Indispensability and Practice

Abstract

* My thanks go to the NSF (DIR-9004168) and to the UC/Irvine Academic Senate Committee on Research for their support.. .. it is applicability alone which elevates arithmetic from a game to the rank of a science," P. Geach and M. Black, eds., Translations from the Philosophical Writings of Gottlob Frege (Cambridge: Blackwell, 1970), p. 187. Although Frege speaks of arithmetic, my focus here will be on analysis, broadly construed. 2 See, e.g., "On What There Is," repr. in From a Logical Point of View, 2nd ed.

The Applicability of Mathematics and the Indispensability Arguments

“…Let us consider the following examples (for more about these examples, see Maddy 1992). It is common, in the analysis of water-wave dispersion, to assume that water depth tends to infinity.…”

Against Mathematical Convenientism

“…Confirmational holism holds that observations confirm not just some parts of a scientific theory but all parts of a scientific theory. Confirmational holism has received severe criticisms from Penelope Maddy (1992) and Jacob Busch (2012). Maddy observes that we do not believe that ideal entities, such as frictionless slope and continuous fluids, are real, although they are indispensable parts of our best scientific theories.…”

Information Systems Foundations Part Three : The Role of Design Science

“…Studies of the actual methods used by researchers in mathematics, IS and other disciplines indicate widespread departures from strict empiricist requirements, creating an implicit tension between 'ideal' and actual practice (see Bealer 1992;Maddy 1992;Smith 2006). In IS research in particular, these differences indicate that IS researchers already view aspects of the research process in transcendental realist terms (Mingers 2004b;Smith 2006), so critical realism could be a more accurate formulation of what researchers really believe and practice.…”