#TPAC (The Paradoxes And Contradictions, August 18, 2017):
How does your tongue taste? What do you take for granted? Can you create randomness? Do you act in the continuum? Can you then reason about racing a tortoise ahead of you? Is there something common to most paradoxes? Can all paradoxes be ‘stated’? Do paradoxes owe something to the nature of Reality? Are dilemma, doubt, disbelief, paradoxes, & contradictions in the same class? Do we necessarily need faith before reasoning? Is there a reasoning process that does not lead to paradoxes? Why isn’t Gödel’s Theorem a Law? Are all paradoxes connected to language? Can a logic be complete but undecidable? Is uncomputability a consequence of self reference? Can discrete cardinality be higher than real numbers’? How did quantum probability uncover the hidden assumptions behind the quantum paradoxes? Is the quantum collapse (still) a physical phenomenon? What is computing? Are paradoxes pictures? Is a paradox free conception of the world possible? What is common knowledge? Are all paradoxes counterintuitive, & will we always keep running into them? Is there likely to be a ‘Law of Reasoning’ in the future? SynTalk thinks about these & more questions using concepts from mathematics (Prof. Luigi Accardi, University of Rome Tor Vergata, Rome, Italy), computer science (Prof. Supratik Chakraborty, IIT Bombay, Mumbai), & philosophy (Prof. Navjyoti Singh, IIIT, Hyderabad).
SynTalk is pleased and privileged to have hosted the following SynTalkrs (in alphabetical order) on its #TPAC show.
Prof. Luigi Accardi (mathematics) teaches at the Economy Faculty of the University of Rome Tor Vergata, Rome, Italy, where he also founded (in 1987) the Vito Volterra Interdepartmental Centre, devoted to a multidisciplinary view of mathematics. His research interests are in mathematics, physics, mathematical economy, philosophy of science and cryptography. Prof. Accardi has taught in various universities, such as, Princeton (1986), & Gainesville (1988-89) in USA, and Meijo University, Nagoya (1996-98), & Tokyo University of Science (1989-95) in Japan. He obtained his degree in Mathematics in the University of Naples (1970) and his Ph.D. (Candidat Nauk) at the Faculty of Mathematics and Mechanics of Moscow University (1974) under the guidance of I.M. Gelfand and R.L. Dobrushin. In his Ph.D. thesis he introduced and constructed the first examples of quantum Markov chains using a solution that was a radical innovation of the notion of ‘quantum conditioning’ and the first time use of the notion of ‘quantum stochastic process’. He developed his theory of relativity of the law of chance in early 1980s &, with the introduction of statistical invariants, it led to the proof of existence of multiplicity of mathematical models for the laws of chance. Prof. Accardi then re-examined the problems of quantum theory & published his conclusions in a book titled ‘Urns and Chameleons’ (1997). He has also published a two volume book, titled, ‘Quantum Theory and its Stochastic Limit’ (co-authors Y.G. Lu, I. Volovich, Springer Tracts in Modern Physics, 2002), which is a collection of results in the fields of quantum dissipative & transport phenomena, stochastic bosonization in higher dimensions, & non classical statistics. He is the managing editor of the journal ‘Infinite Dimensional Analysis, Quantum Probability and Related Topics’ (World Scientific), & is on the editorial board of several other international journals of mathematics and physics.
Prof. Supratik Chakraborty (computer science) is currently Bajaj Chair Professor in the Department of Computer Science and Engineering at Indian Institute of Technology Bombay (IITB), Mumbai. He is also a principal investigator in the Center for Formal Design and Verification of Software (CFDVS) at IITB. Prior to joining IITB, he served as Member of Research Staff at Fujitsu Laboratories of America, Sunnyvale, California, USA. He received a B. Tech. in Computer Science and Engineering from IIT Kharagpur, and an M.S. and Ph.D. in Electrical Engineering (Computer Systems) from Stanford University. His current research interests include formal methods and applications of mathematical logic, with an emphasis on scalable algorithmic techniques for reasoning about hardware, software and biological systems. His interests lie in understanding the decidability and computational complexity of problems that arise in reasoning about different computational models, with a focus on understanding how efficient algorithms with strong approximation guarantees can be designed for these problems. He develops tools and techniques that apply formal methods based reasoning to problems arising from industry and government organizations. Prof. Chakraborty has been awarded the President of India Gold Medal from IIT Kharagpur, James R. Isaac Chair for Young Faculty & an Excellence in Teaching Award from IITB, Indian National Academy of Engineering Young Engineer Award, and an IBM Faculty Award. He has authored a book chapter on the application of automata techniques in reasoning about computer programs, and has published extensively in formal methods (in journals such as Annals of Pure and Applied Logic, ACM Transactions & IEEE Transactions). He serves and has served on several advisory boards (both government and private), including the Executive Councils of the Indian Association for Research in Computing Sciences (IARCS), & the Association for Computing Machinery (ACM).
Prof. Navjyoti Singh (philosophy) is currently Professor and Head, Center for Exact Humanities, International Institute of Technology (IIIT), Hyderabad. His current research interests are theories of arts and aesthetics, computational humanities, formal ontology, Indian philosophy and Indian analytic traditions (Vaisesika, Jaina and Bauddha), history of ideas in foundations of logic, mathematics and linguistics. Prof. Singh received his B. Tech. (Mechanical Engineering) and M. Tech (Nuclear Engineering & Technology) from IIT Kanpur (IITK). Prior to IIIT, he was a Fellow at Indian Institute of Advanced Studies, Shimla (IIAS, 2002-2005), Director PPST Foundations, Chennai (1996-2002), & Scientist, National Institute of Science Technology & Development Studies, New Delhi (NISTADS, 1983-2011). He has been professionally researching on the ‘crossroads of Indian and Greco-European analytic traditions’, an engagement that spans more than three decades. He started with publishing on foundations of logic, mathematics and linguistics & moved towards a prolonged research on the ‘working of the mind’. He has formalized Vaiseshika ontology, written on transfinite mathematics of Jaina and developed formal approach to Buddhist phenomenology. His recent works deal with formal theories of justice, history, society and arts. Prof. Singh labels a wide range of his intellectual pursuits under ‘exact humanities’ and draws heavily from Indian analytical traditions. Prof. Singh has nurtured two networks – FAMOTSIT (Foundations and Methodology of Theoretical Sciences in the Indian Tradition), a research network on Indian analytic tradition, & PPST (Promotional network of Congresses of traditional sciences and technologies of India). He has three book manuscripts under development, tentatively titled, ‘Punctuating Reality’, ‘Spirit of Reason’, & ‘Mechanics of Phantasm’. [Note: Also a SynTalkr on #TFOI (The Firstness Of Ideas)]
Note: Any & all errors in the brief profiles above are SynTalk’s own.
#TPAC mentions: Zeno of Elea, G. W. F. Hegel, Carl Friedrich Gauss, Georg Cantor, Bernhard Riemann, Karl Marx, Joseph Bertrand, David Hilbert, Ludwig Wittgenstein, Kurt Gödel, Alfred Tarski, Alan Turing, Richard Feynman, & Louis de Broglie, among others.