Here is one very simple and very robust argument: Western mathematics and philosophy is founded on the belief that deductive inference is certain and universal. However, deductive inference varies with the logic used, and 2-valued logic is neither (a) culturally universal, nor (b) empirically certain.
People in the West have reacted to it in surprising ways.
One of these surprises was a mail I received on 24 Dec 2007 (note the day) from the editor of a journal asking for a copy of the book to be reviewed. Referring to my book, Cultural Foundations of Mathematics, the mail said:
"...If this book is any good, it should be reviewed in the only learned journal in the world devoted to philosophy of mathematics, Philosophia Mathematica, which I edit and Oxford University publishes. If you'd like to send me a copy I shall try to have it reviewed.
Strange! Normally, it is authors who want journals to review their books. Here, the editor of a journal was writing to the publishers and the author, soliciting a review copy!
The sentence, "if this book is any good...", suggested a crude attempt at psychological manipulation, and corroborated my worst suspicions about the real intentions behind this solicitation.
Clearly, it was no longer credible for scholars in the West to just go on ignoring my strong argument, which has been around for a decade. Something else had to be done to try and fix it!
Now, the stock Western technique to contain opposition involves:
2. physical exclusion (to prevent the misrepresentation from being corrected), and
3. personal abuse (to prejudice people against the opponent).
For example, Augustine misrepresented Origen's arguments, abused him, and Origen was later cursed by the Church. This is central to the entire Western tradition of post-Nicene Christian theology, as I have explained in my earlier book The Eleven Pictures of Time (Sage, 2003).
This stock technique nurtured in the West is rejected by the Indian tradition as not conducive to the truth. The Nyaya sutra, explicitly recognizes (1) misrepresentation, (2) debate-avoidance (through exclusion), and (3) abuse, as 3 of the 23 sure ways of losing an argument. Those who resort to these techniques are well aware of the weakness of their arguments, but know of no better means.
Now, a review "automatically" fulfils the criterion of exclusion, for the author is not expected to respond to a review (though the Jopurnal of Indian Council of Philosophical Research, which I helped to edit, did allow authors to respond). Exclusion enables the easy propagation of misrepresentation and abuse. Western scholars seem afraid to debate with me in an open forum. (As a concrete example, recall the "Petition against Celebrity Justice" signed by a group of leading academics in the Atiyah case where the American Mathematical Society denied me even a single opportunity to put forward my point of view in a matter concerning me.) My blog gives other instances of my experiences with such misrepresentation and personal abuse followed by exclusion, for example, in the "philomathes" list. Indeed, to judge from my experiences, such scurrilous tactics are widespread among Western scholars.
So, I was well prepared for these stock Western tactics when I received this strange mail from the editor of this "learned" journal. Nevertheless, I asked the publishers (Pearson Longman) to send a review copy to the journal. My aim was two-fold. First, I wanted to expose this Western technique of maintaining old lies by generating a constant stream of new ones. Second, I was slightly curious to know what was the best the West could throw against me.
The "review" however has exceeded my wildest imagination!
--The reviewer shamelessly admits that he has ignored the bulk of the book! To justify this strange act he claims that only the first two chapters of the book are relevant to the journal (and to philosophy of mathematics). This is just plain false. There is no way to excuse the reviewer because he has noticed and restated that the book considers history and philosophy together as an integral whole.
Indeed, the new philosophy of mathematics proposed in the book---namely the idea that sunyavada (or zeroism) can be and was historically used as part of a realistic philosophy of mathematics---is proposed and argued only from chapter 3 onwards! The book also compares this new philosophy with the misunderstandings about the calculus which led to the philosophical errors of Descartes, Galileo, Newton, etc., which errors still persist in the Western belief that limits are required and validate the calculus.
The later parts of my book also demonstrate the practical value of the realistic, new philosophy of mathematics in various contemporary contexts. Zeroism throws fresh light on the problem of infinities in the renormalization problem of quantum field theory, or relativistic shocks, which problems cannot be tackled by the European understanding of calculus and limits, or the Schwartz theory of distributions, or even non-standard analysis.
It is irrelevant whether the reviewer's total failure to address the new philosophy was intentional mischief or a mere failure to understand (or a bit of both). Let us give the reviewer the benefit of doubt and suppose that he failed to understand the book from chapter 2 onwards. In that case, he ought not to have accepted the book for review, or, if he did, he ought to have stated up-front that he did not understand most of the book. At the very least, even a 10% honest reviewer would have refrained from commenting on those parts he did not understand. The other possibility that the entire new philosophy of mathematics propounded in the book was suppressed knowingly, and not through ignorance, is equally unpalatable.
