proposition. Universal proposition is defined as the proposition in which the relation between the subject term and the predicate term is without any condition, in which the predicate is either affirmed or denied of the subject unconditionally. In nyaya logic the term vyapti is a universal proposition or invariable relation between the middle term (linga/hetu) and the major term (sadya) . According to the category of relation propositions are divided into categorical and the conditional. Although proposition is a logical entity (...) which is an assertion, either affirm or deny the subject. Truth and falsity are the values of proposition. Universal proposition is of two kinds: universal affirmative proposition and universal negative proposition while universality is the quantity of the subject and affirmation or negation is the quality of the proposition. Anumana (inference) is the knowledge of the objects which follows some other knowledge. In nyaya logic Inference is a combined deductive-inductive reasoning consisting of at least three categorical propositions and in it there are at least three propositions consisting of three terms, viz. the paksa or minor term about which we infer something, the sadhya or major term which inferred object, and the linga(probans) or sadana or middle which is invariably related to the major, and is present in the minor. Indian inference resembles to the categorical syllogism of western logic. In nyaya logic inference consisting of three propositions the first proposition is the conclusion of the syllogism , the second is the minor premise and last the major premise which is totally opposite of western logic. Syllogism of nyaya logic contains five propositions, called its Avayavas or members. These are pratijna, hetu, udarana, upanaya, and nigamana. Middle term have five characteristics in order to make five Figures of syllogism as Figure is the form of the syllogism. These five characteristics, or at least four of them , must be found in the middle term of a valid inference. If not, there will be fallacies(error in reasoning). Nyayikas give us three classifications of inference. According to first inference is of two kinds, namely, svartha and parartha. According to another inference is of three kinds, purvavat, sesavat and samanyatodrsta. According to third classification inference is distinguished into kevalanvayi, kevala-vyatireki and anvaya-vyatireki. (shrink)

The evaluation of arguments was not the sole concern of logicians in ancient India. Early Nyāya and the later Navya-Nyāya provide an interesting example of the interaction between logic and ontology. In their attempt to develop a kind of property-location logic Naiyāyikas had to consider what kind of restrictions they should impose on the residence relation between a property and its locus. Can we admit circular residence relations or infinitely descending chains of properties, each depending on its successor as its (...) locus? Early Naiyāyikas and to some extent also Navya-Naiyāyikas regard these phenomena as a kind of absurdity and they want to rule them out. Their intuitions about properties are close to well-founded systems of set theory, whereas the author of the Navya-Nyāya work Upādhidarpaṇa is a proponent of a non-well-founded property concept. Despite certain similarities with sets properties are still regarded as intensional objects in Navya-Nyāya. In the pre.. (shrink)

Illustrations: Numerous B/w Figures Description: Key questions in the history of Navya-nyaya (New Nyaya) remain unresolved: when did this school of logic begin, who was its founder, what distinguishes Navya-nyaya from Pracina-nyaya (Old Nyaya), and so on. This book attempts to answer these key questions in Part I. Part II provides a translation, analysis, and critical edition of the Lion and Tiger Definitions of Invariable Concomitance Chapter (Simha-vyaghra-laksana: LT Chapter) of the Tattva-cintamani-rahasya (TCR) of Mathuranatha (16th-17th c.). The hypothesis adopted (...) by the author with regard to the first question is that Udayana, who lived in the 11th century, is the founder of Navya-nyaya. This hypothesis is closely linked to the hypothesis offered regarding the second question, which is that the feature that distinguishes Navya-nyaya from the earlier school is its description of concepts and the structure of the world in terms of relation. Early Navya-nyaya authors, who flourished between Udayana and Gangesa (14th c.), devised specific terminology, of which delimitor (avacchedaka) and describer (niËpaka) are the most important, in order to identify or specify relation. This book attempts to illustrate the function of these and other Navya-nyaya terms from the viewpoint of relation. The main sources upon which the author has based his conclusions are Udayana s Laksanavali and the chapters on invariable concomitance or pervasion (vyapti) of the Nyaya-siddhanta-dipa (NSD) of Sasadhara (13rd-14th c.), the Tattva-cintamaÆi (TC) of Gangesa, and the TCR. Of these Sanskrit texts no scholar has worked on the Invariable Concomitance Chapter (Vyapti-vada) of the NSD in detail or the LT Chapter of the TCR. The latter chapter follows in the TCR the Five Definitions of Invariable Concomitance Chapter (Vyapti-pancaka), which Ingalls edited, translated, and analyzed in his epoch-making book Materials for the Study of Navya-Nyaya Logic (1951). One major innovation of this book made in Part II is to explain the structure of Navya-nyaya analysis by employing 86 diagrams based on the dharma-dharmin (property and property-possessor) relation, which serve as a visual aid and help readers to more easily understand the complicated structure of its analysis. The diagrams are also helpful in ascertaining how the definitions of invariable concomitance apply to individual cases and how the entities are connected in the application of the definitions. Another major innovation is: almost every sub-section of the LT Chapter of the TCR contains Mathuranatha s clarification of part of the two definitions; but this clarification does not give the definition incorporating prior clarifications and insertions; this book provides such a definition accompanied by a diagram. In other words, Part II illustrates the structure of the whole definition at every process of the clarification, which (definition) is never presented as such in Mathuranatha s text. (shrink)

