Is it possible to teach mathematics and science with a non-Western epistemology?

C. K. Raju

Indian Institute of Education

and

Indian Institute of Advanced Study

At a lecture in USM, Naquib al Attas made an interesting observation. He pointed out that calculus is today done using the continuum (formal real numbers). However, on the philosophy of al Ashari everything is atomic, and numbers are discrete. Many people might today misunderstand this remark to mean that Islamic philosophers were wrong. But Naquib al Attas meant it in a different way: that an alternative epistemology of the calculus is possible in a way consistent with a discrete number system.

.This struck a chord with me because many years earlier, I had proposed exactly such a possibility of an alternative epistemology of the calculus.¹ I pointed out that most actual applications of the calculus to real-life problems are today done on computers, and computers cannot use formal real numbers and instead use the discrete system of floating point numbers. Further, formal mathematics prohibits the empirical so this preference for formal real numbers is purely a metaphysical preference. Indeed, as I further pointed out, this use of formal real numbers or the continuum to teach calculus is merely an example of a metaphysical bias in our current university teaching,² and it is perfectly possible to teach calculus differently.

The biased Western metaphysics in present-day formal math adds nothing to the practical applications of math to science and engineering, but is the cause of the widespread difficulties of math today. For example, the proof of even a simple thing like 1+1=2 took Bertrand Russell 378 pages.³ Quite obviously, the practical value of 1+1=2 pre-existed, from thousands of years before Russell and most people in the world are perfectly able to carry out everyday transactions without ever learning Russell’s metaphysics.

Metaphysics cannot be universal and the metaphysics of formal mathematics is not even secular.⁴ In particular, the wrong belief in the infallibility of deduction⁵ is based on post-Crusade Christian rational theology (borrowed and twisted from aql-i-kalam). In particular, formal real numbers involve a metaphysics of infinity which is directly tied to political church dogmas about eternity.⁶ However, under the pressure of colonialism and “post-colonial” on universities, all our present-day universities fall in line,⁷ and teach globalised formal mathematics. It is strange that almost no one is even contesting the issue of epistemology in the core sectors of mathematics and science.

In a series of pedagogical experiments, with various groups in various countries, including 4 groups in USM, it was demonstrated that eliminating this metaphysical bias is beneficial even from a purely pragmatic point of view. and teaching mathematics, and especially calculus, with an alternative philosophy makes it easy enough to be taught in a few dys even to students of humanities and social sciences without any background of calculus at the school level.⁸ Making math easy enables students to solve much harder problems not covered in usual university-level calculus courses, as is evident from a glance at a stock tutorial sheet.⁹

The calculus is hardly an isolated example of a metaphysical (and theological) bias against Islam in mathematics and science as currently taught in our universities. Western thinkers have persistently blamed¹⁰ al Ghazali, a prominent Asharite, of “occasionalism”, which (they claim) arrested scientific development in the Muslim world. Specifically, they refer to al Ghazali’s point that Allah is not bound¹¹ by any laws of cause-and-effect, or “laws of nature” contrary to the theological dogma of Aquinas¹² that God rules the world with eternal laws. Though many ordinary academics¹³ understand the fallacy of basing science on such a dogmatic belief, the critique has not found adequate support from authorities and is not being pursued and propagated by any university.

Indeed, through the religiously biased metaphysics of formal math, a variety of metaphysical biased can creep into science. In particular, specifically Judeo-Christian doctrines of creation were promoted as science by Stephen Hawking¹⁴ and others, and this came out prominently in the conflict with Hawking\s co=author, G. F. R. Ellis during the recent ongoing struggle in Cape Town to decolonise mathematics. The pity is that an analysis of the time concept in physics¹⁵ and philosophy,¹⁶ supports (with some modifications) al Ghazali’s idea that there are “uncaused” (or spontaneous¹⁷) events.

The question is whether any university is willing to challenge the hegemony of the West in the epistemology of mathematics and science by actually teaching mathematics and science with a different epistemology using or modifying a model which already exists.