This paper introduces a natural deduction calculus for intuitionistic logic of belief \ which is easily turned into a modal \-calculus giving a computational semantics for deductions in \. By using that interpretation, it is also proved that \ has good proof-theoretic properties. The correspondence between deductions and typed terms is then extended to a categorical semantics for identity of proofs in \ showing the general structure of such a modality for belief in an intuitionistic framework.

The correlation between dialogue and religion, both as conceptual apparatuses and as current practices, has had a long history. The purpose of this essay is to isolate one such instance – the “critical dialogue” taking place amongst scholars of religions – which involves also the dialogue scholars establish with their field of study and/or a given religious tradition. Following a brief clarification of terminology used, I will proceed to discuss concrete examples of critical dialogue within the Study of Religions and (...) how this might be enhanced. Finally, I will draw some partial conclusions which might pave the way for this critical dialogue to improve and continue. (shrink)

This introductory chapter sets out the rationale for the ensuing chapters and their division into different parts. It also provide an overall and comprehensive prologue to the Gramsci-Ambedkar encounter. Indeed, "parallels are strong and very striking for two thinkers who are otherwise so different - in political experience, philosophical background and ideas of effective strategy" (Jon Soske, personal communication). Nevertheless, the moral fabric of their political commitment to Dalits/subalterns bring them very close, particularly in the upholding of Gramsci's 'intellectual and (...) moral reform' and Ambedkar's 'social and moral consciousness of society'. (shrink)

This paper is part of a project that is based on the notion of a dialectical system, introduced by Magari as a way of capturing trial and error mathematics. In Amidei et al. (2016, Rev. Symb. Logic, 9, 1–26) and Amidei et al. (2016, Rev. Symb. Logic, 9, 299–324), we investigated the expressive and computational power of dialectical systems, and we compared them to a new class of systems, that of quasi-dialectical systems, that enrich Magari’s systems with a (...) natural mechanism of revision. In the present paper we consider a third class of systems, that of p-dialectical systems, that naturally combine features coming from the two other cases. We prove several results about p-dialectical systems and the sets that they represent. Then we focus on the completions of first-order theories. In doing so, we consider systems with connectives, i.e. systems that encode the rules of classical logic. We show that any consistent system with connectives represents the completion of a given theory. We prove that dialectical and q-dialectical systems coincide with respect to the completions that they can represent. Yet, p-dialectical systems are more powerful; we exhibit a p-dialectical system representing a completion of Peano Arithmetic that is neither dialectical nor q-dialectical. (shrink)