The strainer tests the strength of a definition of a particular kind. Suppose the definition D is stated in terms of an absence, and x is a definiendum of D. The strainer collects each x-token or x-individual that dissatisfies D in a specific case. Then, all the x-individuals put together would be equivalent to the type x. Hence—one would be forced to conclude that—in a sense, x dissatisfies D. This is a case of under-application of D, since, despite being a (...) definiendum of D, x dissatisfies D. Therefore, D would be too narrow. Similarly, the strainer may detect over-application too. By using the strainer, Raghunātha Śiromaṇi demonstrated that Gaṅgeśa’s conclusive definition of pervasion had a defect, and redefined pervasion. The strainer test is based on intuitive principles. It may disqualify a definition that has an absence in its definiens. Therefore, strainer-proofing becomes an important consideration that must be borne in mind every time we formulate such a definition. (shrink)

The Mīmāṃsā 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, Mīmāṃsā 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 Mīmāṃsā 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 Mīmāṃsā and outlines its relevance, in general, for deontic reasoning. (shrink)

This book is unusual in many respects. It was written by a prolific author whose tragic untimely death did not allow to finish this and many other of his undertakings. It was assembled from numerous excerpts, notes, and fragments according to his initial plans. Zilberman’s legacy still awaits its true discovery and this book is a second installment to it after The Birth of Meaning in Hindu Thought (Kluwer, 1988). Zilberman’s treatment of analogy is unique in its approach, scope, and (...) universality for Western philosophical thought. Constantly compared to eastern and especially classical Indian interpretations, analogy is presented by Zilberman as an important and in many ways primary method of philosophizing or philosophy-building. Due to its universality, this method can be also applied in linguistics, logic, social analysis, as well as historical and anthropological research. These applications are integral part of Zilberman’s book. A prophetic leap to largely uncharted territories, this book could be of considerable interest for experts and novices in the field of analogy alike. (shrink)

Beginning from some passages by Vācaspati Miśra and Bhāskararāya Makhin discussing the relationship between a crown and the gold of which it is made, this paper investigates the complex underlying connections among difference, non-difference, coreferentiality, and qualification qua relations. Methodologically, philological care is paired with formal logical analysis on the basis of ‘Navya-Nyāya Formal Language’ premises and an axiomatic set theory-based approach. This study is intended as the first step of a broader investigation dedicated to analysing causation and transformation in (...) non-difference. (shrink)

The present paper is about three concepts which are crucially involved in Gaṅgeśa's interpretation of a Mīmāṃsā argument against the well-known design inference of the existence of God in Nyāya, namely the concepts “cognition” (jñāna), “certitude” (niścaya) and “doubt” (saṃśaya). According to Maheśa Chandra, the author of the Navya-Nyāya manual Brief Notes on the Modern Nyāya System of Philosophy and its Technical Terms, certitude and doubt are the two varieties of cognition. He illustrates the verbal expression of certitudes by means (...) of declaratives and the verbal expression of doubts by means of interrogatives (functioning as polar or alternative questions). He notes also that different credence levels might be associated with the alternatives involved in a speaker’s doubt. A biassed question in the form of a tag interrogative might be an appropriate way to express such a doubt. In Western logic the idea to treat declaratives and interrogatives on a par, which is anticipated by the Navya-Naiyāyikas' use of the unifying concept of “cognition”, goes back to Frege’s distinction between the semantic content (the “thought”) of a sentence and its force and it was recently elaborated by Ciardelli, Farkas, Groenendijk, Roelofsen et al., the founders of a new branch in logic called “inquisitive logic”. In the present paper we will discuss Maheśa Chandra's succinct exposition of the Navya-Naiyāyikas' innovative approach from the perspective of this type of logic. As an offshoot of our analysis we will try to elucidate Gaṅgeśa's apologetic concerns about the well-known design inference of the existence of God in Nyāya and its liability to be vitiated by a dubious upādhi. (shrink)

