On the Indispensable Premises of the Indispensability Argument

Abstract

International audienceWe identify four different minimal versions of the indispensability argument, falling under four difference varieties: an epistemic argument for semantic realism, an epistemic argument for platonism, and a non-epistemic version of both. We argue that most current formulations of the argument can be reconstructed by building upon the suggested minimal versions. Part of our discussion relies on a clarification of the notion of (in)dispensability as relational in character. We then present some substantive consequences of our inquiry for the philosophical significance of the indispensability argument, the most relevant of which being that both naturalism and confirmational holism can be dispensed with, contrary to what is held by many

The varieties of indispensability arguments

“…page 19, above) is not explicitly relying on a particular notion of indispensability: this seems to us partly due to the fact that the notion of indispensability occurs in it in a schematic way, that should be then made precise according to different determinations. In [Panza and Sereni, 2015] we suggest how the versions of ia commonly discussed can be retrieved by determination of schematic premises from schematic ia's cognate to the ones discussed here.…”

“…As we also have stressed somewhere else (cf. [Panza and Sereni, 2015]), although the indispensability argument, being based on premises that may be established on a posteriori grounds-such as the form that proper formulations of scientific theories must take in order to be suitable for description, explanation or prediction-is usually a powerful tool in the hands of empiricists willing to defend the existence of mathematical abstract objects on empirical grounds, the argument per se does not rule out the availability of other a priori reasons for believing in those objects-in which case, it will at most offer some auxiliary, defeasible, and less than ideal evidence for the wanted conclusion Indispensability considerations: Positing certain objects is sometimes thought to be indispensable to express certain claims about the world, or to provide a systematic description of a certain range of phenomena. [.…”

“…To the best of our knowledge, however, before we tentatively tackled the question in [Panza and Sereni, 2013], (ch. 6) and [Panza and Sereni, 2015], no thorough investigation had been pursued in order to identify and clarify both the traits common to all possible ia's (or to ia itself, considered as a whole family of arguments), those features that are specific to each of them, and the way a single such argument may be obtained through the specification of a general pattern.…”

“…footnote 52 for some remarks on this point.19 This makes the meaning of 'epistemic' in 'epistemic indispensability argument' broader than that we ascribed to it in[Panza and Sereni, 2013], ch. 6, and in[Panza and Sereni, 2015]. This will become clear in § 3.6.20 It goes without saying that arguments in which 'P ' is replaced by an ontological property are likely to presuppose some robust realist understanding of scientific theories as delivering faithful representations of some external reality in agreement with some experimental practice, while arguments in which 'P ' is replaced by an ontological property may be compatible with weaker conceptions, where scientific theories are conceived, for instance, as giving reliable descriptions limited to the observable world and/or as allowing for sufficiently reliable predictions of empirical phenomena.…”

The Applicability of Mathematics and the Indispensability Arguments

“…The idea is that Naturalism tells us that we must commit ourselves to the existence of the entities required by our best scientific theories, and Confirmational Holism prevents us from interpreting part of these theories non-realistically. Both doctrines have been variously called into question, and there is currently a wide debate about the effectiveness of these two thesis in supporting (1 Q ) (see for example Panza & Sereni 2015). However, it is not my intention to focus on these debates.…”