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(2005) Synthese 143 (3).
Remarkably, despite the tremendous success of axiomatic set-theory in mathematics, logic and meta-mathematics, e.g., model-theory, two philosophical worries about axiomatic set-theory as the adequate catch of the set-concept keep haunting it. Having dealt with one worry in a previous paper in this journal, we now fulfil a promise made there, namely to deal with the second worry. The second worry is the Skolem Paradox and its ensuing ‘Skolemite skepticism’. We present a comparatively novel and simple analysis of the argument of the Skolemite skeptic, which will reveal a general assumption concerning the meaning of the set-concept (we call it ‘Connexion M’). We argue that the Skolemite skeptic’s argument is a petitio principii and that consequently we find ourselves in a dialectical situation of stalemate.
Publication details
DOI: 10.1007/s11229-005-0800-0
Full citation:
Muller, F. A. (2005). Deflating Skolem. Synthese 143 (3), pp. 223-253.
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