# The Gettier counter-example: How to formalize its crucial entailment?

The Gettier counter-example to the definition of knowledge employs the claim that d) entails e):

(d) Jones is the man who will get the job, and Jones has ten coins in his pocket.

(e) The man who will get the job has ten coins in his pocket.

See Gettier, Edmund: Is Justified True Belief Knowledge? Analysis, 23 (1966).

How does d) entail e) in a formalized language - probably using predicate calculus?

• Using = rules. If $/phi$ can be deducible and c is a constant in Phi, and c=b, then $\phi$' is also deducible where it is obtained from phi by replacing one or more c by b – Darae-Uri Nov 3 '15 at 2:30

Here is a formalization in quantifier calculus with identity:

Premise: GetJob(Jones) ∧ ∀x(GetJob(x) → x = Jones) ∧ HasCoins(Jones)

Conclusion: ∀x(GetJob(x) → HasCoins(x))

By universal instantiation assume GetJob(a), by the second conjunct in the premise a=Jones, by the last conjunct and substitutivity of identity HasCoins(a). Since a was arbitrary the conclusion follows by universal generalization.

This follows directly using the rule of existential generalization. If we assume our universe of discourse is men (this will save a little bit of space) then we could write the sentences as

WGJ(j) ∧ (∀y)(WGJ(y) → j=y) ∧ HTC(j)

(∃x)[ WGJ(x) ∧ (∀y)(WGJ(y) → x=y) ∧ HTC(x) ]


All one has to do is replace all instances of the name j with an existentially quantified variable x that does not already appear in the sentence.