follows: Alice sees a clock that reads two o'clock and believes that the time is two o'clock. It is, in fact, two o'clock. There's a problem, however: unknown to Alice, the clock she's looking at stopped twelve hours ago. Alice thus has an accidentally true, justified belief. Russell provides an answer of his own to the problem. Edmund Gettier's formulation of the problem was important as it coincided with the rise of the sort of philosophical naturalism promoted by W. V. O. Quine and others, and was used as a justification for a shift towards externalist theories of justification. John L. Pollock and Joseph Cruz have stated that the Gettier problem has "fundamentally altered the character of contemporary epistemology" and has become "a central problem of epistemology since it poses a clear barrier to analyzing knowledge". Alvin Plantinga rejects the historical analysis: Despite this, Plantinga does accept that some philosophers before Gettier have advanced a JTB account of knowledge, specifically C. I. Lewis and A. J. Ayer. Knowledge as justified true belief (JTB) The JTB account of knowledge is the claim that knowledge can be conceptually analyzed as justified true belief, which is to say that the meaning of sentences such as "Smith knows that it rained today" can be given with the following set of conditions, which are necessary and sufficient for knowledge to obtain: The JTB account was first credited to Plato, though Plato argued against this very account of knowledge in the Theaetetus (210a). This account of knowledge is what Gettier subjected to criticism. Gettier's two original counterexamples Gettier's paper used counterexamples (see also thought experiment) to argue that there are cases of beliefs that are both true and justified—therefore satisfying all three conditions for knowledge on the JTB account—but that do not appear to be genuine cases of knowledge. Therefore, Gettier argued, his counterexamples show that the JTB account of knowledge is false, and thus that a different conceptual analysis is needed to correctly track what we mean by "knowledge". Gettier's case is based on two counterexamples to the JTB analysis, both involving a fictional character named Smith. Each relies on two claims. Firstly, that justification is preserved by entailment, and secondly that this applies coherently to Smith's putative "belief". That is, that if Smith is justified in believing P, and Smith realizes that the truth of P entails the truth of Q, then Smith would