Monday, September 27, 2010

Line-by-line commentary to the first few pages of Professor Amartya Sen's book, "The Argumentative Indian"
(written in June 2007)


The Argumentative Indian
Writings on Indian Culture, History and Identity
Amartya Sen


Comment 1: Like Adam Smith’s Invisible Hand and Joseph Schumpeter’s Creative Destruction, Amartya Sen’s concept of an Argumentative Indian may yet prove to have no scientific validity in the long run. By scientific validity, I mean addressing questions of the following type: does it give a rational account of the behavior of a typical Indian? Or is it the best intellectual framework for the progress of India? In fact, as Professor Sen readily admits in the book’s preface, “I am very aware that there are other ways of proceeding.”

Beyond the reasons pointed out in the book in support of the argumentative tradition -- that it promotes democracy and public reasoning, resists social inequality, and removes poverty and deprivation – this tradition has the great strength that it is founded on a non-violent, civil manner of dispute resolution, in contrast to the 'clash of civilizations' approach. In that respect, the argumentative tradition is an authentic representation of Indian culture, history and identity. For the same reason, its outlook, in an age of relative peace and stability, is essentially modern and befits academic scholarship.






PART ONE

Voice and Heterodoxy


I

The Argumentative Indian

Prolixity is not alien to us in India. We are able to talk at some length. Krishna Menon’s record of the longest speech ever delivered at the United Nations (nine hours non-stop), established half a century ago (when Menon was leading the Indian delegation), has not been equalled by anyone from anywhere. Other peaks of loquaciousness have been scaled by other Indians. We do like to speak.


Comment 2: Sure, we do like to speak. But the vast majority of Indians do not have any particular facility with language, tongue-tied as they are with English, and speaking in a guttural, intuitive manner without much emphasis on grammar and syntax when it comes to their own native language.

We do like to speak, and villagers speaking out at panchayats is historical evidence for the tradition of public reasoning in India. But, as a people, Indians do not have the rhetorical training for reasoning in public in a logical manner. To put this in perspective, the public speeches given by the great Western orators like Demosthenes and Pericles in Greece, and Cicero and Crassus in Rome have been studied for their rhetorical nuances for centuries at Schools and Universities in the West. Indians haven’t had the historical benefit of such an education. On the other hand, public narration of fables and puranic myths, and enactment of these stories in the form of musicals and drama on religious occasions is quite common. Even more common among the Indian public are cinematic dialogues and Bollywood songs. Less common, but more important are the public meetings during the time of political elections.

On another note, among caricatures of the typical Indian are the obedient son, the enigmatic sadhu, the suffering housewife, all suggesting a strong undercurrent of a culture of silent penance (mouna vrat). Definitely, Indians are known not only for loud complaining, but also for exercising restraint and accepting defeat sportingly.







This is not a new habit. The ancient Sanskrit epics the Ramayana and the Mahabharata, which are frequently compared with the Iliad and the Odyssey, are colossally longer than the works that the modest Homer could manage. Indeed, the Mahabharata alone is about seven times as long as the Iliad and the Odyssey put together.


Comment 3: This is a double edged sword. At first glance, it appears that putting the Sanskrit epics on a back-patting, leg-pulling camaraderie with the Greek classics serves to establish the authenticity of Indian literature in the eyes of international audience. However, the Indian literary tradition goes back even further to the four Vedas. In fact, the Vedas are quite relevant to the argumentative (spoken) tradition, because they were not just read quietly by individuals, but were chanted loudly in public. There is nothing in Greek literature that compares to the Vedas either from a historical perspective or from a literary perspective.







The Ramayana and the Mahabharata are certainly great epics: I recall with much joy how my own life was vastly enriched when I encountered them first as a restless youngster looking for intellectual stimulation as well as sheer entertainment. But they proceed from stories to stories woven around their principal tales, and are engagingly full of dialogues, dilemmas and alternative perspectives. And we encounter masses of arguments and counterarguments spread over incessant debates and disputations.


