Questions: The Sensitivity Condition and Tracking Truth

Question 1

You believe it is 3:00 PM because you glanced at a clock that happens to be stopped at 3:00. The time really is 3:00 PM. Is your belief sensitive?

• A. Yes — the belief is true and the clock gave the right answer, so it tracks the truth
• B. No — if it were not 3:00 PM, the stopped clock would still read 3:00, and you would still believe it is 3:00 PM
• C. Yes — sensitivity only requires that your belief-forming method is reliable over time
• D. No — because you have no independent justification for trusting the clock

Answer: (B)

The sensitivity test asks: if P were false, would you still believe P? If it were not 3:00 PM, the stopped clock would still display 3:00, and you would still form the belief that it is 3:00 PM. Your belief does not track the truth — it would not vary with reality. This is the classic Gettier-adjacent case that the sensitivity condition is designed to capture. Option A confuses being accidentally right (which happened) with tracking the truth (which requires counterfactual covariance). Option C conflates sensitivity (a modal/subjunctive condition) with reliability (a statistical condition).

Question 2

What distinguishes sensitivity from reliability as conditions on knowledge?

• A. Sensitivity requires true belief; reliability does not
• B. Sensitivity asks about what you would believe in the closest possible world where P is false; reliability asks how often your belief-forming method produces true beliefs across many cases
• C. Sensitivity is a necessary condition for knowledge; reliability is only sufficient
• D. Sensitivity applies to perceptual beliefs; reliability applies to testimonial beliefs

Answer: (B)

Sensitivity is a modal/counterfactual condition: it concerns a specific nearby possible world — the closest world where P is false — and asks whether you would believe P there. Reliability is a statistical claim about the track record of a belief-forming method across many actual or possible cases. A belief-forming method can be statistically reliable (right 95% of the time) yet insensitive if the 5% of errors are concentrated in the worlds closest to the actual one — that is, the belief fails precisely when it is most at risk of failing. These are orthogonal properties.

Question 3

A belief can be statistically reliable — produced by a method that is correct 95% of the time — and yet fail the sensitivity condition.

• T. True
• F. False

Answer: True

Sensitivity is not about frequency of success but about whether your belief would covary with reality in the nearest possible world where reality is different. A stopped clock that happens to be right twice a day is reliable in a trivial sense (it is right twice daily) but completely insensitive (it would display the same time even if the time were different). More seriously: a clairvoyant who is usually right might still form beliefs that would not change if the facts changed, failing sensitivity despite high reliability. The two conditions measure different things.

Question 4

The sensitivity condition applies straightforwardly to mathematical knowledge, such as the belief that 2 + 2 = 4.

• T. True
• F. False

Answer: False

Mathematical truths are necessarily true — there is no coherent possible world in which 2 + 2 ≠ 4. The sensitivity condition asks: 'If P were false, would you still believe P?' But if P is necessarily true, there is no 'closest world where P is false' to evaluate. The counterfactual has a necessarily false antecedent, making it vacuously true or inapplicable. This is a well-known limitation of the sensitivity condition: it works naturally for contingent empirical knowledge but struggles with necessary truths, motivating alternative conditions like safety that handle this case more gracefully.

Question 5

Explain why the stopped-clock belief fails the sensitivity condition, using the counterfactual formulation. What does this show about the relationship between accidental truth and genuine knowledge?

Model answer: The sensitivity condition requires: if P were false, S would not believe P. For the stopped-clock belief: if it were not 3:00 PM, the clock would still show 3:00, and the believer would still form the belief that it is 3:00 PM. The belief would not vary with the facts — it is decoupled from reality. This shows that being accidentally right (true belief by coincidence) is insufficient for knowledge: genuine knowledge requires the belief to track the truth, i.e., to be counterfactually responsive to whether P is actually true. The sensitivity condition captures this 'tracking' requirement.

This is precisely the kind of case Nozick's sensitivity condition was designed to exclude. Gettier cases generally involve beliefs that are true 'by accident' — where the justification and the truth are accidentally aligned. Sensitivity gives a precise modal criterion for what it means to be non-accidentally true: your belief-forming mechanism must be sensitive to the fact in question, so that if the fact changed, your belief would change with it.