Duty and Sacrifice: A Logical Analysis of the Mīmāṃsā Theory of Vedic Injunctions

Abstract

The Mīmāṁ sā school of Indian philosophy has for its main purpose the interpretation of injunctions that are found in a set of sacred texts, the Vedas. In their works, Mīmāṁ sā authors provide some of the most detailed and systematic examinations available anywhere of statements with a deontic force; however, their considerations have generally not been registered outside of Indological scholarship. In the present article we analyze the Mīmāṁ sā theory of Vedic injunctions from a logical and philosophical point of view. The theory at issue can be regarded as a system of reasoning based on certain fundamental principles, such as the distinction between strong and weak duties, and on a taxonomy of ritual actions. We start by reconstructing the conceptual framework of the theory and then move to a formalization of its core aspects. Our contribution represents a new perspective to study Mīmāṁ sā and outlines its relevance, in general, for deontic reasoning.

Mīmāṃsā deontic reasoning using specificity: a proof theoretic approach

“…Since here we are interested in the general properties of Mīmām . sā reasoning, we do not consider this distinction and refer the reader to Freschi et al (2019) for details.…”

“…For G one of G MD , G bMDL we write G Γ ⇒ Δ if there is a derivation of Γ ⇒ Δ in G. The following proposition gives a proof-theoretic proof of the equivalence of the box-free fragment of bMDL and MD. For the original proof using semantical methods, see Freschi et al (2019).…”

“…Traditionally, rituals prescribed by the Vedas are distinguished into fixed (nitya), occasional (naimittika), and elective (kāmya); fixed ritual actions should be performed, in order to obtain the positive result of good karma, regularly throughout the whole life, occasional ones have similar properties, but should be carried out in special occasions, like the birth of a child, whilst the third kind includes rituals to be executed only in order to obtain a specific result. It has been noticed (Freschi et al 2019) that, while the characteristics of the operator O in bMDL are well suited to describe fixed and occasional prescriptions, the elective rituals represent recommendations or instruction for achieving a result in a "Vedic" way, more than proper obligations. We call these weaker obligations recommendations and express them with the operator R(./.).…”

“…We model R(./.) using the dyadic version of the modal logic MP, see, e.g., Chellas (1980), in line with the analysis in Freschi et al (2019) where also the axioms for R(./.) are motivated.…”

“…Notice that it is weaker than D O and D F , as, in contrast with obligations and prohibitions, it is possible to have two recommended rituals for getting the same result which cannot be performed at the same time. In those cases (e.g., in the case of the prescriptions of kāriri sacrifice and twelvenights sacrifice for obtaining the rain, see, e.g., Freschi et al 2019) Mīmām . sā authors assume that one of the two sacrifices is enough to get the intended result, but both recommendations remain in force.…”