# hss-seminar-39

Department of Humanities and Social Sciences

Indian Institute of Technology Ropar

HSS Seminar

The Affinity of Philosophy and Mathematics

by

Dr.. Priyedarshi Jetli

March 1, 2018 (Thursday) at 09:45 AM

Venue: Conference Room 2

Abstract

Common wisdom declares that philosophy is the mother of all disciplines. That is perhaps why the highest academic degree is called “doctor in philosophy.” In the broad use of the term “philosophy” to mean higher order thinking, this may well be true. However, philosophy as an academic discipline does not predate mathematics but the opposite is the case. In the West, the consensus is that systematic philosophy begins with Plato in the 4th Century BCE. The central core of Plato’s thought is the theory of Forms. And the major methodological contribution of Plato was the use of deduction to formulate arguments in order to foster philosophical debates. The history of science and mathematics in the West however goes back at least two centuries in Asia Minor. The Ionian Thales turned to questions about the nature of the world from a scientific perspective. Thales (6th Century BCE) was also a mathematician who introduced deduction in the proof of theorems. Half a century later another Ionian Pythagoras developed deductive mathematics and posited numbers as the ultimate stuff of the universe. Plato acknowledges that he is inspired by both of these thinkers and other Presocratics. Clearly, mathematics and science were the parents who gave birth to philosophy as a discipline. There is no wonder that there was a sign outside Plato’s academy which said: “Let no one ignorant of geometry enter here.” Modern philosophy begins with Descartes. As we all know Descartes was first and foremost a mathematician. He laid down a framework for philosophy, especially for epistemology, that would work from foundational premises much like geometry is built on axioms. Again, then, we see mathematics as the mother of philosophy.

Even though mathematics may be the mother of philosophy, mathematicians do mathematics. They may or may not ask the questions about the nature or foundations of mathematics, or about the history of mathematics or about how mathematical knowledge is possible. The questions and debates in these areas is what constitutes the philosophy of mathematics. And this is a task taken up by philosophers beginning with Plato. Philosophy of mathematics as a formal discipline did not emerge until the 19th century. It centred around two debates:

1. Platonism versus Constructivism: Are numbers and objects of geometry real abstract entities or are they constructions of the human mind? The former view is Platonism and the latter, adopted by Kant, is Constructivism. 2. Leibniz versus Kant: Both agree that mathematics is non empirical, purely a priori, and involves the ability of reason alone. The disagreement is whether or not the foundations of mathematics and mathematical proofs is purely analytic, that is whether mathematics is reducible to logic. Leibniz believed that it was and Kant rejected the reduction. For Kant arithmetic is constructed on the human intuition of time and geometry on the human intuition of space. Though geometry was axiomatized by Euclid in the the 3rd Century BCE, arithmetic could not be axiomatized until the 19th century. Why such a gap? This is good food for thought for everyone and hopefully we can discuss this in the lecture.

Brief Bio-sketch of the speaker

Prof. Jetli completed his PhD in Philosophy in 1987 from Indiana University. He taught at University of Delhi from 1993 to 2006 and at University of Mumbai from 2006 to 2013. He was visiting faculty in institutes such as TISS and JNU. He is interested in Ancient Greek Philosophy, Philosophy of Mathematics, History of Logic; and Philosophy of Law. He is currently working on a book on judicial Affirmative Action decisions in India since Independence. His publications include co-authored (with Monica Prabhakar) book Logic (Pearson, 2012), ‘Relations in Plato’s Phaedo’ (1998), ‘The Completion of the emergence of modern logic from Boole’s The Mathematical Analysis of Logic to Frege’s Begriffsschrift’ (2011), ‘Abduction and model based reasoning in Plato’s Meno’ (2014) and ‘Abduction and model based reasoning in Plato’s Republic’ (2016).