Perhaps the reviewer wanted to suppress my point that Newton's understanding of the calculus was influenced by his religious belief that mathematics is perfect, and that his physics failed for that very reason. (Newton thought, like his contemporaries, that "the Bible is the word of God and the world is the work of God" written in the language of mathematics which must be perfect.) We speak of Newton's "laws" and not "hypotheses", because his contemporaries accepted his claim that the "laws of God" had been revealed to him. Therefore, to be able to use the time derivative in his second "law", Newton needed to "perfect" the calculus. He hence made time metaphysical, in his Principia, and his philosophical error is shown by the way his physics failed (philosophically) and had to be replaced by the theory of relativity based on a new understanding of time.
The point is: Newton's religious beliefs influenced both his mathematics and physics, and led to errors in them. We must recall that the impact of Newton's religious beliefs on this mathematics and physics could not be assessed to date just because Western historians have dishonestly suppressed Newton's real religious views and his 50 years of scholarship leading to his 8-volume History of the Church. (He had documented the changes in Christian doctrine and the Bible after the Nicene council.) My book explains how the early Western philosophy of mathematics was not only explicitly religious, but it agreed with pre-Nicene Christianity. This early (Platonic-Neoplatonic) philosophy of mathematics was transformed during the Crusades, using concoctions like Euclid (for which see below). It was this post-Crusade theology that led to Newton's erroneous religious beliefs about mathematics and physics. (The successful part of Newton work related to the computational technique, the calculus, borrowed from India.)
The availability of a new philosophy of mathematics, brings out the religious undercurrents of formalism also in contemporary terms. Thus, the book explicitly argues that the difficulties of teaching mathematics today arise because the complexities of theology have got interwoven into it, and suggests that casting out the theology from mathematics makes math very easy, while retaining rigour with the help of the new philosophy (as is now being demonstrated in the ongoing teaching course on "Calculus without limits") etc. etc.
But if the reviewer knowingly suppressed the later parts of the book for reasons of religious prejudice, that is equally unacceptable, even if this was done with the complicity of the editor.
So, whichever the way we look at it, the ENTIRE new philosophy articulated and developed in the book has been set aside by the reviewer just because the basic intention never was to review the book, but only to use the book-review as an excuse to articulate falsehoods about my person and to misrepresent my point of view.
Incidentally, one of the conclusions that emerges from the new philosophy in the book is that one can and ought to get rid of set theory---and set theory is what the reviewer has spent a lot of his life on. One understands that this might upset the reviewer, but the right way is to either accept the arguments or to respond with counter-arguments, and not to pretend that the arguments don't exist.
The blatantly false assertion that the later part of the book contains no philosophy provides an easy way out of all difficulties. Such blatant falsehoods, however, are not appropriate for a review. Reviewers are entitled to their opinion, but not to such blatant misrepresentation of the entire contents of the book which is no part of even a moderately dishonest review.
Why was the editor not able (or unwilling) to find any better reviewer, better acquainted with Indian philosophy? This itself speaks volumes for the way non-Westerner are systematically excluded from Western journals, conferences, and the like. This reviewer has obviously never published anything on Indian philosophy, and probably can't even spell or pronounce the name of sunyavada correctly. His ignorance is revealed in the review itself when he goes overboard in his desire to criticize, and criticizes the book for not containing a tutorial on the most elementary aspects of Indian philosophy and bemoans the lack of a "good introduction" to it! My book clearly states that it is intended for experts. Why on earth should a book written for experts contain such an introductory tutorial? If that is what the reviewer wants, he should attend the high-school or undergraduate courses in Indian philosophy designed for this purpose.
One is reminded of the famous remark made by my friend the late Paulos Mar Gregorios to the pope: that one who is unacquainted with Nagarjuna is as illiterate on Indian tradition, as a person unacquainted with Plato would be on the Western tradition.
What would one think of the standard of an Indian journal if the editor were to send a book involving Western philosophy to a reviewer who not only knew nothing of Plato and but declares that what Plato said was not philosophy? This journal from Oxford University has shown that it maintains a worse standard than that. If the journal has no access to experts in non-Western philosophy, it must be because that is its defective editorial policy. But if the editorial policy of this journal is that the philosophy of mathematics can only be Western, it should rename itself appropriately to give a more honest account of its contents and practices. Presumably, however, the editor wants to promote these biased policies in an underhand way. That would also explain why he selected such a reviewer who has no knowledge of the subject of the book which proposes a new philosophy of mathematics from a non-Western perspective. As they say, bandar kya jaane adrak ka swad! Some learned journal this which could find no better reviewer for a book it solicited for review!
