Bryson Brown (Lethbridge) gives a talk at the Conference on Paraconsistent Reasoning in Science and Mathematics (11-13 June, 2014) titled "On the Preservation of Reliability". Abstract: …all models are wrong, but some are useful. (G E.P. Box and N. R. Draper, 1987). C.S. Peirce examined several broad methods for arriving at beliefs in “On the Fixation of Belief”; the central theme of his essay is the importance of having a method that leads to stable agreement amongst the members of a society. Peirce argues that the ‘scientific method meets this standard, generalizing Hobbes’ observation that Harvey’s hypothesis of the circulation of the blood is an important example of a once-controversial view that came to be accepted even by those who initially rejected it, and a demonstration of the special epistemic success of science, in contrast with other forms of inquiry. But stable agreements are sometimes overturned. The brilliant, wide-ranging successes of classical physics made the basic principles of Newton’s theory laws of nature in the eyes of physicists, philosophers and the educated public. Yet they have been superseded by new principles. This pattern of success followed by failure and replacement is the key premise of Laudan’s pessimistic induction argument against scientific realism. Yet we have confidence, often justified confidence, in many scientific inferences, including inferences that begin with models and theoretical principles known to be false. Though the equations used and descriptions of actual systems our models are applied to are false, the results of the calculations (even when only approximate) are considered reliable for many purposes, and with good reason. Thus models provided by orbital mechanics are used to place probes in desired orbits and even land on other planets, while atmospheric GCMs are used to estimate large-scale climate changes likely to occur given various scenarios for human GHG emissions. Neither the equations used nor the descriptions of the systems such models include are true; the results of the calculations (even assuming the calculations are exact) cannot reasonably be taken to be true, either. Yet we do rely on them, and with good reason. Many measurable physical quantities that models allow us to calculate values for turn out to be very close to the results of actual observations under a wide range of specifiable conditions. This paper develops a pragmatic view of theories, models and the inferences we use our models and theories to make. The preservation of reliability allows for the use of incompatible theories and principles in our inferences, along with contextually-determined levels of acceptable approximation, and conceptual shifts in how measurement results are interpreted in the light of the different principles relied on at different points. But it is also compatible with a modest scientific realism: the criteria by which we decide when a theory can be relied on generally include measurable parameters whose values, even though our understanding of them remains imperfect, reliably indicate when and to what extent a given theory is reliable and constitutes reliably settled science in a sense that Peirce might have found satisfying even without an accepted background theory in which we can explain both that reliability and its limits.