Jay Jolly asked:<\/p>\n
“Could you expand more on the the concept of \u201cZeroism\u201das applied in Mathematics?What changes do you foresee in pedagogy of Mathematics if the philosophy is changed from formalism to zeroism?”<\/p>\n
First I have a whole chapter on\u00a0zeroism in my book Cultural Foundations of Mathematics<\/em> (chp. 8 with the subtitle: sunyavada<\/em> vs formalism). (The editor of a Cambridge journal solicited the book for review, and the reviewer then lied that the book did not contain any philosophy beyond chp. 2 to justify the extraordinary procedure of reviewing only 2 chapters of the book. This is in the long Western tradition of suppressing and defaming\u00a0opposing viewpoints when unable to counter them.\u00a0Even today,\u00a0Western universities don’t teach non-Western philosophy presumably just because they are afraid this would damage their own philosophy\u00a0built on the weak foundations of theology.)<\/p>\n What is zeroism?<\/strong><\/p>\n There are three aspects of zeroism which are relevant.\u00a0First,\u00a0zeroism regards\u00a0the empirical (though fallible)\u00a0as an appropriate\u00a0means of proof,\u00a0superior to\u00a0any metaphysics. (This is contrary to formalism which is wholly metaphysical, and regards its particular\u00a0metaphysics as superior to both physics and all other systems of metaphysics.)\u00a0\u00a0Zeroism accepts fallibility, as in the fallibility of science.<\/p>\n Second\u00a0zeroism accepts the impossibility of “perfect” or precise represenation of anything.\u00a0This is the practice in natural language that\u00a0one name\u00a0refers to a multiplicity of entities. When applied to persons, this means that we use one name to refer to a “person” who is, in reality,\u00a0a constantly changing\u00a0entity from childhood to old age.\u00a0 (We cannot even specify, “this person at x instant” because\u00a0the instant cannot be precisely specified, and by the time of the specification, even that specious instant is gone forever beyond observation.) When applied to numbers this means that the number pi can variously refer to 3.14 or 3.1415 etc, as needed for a particular practical problem, with the rest of the infinite\u00a0series being “zeroed”.\u00a0This is similar to the common practice of rounding, though built on a different epistemological foundation.<\/p>\n This was the point of Western confusion about the calculus, as in\u00a0Descartes’ confusion: he thought the infinite series for pi\u00a0must be naively summed. He was right\u00a0that\u00a0physically\u00a0carrying out this\u00a0infinite sum would require an infinite amount of time, which was not available to humans. He was wrong in\u00a0thinking that stopping at any stage was not perfect, hence\u00a0not mathematics: for any<\/em> practical application we will and must stop at some finite stage of precision. So, it is the demand for infinite precision which is mistaken.\u00a0\u00a0This\u00a0persistent\u00a0confusion about math as perfect and infinitely precise\u00a0is what eventually led to the \u00a0formalist solution\u00a0just to postulate that the\u00a0series for pi could be summed metaphysically, which metaphysics\u00a0is\u00a0never needed for any practical purpose.<\/p>\n Third, zeroism brings out the variations in logic, so that the deductive proofs do not constitute certain knowledge, and are of little practical value. The theorems would obviously vary with the logic used. (Even intuitionsists recognized that math would change if proofs by contradiction were abandoned.) Accordingly, the church vision of mathematics as\u00a0\u00a0concerned with proof, and not calculation has to be abandoned. The church focus was on using math to teach reason as a “universal means of persuasion”, since after the failure of the Crusades it tried to convert Muslims using “reason”.\u00a0\u00a0However, for others, the objective of math\u00a0was (and remains)\u00a0commerce, science and\u00a0technology.<\/p>\n