--Let us turn now to the two chapters of the book that the reviewer claims to have read. The second chapter advances a straightforward argument already stated above. Namely, present-day formal mathematics is concerned with proving theorems. These "proofs" assume 2-valued logic; changing logic would change the theorems. But why should logic be 2-valued? The choice is either a (a) cultural or (b) an empirical matter. If logic is chosen on cultural grounds, then 2-valued logic is not universal for Buddhist and Jain logics, for example, are not two valued. If logic is chosen on empirical grounds, one must rely on physics, and quantum logic is not 2-valued. The reviewer says this argument is very weak. So, what is his counter-argument? The reviewer's counter-argument is that logic need not be decided empirically!
Clearly there are two parts to my argument. The nature of logic could be decided (a) culturally OR (b) empirically. But the reviewer reduces my argument to only part (b), pretending that the first part does not exist. That shows that he is unable to contest the real argument at all, and either has an excessively weak understanding of it, or found it necessary to dishonestly distort and misrepresent my argument.
The reviewer should have pondered for a moment before giving such a farcical "counter-argument". If logic is decided purely culturally, AND this choice does not fit into what Buddhists and Jains think, that makes formal mathematics non-secular and a matter pertaining to a particular religion. Anyway, formal mathematics and theorem-proving (unlike arithmetic calculation) has no practical value at all. So this sort of mathematics should be banned from school education in countries like India and US which are obliged by law to be secular. That, incidentally, is exactly what I have told the National Knowledge Commission in India. (Formal mathematics could, of course, continue to be taught in university departments of theology or culture; I have suggested that too.)
--The other argument that the reviewer has is a quote from Hilbert to the effect that mathematics is not arbitrary. Now isn't that a powerful argument? The great Hilbert actually said mathematics is not arbitrary, therefore it is not arbitrary! Wow! Undoubtedly this journal sets wonderful standards of philosophy! This reliance on authority tempts one to quote Adelard of Bath, who tried to communicate to Christians what he had learnt from Muslims:
"you are dazzled by the show of authority and led by a halter. For what is authority to be called, but a halter? As the brute beasts, indeed, are led by the halter, and have no idea by what they are led or why, but only follow the rope that holds them, so also the authority of writers leads not a few of you into danger, tied and bound by brutishI am not at all trying to compare the reviewer to some brute animals, for it is only in Christian theology that animals are regarded as soul-less, while anyone can see that animals have a far better moral sense than those morally guided by priests.
But authority is indispensable to formal mathematics. While the validity of mathematical proof can be decided mechanically, there is no way to assess the value of a mathematical theorem except to rely on authority. Therefore, formal mathematicians, especially professional one's, are haplessly dependent upon authority. And since the reviewer's entire argument is from authority, he punctuates his "argument" with constant attempts to belittle me with personal remarks, in this case the remark that "Raju would be surprised to learn" that Hilbert said so. The reviewer forgot to add that the pope too said the same thing some time back, and in 2006 I published an article on Znet and in the Indian Journal of Secularism explaining the theological and political mileage the pope hoped to derive from this false dogma of Christian absolutism based on the appropriation of reason through concocted history. That article is available at the click of a mouse at Znet.
This similarity between Hilbert's AND Russell's views and the pope's is part of what I mean by saying that the views of Hilbert AND Russell are religious. This is regardless of their personal averments: Russell, of course, was an atheist, and a non-Christian. This is stated explicitly on p. 273 of my book "Bertrand Russell, for example, clearly freed himself from many aspects of religious indoctrination, but accepted uncritically the received historical narrative, and this directly influenced his philosophy of mathematics." (But, of course, the reviewer has ignored all parts of the book after chapter 2, and this comes after chapter 2.)
--So, the reviewer has (1) neglected most of the book, and thoroughly misrepresented its contents. (2) Of the first two chapters of the book, that he claims to have read, he has blundered in his counter-argument.
What about the first chapter?
