| HPS 2682 | Theories of Confirmation | Spring 2021 |
| (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. |
| YES | NO |
| Evidence. Hence, hypothesis. |
Evidence confirms hypothesis. |
| "Induction" "Inductive inference" | "confirmation" |
| 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? |
| 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. |
|
E confirms H |
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. |
| 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) |
| 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.