Comment 4: While there is plenty of evidence in Indian literature for “dialogues, dilemmas and alternative perspectives”, there is nothing in it that demonstrates how these states of ignorance and confusion could resolve themselves to truths and certainties. Certainly, nothing like Euclid’s theorem – proof development of geometry in a self-evident manner, nor like Socrates’ willingness to use purely rational arguments, in dialogues with the skeptical young men of Athens, to arrive at the truth.







Dialogue and Significance

The arguments are also, often enough, quite substantive. For example, the famous Bhagavad Gita, which is one small section of the Mahabharata, presents a tussle between two contrary moral positions – Krishna’s emphasis on doing one’s duty, on one side, and Arjuna’s focus on avoiding bad consequences (and generating good ones), on the other.


Comment 5: The Bhagavad Gita discusses the concept of the soul in a much more sophisticated manner than the rest of the Mahabharata. For this reason, it has often been suggested that the Bhagavad Gita itself was written sometime during or after the advent of the Buddhist and Jainist theologies which discussed the transmigration of the soul rigorously, much after the original compilation of the Mahabharata. In particular, the author(s) of the Bhagavad Gita purportedly favored philosophical clarity to a great extent over historical accuracy. It is true that generation after generation has found inspiration in the ‘transcendental’ clarity of the Gita, most recently the International Krishna Consciousness movement. However, can the Gita, which favors philosophical and ‘transcendental’ clarity in such a lopsided manner, be quoted as the prime example of the argumentative tradition of India? If so, it would imply, as scholars like Sir V. S. Naipaul have pointed out, that Indians have no scientific tools for exploring their identities and achieving self-knowledge. This is why it is important to focus on the four original Vedas rather than the Bhagavad Gita.







The debate occurs on the eve of the great war that is a central event in the Mahabharata. Watching the two armies readying for war, profound doubts about the correctness of what they are doing are raised by Arjuna, the peerless and invincible warrior in the army of the just and honourable royal family (the Pandavas) who are about to fight the unjust usurpers (the Kauravas).


Comment 6: While the text of the Bhagavad Gita deals with extremely deep material, it has to be said that it is not really a debate, or a dialogue in the sense of Plato. There is a certain amount of coercion, in that one of the parties to the dialogue is a supreme being, who is above good and evil, beyond birth and death, and is only condescending to illuminate the other party in some transcendental matters. In particular, the supreme being would not discuss with a human being every time he/she is deeply disturbed by philosophical questions. Only a true devotee like Arjuna would have that privilege. This is in contrast with Plato-type dialogues which can be naturally enacted in daily lives by ordinary people.

On another note, the Mahabharata by itself portrays its characters as larger than life, in keeping with an epic imagery (for example, Arjuna is the ‘peerless and invincible warrior’). Whereas the Gita deals with the doubts and fears of an individual. A doubting warrior-general would be less than heroic in the larger canvas of the Mahabharata, and his state of doubt would not get more than a few lines, by way of attention, in the text of the epic. This is another example where the Mahabharata and Bhagavad Gita do not seem to share the same poetic background and do not address the same themes.







Arjuna questions whether it is right to be concerned only with one’s duty to promote a just cause and be indifferent to the misery and the slaughter – even of one’s kin – that the war itself would undoubtedly cause. Krishna, a divine incarnation in the form of a human being (in fact, he is also Arjuna’s charioteer), argues against Arjuna. His response takes the form of articulating principles of action – based on the priority of doing one’s duty – which have been repeated again and again in Indian philosophy. Krishna insists on Arjuna’s duty to fight, irrespective of his evaluation of the consequences. It is a just cause, and, as a warrior and a general on whom his side must rely, Arjuna cannot waver from his obligations, no matter what the consequences are.


