18. The Basics of Inductive Reasoning

 

Summary

This video opens a new series on inductive reasoning and the scientific method. It reviews the difference between induction and deduction, surveys the main types of inductive arguments, and looks closely at analogy.

Induction versus Deduction

There are two kinds of logic: formal logic, which deals with deductive arguments, and informal logic, which deals with inductive arguments. The key distinction lies in how conclusions follow from premises. A deductive conclusion follows necessarily and with certainty; an inductive conclusion follows only with a degree of probability, never necessary truth. By definition, any argument that is not deductive is inductive, which includes abductive and ampliative reasoning.

Di Donato unpacks several common ways of describing the contrast:

• Induction often moves from the specific to the general (observations of falling bodies to the law of gravity); deduction from the general to the specific (all oaks come from acorns, so this oak did). These descriptions are useful but have exceptions.
• In induction, premises strengthen or weaken the argument; in deduction they provide absolute support.
• An inductive conclusion may contain new information not present in the premises; a deductive conclusion is wholly contained in its premises.
• If all premises of an inductive argument are true, the conclusion may still be false; in a valid deductive argument, true premises guarantee a true conclusion.
• Adding a premise can change the probability of an inductive conclusion but cannot affect a deductive one.
• Inductive strength rests on content (the matter); deductive strength rests on structure (the form).

He stresses that validity belongs only to formal logic: inductive arguments cannot be valid, so "deductively valid" is redundant. An argument is valid if and only if it is impossible for all premises to be true and the conclusion false, something that can never happen inductively. Inductive support therefore comes in degrees: weak, moderate, or strong, with deductive support sitting at the top as absolute.

Key Concepts of Inductive Arguments

An inductive argument applies what is known about familiar objects or situations to unknown ones. Three concepts are central:

• The property under investigation (P): the feature in question.
• The sample: a group already known or believed to possess P.
• The target (target class or population): the individual or group we are asking about.

Every inductive conclusion attributes the property P to the target.

Two Basic Categories

Inductive arguments fall into two families whose similarities outweigh their differences: analogical arguments and generalizations. Both begin with a sample, identify a property of its members, and conclude that something outside the sample shares that property; both are evaluated the same way. The difference lies in the target. In an analogical argument the target is a single item lying outside the sample (Tom is a clown like Dick and Harry, so Tom also wears big shoes and a red nose). In a generalization the target is a class, and the sample is part of that class (humans feel sleepy after big meals, so all animals do).

Five Types of Inductive Argument

1. Inductive analogy (specific to specific): direct comparison, e.g. animals bred in captivity compared with wild populations to infer that nature uses a selection process like breeders. Analogies are not strictly arguments but are used to build them.
2. Inductive generalization (specific to general): moving from instances to a universal conclusion (every Charlotte football fan I know is a Panthers fan, so probably all are). This needs a sampling frame, a precise definition of the population and attribute, and a representative sample.
3. Statistical syllogism (general to specific): falls short of deduction. Strength depends on the proportion in the opening statement (most lawyers are crooks; Joe is a lawyer; Joe is probably a crook). A 95% claim is far stronger than 40%. A universal premise ("all lawyers are crooks") would instead make a valid deductive argument.
4. General to general: works like an inductive analogy but reasons across populations rather than individuals.
5. Inference to the best explanation (abduction): weighs rival explanations to find the most probable. Finding the front door open, we rule out wind and forgetfulness and conclude the owner left it open. Abduction is a leap based on current background knowledge.

A Closer Look at Analogy

Analogy compares something familiar with something unfamiliar; analysis means identifying the two things and how they are similar. The rough form is: X and Y share attributes P, Q, R; X also has S; therefore Y probably has S. X and Y are the analogs. A contrary analog shares some attributes but lacks the attribute of interest S (the problematic extension), and it counts against the conclusion, as when a third Tesla engineer earns less than the others. With analogies we judge not absolute probability but relative strength, set by how similar the analogs are.

Di Donato recommends translating arguments into standard form (sample, target, known similarities, property S, conclusion) to make them easy to analyze, illustrating with examples about salaries and friends' disappointing motorcycles.

Six Rules for Evaluating Analogies

All boil down to one principle: the more similar the sample and target, the higher the probability the conclusion is true.

1. A larger sample gives a stronger argument.
2. A greater percentage of the sample having P strengthens it.
3. More relevant similarities strengthen it.
4. Fewer dissimilarities strengthen it.
5. Greater diversity in the sample helps when a target feature is uncertain.
6. A more guarded conclusion is easier to support (imagine premises as table legs holding up the conclusion).

Relative Strength

Evaluating analogies is somewhat subjective, depending on how relevant and similar the analogs seem. Rather than seeking absolute strength, ask what would make the argument stronger, or compare it with rival analogies. The Sumerian example (Italian and Spanish must be spoken to prove fluency, so Sumerian must be too) is judged weak: the sample is small, not diverse, and ignores that Sumerian is a dead language. The next video will turn to certainty and probability.