Bicontextualism for Truth and Sets : An Intermediate Position between Generality Absolutism and Generality Relativism

Generality absolutism is the claim that quantifiers can range over absolutely everything, while generality relativism insists that quantifiers must always be restricted. Each view offers significant strengths: absolutism is needed to preserve the intended interpretation of fundamental statements in the foundations of semantics and mathematics, whereas relativism provides the most successful and elegant solutions to paradoxes such as Russell’s and the Liar. However, these positions appear fundamentally incompatible. This thesis develops a new intermediate position—bicontextualism—that reconciles the strengths of both views. Bicontextualism holds that domain restrictions must be applied in some cases to avoid paradoxes, while in other, non-paradoxical cases, unrestricted quantification is unproblematic. This framework thus combines the elegant, relativistic solutions to paradoxes with the possibility of unrestricted interpretation for unparadoxical sentences. The thesis proceeds as follows: first, it provides a systematic development of the position of bicontextualism. Next, it explores how this position can be applied to the truth-theoretic paradoxes, including the Liar paradox. Finally, it examines the set-theoretic paradoxes, such as Russell’s paradox. In both cases, bicontextualism offers a coherent and effective framework that combines relativistic solutions of the paradoxes with absolute generality.