Gettier Problem and Circularity of Induction

Edmund L. Gettier - "Is Justified True Belief Knowledge?"

Introduction

  • Gettier challenges the traditional definition of knowledge as justified true belief.
  • The standard formulation:
    • S knows that P IFF (i) P is true, (ii) S believes that P, and (iii) S is justified in believing that P.
  • Examples of philosophers who held similar views:
    • Chisholm: S knows that P IFF (i) S accepts P, (ii) S has adequate evidence for P, and (iii) P is true.
    • Ayer: S knows that P IFF (i) P is true, (ii) S is sure that P is true, and (iii) S has the right to be sure that P is true.
  • Gettier argues that these conditions are not sufficient for knowledge.

Two Key Points

  1. Justification does not guarantee truth:
    • It is possible to be justified in believing a proposition that is false.
  2. Justification is preserved through deduction:
    • If S is justified in believing P, and P entails Q, and S deduces Q from P and accepts Q, then S is justified in believing Q.

Case I

  • Scenario: Smith and Jones have applied for a job.
  • Smith has strong evidence for the following conjunctive proposition (d):
    • (d) Jones is the man who will get the job, and Jones has ten coins in his pocket.
    • Smith's evidence: the company president's assurance and a coin count.
  • Proposition (d) entails:
    • (e) The man who will get the job has ten coins in his pocket.
  • Smith infers (e) from (d) and is justified in believing (e).
  • Unexpected twist: Smith, not Jones, gets the job; Smith also has ten coins in his pocket, unbeknownst to him.
  • Analysis:
    • (e) is true.
    • Smith believes that (e) is true.
    • Smith is justified in believing that (e) is true.
    • However, Smith does not know that (e) is true because his belief is based on false information (Jones getting the job).

Case II

  • Scenario: Smith has strong evidence for:
    • (f) Jones owns a Ford.
    • Smith's evidence: Jones's past car ownership and a recent ride in Jones's Ford.
  • Smith is ignorant of Brown's whereabouts.
  • Smith constructs three propositions:
    • (g) Either Jones owns a Ford, or Brown is in Boston.
    • (h) Either Jones owns a Ford, or Brown is in Barcelona.
    • (i) Either Jones owns a Ford, or Brown is in Brest-Litovsk.
  • Each proposition is entailed by (f).
  • Smith infers (g), (h), and (i) and is justified in believing them.
  • Unexpected twist:
    • Jones does not own a Ford (rented car).
    • Brown is, by coincidence, in Barcelona.
  • Analysis:
    • (h) is true.
    • Smith believes that (h) is true.
    • Smith is justified in believing that (h) is true.
    • However, Smith does not know that (h) is true because his belief is based on the false premise that Jones owns a Ford.

Conclusion

  • Gettier's examples demonstrate that justified true belief is not sufficient for knowledge.
  • Definitions (a), (b), and (c) are all flawed.

Peter Achinstein - "Circularity and Induction"

Circularity of Inductive Arguments
  • Achinstein discusses the circularity in arguments that attempt to support an inductive rule by citing its past success.
Inductive Rule (R)
  • R: To argue from "Most instances of As examined under a wide variety of conditions have been B" to "(probably) The next A to be encountered will be B".
Argument in Favor of R
  • (a): In most instances of the use of R in arguments with true premises examined in a wide variety of conditions, R has been successful.
  • Hence (probably): In the next instance to be encountered of use of R in an argument with a true premise, R will be successful.