Comment 7: There are some very subtle points here. Firstly, Indian literature does not really have a serious theory of morals. At least, it is reasonable to expect one to accept that Panchathantra and Jataka tales are not in the same class as the writings of Aristotle and Plato on morals. What does exist is a pervading sense of mental peace (shanthi) in Indian culture. When an Indian is severely disturbed by philosophical doubts at various moments in his/her life, it is for the seeking of this shanthi that he/she aims for. His/her sense of right and wrong is indicated by the degree of attainment of this shanthi, perhaps in close consultation with a Guru (for more mundane matters, he/she would consult with family members -- Matha, Pitha, Guru, Deivam). From a cultural perspective, it is more plausible that Arjuna’s doubts and questions arose from the necessity to seek this mental peace and from the pressing immediate need to find the will to fight the war, rather than from a broad philosophical framework of morals. Of course, there was also the issue of re-birth, as a common Indian belief, if one committed sins. But what exactly these sins are, is not defined by any of the religious theologies of Ancient India beyond requiring a strict adherence to the rituals, definitely nothing by way of the Ten Commandments. For example, would hesitating to fight before a war constitute a sin?

Secondly, one must note that the recurrence of this ‘principle of action’ -- the priority of doing one’s duty -- in Indian philosophy happens historically only after the Bhagavad Gita. Duty of an individual to an external entity, whether it be the state or a supreme being, is a quintessentially Greek concept, which Socrates paid for with his life. Once the concepts of the ideal state and the duties of its citizens towards that state were developed through centuries of effort by the Greek philosophers in a thoroughly rational manner, it is a relatively easier proposition to assimilate that sense of duty with the indigenous Brahminical, Buddhist and Jainist theologies, under the aegis of a supreme being. That said, one must admit that the Bhagavad Gita is an extremely beautiful and poetic unification of the major philosophies of that time, whose power of motivating the individual to equanimous action is unique and unrivalled. The effectiveness of this transformational power of the Gita can still be observed among the devotees of the Krishna Consciousness movement.

Thirdly, the direct association of Arjuna with the supreme being as his friend, his philosopher and his guide is analogous to Jesus Christ's direct association with God in a father-son relationship. This is the first incidence, in an Indian religious document, where a human associates with God in a give-take, loving relationship. Before this occurrence, idol worship, nirvana, ahimsa, agnosticism, yogic penance, fire worship, animal sacrifice and nature worship were the main religious practices in India, and the conception of God whenever it existed was that of a vengeful one fully dominating the individual’s psyche. In addition, the precepts of the Bhagavad Gita were also the first forays of Indian philosophy into monotheism, an important legacy of the Judeo-Christian religions, going back to Moses and Zoroaster. These are some of the examples that show that the Gita (and the Upanishads) assimilated the major streams of thoughts in the World at that time into Indian culture.







Krishna’s hallowing of the demands of duty wins the argument, at least as seen in the religious perspective. Indeed, Krishna’s conversation with Arjuna, the Bhagavad Gita, became a treatise of great theological importance in Hindu philosophy, focusing particularly on the ‘removal’ of Arjuna’s doubts.


Comment 8: The theological importance of the Gita in subsequent Hindu philosophy is three-fold. Firstly, the Gita and the Upanishads, formed the Vedanta philosophy, which line of investigation led to a great debate within Hinduism, about the concepts of Advaitha and Visishtadvaitha, that prolonged right into the middle ages. Secondly, by subsuming the major tenets of Buddhism and Jainism, the Gita re-established Hinduism as the pre-dominant religion in India. Thirdly, with its other-worldly concerns of the soul and its relationship to God, the Bhagavad Gita pre-occupied the Indian scholar with its transcendental clarity so much, that he/she then did not focus on empirical investigations of the natural world for many centuries. To be fair, empirical investigations did not take off in a serious way in the Western World too until the revolutionary discoveries of Copernicus, Galileo, Descartes and Newton at the end of the middle ages. But by then, the remaining empirical traditions in India were close to extinction. For example, Astronomy had degenerated into Astrology, and Ayurveda was waiting for the British to be replaced by Allopathy. The only phenomenon anywhere close to empirical investigation that India was prepared for at the end of the middle ages was the advent of militant Hinduism and Sikhism. On a different note, it would be interesting to study the influence of Bhagavad Gita on the Mughlai period of Indian history (e.g. Sufism, Din-Illahi, Bhakthi movement).







