Logic Centre, Mumbai

WELCOME

LOGIC INITIATIVEWORK DONE SO FAR

CONFERENCES & WORKSHOPS

• Conferences

• IIT Bombay – 2005 and 2007

• Kolkata – 2007

• Chennai – 2009

• Delhi – 2011

• Winter School

• IIT Bombay – 2006

• IIT Kanpur – 2008

• University of Hyderabad – 2010

ASSOCIATION FOR LOGIC

• The ‘Association for Logic in India’ (ALI) was formed in 2008 with the basic aim of building a logic community in India, and promoting research and education in logic, and its applications.

• ALI now organizes a Biennial Conference / School on Logic in India: ICLA (Indian Conference on Logic and Applications) in the odd years, and ISLA (Indian School on Logic and Applications) in the even years.

PUBLICATIONS

• The papers presented in the 2005 and 2007 conferences at IIT Bombay have been compiled into two books entitled Proof, Computation and Agency & Games, Norms and Reasons (Festschrift for Rohit Parikh), (subtitle ‘Logic at the Crossroads’ for both) by Springer as part of their Synthese Library Series.

• The papers of Kolkata Conferences (2007) have been published by King’s College Publication, London under the series Studies in Logic

• The FoLLI subseries of the Springer Lecture Notes in AI has published the papers presented in the Chennai (2009) & Delhi conferences (2011) i.e. Vol. 5378 and Vol. 6521 respectively.

• In 2010 the Journal of Indian Council of Philosophical Research (JICPR) published Special Issues Vol. XXVII, No. 1 (Jan.-March) and No.2 (April-June) on Logic and Philosophy Today.

WHAT NEXT?

A LONG WAY TO GO• In spite of these achievements we feel that we are far from achieving

our objective of creating appropriate mechanisms, which should facilitate being in close touch with our target groups.

• There are more than 300 Universities and Institutes of Higher learning in India. Large number of students, researchers and teachers still shy away from the Conferences we have been organizing and are unable to make full use of our publications.

• The curriculum in Logic, except in a few Universities and Institutes, is archaic and the standard of courses and research in Logic appalling. This is due to lack of familiarity with basics of formal systems, model theoretic semantics, machine model of effective computability, recursion etc.

• The present state of education and research in Logic in India deserves empathetic understanding and novel approach since its abject neglect is a matter of great concern and agony for all practitioners of logic. We need to think big and in a radical manner to help solve this enormous problem of gigantic proportion.

LOGIC CENTRE, MUMBAI

PROPOSED ACTIVITIES

• Hosting a specially designed interactive Web Site

• Start publishing a bi-annual e-journal

• Hold regular discussion sessions and symposia on logic and its applications

INAUGURATION OF THE WEB SITE

INTRODUCTION

The Logic-Center, Mumbai, through the website to be launched this evening, intends to reach out to every interested student, researcher and teacher of logic, especially in India, in any discipline by using modern online digital technology and accessing global resources with a view to realize the following Vision and Mission

VISION

Unleashing local energies in the field giving rise to contemporary schools of Logic in India and training brilliant Indian minds with a view to taking a rightful place in this rich intellectual community in the world.

MISSION

• To facilitate education and research in Logic to achieve the breadth and depth it should have comparable to the vigor and intensity with which Logic and its relationship with and application in other disciplines is pursued in some of the countries where modern Logic has flourished.

• To bridge the big gap in knowledge and awareness of the current state of Logic between teachers, researchers and students of Logic in Philosophy Departments in India on the one hand and those in Computer Science and Mathematics on the other.

• To nurture the scholarship in Indian Logic as practiced in contemporary times while taking into account the manner in which contemporary logic is being brought to bear on the new ways of interpreting classical texts in Indian Logic resulting in paradigm shifts and emerging distinctive trends / themes.

A CAVEAT

Needless to say that the use of this virtual learning in no way intends to underestimate the importance of live face-to-face exchange and personal vibrant teaching-learning experience of the classroom, but provides an opportunity to all those interested in Logic in availing of the enormous global resources, infusing vitality in learning by unlocking vast reserve of knowledge and in the process “empowering minds.”

BRIEF HISTORY OF LOGIC

ANCIENT LOGIC

• Argumentative traditions in ancient world –

Indian, Chinese, Arabic and Greek

• The Greek tradition• Aristotle (384 BC – 322 BC) Theory of Syllogism For.m / Structure vs. Content

Figure and Mood

256 : 19 Valid forms of syllogistic arguments

• Mathematical Tradition: Pythagoras of Samos

(c. 570 – c. 495 BC)

• The Pythagoreans and the discovery of “incommensurability: the 1st Crisis in

Mathematics. The need for agreement on what can be

taken as basic assumptions. The need for resolution of the crisis and the

need for systematization of stray, discrete facts.

