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"Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascod, so pages of formulae will not get a definite result out of loose date" (Thomas Huxley (1869) Geological Reform, Presidential Address to the Geological Society). Reasoning in science is a rich and complex phenomenon. On one hand, we find detailed, sophisticated and rigorous calculations. But on the other, we encounter a multiplicity of models and approximations whose status has been the subject of extensive debate (See [6] How the Laws of Physics Lie (Oxford, New York, Oxford University Press) and [7] The Dappled World (Cambridge, Cambridge University Press)). Detailed and demanding calculations give the appearance of mathematical rigour, and from a practical perspective, inferences and calculations based on successful models have proven to be reliable guides to our world, predicting the results of many measurements and suggesting interventions in the world that produce startling and impressive novel phenomena ranging from laser light to transistors to monoclonal antibodies and new types of sub-atomic particles. But the logical incompatibility of different models, each making different assumptions and approximations, together with the application of distinct, conflicting models in the course of deriving important results, raise serious questions about the nature and status of the both the premises and the conclusions of scientific reasoning.

DOI: 10.1007/978-3-319-40220-8_4

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