We identify four different minimal versions of the indispensability argument, falling under four different 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.
Andrea Sereni, Marco Panza.On the Indispensable Premises of the Indispensability Argument. Gabriele Lolli, Marco Panza, Giorgio Venturi. Philosophy of Mathematics; from Logic to Practice - Italian Studies in the Philosophy of Mathematics, 208, Springer, pp. 241-276, 2015, Boston Studies in the Philosophy and History of Science, 978-3-319-10433-1, 978-3-319-10434-8. https;//doi.org/10.1007/978-3-319-10434-8_13 .