ORIGINAL ARTICLE Against the Judgment-Dependence of Mathematics and Logic Alexander Paseau Received: 21 January 2009 / Accepted: 3 September 2011 / Published online: 21 September 2011 Ó Springer Science+Business Media B.V. 2011 Abstract Although the case for the judgment-dependence of many other domains has been pored over, surprisingly little attention has been paid to mathematics and logic. This paper presents two dilemmas for a judgment-dependent account of these areas. First, the extensionality-substantiality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the substantiality condition (roughly: non-vacuous specification). Second, the exten- sionality-extremality dilemma: in each case, either the judgment-dependent account is extensionally inadequate or it cannot meet the extremality condition (roughly: absence of independent explanation). The paper concludes with a moral concerning the judgment-dependence of a posteriori areas of discourse that emerges from consideration of these two a priori cases. 1 Introduction The idea behind judgment-dependence is that our best opinion under idealised conditions about some statements constrains or maybe even grounds these statements’ truth. 1 For example, whether a joke is funny seems to depend on our reactions to it, and perhaps the same goes for whether a dish is tasty, an object is red or an act is morally right or wrong. The leading theoretical template for A. Paseau (&) Wadham College, Oxford OX1 3PN, UK e-mail: alexander.paseau@philosophy.ox.ac.uk 1 Wright’s preferred characterisation in his (1992) is ‘conceptual grounding’, e.g. ‘‘the Euthyphronic thesis becomes, correspondingly, that, for the discourse in question, optimally conceived judgment—best opinion—is the conceptual ground of truth.’’ (1992, p. 111). 123 Erkenn (2012) 76:23–40 DOI 10.1007/s10670-011-9320-0