional case of doing X , doing X is not thus and so Thus doing X is not thus and so o Uncle who smoked cigarettes every single day but lived to he was 93 o Smoking cant be bad for health Subcase of the fallacy of a small sample Just one exception , drawing major conclusions Appeal to unqualified authority - So and so said P Therefore P The authority cited must be a relevant authority of the subjet The conclusion must have a claim that can be settled by expert opinion There must be no reason to think that the authority is untrustworthy or biased There must be no SIGNIFICANT DEGREE OF DISAGREEMENT among authorities o Cologne promoted by Michael Jordan cannot be assumed to definitely be good , how can MJ be an authority at the issue o PM Lee said that in moderate qualities, red wine reduces the incidence of heart disease, so drinking a little red wine is probably a good idea After this , so because of this - Immediately after event E1 happened , Event E2 happened So E1 probably caused E2 to happen o After the hyatt hotel decided to change to position of its furniture , its profits increased ten-fold. One must never underestimate the power of geomancy o If A causes B , B usually happens after A (correct) o B happened just after A cannot be the absolute reason to attribute that A cause B, there could definitely be a coincidence or a confound With this , so because of this - E1 type events are usually correlated with E2 type events 29 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - They usually happen around the same time So E1 must have caused E2 Correlation between two things , as one increased , the other one also increased or decreased at the same time CORRELATION DOES NOT EQUATE TO CAUSATION Just because there is a temporal correlation does not mean that there is a causal connection between the two As the frequency of incidents of glue-sniffing has increased over the years, so the ratio of passes to fails in secondary school exams has fallen. So probably glue sniffing in secondary schools is the cause of poor results. Could be related , but should not be the main reason , otherwise , fallacious Mistaking cause for effect and missing a common cause - - - The arguer sees a connection between E1 and E2 but then assumes for no good reason that E1 causes E2 when it could be just as likely for E2 to cause E1 or just as likely that E3 is the common cause of E1 and E2 Unjustified assumptions about which is the cause and which is the effect Students who smoke do less well in exams than students who do not smoke. So if we want better results we must discourage them from smoking. This assumes that smoking is the cause of poor results. But it might be that the stress of poor results is part of the reason why students start, or continue, to smoke. After lightning there is always thunder, so lightning causes thunder. Lightning and thunder are the same event perceived differently (by sight and sound). Both are the same effect of a common cause—an explosion in a cloud. Mistaken Cause may occur in After This, So Because Of This or With This, So Because Causal slippery slope - - Arguer most often claims , that we should not do something , otherwise it will trigger a chain of events which would ultimately led to a negative outcome when in fact the bad outcome is difficult to materialize 2 ways o Some of the effects in the chain are unlikely (links in the chain unlikely to happen) o Chain is quite long , even if the individual causes all seem likely, likelihood that all of them to pass will be quite low We should not let the students have a bar on campus. If we do that, more students will drink. Then more of them will indulge in premarital 30 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 sex. Before long, most of our students will be alcoholics or single mothers. Then the government will close us down. Weak analogy - Two things have everal properties in common Then conclusing that they share some other same property Inductive – never enough to guarantee that any particular property will be shared Strength or argument depends on the number of relevant similarities FALLACY – similarities given NOT RELEVANT TO THE CONCLUSION DRAWN Colour isn’t relevant to the speed and fuel consumption of cars Disanalogy FALLACIES OF PRESUMPTION - Assumptions that we are not allowed make Begging the question - Omission of premise - - A controversial premise is left out that is needed to support the conclusion o Suicide is wrong because murder is wrong o Missing premise: Suicide is murder o Missing premise is highly controversial unfair to opponent to just simply assume it NO FALLACY IS COMMITTED UNLESS THE MISSING ASSUMPTION IS HIGHLY CONTROVERSIAL Begging the question - Restatement - Premise = conclusion in different words It is true that P Therefore it is true that Q ( Q being just another way of saying P) o We cant sell drugs that are not prescribed by the doctor because we are not allowed to retail medication that is not authorized in writing by a physician Begging the question- Circular chain - Someone who refuses to accept the conclusion would refuse to accept the premise The final conclusion is supported by itself There is a chain of reasons for the final conclusion but one of these reasons repeats , restates , in different words or presumes the final conclusion ( such that someone who refuses to accept the conclusion would be refusing to accept the premise too) o P because of q ; q because of r ; r because of p o p because q; q because r; r because s (where s is a restatement of p). o (1) God exists because (2) it says so in the Bible. Furthermore we know that (3) the Bible is true because (4) it is the revealed word of God. Complex question 31 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - - A single answer is demanded for a yes no question that presumes the answer to the second unasked question Same conclusion is drawn upon the answer to a complex question o ‘Have you stopped smoking’ unfairly assumes that without argument thst the answer to the implicit question ‘have you ever smoked’ is yes o Either way that the person replies , the conclusion will be that he has smoked There must be an argument built upon the complex question that relies on the forced answer to the implicit second question complex questions on its own are not mistakes in reasoning I asked Jane if she has stopped plagiarizing. She answered ‘No’. So she has admitted that she has plagiarized. Either way she answers , youre gonna assume that she has plagiarized IF YOU SIMPLY ASK ‘ HAD JANE STOPPED PLAGIARIZING’ that’s not a fallacy False dichotomy - Genuine dichotomy: Either it’s Friday or it’s not Friday. Exhaustive: No third possibility Exclusive: No possibility of both options Overlapping alternatives o Either P or Q ( when both P and Q might be true) o P o Therefore not Q Either Tay is working or at home, so he can’t be home because he’s working But tay could be working at home (unless we add ‘but not both’ to the first premise). We cannot simply assume that the alternatives don’t overlap. Tay might be working from home. o When it comes to geographical locations , there can be no overlaps Cannot both be in paris and London at the same time Overlooking alternatives o Either P or Q ( when no reason has been given that only these two alternatives are possible) o Not P o Therefore Q Either John wants to learn astrology or he wants to continue bungling through life as he has been. Now, I'm sure he doesn't want to continue bungling through life, so he'll be glad to learn astrology. He might not want to learn astrology , even though he doesn’t want to continue bungling through life 32 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Although the argument is valid (disjunctive syllogism), the mistake was to assume, for no reason, that the first premise is true when there could easily be a third option: John might not want to learn astrology or to continue bungling through life but instead join a Church CAN BE VALID BUT BE FALLACIOUS MISCESLLANEOUS FALLCIES Equivocation - When an argument uses a word or phrase that is ambiguous, in other words , has more than one meaning , and slides from one meaning to another Words that have double meaning , taking on two different meanings in the same argument It’s not wrong for newspapers to pass on rumors about sex scandals. Newspapers have a duty to print stories that are in the public interest, and the public clearly has a great interest in rumors about sex scandals. ‘interest’ = curiosity versus benefit. Anything that is orange is guaranteed to cheer you up, they even provide more vitamins than apples ! Missing comparative - - Such and such is a good thing of X Therefore X is better than Y Emphasis is placed o nsomething being highly significant without making clear what it is supposed to be compared with o A recent has shown that 20% of first-year students at the National University of Temasek in Sweden (NUTS) this year had great difficulty in writing grammatically correct essays. Clearly this cohort is much worse than in previous years. o To say that this cohort is much worse than in previous years would require you having to compare to the performance in other years Element of time and space sometimes the comparison might not be against time but with other competitors Composition - Each part of X has property F Therefore X has property F 33 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 - o This bag of chains are made up of many chains that are super light , therefore the bag must be light – Sometimes its correct : each tile on this floor is white , thus the floor must be white Involves the transference of the property from the subgroup to the big group but the transference is not logical ! Each member of group G has property F Therefore G has property F o Each member of the soccer team is a world-class player, so the team is a world-class team. o Suppose each player is a world-class goalkeeper! The argument is invalid. Division - - X has property F Therefore each part of X has property F o Poverty isn’t a problem in amercia because America is a rich country o Just because this is a property of the whole does not mean that it is the property of the smallest components Sometimes it is correct too : this floor is completely white , It must be made up of white tiles Accident - Arguer applies a general or moral rule to an exception that the rule was never meant to account for o People who cut other people up with knives should be locked up, so surgeons should be locked up because they cut other people up with knives. o Moral rule: Don’t cut people up with knives. Identification of fallacies - Identifying the fallacy (1m) , addressing the specifically how to fallacy is being committed (3m) cannot restate the structure , must specifically address the context of the question Only need to identifying the fallacy , not the subtypes Man is a fighting animal; therefore the nation, being a community of fighters, must be a fighting unit. (Winston Churchill) o Fallacy of composition(1m). conclusion depends on the transference of the attribute from the subpart to the whole , but this transference is logically unwarranted. A fighting unit is a group of men that disciplined to fight together as a team ,and to take orders and go for missions. From The assumption that every man is a fighting animal, it does not follow that a bunch of fighting men will naturally be a fighting unit ,for it is not a natural instinct for humans to be fighting together as a unit. Compare a riot with a team of assasins, the former a bunch of fighting men , the latter , a fighting unit o Counterexample to Churchill’s argument: Man is a singing animal; therefore the nation, being a community of singers, must be a choir. Part 2 34 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Provide only one argument for or against this conclusion using at least two deductively valid forms of argument