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In this article I develop a model of theoretical understanding in science. This is a philosophical theory that specifies the conditions that are both necessary and sufficient for a scientist to satisfy the construction ‘S understands theory T ’. I first consider how this construction is preferable to others, then build a model of the requisite conditions on the basis of examples from elementary physics. I then show how this model of theoretical understanding can be made philosophically robust and provide a more sophisticated account than we see from models of a similar kind developed by those working in the psychology of physics and artificial intelligence. 1. Introduction2. The Explicandum/Analysandum3. Analysis of ‘S understands T’4. The Inferential Model 4.1. Which problems are we talking about?4.2. Does the solution have to be true?4.3. Does each cycle have to be correct for S to understand T?4.4. What is problem-solving reliability?4.5. Does every specific inference of a cycle have to be correct?4.6. Does each inference have to use a principle that is part of the theory?5. Theoretical Understanding and Conceptual Expertise: Empirical Considerations6. Conclusion: Inferential Model of Scientific Understanding and Our Traditional Problems
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