problem in first-order logic, but the introduction by Gettier of terms such as believes and knows moves the discussion into the field of epistemology. Here, the sound (true) arguments ascribed to Smith then need also to be valid (believed) and convincing (justified) if they are to issue in the real-world discussion about justified true belief. Responses to Gettier problems have fallen into three categories: Affirmations of the JTB account: This response affirms the JTB account of knowledge, but rejects Gettier cases. Typically, the proponent of this response rejects Gettier cases because, they say, Gettier cases involve insufficient levels of justification. Knowledge actually requires higher levels of justification than Gettier cases involve. Fourth condition responses: This response accepts the problem raised by Gettier cases, and affirms that JTB is necessary (but not sufficient) for knowledge. A proper account of knowledge, according to this type of view, will contain some fourth condition (JTB + ?). With the fourth condition in place, Gettier counterexamples (and other similar counterexamples) will not work, and we will have an adequate set of criteria that are both necessary and sufficient for knowledge. Justification replacement response: This response also accepts the problem raised by Gettier cases. However, instead of invoking a fourth condition, it seeks to replace Justification itself for some other third condition (?TB) (or remove it entirely) that will make counterexamples obsolete. One response, therefore, is that in none of the above cases was the belief justified because it is impossible to justify anything that is not true. Conversely, the fact that a proposition turns out to be untrue is proof that it was not sufficiently justified in the first place. Under this interpretation, the JTB definition of knowledge survives. This shifts the problem to a definition of justification, rather than knowledge. Another view is that justification and non-justification are not in binary opposition. Instead, justification is a matter of degree, with an idea being more or less justified. This account of justification is supported by mainstream philosophers such as Paul Boghossian and Stephen Hicks. In common sense usage, an idea can not only be more justified or less justified but it can also be partially justified (Smith's boss told him X) and partially unjustified (Smith's boss is a liar). Gettier's cases involve propositions that were true, believed, but which had weak justification. In case 1, the premise that the testimony of Smith's boss is "strong