ABSTRACT
The model is a mathematical system which represents the physical system as well as possible. There are good and bad models. How good the model is will be judged on the basis of how well it predicts the behaviour of the physical system. To simplify matters let mathematicians suppose that they can rid their minds of the doubts raised in them by the last section of Dr Pym's article about the nature of proof in mathematics, and let them agree that mathematics is a structure obtained by rigorous deduction from a consistent set of axioms. It will be convenient to use the term 'mathematical system' to mean a particular set of axioms together with the deductions that may be made from it. The trouble started, perhaps paradoxically, in one of the most productive periods of mathematical and logical innovation, the period from Pythagoras to Euclid.
