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The Sensitivity Condition and Tracking Truth

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Core Idea

The sensitivity requirement states that if the proposition known were false, the believer would not believe it—the belief appropriately tracks the truth. Unlike safety, which asks about false beliefs one could have made, sensitivity focuses on whether one's actual belief would vary with the truth-value of the proposition. Together with safety, sensitivity attempts to capture when true justified belief constitutes genuine knowledge rather than lucky guessing.

How It's Best Learned

Practice checking whether a belief would vanish if the proposition were false. Apply to perceptual knowledge, testimony, and inference. Note cases where sensitivity fails even with true justified belief (like normal logical deduction).

Common Misconceptions

Explainer

You already understand Gettier cases: situations where you have justified true belief but intuitively lack knowledge, because your belief is true "by accident." Various responses have attempted to add conditions that rule out such accidents. The sensitivity condition, developed most influentially by Robert Nozick, approaches this by asking a counterfactual question: would you still believe it if it were false?

The formulation uses a subjunctive conditional: S's belief that P is *sensitive* if and only if, were P false, S would not believe P. This tests whether your belief tracks the truth — whether your belief-forming mechanism is genuinely responsive to how things actually are. Consider a simple case: you see your cat on the mat and believe the cat is there. If the cat were not on the mat, you would look, see no cat, and not believe it. Your belief tracks the truth. Now contrast a Gettier-style case: you correctly believe it is 3:00 PM because you glance at a stopped clock that happens to read 3:00. If it were not 3:00 PM, the clock would still read 3:00, and you would still believe it is 3:00 PM. Your belief does not track the truth — it fails the sensitivity condition.

Your background in modal logic is directly relevant here. The sensitivity condition checks what happens in the closest possible world where P is false — the scenario minimally different from ours where the proposition doesn't hold. This is fundamentally different from asking about reliability across many actual cases (a statistical question). Sensitivity is a modal claim: it asks about what you *would* believe in a nearby counterfactual scenario. A belief can be statistically reliable and yet insensitive — if, for example, you're right 95% of the time but the 5% of errors are clustered in exactly the worlds closest to the actual one.

The sensitivity condition runs into a well-known problem with logical and mathematical knowledge. Consider your belief that 2 + 2 = 4. Were 2 + 2 not to equal 4 — which is arguably incoherent, since mathematical truths hold necessarily — what would you believe? Because there is no coherent closest world where the proposition is false, the sensitivity test becomes inapplicable. This suggests sensitivity works well for empirical knowledge (perceptual beliefs, contingent testimony) but struggles with necessary truths. That limitation motivates comparing sensitivity with alternative tracking conditions: safety (your belief couldn't easily have been false — a subtly different modal claim) and proper function (your belief-forming faculties are working as they were designed to). Together, these conditions map out the space of what it might mean for a true belief to be non-accidentally connected to the facts it represents.

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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 → The Sensitivity Condition and Tracking Truth

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