Here, the reviewer takes up only one point: namely that Euclid did not exist. Note that this is a historical issue not a philosophical one, but the reviewer engages with it anyway. He seemingly concedes the point, only to quibble that some other persons or group of persons could have systematised the Elements before the Christian era! That is, if Euclid did not write the book, Euclid1 could have written it! (And if Euclid1 did not exist, then Euclid2 could have written it, or maybe it was Euclid1+Euclid2 and so on!) Presumably, as a formal logician the reviewer is immensely satisfied with such postulates and quibbles, and regards them as a way to work around my argument without addressing any evidence. This is doubtless a genuine failure to comprehend a very simple argument. The reason I regard it as a genuine failure is that another "professor" on the philomathes list had displayed the same level of aql, and put forward a similar simplistic counter-argument, which distinctly crosses the borderline of the facetious: the accumulation of hypotheses (a stock theological tactic) is bad enough, but here even the accumulated hypotheses do not even remotely meet my argument!
So, let me explain things at the kindergarten level. My first claim is that Euclid was concocted during the Crusades in order to concoct a theologically correct early-Greek origin for the Elements, obtained from Arabs (since neither Arabs nor late Greeks such as Porphyry, Theon, and Proclus were theologically correct). In addition to a theologically-correct origin, the fear of heresy during the Inquisition made it mandatory to provide a theologically correct interpretation of any book for it to be acceptable. So the second claim is that the Elements was reinterpreted (exactly like the Bible) to suit post-Crusade Christian theology. The attribution of the text to a Euclid about whom nothing is known facilitated this reinterpretation (which could be passed off as the philosophy of the unknown Euclid). Such concoctions are a common trick used by priests to lend authority to their theological interpretations. The question is why should anyone believe an iota of this history put forward by religious fanatics during the Crusades and the Inquisition, and developed by later-day colonial and racist historians?
As emphasized in my book (p. 25) we can can believe neither in Euclid NOR in his purported philosophy. The purported evidence for both claims is the same single forged remark from a late text:
"In particular, irrespective of whether Euclid was real or invented, the Monacensis remark about his alleged philosophy of “irrefragable demonstration” is obviously a later-day interpolation."
The circumstances of this forgery are very suspicious.
There is no other evidence that the philosophy of mathematics (attributed to Euclid) existed prior to Proclus. From Plato to Proclus there prevailed an understanding of geometry that was explicitly linked to their religious beliefs about the soul, virtue, and so on.
These religious beliefs, though in agreement with pre-Nicene Christianity, sharply conflicted with post-Nicene (Western) Christian theology (p. 4):
"Since Proclus, like Plato and Socrates, regarded all learning as reminiscence of knowledge that the soul had acquired in previous lives, this closely tied mathematics to his religious beliefs about the soul and reincarnation. Proclus thought the soul, being eternal, was sympathetically stirred by eternal mathematical truths---which entailed the eternity of the cosmos. These beliefs about the soul and cosmos, though compatible with the early Christianity of Origen, were in sharp conflict with the later-day Augustinian doctrines of resurrection, creation, and apocalypse."
Living in a time of such intense attacks by Christians against those "pagan" beliefs, which led to the destruction of all "pagan" temples in the Roman empire, the systematic burning of their books, and the lynching of Hypatia, Proclus could hardly have been unaware of this conflict. And indeed my book asserts (p. 25) that Proclus' commentary relates the philosophy of mathematics to this religious war for it
"brings out, point by subtle point, all the key elements that refute the revised Christian doctrine" eternity vs apocalypse, "past lives vs creation, reincarnation vs resurrection, , immanence vs transcendence, equity vs inequity, images vs charges of idolatry."The importance of some of the distinctions here was explained in my earlier book, The Eleven Pictures of Time, and particular in the chapter on "The curse on cyclic time".
Proclus was HENCE declared a heretic by the church (which then closed all schools of philosophy). Had there then been any other way of understanding mathematics, wouldn't the church have seized upon it?
How, then, did the prevailing philosophy of mathematics, which was in such sharp conflict with post-Nicene theology get transformed into agreement with post-Crusade Christian theology? This is my central argument. This argument cannot be met by concocting a new Euclid1 or Euclid2 or Euclid1+Euclid2, or even a whole infinite series of Euclids "from before the Christian Era" as a new theologically acceptable substitute for the now defunct Euclid.
