Mathematical formalisms in scientific practice: From denotation to model-based representation

The present paper argues that ‘mature mathematical formalisms’ play a central role in achieving representation via scientific models. A close discussion of two contemporary accounts of how mathematical models apply—the DDI account (according to which representation depends on the successful interplay of denotation, demonstration and interpretation) and the ‘matching model’ account—reveals shortcomings of each, which, it is argued, suggests that scientific representation may be ineliminably heterogeneous in character. In order to achieve a degree of unification that is compatible with successful representation, scientists often rely on the existence of a ‘mature mathematical formalism’, where the latter refers to a—mathematically formulated and physically interpreted—notational system of locally applicable rules that derive from (but need not be reducible to) fundamental theory. As mathematical formalisms undergo a process of elaboration, enrichment, and entrenchment, they come to embody theoretical, ontological, and methodological commitments and assumptions. Since these are enshrined in the formalism itself, they are no longer readily obvious to either the novice or the proficient user. At the same time as formalisms constrain what may be represented, they also function as inferential and interpretative resources.     

Introduction to values and pluralism in the environmental sciences: From inferences to institutions

Philosophers of science continue to elaborate our understanding of the roles that values play in scientific reasoning, practice, and institutions. This special issue focuses on the environmental sciences, a mosaic of fields ranging from restoration ecology to forestry to climatology, unified by its attention to the relationships between humans and their habitats. It is a field that revolves around ameliorating environmental problems, aiming to support the provision of social goods and provide guidance to policymakers about how to regulate individuals and industries. Values abound in such judgments as setting the boundaries of an ecosystem, integrating the human dimensions of social-ecological systems, and collaborating with stakeholders. Since few in the field are likely to insist that these judgments can be made without reference to social values, environmental science can serve as fertile ground for exploring the ethical, social, and political terrain at the frontier of the science and values discourse.