Modern Formalisms for Pre-Modern Indian Logic and Epistemology
Hamburg (Germany); 4-6 June 2010


Anekantavada between Logic, Epistemology and Religion

Unlike other elements of Indian logic, the Jaina teaching of the manysidedness of reality is still very much part of an active religious community. Anekantavada and syadvada are sometimes used almost as synonyms for Jaina philosophy and religion. They are associated not only with logic, ontology and epistemology but also with environmental ethics, interreligious tolerance and even 'modern' science. My research tries to show that while many of these associations seem rather far-fetched, the plurality of spheres into which anekantavada extends is of relevance also for attempts to formalize Jaina logic. The problem of the apparently redundant elements of the saptabhangi can, for example, be understood in the context of the religious concept of the omniscient, i.e., when taken not only as a logical model but also as a kind of spiritual 'visualisation aid' on the path to perfect knowledge.

Melanie Barbato
München, Germany
Jonardon Ganeri, Argumentation, Dialogue and the Kathavatthu: PDF file
Jonardon Ganeri
Brighton, United Kingdom
Tailoring symbolic clothes for ancient logic

In order to assess the applicability of modern formal systems to ancient Indian logic, it is worth looking into the development of European logic, where, earlier than in indology, tools of modern formal logic have been used for the research into ancient logical systems. Frege's quantifier logic, invented during the last quarter of the 19th century, not only led to a revolution regarding the utilization of formal logic in the area of the foundations of mathematics, but also with regard to the use of formal logical methods as a tool for the interpretation of ancient logical texts. Whereas the triumphal march of quantifier logic in the field of mathematics for which it had been designed was doubtlessly justified, the situation in the area of history and philosophy of logic encountered obstacles. Not until Frege's interpretation of Aristotelian syllogistics, which was subsequently copied into almost every elementary logic textbook, had been overthrown by the eminent modern formal logician Jan Łukasiewicz, did the new ill-fitting Fregean clothes of ancient logic fall off, and the field for a new debate on the formal aspects of Aristotle's logic become open again. This led in 1972 to John Corcoran's now widely accepted formal interpretation of Aristotelian syllogistics. Starting with Łukasiewicz's student Stanisław Schayer around 1930, research in the field of ancient Indian logic also switched tools from Aristotelian syllogistic to modern symbolical logic. As in the case of ancient European logic, there is a risk that philosophically insensitive misapplication of this method distorts ancient texts and injects artificially generated problems, thus creating obscurity and confusion instead of clarity and precision.

Klaus Glashoff
Lugano, Switzerland
Jain context-sensitive approach to knowledge in the light of argumentative practices

From the seventh to the eleventh centuries approximately, Jain philosophers have developed a context-sensitive approach to knowledge (nayavâda) according to which given contextual elements are decisive in the determination of the meaning and validity of a thesis.

In western modern terms, it would be quite natural to understand this theory from a modal perspective, see Ganeri [2002]. Promising studies on new ways to conceive contextual validity have been developed by Priest [2008] and Humberstone [2008] in this line. The problem is that the conceptions of Jain philosophers do not seem to match the standard conceptions of modal logic, because the contextualisation process is not about propositions but about objects that are subjects of a predication and is performed outside the object language.

Using a pragmatic semantics that provides a general theory for meaning based on argumentative practices, I propose in this talk a new reading on Jain theory of viewpoints such as presented in Prabhcandra's Prameyakamalamârtanda, The Sun of the Lotus of the Knowables, a 10th century work in the line of Akalanka?s philosophical tradition. The main idea of this reading is to make explicit the ontological assumptions handled by an agent when she asserts a given thesis. This talk is based on a joint paper with Clerbout and Rahman.

Marie-Hélène Gorisse
Lille, France
Ibn Sina's Cyclotron

In around 1025, early in his major commentary on Aristotle's Prior Analytics, Ibn Sina describes a geometric construction. It bears an uncanny resemblance to the design for a cyclotron collider which Rolf Wideroe tried and failed to patent in 1943. Ibn Sina believed that this and related examples did serious damage to Aristotle's view of logic. But exactly what conclusions did Ibn Sina expect his readers to draw from the examples? A modern answer might well mention multiple quantification, dynamic predicate logic and the failure of o-minimality in the reals with sine function. But clearly Ibn Sina didn't expect his readers to know these modern theories. The question requires us to understand what Ibn Sina thought logic consists of. Two other questions that we need to answer along the way are: (1) Why did Ibn Sina continue to teach and use a logic that he regarded as misconceived? (2) What follows for standard accounts of the difference between aristotelian and modern logic?

