UGRC 150 Lecture Notes PDF

UGRC 150: CRITICAL THINKING AND PRACTICAL REASONING LECTURE 5: Deduction versus Induction (Unit 6) Dr. (Mrs.) Nancy Myles B. Gyamfi Senior Lecturer Philosophy and Cl...

UGRC 150: CRITICAL THINKING AND PRACTICAL REASONING LECTURE 5: Deduction versus Induction (Unit 6) Dr. (Mrs.) Nancy Myles B. Gyamfi Senior Lecturer Philosophy and Classics, (Arts, Humanities, U.G) Jan- April 2023 [email protected] 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 1  Outline CONTRASTING DEDUCTIVE AND INDUCTIVE ARGUMENTS – Particular and general statements Reference class and attribute class – Types of generalizations – Universal generalizations as disguised conditionals DEDUCTIVE ARGUMENT AND INDUCTIVE ARGUMENT 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 2  Outline Cont’d FOUR VALID SYLLOGISTIC PATTERNS Understanding syllogisms Understanding negation – Modus Ponens (affirming the antecedent) – Modus Tollens (negating the consequent) – Disjunctive Syllogism – Hypothetical Syllogism FORMAL FALLACIES – Fallacy of affirming the consequent – Fallacy of negating the antecedent – False hypothetical syllogism VALID ARGUMENT AND SOUND ARGUMENT 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 3  Deduction vs. Induction These terms describe two types of arguments. (two ways of reasoning; two ways of supporting a claim with evidence(s)) Deductive argument: In a valid deduction if the premises are true, then the conclusion is also necessarily true already. Inductive argument: The conclusion may not necessarily follow(may not be true) even if the premises are true. Recall premises and conclusion! 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 4  Recall Argument Argument: a passage that contains a single conclusion that is presented as a logical consequence of reasons (premises/evidence) offered. ▪ Thus, hence, therefore, so, indicate conclusion ▪ Since, if, given that, provided, indicate premises (reasons/evidence). ▪ Refer to the text for examples!! Discuss during interactions 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 5  COMPARE TWO TYPES OF ARGUMENTS Deductive 1. All students write exams Ama is a student So, she writes exams Inductive 2. Most Ghanaians are hospitable My mother is a Ghanaian Therefore, she is hospitable 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 6  Discuss types of argument cont’d – Inductive argument 3. Since the security man was the last person who left the building yesterday, he stole the project leader’s laptop. – Deductive argument 4. All mangoes are fruits My pen is not a fruit So, it is not a mango 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 7  CORRECT DISTINCTION: DEDUCTIVE AND INDUCTIVE ARGUMENTS Deductive argument: an argument is deductive when the truth of the premises guarantee(proves) the truth of the conclusion. In a good (valid) deductive argument, if the premises are assumed to be true, then the conclusion must be necessarily true. In a valid deductive argument, it is impossible for the premises to be true, and the conclusion to be false at the same time. If not, you create a contradiction!!! 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 8  CONTRASTING DEDUCTION AND INDUCTION It is wrong to say deductive arguments move from general premises to particular conclusions while inductive move from particular to general. That is ambiguous!!! Note that deduction is topic-neutral but induction depends on subject matter! Deduction is about form/pattern/structure but induction is about content. See text for more examples! 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 9  TYPES OF VALID DEDUCTIVE ARGUMENTS Your textbook lists 4 types of VALID deductive syllogistic arguments, but there are more: 1.Modus Ponens (affirming the antecedent) 2. Modus Tollens (denying or negating the consequent) 3. Disjunctive Syllogism 4. Hypothetical Syllogism See examples from text! Note: A syllogism is a form of deductive argument with two premises and one conclusion 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 10  Understanding particular vs general statements Every statement (proposition) has two parts : the reference class and the attribute class. e.g. That man is a bully. ‘That man’ is the reference class (since ‘that man’ is specific, countable and finite, we describe this statement as a particular statement) e.g. Men are bullies. ‘Men’ is the reference class (since ‘men’ is not specific, not countable and is infinite, we describe this statement as a generalization) 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 11  Types of generalizations universal and statistical Universal/lawlike generalization: The attribute applies to all members of that infinite reference class. (No one is exempted!) E.g. Men are bullies. Statistical generalization: The attribute applies only to a subset of the infinite reference class. (some are exempted but the class is still infinite, therefore a generalization). E.g. Some men are bullies. NOTE: The reference class tells you whether a statement is general or particular; as well as the type of generalization 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 12  Practice! particular vs. general statements: See pg. 191 1. The disease is contagious. verifiable 2. Few Ghanaians are allergic to pineapples. confirmable 3. The liquid in that ball is poisonous. verifiable 4. Green tables are scarce these days. confirmable 5. Kofi is the new SRC president. verifiable 6. All voters prefer a recount of ballots. confirmable 7. All the voters interviewed said they will prefer a recount of the ballot. verifiable 8. No student registers unless forced. confirmable 9. None of the students in that class registered for the course. verifiable 10. 