Research in animal behavior begins by identifying what animals are doing. In the course of observation, the observer comes to see animals as performing a particular activity. How does this process work? How cn we be certain that behavior is identified correctly? Wittgenstein offers an approach to these questions. looking at the uses of certainly rather than attempting to find rules that guarantee it. Here two stages in research are distinguished: first, watching animals, and second, reporting the results to other (...) scientists. Certainly about what animals are doing, has different uses at each stage. (shrink)

In this paper I assess the obstacles to a transfer of Lakatos's methodology of scientific research programmes to mathematics. I argue that, if we are to use something akin to this methodology to discuss modern mathematics with its interweaving theoretical development, we shall require a more intricate construction and we shall have to move still further away from seeing mathematical knowledge as a collection of statements. I also examine the notion of rivalry within mathematics and claim that this appears to (...) be significant only at a high level. In addition, ideas of ‘progress’ in mathematics are outlined. (shrink)