Krishna’s moral position has also been eloquently endorsed by many philosophical and literary commentators across the world, such as Christopher Isherwood and T. S. Eliot. Isherwood in fact translated the Bhagavad Gita into English. This admiration for the Gita, and for Krishna’s arguments in particular, has been a lasting phenomenon in parts of European culture. It was spectacularly praised in the early nineteenth century by Wilhelm von Humboldt as ‘the most beautiful, perhaps the only true philosophical song existing in any known tongue’. In a poem in Four Quartets, Eliot summarizes Krishna’s view in the form of an admonishment: ‘And do not think of the fruit of action. / Fare forward.’ Eliot explains: ‘Not fare well, / But fare forward, voyagers.’


Comment 9: The Bhagavad Gita has had major influences on many World famous figures, notably Mahatma Gandhi and Albert Einstein. However, its most important influence on the great thinkers in the 20th century has been on mathematicians. Andre Weil, a giant of 20th century mathematics adopted the Gita as his system of belief. In fact, by the end of the 19th century in Europe, the individual’s duties to the state as advocated by ancient Greek philosophy had been replaced, in the public’s conscience, by the emphasis on the freedom and rights of the individual as advocated by the Renaissance Enlightenment. As an unfortunate and unlikely result of this development, during the 1930’s in France, individual glory and prize-driven egomania were the common attitudes among the pioneers and thinkers of science. To counter this malaise, Andre Weil formed the Bourbaki group of mathematicians, all of whom were anonymous members (while they were members), and got no individual credit for their publication. Yet the mathematical research of Bourbaki had a profound impact on 20th century mathematics. To wit, this group alone produced three Fields Medallists. To be truly devoted to one’s research without craving for the fruits of action is very much in the spirit of Bhavagad Gita.

Another mathematician Kurt Godel had also adopted the Gita as the foundation of his beliefs. He was one of the greatest, if not the greatest, logician of the 20th century. In fact, some concepts like the different levels of consciousness found in the Bhagavad Gita have direct bearings on Godel's research work in logic, for example, on the different levels of certainties in mathematical logic, from a theorem to a contradiction.

Other major developments in 20th century mathematics in the spirit of Bhagavad Gita were (i) in unifying the concepts of number and geometry through algebra. It is notable here that the success of mathematicians (primarily Grothendieck, Serre, Weil, Zariski), in establishing deep unifying connections between number and geometry is in striking contrast with centuries-old problems resisting attempts to unify the concepts of number and motion (ref., Riemann Hypothesis), (ii) recall G. H. Hardy’s comment on Srinivasan Ramanujan: “… But with his memory, his patience, and his power of calculation, he combined a power of generalization, a feeling for form, and a capacity for rapid modification of his hypotheses, that were often really startling, and made him, in his own peculiar field, without a rival in his day.” It must be said though, that Hardy’s comments do not fully capture Ramanujan as a mathematician. Ramanujan was a powerfully original and penetratingly insightful mathematician, not just a grand unifier with an eye for elegance. There is always this restlessness and manic energy about Ramanujan, which is quite in contrast to the ideals of mukthi in Hindu scholarship or nirvana in Buddhist scholarship. In that sense, he was a truly modern thinker who just happened to be from India.







And yet, as a debate in which there are two reasonable sides, the epic Mahabharata itself presents, sequentially, each of the two contrary arguments with much care and sympathy.


Comment 10: Perhaps a large part of the care and sympathy can be attributed to the fact that for the first time in Indian religious mythology, a human being was in direct conversation with the supreme being, the sole and single God, under whose command the universe functions. Also, the brotherly love that Arjuna shares with Krishna is similar to Jesus Christ’s filial love for the Christian God. The love in the relationship between the God and the devotee also accounts for the care and sympathy in the conversation. The third factor is that the philosophical depth of the material discussed, by itself, demands much care and caution. This third factor, while present, is not as central as in Plato’s dialogues.







