Groundedness, Truth and Dependence
Leitgeb (2005) proposes a new approach to semantic paradoxes, based upon a direct definition of the set of grounded sentences in terms of dependence upon non-semantic state of affairs. In the present paper, we account for the extensional disagreement between this dependence approach and more familiar alethic approaches. In order to do so, we study the behavior of dependence jumps and alethic jumps, and provide an equivalence result for the two approaches.
KeywordsDependence Supervaluations Groundedness Jump.
We would like to thank Serge Bozon, Paul Égré, Hannes Leitgeb, Øystein Linnebo, Philippe de Rouilhan, and Jönne Speck for their insightful comments on earlier versions of this research. We are particularly grateful to Øystein Linnebo who greatly helped us clarify the rationale behind results proven in (van Vugt 2009). We also need to thank various audiences in Gothenburg, London and Paris for their helpful feedback. The present work originates in the second author’s master thesis under the supervision of the first author (van Vugt 2009). Results in the present work were obtained independently of (Meadows 2013), which proves Proposition 8 supra as its main result (see Footnote 6 for a more detailed discussion). The work of the first author was partly supported by the ESF-funded project ‘Logic for Interaction’, a Collaborative Research Project under the Eurocores program LogICCC.
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