Many philosophers have claimed that extensive or additive measurement is incompatible with the existence of "higher values", any amount of which is better than any amount of some other value. In this paper, it is shown that higher values can be incorporated in a non-standard model of extensive measurement, with values represented by sets of ordered pairs of real numbers, rather than by single reals. The suggested model is mathematically fairly simple, and it applies to structures including negative as well (...) as positive values. (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.