The No-False-Lemmas and Defeasibility Responses

These two early responses to the Gettier problem add a fourth condition to justified true belief: one demands that the believer's reasoning rest on no false assumption, the other that the justification not be defeated by some truth the believer has overlooked.

Definition

The no-false-lemmas response holds that a justified true belief is knowledge only if it is not inferred from any false premise; the defeasibility response holds that it is knowledge only if the justification is not defeated by any true proposition that, were it added to the believer's evidence, would undermine the justification.

Scope

This topic covers the no-false-lemmas (or no-false-grounds) proposal and the defeasibility analysis of knowledge. It examines how each blocks the standard Gettier cases, the counterexamples that each faces — Gettier cases not based on inference for the first, and the problem of misleading defeaters for the second — and refinements such as the distinction between genuine and misleading defeaters. Modal and reliabilist responses are treated in separate topics.

Core questions

• Can Gettier cases be blocked by ruling out reliance on false premises?
• Are there Gettier cases that involve no false lemma at all?
• What is a defeater, and when does an overlooked truth defeat justification?
• How can a defeasibility theory exclude merely misleading defeaters?

Key theories

No false lemmas

Knowledge is justified true belief whose justification does not essentially depend on any false belief; since Gettier's subjects infer their true conclusions from false premises, the condition excludes those cases.

Defeasibility analysis

Lehrer and Paxson require that the justification be undefeated — that there be no true proposition such that, if the believer were aware of it, the justification would be destroyed — capturing Gettier cases as ones with such a defeater.

History

Within a year of Gettier's paper, Clark proposed that knowledge requires fully grounded belief with no false grounds. Lehrer and Paxson's 1969 defeasibility analysis offered a more general diagnosis in terms of undefeated justification. Both proposals shaped the agenda, but each met counterexamples — non-inferential Gettier cases for the first, misleading defeaters for the second — that drove the search for further conditions.

Debates

Genuine versus misleading defeaters

Defeasibility theories must distinguish truths that genuinely undermine knowledge from misleading truths whose addition would mislead the believer; getting this distinction right without circularity or new counterexamples remains the central difficulty for the approach.

Key figures

• Michael Clark
• Keith Lehrer
• Thomas Paxson
• Peter Klein

Seminal works

• lehrerpaxson1969
• clark1963

Frequently asked questions

What is a false lemma?

A false lemma is a false premise on which a person's reasoning to a true conclusion depends. The no-false-lemmas response says that knowledge requires that no such false premise figure essentially in the justification, which excludes the inferential Gettier cases.

Why isn't the no-false-lemmas condition enough?

Because some Gettier cases involve no inference from a false premise at all — for instance perceptual cases like the fake-barn scenario — so a belief can be Gettiered while resting on no false lemma, showing the condition does not cover every case.