The Mīmā ṃ sā school of Indian philosophy elaborated complex ways of interpreting the prescriptive portions of the Vedic sacred texts. The present article is the result of the collaboration of a group of scholars of logic, computer science, European philosophy and Indian philosophy and aims at the individuation and analysis of the deontic system which is applied but never explicitly discussed in Mīmā ṃ sā texts. The article outlines the basic distinction between three sorts of principles —hermeneutic, linguistic and (...) deontic. It proposes a mathematical formalization of the deontic principles and uses it to discuss a well-known example of seemingly conflicting statements, namely the prescription to undertake the malefic Śyena sacrifice and the prohibition to perform any harm. (shrink)

According to a longstanding philosophical tradition dating back to Aristotle, certain proofs do not only certify the truth of their conclusion but also explain it. Lately, much effort is being devo...

The notion of grounding is usually conceived as an objective and explanatory relation. It connects two relata if one—the ground—determines or explains the other—the consequence. In the contemporary literature on grounding, much effort has been devoted to logically characterize the formal aspects of grounding, but a major hard problem remains: defining suitable grounding principles for universal and existential formulae. Indeed, several grounding principles for quantified formulae have been proposed, but all of them are exposed to paradoxes in some very natural (...) contexts of application. We introduce in this paper a first-order formal system that captures the notion of grounding and avoids the paradoxes in a novel and non-trivial way. The system we present formally develops Bolzano’s ideas on grounding by employing Hilbert’s ε-terms and an adapted version of Fine’s theory of arbitrary objects. (shrink)