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Multi-Case Analysis and Knowledge Conditions

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Gettier Cases and Formal AnalysisMargin for Error and Knowledge ConditionsDefeasibility Conditions and Knowledge
knowledge formal-analysis methodology cases

Core Idea

Multi-case analysis systematically compares intuitions across related cases that differ in subtle ways to identify necessary and sufficient conditions for knowledge. By varying one feature at a time and noting how intuitions change, epistemologists create a formal landscape of knowledge conditions. This methodology has proven invaluable in responding to Gettier and in developing anti-luck accounts.

How It's Best Learned

Take a proposed knowledge condition and construct case pairs that test it: one where the condition holds and knowledge seems present, one where it doesn't and knowledge seems absent. Use this to refine the condition. This systematic approach builds intuitions about what knowledge fundamentally requires.

Common Misconceptions

Explainer

From your formal analysis of Gettier cases, you know how a single carefully constructed scenario can overturn a philosophical theory that had stood for millennia. The original Gettier cases were not just counterexamples — they were existence proofs that the three conditions of the JTB analysis (truth, belief, justification) are individually necessary but jointly insufficient. Once that was established, the question became: what further conditions are needed? Multi-case analysis is the systematic methodology for answering that question — not by finding one perfect case, but by building up a dense landscape of cases that collectively triangulate where the real conditions lie.

The core technique is controlled variation: you take a scenario and change exactly one feature, then ask whether your intuition about whether the agent knows changes. Suppose a proposed condition says "an agent knows P only if their belief is sensitive to P's truth" (roughly: if P were false, they would not believe P). You can test this by constructing pairs of cases — one where sensitivity holds and one where it does not — while keeping everything else identical. If knowledge tracks sensitivity in both directions (present when sensitivity holds, absent when it fails), that is evidence the condition is onto something. If you can construct a case where sensitivity holds but knowledge clearly doesn't (or vice versa), that tells you the condition is not quite right.

What makes this methodology powerful is accumulation. A single case can always be dismissed as an intuition pump, a misleading special case, or a confusion about the scenario's details. But when dozens of carefully varied cases all point in the same direction — when manipulation, justified falsehood, barn façade counties, and doxastic incontinence cases all exhibit the same pattern — the convergence is hard to ignore. The methodology treats philosophical intuitions about cases as data points: individually fallible, but collectively informative about the underlying structure of our concept of knowledge. This is why the post-Gettier literature produced such a proliferation of cases rather than simple arguments — cases are the medium of evidence in analytic epistemology.

The methodology also has important limits that disciplined practitioners keep in mind. Intuitions vary across individuals and cultures, so what seems obviously knowledge to one philosopher may not to another. A case designed to test one variable may inadvertently change others, making the result harder to interpret. And there is a deep question about whether our intuitions about artificial philosophers' cases track anything important about real knowledge, or merely track our folk-psychological reactions to stylized thought experiments. These limits do not abandon the method — they are reasons to practice it carefully, with multiple cases, explicit attention to what each case varies, and epistemic humility about what the pattern of intuitions establishes.

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Prerequisite Chain

Understanding ZeroThe Number ZeroCounting to FiveCounting to 10Counting to 20Counting a Set of Objects Up to 20Cardinality: The Last Number CountedMatching Numerals to QuantitiesSubitizing Small QuantitiesAddition Within 10Number Bonds to 10Addition Within 20Doubles and Near DoublesDoubles Facts Within 10Near Doubles Facts Within 20Mental Math Strategies for AdditionMental Math: Adding and Subtracting TensAddition Within 100Repeated Addition as MultiplicationMultiplication as Equal GroupsMultiplication: ArraysBasic Multiplication Facts (0s, 1s, 2s, 5s, 10s)Multiplication Facts Within 100Division as Equal SharingDivision as Grouping (Measurement Division)Division: Grouping (Repeated Subtraction) ModelDivision: Fair Sharing ModelDivision as Equal SharingDivision as GroupingBasic Division FactsDivision Facts Within 100Multiplication and Division Fact FamiliesRelationship Between Multiplication and DivisionDivision Facts as Inverse of MultiplicationRemainders and Quotients in DivisionDivision Word ProblemsMulti-Step Word ProblemsSolving Multi-Step Word ProblemsMultiplication Word ProblemsDivision Word ProblemsIntroduction to Long DivisionFactors and MultiplesPrime and Composite NumbersEquivalent FractionsRelating Fractions and DecimalsDecimal Place ValueIntegers and the Number LineComparing and Ordering IntegersAbsolute ValueAdding IntegersSubtracting IntegersMultiplying IntegersIntroduction to ExponentsOrder of OperationsInteger Order of OperationsVariable ExpressionsThe Distributive PropertyVariables and Expressions ReviewIntroduction to PolynomialsAdding and Subtracting PolynomialsMultiplying PolynomialsFactorialPermutationsCombinationsCounting Principles: Addition and Multiplication RulesIntroduction to Graph TheoryPropositional Logic FoundationsLogical EquivalencesBoolean AlgebraIntroduction to Propositional LogicIntroduction to Predicate Logic (First-Order Logic)First-Order Logic SyntaxTerms and Atomic Formulas in FOLVariable Binding and ScopeOpen and Closed Formulas in First-Order LogicVariable Substitution and Capture-Avoidance in First-Order LogicQuantifier Instantiation Rules in First-Order Proof SystemsUniversal Quantification: Meaning and ScopeFree Variables and Bound VariablesSubstitution and Instantiation in Predicate LogicTerms and Atomic FormulasFormulas and Well-Formed ExpressionsStructures and InterpretationsModel Interpretation and SatisfactionInterpretation, Truth, and Satisfaction of FormulasLogical Consequence and EntailmentSoundness Theorem and Validity of Proof SystemsDeductive Reasoning and Formal Proof SystemsFirst-Order ResolutionPropositional ResolutionSemantic Tableaux (Propositional)Semantic Tableaux (First-Order)Decidable Fragments of First-Order LogicGödel's Completeness Theorem for First-Order LogicGödel's Incompleteness TheoremsIntroduction to Intuitionistic LogicIntroduction to Modal LogicA Priori and A Posteriori KnowledgeRationalism vs. EmpiricismFoundationalismResponses to External World SkepticismEpistemic ContextualismContextualism and Knowledge AttributionsThe Relevant Alternatives TheoryContextualism as Indexicalism in EpistemologyMargin for Error and Knowledge ConditionsMulti-Case Analysis and Knowledge Conditions

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