Then there is the archaeological evidence of papyri which shows that the Elements was NOT standardised until the 3rd c. CE. This is supported by the goof-up between the Eastern and Western church: the name Euclid is found only in the Latin manuscripts (from the 12th c. onwards), but the Greek manuscripts (until the 19th c.) all insist that the Elements is based on the lectures of Theon. Unable to address this evidence, the reviewer predictably shifts to a personal attack imputing motives to me, and saying that I want to insist that Theon was the author! Of course, this attack is bogus. Actually, I think Theon's daughter Hypatia gave final shape to the Elements, and that is why she was lynched by a Christian mob because her philosophy of the Elements was in sharp conflict with post-Nicene theology. (That is also presumably why Proclus speaks of the "author of the Elements" instead of naming the author, so as to avoid arousing Christian prejudices about women.) Also, I have explicitly stated on the same page (p. 25) that this "final shape" only involved a standardisation (NOT systematisation) of the previously-existing Egyptian mystery geometry, so I have no difficulty at all with the prior existence of such geometry!
So the reviewer has got EVERYTHING wrong, even in the first chapter, and hopes to hide these larger issues of mathematical philosophy and its massive religious conflict with post-Nicene Christian theology with an inane quibble about Euclid1+Euclid2. What a wonderful display of the level of philosophical sophistication and learning that one can expect from the reviewer of a learned journal brought out by Oxford university!
I would have welcomed a reviewer expressing a well-argued contrary opinion, leading to a serious debate, and the reviewer's "counter arguments" are excellent material, but only for a farce.
Of course, there is a lot more to the first chapter than just the thesis about Euclid, for this book is written for experts, so it naturally presents a whole lot of complex information, and assumes that the reader has enough background to understand those complexities. For example, the chapter also covers Islamic rational theology and how it led to the formation of post-Crusade Christian rational theology and it also indicates how the appropriation of reason during the Crusades was used against Muslims (as pope Benedict still does); so the reader is expected to be familiar with all that too. But it is perhaps futile to expect this reviewer to know such things.
Incidentally, yet another false statement the reviewer desperately tries to pass off is that the relation of time, values, and logic is confined to Indian thought. Can one take away creation from Christian theology? Even school children understand this connection which the reviewer tries so hard to suppress. The first chapter of this book has a whole section on Proclus and Origen. (My earlier book, cited in this one, elaborates how Proclus' notion of the soul depended upon past lives in the context of quasi-cyclic cosmos, and explains the Christian curse on cyclic time, against Origen, which encapsulates the decisive feature of post-Nicene theology.) Of course, it is quite possible that the reviewer is too ignorant about Christian theology to differentiate between Augustine and Origen, and the change in the Western Christian perception of time between them.
To summarise, the reviewer did not understand any part of the book---neither the main part of the book, advocating a new philosophy of mathematics, nor even the first two chapters---or was interested in deliberately spreading a whole bunch of falsehoods about it (or both). If such a methodology were permissible, one could call the reviewer "Fie" on the grounds that the latter part (of his name) is not relevant, and the first part can be distorted as one wishes!
But what about the biodata? One tends to suppose that the reviewer of a learned journal brought out by Oxford university, which started as a leading Christian madarsa, can understand at least the biodata of the author. Could the reviewer manage that at least?
Unfortunately not. Instead of saying that I have a broad range of interests which includes mathematics, physics, philosophy, computers, and history of science, the reviewer comes up with the false statement: "The author is a statistician and computer scientist by training, who has concentrated on historical matters for the last ten years or so." Natural languages too do NOT embody a 2-valued logic. However, 2-valued logicians interpret English sentences propositionally. So, what the reviewer, a 2-valued logician, means, of course, is the implicit contrapositive: that the author is neither a mathematician nor a philosopher. Whichever way we look at it, this is just a false statement from the reviewer. That is it is false that I trained as a statistician and a computer scientist , and it is false that I have concentrated exclusively on historical matters for the last ten years or so.
This falsehood is deliberate and mischievous: it is very hard to give the reviewer benefit of doubt by further downgrading estimates of his intelligence.
That my basic degrees are in physics and mathematics is knowledge available at the click of a mouse.
Again, a number of my publications in the last ten years are on philosophy, and in philosophy journals, one of which I happened to be on the editorial board of. All these articles and books are clearly listed in the preface itself. So the reviewer knows perfectly well that he is making a deliberately false and misleading statement about my person. These falsehoods are critical to provide a basis for what the reviewer passes off as his "opinion" about the book. Planting these falsehoods and misrepresentations about the book and my person indeed seems to be the basic objective of the so-called "review".
(The preface does not mention my 2004 paper on the solution of functional differential equations--and it is noteworthy that the best mathematician that Oxford had claimed towards the end of his life to have "independently rediscovered" the ideas explained in my 1994 book. So, if I am not a mathematician one wonders what sort of mathematical tradition Oxford has! One presumes and hopes that episode had nothing to do with this "review".)
