The Doomsday Argument, Self-Sampling Assumption, and Self-Indication Assumption are wrong; J. Richard Gott III's delta t argument underestimates longevity, providing lower bounds on probabilities of longevity, and is equivalent to Laplace's Rule of Succession; but Non-Parametric Predictive Inference based on the work of Bruce M. Hill and Frank P.A. Coolen is consistent with a plausible theory of induction; and Ayn Rand's identification of characteristics as ranges of measurement establishes a philosophical foundation for such a theory of induction.This monograph is a much-revised and much-expanded version of the author's article, "Past Longevity as Evidence for the Future," published in Philosophy of Science (January 2009), often recognized as the leading peer-reviewed journal in its field. Since its publication, that article has been cited favorably in these top-ranked philosophical journals: Journal of Philosophy, Analysis, Synthese, and Ratio.