and one inductively strong form of argument Example typed : (1) There have been many cases in the past where those who were executed for a crime were subsequently found to be innocent. So (2) it is likely that capital punishment will sometimes involve the death of an innocent suspect in the future (strong induction). (3) Any form of punishment that will involve the death of an innocent suspect is unjust. (4) So capital punishment is unjust (from 2 and 3 by valid deduction). [VALID DEDUCTION , if for the sake of the argument, the premise is true, then the conclusion is true] (5) If capital punishment is unjust, then it is wrong. So (6) capital punishment is wrong (from 4 and 5 by modus ponens) [IF P THEN Q , P THEREFORE P] As a separate consideration, (7) the punishment that offenders deserve must fit the crime. But (8) some drug smugglers are punished with the death penalty. (9) This crime does not fit the punishment. So (10) not all those guilty of crimes punishable by death deserve death (from 7, 8 and 9 by valid deduction) [IF PREMISES ARE ASSUMED TO BE TRUE FOR THE ARGUMENT , THEN THE CONLCLUSION IS LOGICALLY GUARANTEED] (11) If capital punishment is not wrong, then all those guilty of crimes punishable by death deserve death. So (12) capital punishment is indeed wrong (from 10 and 11 by modus tollens). [IF P THEN Q , BUT NOT Q , THEREFORE NOT P] Argument against ‘capital punishment is wrong’ (1) According to nearly all expert criminologists around world, the death penalty has a significant effect in preventing other would-be murderers from committing murders. So (2) capital punishment probably has a significant deterrent effect (from 1 by strong argument from authority). (3) Any punishment has overall benefits for society if it has benefits for society and these are not outweighed by the costs. (4) If capital punishment has a significant deterrent effect, then it has benefits for society. So (5) it has benefits for society (from 2 and 4 by modus ponens). (6) These are not outweighed by the costs (such as the suffering of the offender’s relatives). So (7) capital punishment has overall benefits for society (from 3, 5 and 6 by modus ponens). (8) If capital punishment is wrong then it does not have overall benefits for society. So capital punishment is not wrong (from 7 and 8 by modus tollens) End of (3) overall benefits for society IF has benefits for society AND do not outweigh costs 35 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 (4) If capital punishment has significant deterrent effect (P) , it has benefits for society(Q) (5) taking 2 and 4 , modus ponens to establish that capital punishment has benefits to society. (7) taking structure of (3) , including the fact that benefits are not outweighed by costs from (6) AND from (5) , that capital punishment has benefits to society capital punishment has overall benefits (8) if capital punishment is wrong (p) , then it does not have overall benefits to society (q) But if does have benefit to society (not q) Therefore , capital punishment is not wrong ( not p) [modus tollens] (1)Many graduate students of the study of Literature do not find the skills they have learnt in studies have prepared them for actual working life as (2) most of them are not working in jobs that require them to apply their skills from literature studies.(3) It is thus likely that the study of literature may not sufficiently prepare students with the necessary skills to meet the demands of future working life.(moderately strong induction from 1 and 2) (4)If there are necessary skills for students to acquire for the workforce ,they should devote time to acquire them. (5) Working adults in Singapore are required to be competent in cognitive thinking and oratorical skills. (6) Therefore, students should devote their time to acquiring the necessary competencies in cognitive thinking and cognitive skills (from 4 and 5 through modus ponens ). (8) Students should either dedicate their time wholeheartedly in the pursuit of an education in the fine use of literature,(9) or be focused on developing skills that are necessary for their working lives (10) because they cannot achieve both in their short span of time in school. (11) Therefore, the students should not dedicate their time in pursuit of studying literature.(disjunctive syllogism from 7 and 8 and 9 ) (12)The pursuit of literature is not worth dedicating our time ,(13) therefore the pursuit of literature is not worthwhile. (from 11 and 12 via valid deduction) Five useful forms of argument in propositional logic Modus ponens (MP) IF P THEN Q P THEREFORE Q 36 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 Modus Tollens IF P THEN Q NOT Q THEREFORE NOT P Disjunctive Syllogism EITHER P OR Q (and not both) P , therefore not Q Hypothetical Syllogism If p then Q If q then R Therefore if P then R Transposition If P then Q If not q then not P Five Useful Forms of Categorical Syllogisms 1. All M are P All S are M All S are P All mammals are vertebrates All cats are mammals All cats are vertebrates 2. No M are P All S are M No S are P No dogs are insects All poodles are dogs No poodles are insects 3. All M are P Some S are M Some S are P All ministers are politicians Some corrupt individuals are ministers Some corrupt individuals are politicians 4. All P are M Some S are not M Some S are not P All lawyers are graduates Some civil servants are not graduates Some civil servants are not lawyers 5. No M are P Some S are M Some S are not P No Muslims are drinkers Some professors are Muslims Some professors are not drinkers equivalences All S are P = If it’s an S then it’s a P All cats are mammals = If it’s a cat then it’s a mammal 37 Downloaded by Soch By MM (contact@mohakmangal.com) lOMoARcPSD|50811939 No S are P = If it’s an S then it’s not a P insect No cats are insects = If it’s a cat then it’s not an 38 Downloaded by Soch By MM (contact@mohakmangal.com)
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