In the classical account of knowledge, S knows that P if and only if S believes that P, S is justified in believing that P, and P is true (JTB).. In 1963, Gettier presented two problems that casted doubt on this account. Since then, numerous authors proposed modifications or clarifications of JTB, however, these efforts have not produced a satisfactory solution.
In this paper, the focus is on logical properties of justification. The Gettier problem Case II is expressed in sentential logic and Gettier Minimal Assumption (GMA) is introduced. It is shown that Gettier must have used GMA or some other assumption that entails GMA in his construction of Case II. Rejection of GMA solves Gettier problem Case II and it is a step towards a better understanding of the logical properties of justification and knowledge.
Due to Gettier problems, many authors assumed that “justified true belief” JTB is an inadequate account of knowledge. However instead of that, the Gettier problem Case II can be understood to be a counterexample that invalidates certain simplistic assumptions about the logical properties of justification. In the paper, several such assumptions are listed:
Gettier minimal assumption (GMA)
J(F) ⋀ ¬J(B) => J(F ⋁ B)
Extension of justification (EoJ)
J(F) => J(F ⋁ B)
Distribution of Justification (DoJ)
J(F) ⋁ J(B) => J(F ⋁ B)
Transmissibility of Evidence (ToE)
J(Q) ∧ (Q => R) => J(R)
Rejection of GMA and of assumptions that entail it (including EoJ, DoJ, ToE), solves Get-tier problem Case II without modification of JTB. This rejection of GMA leads towards a better understanding the nontrivial logical properties of justification and knowledge.