The later Wittgenstein’s perspective on mathematical sentences as norms is motivated for sentences belonging to Hilbertian axiomatic systems where the axioms are treated as implicit definitions. It is shown that in this approach the axioms are employed as norms in that they function as standards of what counts as using the concepts involved. This normative dimension of their mode of use, it is argued, is inherited by the theorems derived from them. Having been motivated along these lines, Wittgenstein’s perspective on (...) mathematical language may appeal also to those who are not friends of or experts on Wittgenstein’s later philosophy of mathematics. (shrink)

This paper examines the relationship between simulation and experiment. Many discussions of simulation, and indeed the term "numerical experiments," invoke a strong metaphor of experimentation. On the other hand, many simulations begin as attempts to apply scientific theories. This has lead many to characterize simulation as lying between theory and experiment. The aim of the paper is to try to reconcile these two points of viewto understand what methodological and epistemological features simulation has in common with experimentation, while at the (...) same time keeping a keen eye on simulation's ancestry as a form of scientific theorizing. In so doing, it seeks to apply some of the insights of recent work on the philosophy of experiment to an aspect of theorizing that is of growing philosophical interest: the construction of local models. (shrink)

The Aleph Zero or Zero Dichotomy is a strong version of Zeno's Dichotomy II which being entirely derived from the topological successiveness of the w-order comes to the same Zeno's absurdity.