HPS 2154

Theories of Confirmation

Fall 2024

A Little Survey of Induction

Definitions

Inductive inference is . . .

(Overwhelming Majority view)
. . . Ampliative inference	Evidence lends support to an hypothesis, while not establishing it with deductive certainty.
(Minority view, largely historical)
. . . Generalization	Inference from less general to the more general. May also be deductive. Example: "Perfect induction."
(Commonly among epistemologists)
. . . Habits of mind	Some expectation that done well habits match good logical relations.

Rules of Detachment?

YES	NO
Evidence. Hence, hypothesis.	Evidence confirms hypothesis.
"Induction" "Inductive inference"	"confirmation"

Three basic ideas

drive all accounts of inductive inference

Family	Inductive Generalization	Hypothetical Induction	Probabilistic Induction
Principle	An instance confirms the generalization.	Ability to entail the evidence is a mark of truth.	Degrees of belief governed by a calculus.
Archetype	Enumerative induction	Saving the phenomena in astronomy.	Probabilistic analysis of games of chance
Weakness	Limited reach of evidence	Indiscriminate confirmation	Applicable to non-stochastic systems?

Inductive generalization elaborated

Analogical inference	Agreement or source and target in some properties generalized to others.
Hempel's Satisfaction Criterion	Extend basic principle from simple syllogistic logic to first order predicate logic.
Mill's Methods	Generalize instances of necessary and sufficient conditions and interpret as causes.
Glymour's Bootstrap	Derive instance of hypothesis with assistance of any available theory.
Demonstrative Induction	Deduce hypothesis from evidence using auxiliary theory.

Hypothetical induction elaborated

	E confirms H if H (and auxiliaries) entail E AND…	Examples
Exclusionary accounts. Error statistics (Mayo)	. . . E most likely wouldn't be true, if H were false	Controlled studies.
Simplicity Akaike criterion, Bayes information criterion.	. . . H is the simplest.	Curve fitting.
Abduction: Inference to the best explanation (Pierce, Harman, Lipton)	. . . H is the best explanation.	Galactic red shift. Controlled studies of telepathy.
Inference to common cause (Salmon, Janssen)	. . . the common cause is the best explanation.	Perrin's arguments for atoms.
Reliabilism (Popper, Lakatos)	. . . H has been generated by a reliable method.	Any expert investigating.

Probabilistic induction elaborated

Full-blown Bayesianism	Interpretive agonies: Subjective, objective, logical? Justifications: Dutch book arguments, representation theorems, scoring rules. Limit theorems: Washing out of the priors.
Extended Bayesianism	Convex sets of probability distributions. Improper prior probabilities. Jeffrey's conditionalization.
Alternative Calculi	Shafer-Dempster theory. Possibility theory. Deductively definable logics of induction (Norton)

Properties and Tendencies

Family	Distance between evidence and hypothesis	Justification
Inductive Generalization ("bottom up")	Close. Invites logic of discovery.	Self evidence. Case studies.
Hypothetical Induction ("top down")	Distant. Leans towards under-determination.	Self evidence. Case studies.
Probabilistic Induction ("relational")		Elaborate and sophisticated.

The Material Theory of Induction

There are no universally applicable formal rules for inductive inference.
An inductive inference is warranted not by conformity with some universal schema but by a background fact.
There are no universal background facts. No factual principle of the uniformity of nature.
"All Induction is Local." Warranting facts differ in different domains.

Inductive inference	Warranting fact
Generalizations on properties of elements	Elements are generally uniform in the property generalized (e.g. metallic elements are generally solids at room temperatures.)
Darwin's analogical inference from domestic to natural selection	Domesticated pigeons and animals in the wild have naturally varying, heritable characteristics.
Error statistical accounts (severe testing)	Fact that assures "E most likely wouldn't be true, if H were false" such as randomization of subjects in controlled trial.
Inference to the simplest explanation, simplest to fit all elliptical orbit to a new comet.	Comets in bound (elliptical) orbits are more common.
Very probable that DNA match supports identity of suspect and perpetrator	Facts about distribution of DNA in population and that suspect is a random sample of the population
Prudence of probabilistic credences	You are placing bets with a Dutch bookie by specified rules for converting credences into actions.

Formal Problems Solved

Problem	Solution
Each formal theory of inductive inference works somewhere	For each rule, there is some domain in which it is warranted by background facts.
No formal theory works everywhere (hence proliferation)	There is no universal background fact warranting all inductive inferences.
Hume's problem of induction	The problem is formulated in terms of universal rules of inductive inference. There are none in the material theory.

Source: John D. Norton, "A Little Survey of Induction," in P. Achinstein, ed., Scientific Evidence: Philosophical Theories and Applications. Johns Hopkins University Press, 1905. pp. 9-34.