Reflecting on believability: on the epistemic approach to justifying implicit commitments

Abstract By definition, the implicit commitment of a formal theory $$\textrm{Th}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>Th</mml:mtext> </mml:math> consists of sentences that are independent of the axioms of $$\textrm{Th}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>Th</mml:mtext> </mml:math> , but their acceptance is implicit in the acceptance of $$\textrm{Th}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mtext>Th</mml:mtext> </mml:math> . In Cieśliński (2017, 2018), the phenomenon of implicit commitments was studied from the epistemological perspective through the lenses of the formal theory of believability. The current paper provides a comprehensive proof-theoretic analysis of this approach and compares it to other main theories of implicit commitments. We argue that the formal results presented in the paper favour the believability theory over its main competitors. However, there is still a fly in the ointment. We argue that in its current formulation, the theory cannot deliver all the goods for which it was defined. In particular, being amenable to a generalised conservativeness argument, it does not support the view that the notion of truth is epistemically light. At the end of the paper, we discuss possible ways out of the problem.