• Euclid (300 BC): Axiomatization The Elements

Anselm of Canterbury (1033 - 1109)

Avicenna (Ibn Sina) (c. 980 - 1037)

Peter Abelard (1079 - 1142)

John of Salisbury (c. 1120 - 1180)

Roger Bacon (1215 – 1294)

John Duns Scotus (c. 1266 - 1308)

William of Ockham (c. 1287 - 1347)

John Buridan (c. 1300 - after 1358)

The core of the logic from the 12th century onwards was provided by the logical works of Aristotle. These represented

(1)the material for the study of types of predication, the analysis of simple propositions or statements

(2)(2) and their relations of inference and equivalence, the analysis of modal propositions, of the structure and the types of the syllogism, dialectical topics, fallacies and scientific reasoning as based on the demonstrative syllogism.

MEDIEVAL LOGICA FEW IMPORTANT NAMES

Inductive LOGIC & SCIENTIFIC METHOD: The Royal Society and “the New Philosophy”

• Francis Bacon

• New Atlantis (1626)

• Scientific Method, logic & empirical science

• The Royal Society (1660) and

“the New Philosophy”

• Mill’s Methods

• Induction and Probability

• David Hume(1711 – 1776)

• Blaise Pascal (1623 – 1662)

• Thomas Bayes (1702 – 1761)

ALGEBRAIC ANALYSIS OF LOGIC &RISE OF LOGICAL SYSTEMS

• George Boole (1815 – 1864) and logical relations

• Georg Cantor (1845-1918) and Set Theory & 2nd Crisis in Mathematics

• Gottlob Frege (1848 -1925) Frege’s Logicism

LOGICISM & FORMALISMTHEIR LIMITATIONS

• Bertrand Russell (1872-1970) Russel’s Paradox Principia Mathematica

• David Hilbert (1862 – 1943) Hilbert’s Program and the

Entscheidungsproblem

• Kurt Gödel (1906 – 1978) Godel’s Incompleteness

Theorem

FOUR BRANCHES OF LOGIC

• Proof Theory

• It is the study of “Proofs” / derivations / arguments as formal syntactic objects facilitating their analysis by using mathematical techniques.

• Model Theory

• It is the study of (mathematical) structures that provide meaning to sentences of a formal logical language.

• Computability Theory

• Defining “effective” computation and “decidability.”

• Set Theory

• Foundation of mathematics

LOGIC AT THE CROSS ROADS

• “Deviant Logic”

• Modal Logic: possibility and necessity

• Tense Logic: time and reasoning

• Deontic Logic: obligation and permission

• Fuzzy Logic: degree of surety

• Other disciplines where Logic plays an important role:

• Computer Science: program verification, algorithms, AI

• Social Sciences: Rational agents, Social choice theory, Game theory

• Linguistics, Natural Languages and Natural Logic

STRUCTURE OF WEB SITE

SOMETHING FOR EVERYONE

• Mainstream Logic Researcher & Researcher on Logic in the Allied Disciplines

• Researcher in Indian Logic

• Advanced Level Students

• Basic Level Students

• Lay person

• Children

RESEARCHERS – LOGIC AND ALLIED BRANCHES

• Provide an idea of the scope of research in mainstream logic

• Current areas of research-focus across the world both in Logic & other disciplines interfacing with it, including applied logic

• Initiatives in progress: drafts of papers / unpublished papers

• Open problems

• Provide direction to logic students in India and help connect them to scholars

RESEARCH IN INDIAN LOGIC

• Paradigm 1: Hindu syllogism

• Paradigm 2: Interpretation in terms of Frege-Russell tradition

• Paradigm 3: Interpretation in terms of Quine contributions

• Paradigm 4: Interpretation on basis of the following approaches

• Case Based

• Dialogical

• Intensional

• Nonmonotonic Logic

ADVANCED LEVEL STUDENT

• Links to various course materials, annotated books and papers, online lectures, videos,

.ppt presentation of lectures

• Opportunity to interact and discuss with renowned faculty and improve understanding

• Provide necessary material and guidance to various rigorous approaches to logic

BASIC LEVEL STUDENT

• Links to preliminaries to formal logic, videos and books on a first course on formal logic

• Prepare a student to learn formal logic

• Introduce a student to formal logic

• Provide guidance for further study in logic

LAY PEOPLE

• History of logic

• Links to introductory materials on logic including various puzzles and paradoxes

• Give a non technical introduction to logic

• Motivate and develop further interest in logic

CHILDREN

• Proposed framework for logic education at school and junior college level

• Provide resources for parents, guardian or others interested in introducing logic to children in an interesting manner

• Provide puzzles and paradoxes to initiate logic related thinking and curiosity in children.

Prof. S. D. Agashe

Prof. Ramasubramanian Sharma

Mr. Nirmesh Mehta

Mr. Abhisekh Sankaran

Dr. Hari Priyadarshan

Ms. Jyotsana Mehta

Ms. Chaitali Gupta

Prof. Amitabha Gupta

CORE GROUPLOGIC CENTRE, MUMBAI