Reasoning at the frontier of knowledge: Introductory essay -- Why should the logic of discovery be revived? A reappraisal -- Are Heuristics Knowledge-Enhancing?Abduction, Models, and Fictions in Science -- Heuristic Appraisal at the Frontier of Research -- Why do Scientific Revolutions begin? -- Withstanding Tensions: Scientific Disagreement and Epistemic Tolerance -- Heuristics as Methods:  Validity, Reliability and Velocity -- Dynamic generation of hypotheses: Mandelbrot, Soros and Far-From-Equilibrium.