Lecture Notes

1. Lecture Notes Chapter 8 Invitation to Critical Thinking Chapter 8

2. Overview Inductive inferences and analogies • Assessing inductive strength • Statistical generalizations • Margin of error • Reasoning with analogies • Argument by analogy • Evaluating reasoning by analogy • Relevance • Refutation by analogy Invitation to Critical Thinking Chapter 8

3. Inductive Inferences • The difference between deductive and inductive reasoning • Deductive inferences designed to achieve “absolute inferential security” • Inductive inferences designed to manage risk of error where absolute inferential security is unattainable Invitation to Critical Thinking Chapter 8

4. Assessing Inductive Strength • A deductive argument is either valid or not valid • Inductive strength in an argument is relative • It admits of degrees • Some valid inductive arguments are stronger than others • In the absence of absolute inferential security • the premises, even if true, leave room for doubt about the conclusion • the essential question becomes “How much room for doubt?” • To evaluate inductive reasoning, we must estimate the relative security of inferences. Invitation to Critical Thinking Chapter 8

5. Inductive generalizations • The simplest type of inductive reasoning • The most common type of of inductive reasoning • Inductive strength depends on variables • Variables affect the strength of an inductive inference • The more representative the sample is of the population as a whole, the stronger the induction • Vary the sample as widely and in as many different relevant dimensions as possible • Consider these two factors—sample size relative to population size and representativeness of the sample Invitation to Critical Thinking Chapter 8

6. Statistical Generalizations Avariation on simple inductive generalization • Commonly called statistical generalization • Involves projecting trends or percentages observed in the sample onto other instances or onto the population as a whole • Use the same principles for evaluating the strength of simple inductive generalizations to evaluate the strength of statistical generalizations • In both simple inductive generalization and statistical induction • The strength of the inference increases with the size of the sample relative to the population • The strength of the inference increases with the degree to which the sample is representative of the population as a whole Invitation to Critical Thinking Chapter 8

7. Margin of Error An estimate of the likelihood of error • In the conclusion of an inductive inference • In an estimate of how well you think the research has controlled the variables • Variables affect the strength of statistical generalizations • Variables include the degree of precision and certainty attached to the conclusion relative to the evidence contained in the premises • A statistical generalization can generally be strengthened • by hedging the conclusion with appropriate qualifications • essentially by toning down the language with which the conclusion is presented Invitation to Critical Thinking Chapter 8

8. Reasoning with Analogies Analogies are comparisons applied to some specific intellectual purpose • Used to explain by comparison • new and unfamiliar to more familiar • abstract and intangible to tangible things • Used simply to give a vivid description or to spice up a narrative Reasoning with analogies involves • Similarity • Difference • Relevance Invitation to Critical Thinking Chapter 8

9. Argument by Analogy Argument by analogy or reasoning by analogy • Inferential: to infer conclusions • Argumentative: to support or defend controversial positions • Useful to distinguish the items compared by the roles they play in the comparison • Analogue(s): the item(s) used as the basis of the comparison • Target(s): the item(s) about which conclusions are drawn or explanations are offered Invitation to Critical Thinking Chapter 8

10. Evaluating Reasoning by Analogy • Variables that affect the strength of inductive inferences generally also pertain in evaluating reasoning by analogy • The number of analogues relative to the number of targets affects the strength of an argument by analogy • just as the size of the sample relative to the size of the population affects the strength of an inductive generalization Invitation to Critical Thinking Chapter 8

11. An argument based on a large series of analogous cases will tend to be stronger than one based on a single analogue • just as an inductive generalization based on many instances will be stronger than one based on a tiny sample • The number of observed similarities between analogue and target affects the strength of the analogy • just as the representativeness of the sample relative to the population affects the strength of an inductive generalization Invitation to Critical Thinking Chapter 8

12. Relevance • Affects both similarities and differences • More important than either similarities or differences by themselves • The more relevant the observed similarities between analogue and target are to the conclusion being inferred, the stronger the analogy • The more relevant the differences between analogue and target are to the conclusion being inferred, the weaker the analogy   Invitation to Critical Thinking Chapter 8

13. To Evaluate an Argument by Analogy • Identify the similarities between the analogue and the target • Determine whether this similarity is relevant to the conclusion • Determine whether there are significant relevant differences between the analogue and the target • Use these determinations to evaluate the strength of the argument inferred by analogy Invitation to Critical Thinking Chapter 8

14. Refutation by Analogy In refutations of arguments by comparison • The target is usually an argument (occasionally the thesis of an argument) • The goal is to discredit the target by showing that it is analogous to some other argument (or thesis) that is obviously weak or objectionable Invitation to Critical Thinking Chapter 8