HPS 2682       Theories of Confirmation        Fall 2010
Phil 2690

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."


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

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.

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.