1
Test a definition against cases
Write the conditions of an analysis of knowledge, record a verdict for each case, and find the row where the definition and the verdict part company — and say whether the definition is too broad or too narrow there.
Course · Philosophy
Knowledge and Evidence
What it takes to know something, and what it takes to believe it to a degree. A definition of knowledge is tried against cases until one row disagrees; skepticism and the regress are written as arguments and sets of claims; and credence is computed with exact fractions, from a Dutch book to a posterior.
a definition: tested by cases, row by row
credence: the price of a bet that pays 1
P(H | E) = P(E | H)·P(H) / P(E)
independent witnesses: Bayes factors multiply
belief at a threshold is not closed under ∧
What this course is about
- Subject
- Philosophy
- Lessons
- 12
- Format
- Interactive
Overview
What you will be able to do
By the end you can test a theory of knowledge against a table of cases, and you can compute with degrees of belief instead of arguing about them.
2
Formalise a skeptical argument and its reply
Write the brain-in-a-vat argument and Moore’s answer as two valid arguments over one conditional, and say what choosing between them requires that validity cannot give.
3
Locate the exits from the regress
Write Agrippa’s trilemma as a set of claims that cannot all be true, and name the position that each single deletion yields.
4
Check credences for coherence
Assign degrees of belief to the events of a small outcome space, test them against the rules of probability, and construct the bets that lose for certain when the rules are broken.
5
Compute what evidence does
Work out a posterior from a prior and likelihoods, read the Bayes factor as the weight of the evidence, and combine independent witnesses by multiplying their factors.
6
Explain why belief and credence come apart
Show with the lottery and the preface that accepting every claim above a threshold does not leave a set of acceptances whose conjunction is likely.
Lessons
12 lessons
Knowledge is analysed first, then justification is put under pressure, then belief is measured, and last the measure is turned on statistics and on the two paradoxes where it fails to match belief.
Belief, Truth and JustificationKnowledge as three conditions, and a definition tested against cases until one row disagrees.Not marked
Gettier Cases and the Fourth ConditionA case with justification, truth and belief that is not knowledge, and a repair that the next case breaks.Not marked
Reliabilism and the ClairvoyantJustification as a reliable process, tested against Norman the clairvoyant and the brain in a vat.Not marked
Skepticism and the Closure ArgumentThe brain-in-a-vat argument as modus tollens, Moore’s reply as modus ponens, and what validity cannot choose.Not marked
The Regress of JustificationAgrippa’s trilemma as six claims that cannot all be true, and the position each deletion yields.Not marked
Credence and the Dutch BookDegrees of belief as prices of bets, and the sure loss that incoherent prices allow.Not marked
Conditional Credence and Base RatesWhy a test that is right 99 times in 100 can leave most of its positives false.Not marked
Updating on EvidenceA prior, the likelihood of what was seen, and the Bayes factor that measures the weight of the evidence.Not marked
Testimony and Independent WitnessesWhat a witness of stated reliability does to a prior, and why independent witnesses multiply.Not marked
Reference Classes and Statistical EvidenceWhy the probability for an individual depends on the group the individual is placed in.Not marked
The Lottery ParadoxA belief threshold that accepts every ticket’s losing, and a lottery with a winner.Not marked
The Preface ParadoxA hundred well-supported claims that could all be true, and probably are not.Not marked
Recommended background
Arguments and Validity, which supplies validity, the counterexample row and consistency; no probability is assumed.
Practice suggestions
Work forward, and keep the tables. “Belief, Truth and Justification” sets the method that “Gettier Cases and the Fourth Condition” and “Reliabilism and the Clairvoyant” reuse: a definition, a column of verdicts, and the first row where they differ. The verdicts are yours. The lab checks that the definition agrees with them, not that they are right.
Treat each valid argument as a map of choices rather than a result. “Skepticism and the Closure Argument” and “The Regress of Justification” have labs that say an argument is valid or a set inconsistent, and then stop. Which premise to give up is the question the lesson leaves open on purpose.
Do the credence arithmetic by hand once before the lab does it. “Credence and the Dutch Book”, “Conditional Credence and Base Rates” and “Updating on Evidence” each have a worked example small enough to finish on paper, and a result you will not believe until you have. Every number here is an exact fraction; nothing is rounded unless the lesson says so.
Read the last three lessons as a single argument. “Reference Classes and Statistical Evidence”, “The Lottery Paradox” and “The Preface Paradox” turn the credence tools on belief itself, and both paradoxes end by asking which of two reasonable principles to give up.
What it does not cover
The history of epistemology as history. Descartes, Hume and Gettier appear as arguments and cases to be tested, not as names with dates; who said what first is not something a lab can compute.
Every theory of knowledge. Contextualism, virtue epistemology, knowledge-first epistemology and safety and sensitivity conditions are named at most in passing. The course teaches the method of cases on the tripartite analysis, its repair and one rival, and the method carries over.
Formal epistemology beyond coherence. Imprecise credences, accuracy arguments and the logic of knowledge and announcement are not built. Credence here is a number on a finite outcome space.
Statistics as inference. Significance tests, confidence intervals and regression estimate things from data; this course only updates exact priors on exact likelihoods over a few hypotheses, with no densities and no integrals.