Indeed, the tragic desolation that the post-combat and post-carnage land – largely the Indo-Gangetic plain – seems to face towards the end of the Mahabharata can even be seen as something of a vindication of Arjuna’s profound doubts. Arjuna’s contrary arguments are not really vanquished, no matter what the ‘message’ of the Bhagavad Gita is meant to be. There remains a powerful case for ‘faring well’, and not just ‘forward’.[1]


Comment 11: The tragic desolation of the post-combat land in the Mahabharata does indeed remind one of common every day tragedies of poverty and deprivation in the real world. Yes, the theory of morals, as developed in the West, provides a powerful case and clear directions (in the form of political platforms like Social Justice) for 'faring well'.

In addition, modern economic theories and techniques have made it possible to reliably measure the extent to which the people are 'faring well' and to make the right choice of policies for the welfare of the people. So, it is extremely important for governments to concentrate on economic policies.

But, there is also a third lesson here. That is, the repeated occurrence of convincing the doubter through some wild-card entry, like the Vishwaroopa, in Indian philosophical arguments is quite detrimental in the long run. The student of Indian philosophy can not verify the arguments in the Bhagavad Gita or those in the later philosophical developments like Advaitha-Visishtadvaitha through empirical means -- how is he to re-enact the conversation with the supreme being, or to verify the existence of the soul? Also, being enamored with the transcendental clarity of the Bhagavad Gita, the Indian scholar did not venture into exploring the natural world for nearly two thousand years. This is the price paid for the lack of logical rigor and a disregard for rationalism in Indian philosophical arguments, something the Western philosophical tradition has managed to avoid through Aristotle's rigorous development of the concept of logic and his emphasis on empirical verification.







J. Robert Oppenheimer, the leader of the American team that developed the ultimate ‘weapon of mass destruction’ during the Second World War, was moved to quote Krishna’s words (‘I am become death, the destroyer of worlds’) as he watched, on 16 July 1945, the awesome force of the first nuclear explosion devised by man.


Comment 12: Oppenheimer might as well have quoted from Revelations 22:13 of the Holy Bible, ‘I am the alpha and the omega, the first and the last, the beginning and the end’. Historically, India hasn’t really seen the grand scale of war and destruction that the West has repeatedly seen, whether it is for building empires or as a clash of civilizations. So we don’t really know what it is to be put in a situation where one has to make critical choices between scarce resources, among immediate and pressing needs, while great destruction is being wrought all around. That is why, it is wise to accept that the theological treatment of death and destruction in the Bhagavad Gita is a second-hand, re-hashed one. Indian philosophy is not good with explaining death, definitely not in the profound way that the foundations of the Western civilization could be re-organized in modern times around concepts like death wish (along with id, ego and super ego) by Sigmund Freud, or creative destruction by Joseph Schumpeter. On the other hand, Indian philosophy is good in preserving what one already has and in extending the non-violent, positive life force that people experience in their daily lives (e.g. ahimsa, nirvana, yoga, ayurveda). In fact, the ability to control one’s anger and maintain calm is seen as a necessary step towards achieving knowledge and wisdom in India, in contrast to the stereotype of the restless genius which is quite prevalent in Western culture.







Like the advice that Arjuna had received about his duty as a warrior fighting for a just cause, Oppenheimer the physicist could well find justification in his technical commitment to develop a bomb for what was clearly the right side.


Comment 13: It is more instructive to, instead, try to understand why many physicists, chemists and mathematicians in the mid-20th century were frequently led to reading the Bhagavad Gita. If the sole reason was that the Bhagavad Gita discussed finding motivation to fight a nuclear war and to do one’s duty amidst all-around destruction, then it would have found an equally good reception amidst military generals. But, it did not. So, it seems reasonable that it was admired among the scientists for other reasons as well. What are they? It would be interesting to conduct a thorough study in this direction.







Scrutinizing – indeed criticizing – his own actions, Oppenheimer said later on: ‘When you see something that is technically sweet, you go ahead and do it and you argue about what to do about it only after you have had your technical success.’