80% of all retailed stones are not real diamonds. confirmable 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 13  NOTE: Universals are either affirmative or negative Universal Affirmative Ghanaians are hospitable. Christians worship on Sundays. Alcoholics are womanizers. Ghanaians approve of same-sex marriage. Universal negative No man is perfect. No cat is a dog No goats require vaccinations 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 14  Universal generalizations as disguised conditionals Note: any universal generalization is actually a disguised conditional which has an antecedent and a consequent. All men are bullies is the same as if x is a man then x is a bully. Every student cheats is the same as if x is a student then x cheats 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 15  Universal generalizations as disguised conditionals cont’d We can clearly determine the antecedent and the consequent of our statement when written as a conditional (if…then statement). Antecedent: the ‘if clause’ Consequent: the ‘then clause’ E.g. If x is a man then x is a bully. (antecedent is x is a man; consequent is x is a bully) E.g. If x is a student then x cheats. (antecedent is x is a student; consequent is x cheats) 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 16  Universal negations as conditionals For the expression “No man is perfect”, the conditional form reads thus: “if x is a man, then x is not perfect’. For the expression, “No cats are dogs”, the conditional form reads thus: “if x is a cat, then x is not a dog” For the expression, “No humans have feathers”, the conditional form reads thus: “if x is a human then x has no feathers ” 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 17  A note on syllogism A syllogism simply refers to a deductive argument with two premises and a conclusion. All the valid forms we will study are syllogisms. 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 18  A note on interpreting negation Note: if the original statement is a negation, then its negation will be positive, and vice versa. E.g. the negation of the statement “Kofi is not a student” is “Kofi is a student”, while the negation of the statement “Kofi is a student” is “Kofi is not a student”. This note is useful for affirming and denying antecedent and consequent. 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 19  Types of valid deductive forms (valid syllogistic forms) Modus Ponens (affirming the antecedent) All mangoes are fruits This thing is a mango So it is a fruit Modus Tollens (negating the consequent) All mangoes are fruits This thing is not a fruit So, this thing is not a mango 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 20  valid deductive forms cont’d Hypothetical Syllogism All mangoes are fruits All fruits are edible So, all mangoes are edible Disjunctive Syllogism You either save at Barclays or Stanchart You do not save at Barclays Therefore, you save at Stanchart 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 21  Formal/Syllogistic FALLACIES Formal fallacies simply refer to an error in the form of deduction (i.e. you do not deduce according to the correct form or pattern) 1. The fallacy of affirming the consequent. When you affirm the consequent instead of the antecedent. All Xs are Ys This thing is a Y So, this thing is an X 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 22  Formal fallacies cont’d 2. The fallacy of denying or negating the antecedent. When you negate the antecedent instead of the consequent. All Xs are Ys This thing is NOT an X So, this thing is NOT a Y 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 23  Formal fallacies cont’d 3. False hypothetical syllogism: If two different antecedents share a common consequent, it does not mean the two antecedents are the same or identical. “E.g. Every table is a furniture. Every chair is a furniture. So, every table is a chair.” That is a fallacy!!! All Xs are Ys All Zs are Ys So, all Xs must be Zs 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 24  Compare! VALID FORM ITS INCORRECT FORM (FALLACY) MODUS PONENS (affirming the antecedent) Affirming the consequent Heavy smokers have lung issues Heavy smokers have lung issues Kofi is a heavy smoker Kofi has lung issues So, he has lung issues So, he is a heavy smoker MODUS TOLLENS(denying the consequent) Denying the antecedent Heavy smokers have lung issues Heavy smokers have lung issues Kofi does NOT have lung issues Kofi is NOT a heavy smoker So, he is NOT a heavy smoker So, he does NOT have lung issues HYPOTHETICAL SYLLOGISM False Hypothetical Syllogism All mangoes are fruits. All mangoes are fruits All fruits are edible All bananas are also fruits So, all mangoes are edible So, all mangoes are bananas 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 25  Recall! Validity vs. Soundness of a deductive argument Valid and true premises = sound 1. All men are mortal. Socrates is a man. Therefore, Socrates is mortal. Valid but false premises = not sound 2. All human beings have feathers. This table is a human being So, this table has feathers 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 26  SOUND ARGUMENT A sound argument must first be valid and then its premises must be true. 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 27  END OF LECTURE 5 (UNIT 6) BLESSED, SAFE WEEK!! Dr. Nancy Myles B. Gyamfi 🌸 2/14/2023 Dr. (Mrs.) Nancy Myles Gyamfi 28