 Objectivity features prominently in the private language argument. Both Neurath’s argument and Wittgenstein’s earlier one are laid out for the case of an individual epistemic agent understanding himself before he needs to understand others (Uebel 1995b). For both, the constancy and consistency of language use is paramount. It can only be ensured by an intersubjective, that is, objective and social, language, namely the language of physicalism, about ‘spatio-temporal structures’. For Wittgenstein, especially in the Philosophical Investigations, the social dimension of language is a key element of its extrinsic character and therefore its proper justification, the normative condition of possibility and intelligibility of success, and likewise for the more general case of rule-following. The scope of Neurath’s argument is more particularly directed to the case of scientific language in the scientific community.