Comment 14: May be I am wrong here. But Oppenheimer’s comment seems to be about the modern scientific research environment where the scientist is looking for instant gratification through technical discoveries, but the scale of operation is so small at any given moment, that there is hardly any room for moral concerns until later. Even when that later time of reckoning arrives, one is only required to argue one’s case with one’s peers who are seated in a committee or one only sends in a grant proposal. One does not really go through any process of personal soul searching about the potential destruction caused by one’s discoveries and developments. In particular, Oppenheimer might not be criticizing himself in these comments.







Despite that compulsion to ‘fare forward’, there was reason also for reflecting on Arjuna’s concerns: How can good come from killing so many people? And why should I seek victory, kingdom or happiness for my own side?


Comment 15: If Professor Sen’s aim in quoting the Bhagavad Gita as an example in this essay is to emphasize, in the cause of heterodoxy, that the defeated argument for faring well is actually the more sound one, then he is definitely correct in his approach. In fact, the direction the ‘debate’ proceeds in the Gita is a dangerous and irresponsible one, especially in this age of terrorism. Professor Sen definitely succeeds here in showing that the healthy respect shown for a dissenting, defeated view in the argumentative tradition would prevent young people taking to violent causes in favor, supposedly, of the victorious, majority view. Thus the Gita example shows how the argumentative tradition discourages sectarian violence and terrorism. However, there are many ills of today’s society that are not so strikingly and starkly presented as the pre-war scene was to Arjuna. Environmental degradation, AIDS and malarial diseases, political corruption, sexual exploitation, domestic violence, smoking and alcoholism are some examples of silent, small-scale evils at the individual level that add up to enormous proportions at the level of society over time. These evils are working in a more subtle manner than terrorism or communal violence. It would have been good to see Professor Sen give examples for illustrating how the significance of the dialogue in the argumentative tradition helps to deal with these silent evils.







These arguments remain thoroughly relevant in the contemporary world.


Comment 16: No, they don’t. Today, India is so disorganized and chaotic not because millions of Arjunas are moved to inaction due to profound doubts about doing their duty in the wake of moral compunctions. Rather, it is because abstract concepts like the state, health, environment, property, education, justice, family and neighborhood are still only intuitively understood by the average Indian. We haven’t had a really serious age of enlightenment since the compilation of the Bhagavad Gita! If anything, Indian scholarship needs to first understand these concepts better. Hopefully, then more natural arguments would emerge that bear scientific validity and address every day concerns more directly.







The case for doing what one sees as one’s duty must be strong, but how can we be indifferent to the consequences that may follow from our doing what we take to be our just duty?


Comment 17: As such, this question is only relevant today for the extremists in India, both Hindu and Islamic, who take to violence as a just cause. The ordinary Indian is not bothered so much by any call of duty. Now, the extremists too do not have any clear conception of duty. They are simply looking to give vent to their barbaric instincts.







As we reflect on the manifest problem of the global world (from terrorism, wars and violence to epidemics, insecurity and grueling poverty), or on India’s special concerns (such as economic development, nuclear confrontation or regional peace), it is important to take on board Arjuna’s consequential analysis, in addition to considering Krishna’s arguments for doing one’s duty.


Comment 18: India has not been particularly good at this. Clear and incisive consequential analysis that prevents unfavorable results for the nation died with Chanakya. India’s inability to keep up with developments in the rest of the world has been exposed repeatedly throughout our history, rather brutally, through invasions and occupations. However, its long tradition of scholarship and respect for knowledge, combined with non-violence and friendliness, is now finally coming to pay off hugely. Moreover, the success of Indian democracy has ensured that catastrophic consequences of government policies are quickly mitigated (e.g. Indira Gandhi’s emergency, Sanjay Gandhi’s forced vasectomies, and the 2002 sectarian violence in Gujarat. The last example has not been fully corrected since the state government is still occupied by the same party in question).







The univocal ‘message of the Gita’ requires supplementation by the broader argumentative wisdom of the Mahabharata, of which the Gita is only one small part.


