How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism. But several difficulties arise when one tries to naturalize (...) in this way the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method. This paper suggests that, in order to naturalize mathematics through Darwinism, it is better to take the method of mathematics not to be the axiomatic method. (shrink)

Amalgamating evidence from heterogeneous sources and across levels of inquiry is becoming increasingly important in many pure and applied sciences. This special issue provides a forum for researchers from diverse scientific and philosophical perspectives to discuss evidence amalgamation, its methodologies, its history, its pitfalls, and its potential. We situate the contributions therein within six themes from the broad literature on this subject: the variety-of-evidence thesis, the philosophy of meta-analysis, the role of robustness/sensitivity analysis for evidence amalgamation, its bearing on questions (...) of extrapolation and external validity of experiments, its connection with theory development, and its interface with causal inference, especially regarding causal theories of cancer. (shrink)

I argue that philosophical issues concerning reductive explanations help constrain the construction of quantum theories with appropriate state spaces. I illustrate this general proposal with two examples of restricting attention to physical states in quantum theories: regular states and symmetry-invariant states. 1Introduction2Background2.1 Physical states2.2 Reductive explanations3The Proposed ‘Correspondence Principle’4Example: Regularity5Example: Symmetry-Invariance6Conclusion: Heuristics and Discovery.

In current philosophical discussions on evidence in the medical sciences, epidemiology has been used to exemplify a specific version of evidential pluralism. According to this view, known as the Russo–Williamson Thesis, evidence of both difference-making and mechanisms is produced to make causal claims in the health sciences. In this paper, I present an analysis of data and evidence in epidemiological practice, with a special focus on research on the exposome, and I cast doubt on the extent to which evidential pluralism (...) holds in this case. I start by focusing on the claim that molecular data allows for the production of mechanistic evidence. On the basis of a close look at the ways in which molecular data is used in exposome research, I caution against interpretations in terms of mechanistic evidence. Secondly, I expand my critical remarks on the thesis by addressing the conditions under which data is categorised as evidence in exposome research. I argue that these show that the classification of a dataset as a type of evidence is dependent on the ways in which the data is used. This is in contrast with the approach of evidential pluralism, where evidence is classified in different types on the basis of its intrinsic properties. Finally, I come back to what I consider the core of the thesis and suggest that the epidemiological research analysed in the paper indicates different interpretations of evidential pluralism and its applicability in the health sciences. (shrink)