According to the members of the Wiener Kreis, there was a strong connection between logic, reasoning, and rationality. They believed that human reasoning (and in particular scientific reasoning) is rational in so far as it is based on logic (which meant for them Classical Logic). It was also believed that scientific reasoning (for them the hallmark of human reasoning) was in general rational. In the second half of the twentieth century, both beliefs came under attack. One of the motors for this change was the turn in history of science, that was initiated by Alexandre Koyré. In the ‘old history of science’ success stories were told, usually on the basis of published papers and even textbooks, and only theories were considered that had survived (Galileo’s law of free fall, Kepler’s three laws, Newton’s gravitation theory, . . . ). Moreover, no attention was paid to mistaken paths, nor to the contexts in which the original theories were formulated and accepted. So, what happened was that nice and polished reconstructions were made, with Classical Logic as the underlying logic, and that the results were deemed to be rational. In the ‘new history of science’, things changed radically. Theories were studied in their historical setting, and explicit attention was directed not only to theories that were abandoned (such as the phlogiston theory), but also to flaws, and to elements that played a crucial role in the construction of new theories, but that are today considered as non-rational—examples are Kepler’s work on astrology and on the harmony of the spheres, and Newton’s work on alchemy. In the aftermath of Koyré, also philosophers of science, such as Hanson and Kuhn, followed this new trend and started basing their philosophical analysis on actual examples from the history of science. Two central lessons came out of all this. First, the so-called ‘context of justification’, which was the sole concern of the members of the Wiener Kreis, is less straightforward and less ‘logical’ than was traditionally accepted. Next, the ‘context of discovery’ is much more structured and methodical than was believed within the Wiener Kreis, even though it is not understandable from the point of view of Classical Logic. The conclusion was that logic is inadequate to explicate actual examples of human reasoning, whether in the sciences or in everyday life. There were several reactions to this situation. Some scholars held on to the link between (classical) logic and rationality, but concluded that scientific reasoning (especially as it occurs in the context of discovery) is inherently nonrational or even irrational. Others gave up the connection between logic and rationality. They looked for tools elsewhere (mainly in psychology and cognitive science) to analyse the rational character of scientific reasoning, often at the expense of rigour and formal accuracy. Times have changed, however. Today, a multiplicity of formal frameworks (ranging from non-classical logics over probability theory to Bayesian networks) is available in addition to Classical Logic. Also, historians and philosophers of science as well as psychologists have described a rich variety of patterns in both scientific and common sense reasoning. The aim of LRR10 is to stimulate the use of formal frameworks to explicate concrete examples of human reasoning, and conversely, to challenge scholars in formal studies by presenting them with interesting new examples of actual reasoning. Therefore, we welcome papers in all areas related to non-classical logics and non-classical formal frameworks. We also welcome case studies from history and philosophy of science, as well as from psychology, that enhance our apprehension of concrete reasoning patterns that occur in the sciences and in everyday life. Finally, we welcome contributions that deal with the philosophical and methodological implications of the present-day insights for our understanding of the notions of reasoning and rationality.