cannot be refuted, and after 1963, that fellow mathematician Paul Cohen revealed, through the method of forcing, that the continuum hypothesis cannot be proved either. In spite of the undecidability, both Gödel and Cohen suspected the continuum hypothesis to be false. This sense of suspicion, in conjunction with a firm belief in the consistency of ZFC, is in line with mathematical fallibilism. Mathematical fallibilists suppose that new axioms, for example the axiom of projective determinacy, might improve ZFC, but that these axioms will not allow for dependence of the continuum hypothesis. The second type of undecidability is used in relation to computability theory (or recursion theory) and applies not solely to statements but specifically to decision problems; mathematical questions of decidability. An undecidable problem is a type of computational problem in which there are countably infinite sets of questions, each requiring an effective method to determine whether an output is either "yes or no" (or whether a statement is either "true or false"), but where there cannot be any computer program or Turing machine that will always provide the correct answer. Any program would occasionally give a wrong answer or run forever without giving any answer. Famous examples of undecidable problems are the halting problem and the Entscheidungsproblem. Conventionally, an undecidable problem is derived from a recursive set, formulated in undecidable language, and measured by the Turing degree. Undecidability, with respect to computer science and mathematical logic, is also called unsolvability or non-computability. In essence, all problems stay intrinsically undecidable even when they appear to have been solved – take for example the solution to the continuum hypothesis itself. In the end, both types of undecidability can help to build a case for fallibilism, by providing these fundamental thought-experiments. Philosophical skepticism Fallibilism improves upon the ideas associated with philosophical skepticism. According to philosophy professor Richard Feldman, nearly all versions of ancient and modern skepticism depend on the mistaken assumption that justification, and thus knowledge, requires conclusive evidence or certainty. An exception can be made for mitigated skepticism. In philosophical parlance, mitigated skepticism is an attitude which supports doubt in knowledge. This attitude is conserved in philosophical endeavors like scientific skepticism (or rational skepticism) and David Hume's inductive skepticism (or inductive fallibilism). Scientific skepticism questions the veracity of claims lacking empirical evidence, while inductive skepticism avers that inductive inference in forming predictions and generalizations cannot be conclusively justified or proven. Mitigated