In scientific modeling, continuum idealizations bridge scales but at the cost of fundamentally misrepresenting the microstructure of the system. This engenders a mystery. If continuum idealizations are dispensable in principle, this de-problematizes their representational inaccuracy, since continuum properties reduce to lower-scale properties, but the mystery of how this reduction could be carried out endures. Alternatively, if continuum idealizations are indispensable in principle, this is consistent with their explanatory and predictive success but renders their representational inaccuracy mysterious. I argue for a (...) deflationary solution, enlisting the applied scientific method of upscaling as demonstrated in a case from soil hydrology. (shrink)

The history of economic thought witnessed several prominent economists who took seriously models and concepts in physics for the elucidation and prediction of economic phenomena. Econophysics is an emerging discipline at the intersection of heterodox economics and the physics of complex systems, with practitioners typically engaged in two overlapping but distinct methodological programs. The first is to export mathematical methods used in physics for the purposes of studying economic phenomena. The second is to export mechanisms in physics into economics. A (...) conclusion is drawn that physics transfer is often justified at the level of mathematical transfer but unjustified at the level of mechanistic transfer. (shrink)

In this paper I study the activity of mathematical problem-solving in scientific practice, focussing on enquiries in mathematical social science. I identify three salient phases of mathematical problem-solving and adopt them as a reference frame to investigate aspects of applications that have not yet received extensive attention in the philosophical literature.

Cell biologists, including those seeking molecular mechanistic explanations of cellular phenomena, frequently rely on experimental strategies focused on identifying the cellular context relevant to their investigations. We suggest that such practices can be understood as a guided decomposition strategy, where molecular explanations of phenomena are defined in relation to natural contextual (cell) boundaries. This “top-down” strategy contrasts with “bottom-up” reductionist approaches where well-defined molecular structures and activities are orphaned by their displacement from actual biological functions. We focus on the central (...) role of microscopic imaging in cell biology to uncover possible constraints on the system. We show how identified constraints are used heuristically to limit possible mechanistic explanations to those that are biologically meaningful. Historical examples of this process described here include discovery of the mechanism of oxidative phosphorylation in mitochondria, molecular explanation of the first steps in protein secretion, and identification of molecular motors. We suggest that these instances are examples of a form of downward causation or, more specifically, constraining relations, where higher-level structures and variables delimit and enable lower-level system states. The guided decomposition strategy in our historical cases illustrates the irreducibility of experimentally identified constraints in explaining biological activities of cells. Rather than viewing decomposition and recomposition as separate epistemic activities, we contend that they need to be iteratively integrated to account for the ontological complexity of multi-level systems. (shrink)