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Multi-Case Analysis and Knowledge Conditions

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Gettier Cases and Formal AnalysisMargin for Error and Knowledge Conditions→→Defeasibility 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 Zero → The Number Zero → Counting to Five → Counting to 10 → Counting to 20 → Counting a Set of Objects Up to 20 → Cardinality: The Last Number Counted → Matching Numerals to Quantities → Subitizing Small Quantities → Addition Within 10 → Number Bonds to 10 → Addition Within 20 → Doubles and Near Doubles → Doubles Facts Within 10 → Near Doubles Facts Within 20 → Mental Math Strategies for Addition → Mental Math: Adding and Subtracting Tens → Addition Within 100 → Repeated Addition as Multiplication → Multiplication as Equal Groups → Multiplication: Arrays → Basic Multiplication Facts (0s, 1s, 2s, 5s, 10s) → Multiplication Facts Within 100 → Division as Equal Sharing → Division as Grouping (Measurement Division) → Division: Grouping (Repeated Subtraction) Model → Division: Fair Sharing Model → Division as Equal Sharing → Division as Grouping → Basic Division Facts → Division Facts Within 100 → Multiplication and Division Fact Families → Relationship Between Multiplication and Division → Division Facts as Inverse of Multiplication → Remainders and Quotients in Division → Division Word Problems → Multi-Step Word Problems → Solving Multi-Step Word Problems → Multiplication Word Problems → Division Word Problems → Introduction to Long Division → Factors and Multiples → Prime and Composite Numbers → Equivalent Fractions → Relating Fractions and Decimals → Decimal Place Value → Integers and the Number Line → Comparing and Ordering Integers → Absolute Value → Adding Integers → Subtracting Integers → Multiplying Integers → Introduction to Exponents → Order of Operations → Integer Order of Operations → Variable Expressions → The Distributive Property → Variables and Expressions Review → Introduction to Polynomials → Adding and Subtracting Polynomials → Multiplying Polynomials → Factorial → Permutations → Combinations → Counting Principles: Addition and Multiplication Rules → Introduction to Graph Theory → Propositional Logic Foundations → Logical Equivalences → Boolean Algebra → Introduction to Propositional Logic → Introduction to Predicate Logic (First-Order Logic) → First-Order Logic Syntax → Terms and Atomic Formulas in FOL → Variable Binding and Scope → Open and Closed Formulas in First-Order Logic → Variable Substitution and Capture-Avoidance in First-Order Logic → Quantifier Instantiation Rules in First-Order Proof Systems → Universal Quantification: Meaning and Scope → Free Variables and Bound Variables → Substitution and Instantiation in Predicate Logic → Terms and Atomic Formulas → Formulas and Well-Formed Expressions → Structures and Interpretations → Model Interpretation and Satisfaction → Interpretation, Truth, and Satisfaction of Formulas → Logical Consequence and Entailment → Soundness Theorem and Validity of Proof Systems → Deductive Reasoning and Formal Proof Systems → First-Order Resolution → Propositional Resolution → Semantic Tableaux (Propositional) → Semantic Tableaux (First-Order) → Decidable Fragments of First-Order Logic → Gödel's Completeness Theorem for First-Order Logic → Gödel's Incompleteness Theorems → Introduction to Intuitionistic Logic → Introduction to Modal Logic → A Priori and A Posteriori Knowledge → Rationalism vs. Empiricism → Foundationalism → Responses to External World Skepticism → Epistemic Contextualism → Contextualism and Knowledge Attributions → The Relevant Alternatives Theory → Contextualism as Indexicalism in Epistemology → Margin for Error and Knowledge Conditions → Multi-Case Analysis and Knowledge Conditions

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