This essay is an attempt to analyze, classify and illustrate different scholarly approaches to the Sanskrit philosophical commentaries as reflected in some influential and especially thoughtful studies of Indian philosophy; at the same time it highlights some specific features involving commentary and annotation in general, drawing from results of studies on commentaries conducted in other disciplines and fields, such as Classical and Medieval Studies, Theology, and Early English Literature. In the field of South Asian Studies, philosophical commentaries may be assessed (...) from various overlapping and not always exclusive points of view, such as preservation of otherwise lost historical information, historical authenticity and reliability, interpretational innovation, spiritual or experiential insight, philosophical creativity, intellectual liveliness, doxographic intent, degree of incidentality, expository breadth and explanatory depth. The essay provides numerous examples taken from classical to early modern philosophical literature, especially of the Brahminical and Buddhist traditions, and also discusses their diverging perception by modern scholars and interpretators. (shrink)

I dare say, a set is contranatural if some pair of its elements has a nonempty intersection. So, we consider only collections of disjoint nonempty elements and call them totalities. We propose the propositional logicTT, where a proposition letters some totality. The proposition is true if it letters the greatest totality. There are five connectives inTT: , , , , # and the last is called plexus. The truth of # means that any element of the totality has a nonempty (...) intersection with any element of the totality . An imbeddingG of the classical predicate logicCPL inTT is defined. A formulaf ofCPL is a classical tautology if and only ifG(f) is always true inTT. So, mathematics may be expounded inTT, without quantifiers. (shrink)

The present paper is a continuation of a previous one by the same title, the content of which faced the issue concerning the relations of coreference and qualification in compliance with the Navya-Nyāya theoretical framework, although prompted by the Advaita-Vedānta enquiry regarding non-difference. In a complementary manner, by means of a formal analysis of equivalence, equality, and identity, this section closes the loop by assessing the extent to which non-difference, the main issue here, cannot be reduced to any of the (...) former. The following sections of this study will focus on the assessment of the eventual possibility of causation and transformation in non-difference. (shrink)

The section we have examined is a persuasive and sustained demolition of the realist strategy of deriving an invariable concomitance between the existenthood of the world and the system of validation (a system accepted by both parties as being the regulator of epistemic activity). This leaves the Advaitin with an absence of invariable concomitance. This is where the Advaitin wants to be. On his view, the absence of this concomitant dependence of the system of validation on an ‘existent’ world points (...) to the possibility that the cognized world is not that independent world which Nyāya takes to be the determinate reality. If that world is not philosophically proven to be so independent, then there is at least aprima facie case for the Advaitic soteriological claim that it is Brahman alone which is ultimately real, even though the commonly cognized world allows of coherent epistemic activity. It is fair to say that such a view is established by the failure of the opponent to prove invariable concomitance between inquiry, validation and an independent world. It is the inability of the opposing view to prove a metaphysical claim which itself points to the nature of the Advaitic position; the position, that is, which suspends the need to make an ontic commitment to the extrinsic world as a determinate reality. Whether the critique of the Nyāya concept ofsattā takes us to the refutation of the Nyāya concept of a determinate world (and whether the Advaitic rejection ofsattā is of a piece with the concept of an ‘indeterminate’ world) is another issue, dealt with in detail by Śrī Har $$\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{s} $$ a elsewhere in his book, but beyond the purview of this paper. (shrink)

This paper investigates Vācaspati Miśra’s remarkably complex argumentative architecture in support of non-difference by means of a microsimulation model, the classical gold-crown case. A full range of positions, including instantaneism, transformative continuum, indeterminate common basis reference, difference and non-difference coordination, etc., is put under the scrutiny of the Vācaspati Miśra’s dialectic effort. The possibility of coexistence of multiple properties with a single referent is then formally explored. The analysis is carried out in compliance with the ‘Navya-Nyāya Formal Language’ extensional set-based (...) approach and its non-predicative, and variables free, relational syntax. Repeatable modules and structures of reasoning are identified and designed in the form of hypothesis frameworks, axioms and theorems to allow more accurate inferences, in particular regarding transformation and permanence, together with possible or impossible plexuses of properties. Identity and difference qua mutual absence are thoroughly defined with the aid of these formal tools, which conjointly might cast new light on the heuristic and expressive power of Navya-Nyāya logic, as well as on the theoretical potentialities of the non-dualistic account. (shrink)