When the editor of a journal has solicited a book for review, and the reviewer then goes about making such a series of materially false statements about the book and person of the author, this is a clear case of yellow journalism--at best one could call it yellow "learned" journalism, for, after all, this is a learned journal from Oxford university. Although I subscribe to the Jain ethic that in such matters intentions are irrelevant, the intentions are perfectly clear from the numerous belittling personal statements about me, which pepper the review, and which include unscrupulous speculations on how I might have learnt something, "in my university days".
Incidentally, I have encountered this Western method of yellow scholarship so frequently, it is already anticipated in the book, in the Introduction:
"This book, since it presents a new account of Indian history, inevitably involves a critique of Western history. However, some Western scholars, recognizing the intrinsic weakness of that history, tend to respond to any critique of Western history not by examining the evidence (which would expose it) but by launching personal attacks on the critic with labels...".(Note incidentally how the above gives the lie to yet another one of the reviewer's statement that the book is primarily against Eurocentric history: the aim is to give a true account of Indian history; as a side-effect it is necessary to cast off all the voluminous falsehoods of racist history which have piled up like the horse-manure in the Aegean stables.) The review itself is a good example of how Westerners pile up these falsehoods.
Some friends have strongly suggested that I should take legal action against those who tell such falsehoods. But I would get little satisfaction from seeing a few Western scholars declared as criminals or locked up in jail. My quarrel is not with any individual but with a biased point of view.
The reviewer has given an excellent example of how many falsehoods can be packed in one short piece. If the reviewer arrived at those falsehood through a process of logical deduction, it demonstrates the Lokayata point about the utter fallibility of deduction. If, on the other hand, those falsehoods were deliberate, that is a manifest demonstration of how the falsehoods of Western history were deliberately constructed.
THAT is what I would prefer to expose, that racist history originated not because of any unconscious Eurocentric biases, but because of deliberate lies which Western scholars thought they could develop and get away with. The uninterrupted tradition since Eusebius and Orosius has been to glorify themselves and belittle all others, through falsehoods, misrepresentations etc.
What is also of great satisfaction is that the reviewer can do no better than invent a stream of falsehoods about me and apply a variety of adjectives; he could not seriously address A SINGLE PIECE OF evidence or a SINGLE actual argument in the book, and has blundered badly where he tried to do so. That is certainly a matter to rejoice about, for that is presumably the best the West has. And this information is now on record for future generations to laugh at.
Lastly, the reviewer does say one or two positive things. Now, of course, it is a well-known priestcrafty trick to wrap poison in sugar hoping that a gullible person will mistake the contents and swallow the whole thing on faith.
However, I have another possible interpretation. The new mathematical philosophy I have put out is historically compelling, and its practical advantages at this epoch are so great that it is very likely to be adopted in the near future. So, what the reviewer is really saying is that (as in the case of the calculus) all that is needed for its acceptance by the West is that a theologically-correct Western source should be assigned or concocted for it, and it should be reinterpreted in a theologically-correct way!
There are far too many misrepresentations and falsehoods in the review to address all of them individually. However, here are a few more points.
1. The reviewers uses the term "deviant" for logic and history of the calculus. Now, during the Inquisition, Christian priests horribly tortured and killed anyone who "deviated" from what they ordained. In fact, the book argues that that is precisely the reason why Europeans made it a practice never to acknowledge non-Christian sources, for they were afraid of attracting charges of heresy with all the consequences. One also understands that this fear of "deviance" still lurks in the mind of the reviewer. However, by what logic (apart from his personal fears) did the reviewer arrives at what he implicitly declares to be the norm? Did he conduct a survey which included the billions of Indians, Chinese and Africans? Also, my book throws out long-standing falsehoods about history and logic. Those falsehoods of Western history were articulated just because the truth was regarded as a terrible "deviation" which could destroy them!
2. The mechanistic view of the world as God's clockwork was a key ingredient of post-Crusade Christian rational theology, and is still reflected in current terminology such as Newton's "laws". It was natural for this to creep into mathematics. After all a formal proof is necessarily something that can be validated by a moron or a machine. Conversely, the present-day theory of computation is directly based on formalism. Formal mathematics is also mechanical in the sense of being obviously "soul-less", for there is no place in it for "learning" or the "soul" or past lives for which Plato and Proclus valued mathematics. So, the reviewer is ill-informed even about the philosophy of formal mathematics which he sets out to defend.