Decolonizing mathematics | Decolonial International Network (Full Article)

These are just some of the selected quotes

** “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. This makes matters very complicated: Whitehead and Bertrand Russell took 368 pages to deductively prove 1+1=2 in their book. Decolonised mathematics eliminates this needless complexity and accepts the natural and empirical way; it is simple and easy.”**

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Indeed, that is how I learned mathematics using deductive proofs. The famous example is: “All men are mortal. Socrates is a man. Therefore Socrates is mortal.” So what is wrong with that method of deduction? Why is this Eurocentric, apart from the fact that a male is used in this example?

Raju: “First of all, I don’t use the term ‘Eurocentric’ because it wrongly suggests that a massive piece of deliberate mischief was an innocent mistake. Second there is nothing wrong with the method of deduction as such, which was used also, for example, in India. Of course, attributing this syllogism to Aristotle is the usual false Western history: there is nil evidence to link the syllogism to Aristotle. What is uniquely Western and wrong are the claims that (a) deduction is infallible, (b) that it is universal (c) that deductive proof is superior to empirical proof, and that (d) it is possible to arrive at valid knowledge without any empirical inputs, as in formal mathematics. All these 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. Our senses might mislead us. To use a classical example from Indian philosophy: I might mistake a rope for a snake or a snake for a rope. But deductive proof too is fallible: one may easily mistake an invalid deductive proof for a valid one. For example, the very first proposition of “Euclid’s” Elements has an invalid deductive proof. But for 8 centuries that book was mistakenly regarded by all the foremost minds in the West as the model of deductive proof, when, in fact, there isn’t a single valid deductive proof in it, as Bertrand Russell too emphasized. How do you know that his own 368 page proof of 1+1=2 is valid? You just blindly trust authority, and such blind trust can be very fallible. Empirical proofs are never so fallible: one might mistake a rope for a snake, but the Western error about “Euclid’s” Elements, is like mistaking a rope for an elephant.”**

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“No, on the contrary they are inferior. 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.”**

to summarize, he is arguing that Western Mathematics reliability on the Deductive method is inferior to the empirical method

thoughts?