Wilfrid Hodges, Ibn Sina on analysis: 1. Proof Search. Or: Abstract State Machines as a tool for the history of logic. PDF file

Wilfrid Hodges
London, England
Lessons from Nâgârjuna

For the modern reader interested in argumentation theory, or more generally in logic conceived as a theory of justification through linguistic interaction, Nâgârjuna presents some strikingly interesting features. In this talk, we present some of these:

  1. the relations between the notion of thesis (or claim), the notion of burden of the proof and the notion of proposition;
  2. presupposition handling and negation(s);
  3. "universally" and "conventionally" adverbs as modalities.
We show how to capture these features in a modern conceptual framework (namely Dialogical logic) and comment on the light it sheds on some of Nâgârjuna's famous and controversial philosophical tenets.

Laurent Keiff
Lille, France
Are there cognitive predicates in Dharmakīrtian inferences from non-perception?

This paper deals with a particular pattern of reasoning formulated and analyzed by the South Asian Buddhist logician Dharmakīrti (ca. 600-660 CE): from the ascertained fact that a particular object like a jar (which would necessarily be perceived if it existed) is not perceived, one infers that this object does not exist. Such inferences, in which the non-cognition and non-perception (anupalabdhi) of an object serves as evidence, seem to differ crucially from other inferences envisioned by Buddhist logicians, such as the one from smoke rising above a hill to the presence of fire-they involve cognitive predicates. In this paper I am going to present how Dharmakīrti and other logicians dealt with this (perhaps only apparent) peculiarity.

Birgit Kellner
Heidelberg, Germany
Some methodological aspects of formalization with respect to Indian philosophical teachings

Aim of the lecture is to explicate a concept of formal description and to explore its relevance for investigations on non-Western traditions of thought and in particular with respect to teachings assigned to the tradition of Indian philosophy. It will be claimed that in the context of studies of Indian theoretical systems formal descriptions can possess (at least) three significant functions which could be characterized by the terms: 1) representative, 2) analytic and 3) critical function. Apart from presenting a more elaborate explication of the pertinent functions methodological issues pertaining to the derivation of formal descriptions from formulations occurring in textual sources constitute a major topic of the paper.

Claus Oetke
Stockholm, Sweden
The Catuskoti

In early Buddhist logic, it was standard to assume that for any state of affairs there were four possibilities: that it held, that it did not, both, or neither. This is the catuskoti (or tetralemma). Classical logicians have had a hard time making sense of this, but it makes perfectly good sense in the semantics of various paraconsistent logics, such as First Degree Entailment. Matters are more complicated for later Buddhist thinkers, such as Nagarjuna, who appear to suggest that none or these options, or more than one, may hold. The point of this talk to to examine the matter, including the formal logical machinery that may be appropriate.

Graham Priest
Melbourne, Australia
The Interactive and Epistemological Turn in Logic

The recent trend in logic has been to shift emphasis from static systems developed for purely theoretical reasons to dynamic systems designed for application to real world situations, such as modelling knowledge and belief, interaction, and reasoning in multi-agent systems. This emphasis on the situational and applied aspects of logic and reasoning is relatively new in contemporary logic, but it was the dominant approach to logic by logicians in the high Middle Ages, especially in mid-13th to mid-14th C. Medieval logic was concerned with techniques of reasoning that could be applied in real reasoning contexts, and thus which could vary from context to context. This pragmatic approach to logic was complimented with a strong interest in modelling dynamic, interactive systems, where reasoning is not an armchair process of a single agent but is instead a dispute or debate between two or more agents, each of which have different knowledge and different roles in the disputation. In this respect, medieval Western logic and medieval Indian logic, particularly in the Navya-Nyāya tradition have much more in common than either of these have with the mathematical logic of the early 20th century. Recently scholars of logic have approached both traditions in a similar fashion, using the new tools and techniques developed in recent decades. We survey and discuss these tools and techniques with a view towards their possible applications in formalizing pre-modern logical theories.

PDF file of the slides
Sara L. Uckelman, Aristotelian Syllogistics with Abelardian Truth Conditions. Notes on the formalization of existential import, triggered by a discussion after Klaus Glashoff's talk: PDF file.

Sara L. Uckelman
Amsterdam, The Netherlands