Chapter 10- Induction

Inductive reasoning

Reasoning whose premises support a probable conclusion without guaranteeing it, even when the premises are true.

Deductive reasoning

Reasoning in which a valid argument guarantees a true conclusion if all its premises are true.

Inductive strength

The degree of support that an inductive argument’s evidence provides for its conclusion.

Inductive generalization

Using observations of a sample to draw a probable conclusion about a whole population.

Population

The entire group an investigation aims to draw conclusions about.

Sample

The portion of a population actually observed or examined.

Sampling

Examining part of a population to draw conclusions about the whole population.

Representative sample

A sample that reflects the relevant characteristics of its population.

Biased sample

A sample that misrepresents its population in ways that could affect the conclusion.

Sample size

The number of cases or members examined in a sample.

Homogeneous population

A population whose members are similar in relevant characteristics.

Assessing an inductive generalization

Check whether the sample is representative and large enough.

Statistical syllogism

Using a population statistic to estimate the probability that a characteristic applies to an individual member.

Inductive generalization versus statistical syllogism

Generalization moves from sample to population; statistical syllogism moves from population statistics to an individual.

Assessing a statistical syllogism

Check whether additional relevant information about the individual has been overlooked.

Criterion of adequacy

The requirement that premises provide enough support for the conclusion.

Criterion of relevance

The requirement that premises bear on whether the conclusion is true.

Hypothesis

A statement or principle that would explain an event or situation if true.

Observation statement

An empirical prediction stating what should be observed under specified conditions.

Induction by confirmation

Supporting a hypothesis by observing that predictions derived from it are true.

Form of induction by confirmation

If h, then o. o is observed. Therefore, h is probably true.

Confirming instance

An observation that matches a prediction derived from a hypothesis.

Disconfirming instance

An observation showing that a prediction required by a hypothesis is false.

Confirmation versus disconfirmation

Confirmation adds probable support; a genuine disconfirmation of a required prediction can refute the hypothesis.

Assessing induction by confirmation

Check the number and variety of confirming instances and look for disconfirming instances.

Negative result

A test result that fails to match a hypothesis’s prediction.

Hypothesis revision

Changing a hypothesis to address evidence; the revised version is technically a different hypothesis.

Affirming the consequent

The invalid deductive form: If h, then o. o. Therefore, h.

Denying the consequent or modus tollens

The valid deductive form: If h, then o. Not-o. Therefore, not-h.

Analogical reasoning

Using relevant similarities between cases to support a probable conclusion about a further similarity.

Analogy

A comparison between objects, situations, or relationships.

Analogue case

The familiar case used as evidence in an analogical argument.

Subject case

The case about which an analogical argument draws its conclusion.

Target feature

The particular characteristic or relationship inferred about the subject case.

Property

A characteristic of a thing considered on its own, such as colour or size.

Relation

A connection between two or more things, including parts of one object.

Analogical argument by properties

Inferring that cases sharing some properties probably share another property.

Form of analogy by properties

x has A, B, and C. y has A and B. Therefore, y probably has C.

Analogical argument by relations

Inferring that a relationship found in one case probably also occurs in a comparable case.

Relevant similarity

A shared feature that matters to the target feature or conclusion.

Relevant dissimilarity

A difference that matters to the target feature or conclusion.

Strong analogy

A comparison whose relevant similarities provide substantial support despite its relevant differences.

Weak analogy

A comparison whose relevant differences or lack of relevant similarities leave the conclusion poorly supported.

Assessing an analogical argument

Identify the target feature and weigh relevant similarities against relevant differences.

Three uses of analogy

Clarifying an idea, suggesting a hypothesis, and providing probable support for a conclusion.