Keeping Globally Inconsistent Scientific Theories Locally Consistent
Most scientific theories are globally inconsistent. Chunk and Permeate is a method of rational reconstruction that can be used to separate, and identify, locally consistent chunks of reasoning or explanation. This then allows us to justify reasoning in a globally inconsistent theory. We extend chunk and permeate by adding a visually transparent way of guiding the individuation of chunks and deciding on what information permeates from one chunk to the next. The visual representation is in the form of bundle diagrams. We then extend the bundle diagrams to include not only reasoning in the presence of inconsistent information or reasoning in the logical sense of deriving a conclusion from premises, but more generally reasoning in the sense of trying to understand a phenomenon in science. This extends the use of the bundle diagrams in terms of the base space and the fibres. We then apply this to a case in physics, that of understanding binding energies in the nucleus of an atom using together inconsistent models: the liquid drop model and the shell model. We draw some philosophical conclusions concerning scientific reasoning, paraconsistent reasoning, the role of logic in science and the unity of science.
We are grateful to Diderik Batens, Koen Lefever, Elías Okón Gurvich, Paweł Pawłowski and Elisángela Ramírez-Cámara for the feedback offered throughout the development of this research. Special thanks are deserved to the anonymous referees for their comments and suggestions. The first author would like to acknowledge active support from the Vrije Universiteit Brussel and the Research Stays Program (PREI)-UNAM. The second author was supported by the PAPIIT Projects IA401117 “Philosophical Aspects of Contra-Classical Logics” and IA401717 “Pluralism and Normativity in Logic and Mathematics”.
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