1
Compute what a run of observations licenses
Given a prior over hypotheses and a run of data, compute the exact probability of the next observation, and name the premise the prior supplies that no number of observations can.
Course · Philosophy
Science, Induction and Causation
Hume said the future cannot be deduced from the past; here is exactly what must be added, and what it costs. Weigh evidence by a Bayes factor, see what a theory forbids, find what a failed test refutes, search a table of cases for a cause, watch a pooled rate reverse, and test a cause by flipping it in a model.
BF = P(E | H) / P(E | ¬H) weight of E
P(E | H) = 0 and E seen: H is refuted
grue and green: same rows, BF = 1
a failed test refutes the whole set
pooled rates can reverse every group's
cause: flip C and E flips, others held
What this course is about
- Subject
- Philosophy
- Lessons
- 10
- Format
- Interactive
Overview
What you will be able to do
By the end you can take a claim about evidence or about a cause, put it in a form that can be computed, and say which assumption the answer rests on.
2
Measure the weight of evidence
Compute a Bayes factor, classify evidence as confirming, disconfirming or neutral, and explain why a surprising result weighs more than an expected one.
3
Locate what a failed prediction refutes
Write a prediction as a set of claims that cannot all be true, find its smallest inconsistent subset, and say why the observation refutes the set and not one member of it.
4
Search a case table for a cause
Apply the methods of agreement and difference to a table of cases, list every formula that fits, and say what the table cannot rule out.
5
Detect and explain a reversal
Compute rates within groups and pooled, decide whether they reverse, and name the variable that explains the reversal.
6
Test a cause by flipping it
Write a situation as Boolean equations, compute the actual values, and decide by recomputation whether a variable is a but-for cause, a cause once something is held fixed, or neither.
Lessons
10 lessons
Induction comes first because every later lesson needs its answer, confirmation comes second because it measures evidence, and causation comes last because it asks what evidence is evidence of.
Enumerative Induction and Hume's ProblemA run of sunrises is not a deduction of the next one, and what must be added is a prior.Not marked
Grue and the New RiddleTwo hypotheses can fit every observation and differ in the future, and the data cannot choose.Not marked
Confirmation and the Weight of EvidenceEvidence confirms a hypothesis when it raises its probability, and the Bayes factor measures how much.Not marked
Falsification and What a Theory ForbidsAn outcome a hypothesis forbids refutes it for good; no run of allowed outcomes proves it; and a hypothesis that predicts exactly what its rival predicts is never moved.Not marked
The Raven ParadoxA white shoe confirms that all ravens are black, by a factor so close to 1 that it barely counts.Not marked
The Duhem–Quine ProblemA failed prediction refutes the theory together with its auxiliaries, and logic cannot say which to give up.Not marked
Mill's Methods and the Common FactorThe factor present in every positive case and absent from every negative one is a candidate for the cause, and no more.Not marked
Correlation, Confounding and Simpson's ParadoxA treatment can do better in every group and worse overall, and the group variable explains why.Not marked
Counterfactual Causation and the But-For TestWrite a situation as equations, flip a variable, recompute, and see whether the effect flips with it.Not marked
Preemption, Overdetermination and Redundant CausesWhen a backup would have produced the effect anyway, the but-for test fails, and holding the backup fixed repairs it.Not marked
Recommended background
Knowledge and Evidence, which teaches credence and updating by Bayes' rule, and through it Arguments and Validity, whose truth tables and consistency test return here; nothing beyond fractions.
Practice suggestions
Read the first two lessons together. “Enumerative Induction and Hume's Problem” shows what a prior supplies, and “Grue and the New Riddle” shows that the supply cannot come from the data. The confirmation lessons then treat the prior as given and ask only what the evidence adds.
Change the prior and the likelihoods, not only the data. Almost every figure in the confirmation lessons is a ratio of two likelihoods, and the quickest way to see which one matters is to move it and watch the Bayes factor follow.
Expect the causal lessons to be exact rather than intuitive. The structural models are small Boolean equations written out in full, and a verdict such as “a cause once something is held fixed” is the result of a recomputation you can repeat by hand in a minute.
Keep Knowledge and Evidence to hand. “Updating on Evidence” is the one procedure used in every lesson of the first half, and nothing here re-derives it.
What it does not cover
Statistical inference. Significance tests, confidence intervals and regression estimate a quantity from data; nothing here is estimated. Simpson's paradox is computed from counts, and every update runs over a handful of hypotheses stated in full.
Continuous priors. The rule of succession appears as its five-point discretisation and says so. No densities, no integrals, and the lab will not tell you what the answer would be over a continuum.
Causal inference from data, including the do-calculus and the question of when a cause is identifiable. The structural models here are Boolean and given; the labs do not learn them.
The history and sociology of science. Paradigms, revolutions and the question of how scientists actually choose between theories are real subjects, but they are not of a shape a lab can compute without misrepresenting them. The Duhem–Quine lesson takes one episode as an example of the logic and says no more about the history.