Mathematics as Quasi-Matter to Build Models as Instruments

Mathematical models are instruments of investigation, epistemological equivalent to the microscope and the telescope. In comparing the epistemological difference between models and experiments, Morgan (2005) argues that experiments offer greater epistemic power than models as a means to investigate the world. This outcome rests on the distinction that whereas experiments are versions of the real world captured within an artificial laboratory environment, models are mathematical worlds built to represent the real world. This difference in ontology has epistemic consequences: experiments have greater potential to make strong inferences back to the world. This latter power is manifest in the possibility that whereas working with models may lead to ‘surprise’, experimental results may be unexplainable within existing theory and so ‘confound’ the experimenter. This paper will show that mathematical models are quasi-empirical objects, objects that are made of quasi-material mathematics, and so have potential to confound the modeller because of the indeterminateness of the mathematical matter. Mathematical matter is indeterminate in two different ways: 1) indeterminate with respect to ignorance: the possibility of having false or incomplete theories of the mathematical structures; 2) indeterminate with respect to potential independence: despite the structure may be determined, there is still a certain degree of freedom, of indeterminacy, for the patterns of behaviour of the mathematical objects