In 1959, mathematician Mark Kac introduced a model, called the Kac ring, in order to elucidate the classical solution of Boltzmann to the problem of macroscopic irreversibility. However, the model is far from being a realistic representation of something. How can it be of any help here? In philosophy of science, it is often argued that models can provide explanations of the phenomenon they are said to approximate, in virtue of the truth they contain, and in spite of the idealisations (...) they are made of. On this view, idealisations are not supposed to contribute to any explaining, and should not affect the global representational function of the model. But the Kac ring is a toy model that is only made of idealisations, and is still used trustworthily to understand the treatment of irreversible phenomena in statistical mechanics. In the paper, my aim is to argue that each idealisation ingeniously designed by the mathematician maintains the representational function of the Kac ring with the general properties of macroscopic irreversibility under scrutiny. Such an active role of idealisations in the representing has so far been overlooked and reflects the art of modelling. (shrink)

Empirical agreement is often used as an important criterion when assessing the validity of scientific models. However, it is by no means a sufficient criterion as a model can be so adjusted as to fit available data even though it is based on hypotheses whose plausibility is known to be questionable. Our aim in this paper is to investigate into the uses of empirical agreement within the process of model validation.

Engineering deals with different problem situations than science, and theories in engineering are different to theories in science. So, the growth of knowledge in engineering is also different to that in science. Nonetheless, methodological issues in engineering epistemology can be explored by adapting frameworks already established in the philosophy of science. In this paper I use critical rationalism and Popper’s three worlds framework to investigate error elimination and the growth of knowledge in engineering. I discuss engineering failure arising from the (...) falsification of engineering theories, and present taxonomies of the sources of falsification and responses to falsification in engineering. From this I discuss contexts of research and design in engineering, ad hoc rescue of engineering theories, and engineering assurance. (shrink)

The technological sciences have at least six defining characteristics that distinguish them from the other sciences. They have human-made rather than natural objects as their study objects, include the practice of engineering design, define their study objects in functional terms, evaluate these study objects with category-specified value statements, employ less far-reaching idealizations than the natural sciences, and do not need an exact mathematical solution when a sufficiently close approximation is available. In combination, the six characteristics are sufficient to show that (...) the technological sciences are neither branches nor applications of the natural sciences, but form a different group of sciences with specific characteristics of their own.Keywords: Technological sciences; Technology; Functional concepts; Idealization; Design. (shrink)

An early version of the work on mathematics as the science of structure that appeared later as An Aristotelian Realist Philosophy of Mathematics (2014).

Engineering is often said to be ‘scientific’, but the nature of knowledge in engineering is different to science. Engineering has a different ontological basis—its theories address different entities and are judged by different criteria. In this paper I use Popper’s three worlds ontological framework to propose a model of engineering theories, and provide an abstract logical view of engineering theories analogous to the deductive-nomological view of scientific theories. These models frame three key elements from definitions of engineering: requirements, designs of (...) artefacts, and theories for reasoning about how artefacts will meet requirements. In a subsequent paper I use this ontological basis to explore methodological issues in the growth of engineering knowledge from the perspective of critical rationalism. (shrink)

The Scientific Revolution spawned not just one methodology, but two. We have emphasized Bacon's inductivism at the expense of Galileo's more abstract, sophisticated method of successive approximation, and so have failed to appreciate Galileo's contribution to the ceteris paribus problem in philosophy of science. My purpose here is to help redress this imbalance. I first briefly review the old unsolved problems, and then point out the Baconian basis of ceteris paribus, as this clause is conventionally understood, and its history from (...) Aristotle to twentieth century Positivism. Then I explore Galileo's method of dealing with unwanted impediments, and the more general problem of 'accidents.' I trace his methodology back to Archimedes and forward through the economic theories of Adam Smith (18th century), J. S. Mill (19th) and Milton Friedman (20th). Finally, I point out ways in which I think Galileo's scientific method sheds light on, and provides a partial solution to, the ceteris paribus problem. (shrink)

It’s uncontroversial that notions of idealization and approximation are central to understanding computer simulations and their rationale. So, for example, one common form of computer simulation is to abandon a realistic approach that is computationally non-tractable for a more idealized but computationally tractable approach. Many simulations of systems of interacting members can be understood this way. In such simulations, realistic descriptions of individual members are replaced with less realistic descriptions which have the virtue of making interactions computationally tractable. Such simulations (...) can be supplemented with empirically determined correction factors which render the output produced by means of the idealizations more in accord, one hopes, with what the more realistic approach would have produced had it been computationally tractable. Another way to utilize computers is to replace an idealized but analytically tractable account of some phenomenon with a less idealized account which has no closed form or analytical solutions but where the computer can be used generate approximations to the desired solutions. (shrink)