Prof. C.K. Raju: “Decolonizing mathematics leads to better mathematics”

In school our children are being taught two conflicting systems of mathematics. In primary school they learn to calculate in an empirical way: one apple and one apple makes two apples. But later on they they are told that is wrong, and learn some formal mathematics where you postulate some axioms and use the deductive method to arrive at conclusions from the axioms.

I don’t use the term ‘Eurocentric’ because it wrongly suggests that a massive piece of deliberate mischief was an innocent mistake. Wrong claims lead to the wrong belief that Western (formal) mathematics is superior and the only right way to do mathematics.

Empirical proof is rejected by Western mathematics on the grounds that empirical proof is fallible. But deductive proof too is fallible: one may easily mistake an invalid deductive proof for a valid one.

Divorced from the empirical, even a valid deductive proof does not lead to valid knowledge or even to approximately valid knowledge,” states Raju. “Using the deductive method any silly proposition whatsoever can be proved as a mathematical theorem from some postulates.”

Raju likes to poke fun at Western philosophers and mathematicians like Bertrand Russell (1872-1970). Raju: “I could easily give a valid deductive proof that Russell is a racist. I would start with ‘All western philosophers from the 17th to the 20th century were racist. Russell was a 20th century western philosopher. So Russell was a racist.’ This is a valid deductive proof. But is it valid knowledge? No, if it is detached from empirical evidence it is not valid knowledge.

Yet another problem with formal mathematics is that it is based on a particular logic: the two-valued logic, which Western philosophers such as Kant took to be god-given or a priori. In this logic a proposition is either true or false. But there are many other logical systems Kant was ignorant of. Raju: “Take the Buddhist catuskoti logic. This is based on four alternatives. For example: the world is finite; the world is infinite, the world is both finite (in one direction) and infinite (in another direction), and the world is neither finite nor infinite (there can be other ways to look at the world). And Buddhist logic is just one of the many logical systems, there are others such as Jaina syadavada logic. In fact, one can conceive of an infinity of possible logics. This was not known to the West when formal mathematics developed in the early 20th c. Given the different systems of logic, one should select the right logic, on scientific grounds. But science inevitably involves empirical proofs.

Decolonised math shifts the whole focus away from the wrong idea that math is about metaphysical proof and persuasion which were church requirements. Decolonised mathematics focuses on practical value; it eliminates the superficial metaphysics that the West retrospectively added to imported practical math. Students find math difficult today just because of that useless Western metaphysics; eliminating it retains all practical value, but makes decolonised math very easy.

“Professor Raju's views are a departure point for debate. Raju challenges existing dogma at a time when we as a university are reflecting on our colonial history and the ways in which we as a country have embraced colonial epistemology. Raju’s message to students is that they should question Western Authority on science and insist instead on empirical evidence on truth. To faculty, he asks that if we teach the exact similar science as taught in the West, we should be able to justify why that is so. First - we must explain our exclusion of other approaches to science from other parts of the world. Secondly, we should demonstrate the benefits of science as taught and understood in the West, and explain why local communities may be rendered only beneficiaries, and never co-producers of scientific knowledge. Professor Raju essentially rejects the notion that the Western philosophy of science and maths is objective and universal. This aligns with the decolonial questioning of Western thought as the singular truth. Professor Raju invites us to think about philosophy other than that which originated in the West, Eastern and African philosophies of science and maths. It seems to me like a constructive way to engage in a discussion on decolonial thinking, regardless of the discipline.”

https://www.din.today/prof-c-k-raju-decolonizing-mathematics-leads-to-better-mathematics/

In school our children are being taught two conflicting systems of mathematics. In primary school they learn to calculate in an empirical way: one apple and one apple makes two apples. But later on they they are told that is wrong, and learn some formal mathematics where you postulate some axioms and use the deductive method to arrive at conclusions from the axioms.

I don’t use the term ‘Eurocentric’ because it wrongly suggests that a massive piece of deliberate mischief was an innocent mistake. Wrong claims lead to the wrong belief that Western (formal) mathematics is superior and the only right way to do mathematics.

Empirical proof is rejected by Western mathematics on the grounds that empirical proof is fallible. But deductive proof too is fallible: one may easily mistake an invalid deductive proof for a valid one.

Divorced from the empirical, even a valid deductive proof does not lead to valid knowledge or even to approximately valid knowledge,” states Raju. “Using the deductive method any silly proposition whatsoever can be proved as a mathematical theorem from some postulates.”

Raju likes to poke fun at Western philosophers and mathematicians like Bertrand Russell (1872-1970). Raju: “I could easily give a valid deductive proof that Russell is a racist. I would start with ‘All western philosophers from the 17th to the 20th century were racist. Russell was a 20th century western philosopher. So Russell was a racist.’ This is a valid deductive proof. But is it valid knowledge? No, if it is detached from empirical evidence it is not valid knowledge.

Yet another problem with formal mathematics is that it is based on a particular logic: the two-valued logic, which Western philosophers such as Kant took to be god-given or a priori. In this logic a proposition is either true or false. But there are many other logical systems Kant was ignorant of. Raju: “Take the Buddhist catuskoti logic. This is based on four alternatives. For example: the world is finite; the world is infinite, the world is both finite (in one direction) and infinite (in another direction), and the world is neither finite nor infinite (there can be other ways to look at the world). And Buddhist logic is just one of the many logical systems, there are others such as Jaina syadavada logic. In fact, one can conceive of an infinity of possible logics. This was not known to the West when formal mathematics developed in the early 20th c. Given the different systems of logic, one should select the right logic, on scientific grounds. But science inevitably involves empirical proofs.

Decolonised math shifts the whole focus away from the wrong idea that math is about metaphysical proof and persuasion which were church requirements. Decolonised mathematics focuses on practical value; it eliminates the superficial metaphysics that the West retrospectively added to imported practical math. Students find math difficult today just because of that useless Western metaphysics; eliminating it retains all practical value, but makes decolonised math very easy.

“Professor Raju's views are a departure point for debate. Raju challenges existing dogma at a time when we as a university are reflecting on our colonial history and the ways in which we as a country have embraced colonial epistemology. Raju’s message to students is that they should question Western Authority on science and insist instead on empirical evidence on truth. To faculty, he asks that if we teach the exact similar science as taught in the West, we should be able to justify why that is so. First - we must explain our exclusion of other approaches to science from other parts of the world. Secondly, we should demonstrate the benefits of science as taught and understood in the West, and explain why local communities may be rendered only beneficiaries, and never co-producers of scientific knowledge. Professor Raju essentially rejects the notion that the Western philosophy of science and maths is objective and universal. This aligns with the decolonial questioning of Western thought as the singular truth. Professor Raju invites us to think about philosophy other than that which originated in the West, Eastern and African philosophies of science and maths. It seems to me like a constructive way to engage in a discussion on decolonial thinking, regardless of the discipline.”

https://www.din.today/prof-c-k-raju-decolonizing-mathematics-leads-to-better-mathematics/