invitation to critical thinking chapter 8 lecture notes chapter 8

Invitation to Critical Thinking Chapter 8

Lecture Notes

Chapter 8


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


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


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.


• 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


Statistical GeneralizationsA variation 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


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


Reasoning with AnalogiesAnalogies 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


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


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


• 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


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


To Evaluate an Argument by Analogy

1. Identify the similarities between the analogue and the target

2. Determine whether this similarity is relevant to the conclusion

3. Determine whether there are significant relevant differences between the analogue and the target

4. Use these determinations to evaluate the strength of the argument inferred by analogy


Refutation by AnalogyIn 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 lecture notes chapter 8

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