Comment 19: No, again. The broader argumentative wisdom of the Mahabharata mainly concerns an inter-clan war. Is it really relevant for the India of the 21st century? What we need to do is to focus on more authentic, scholarly documents, like the four Vedas, which can withstand scientific scrutiny. If anything, an anthropological study comparing the Vedas and the ancient religions of Egypt, Greece, Babylon and Persia would give clear and definite authenticity to the Vedas. The Bhagavad Gita can be taken as an authoritative commentary on the Vedas, but it cannot be taken as the be-all and the end-all reference to Hinduism, the way it has been done by Westerners so far. Perhaps, Westerners have got such an attitude about the Gita from the adherence of the Judeo-Christian religions, these being the religions they are usually brought up with, to the Holy Bible and the Old Testament as the main documentary references for their faith.

We need to figure out how the inclusive wisdom and the scientific temperament exhibited in the Vedas can be combined with (i) later religious influences like Budhism, Jainism, Islam, Christianity, Sikhism and other religions, (ii) later scientific advancements like Calculus, Computers, Medicine, Engineering and Biology, (iii) later humanistic influences like music, arts, architecture, the English language, Urdu poetry and regional literature, (iv) later administrative and political institutions like those of the British and the Mughals, (v) later intellectual developments like the state, empire, university, civilization, globalization, and various other aspects of one’s identity. What Indian culture also needs is a healthy dose of experimentation and empirical research, especially to overcome an age-old ignorance of biological concerns like personal health, cleanliness and sports. It is obvious that such a great intellectual advancement is not happening anytime in the next one hundred years. But, it is certainly good to have a go at it, in a non-violent, civil manner. And this seems to be the right direction for India to proceed.

On another note, a unifying message is not bad, by itself. It may be a natural, anthropological process for humans to find issues in common with other people. Hence, a modern outlook for unity and diversity in India emulating the natural unity and diversity observed in the biological world is a more robust framework, than ad-hoc policies on unity and diversity based on the political theories of the day.







There will be an opportunity in this essay, and in the others to follow, to examine the reach and significance of many of the debates and altercations that have figured prominently in the Indian argumentative tradition. We have to take note not only of the opinions that won – or allegedly won – in the debates, but also of the other points of view that were presented and are recorded or remembered. A defeated argument that refuses to be obliterated can remain very alive.


Comment 20: The argumentative tradition does keep alive all sides of a debate, in contrast to the clash of civilizations approach which is not quite relevant to the Indian context. However, one must note the following points on the argumentative tradition which were already raised in the previous comments: (i) lack of logical rigor and crudeness of arguments in Indian literature, (ii) lack of training among the general public to appreciate rhetorical nuances in public reasoning, (iii) danger of disenfranchisement of people who have a silent disposition, (iv) too much heterodoxy without the benefit of unifying principles leads to post-modern disillusionment. Science develops as much due to individual creativity as it does due to engaging debates. So, doing one’s work quietly is equally important as arguing one’s point with others.




[1] As a high-school student, when I asked my Sanskrit teacher whether it would be permissible to say that the divine Krishna got away with an incomplete and unconvincing argument, he replied: ‘Maybe you could say that, but you must say it with adequate respect.’ I have presented elsewhere a critique – I hope with adequate respect – of Krishna’s deontology, along with a defence of Arjuna’s consequential perspective, in ‘Consequential Evaluation and Practical Reason’, Journal of Philosophy 97 (Sept. 2000).

Friday, September 24, 2010

Book review: George P. Lakoff and Raphael E. Nunez, "Where Mathematics Comes From: How the Embodied Mind Brings Mathematics into Being"

(Dated: October 18, 2007. Note that this review was originally written as a postal correspondence with Professor Dana Scott, co-winner of the 1976 ACM Turing Award. The initial few paragraphs in the correspondence are not directly related to the review of the Lakoff-Nunez book. The book review, proper, starts from the sixth paragraph of the correspondence given below).


Urbana-Champaign, IL
October 18, 2007
Thursday


Dear Professor Dana Scott,

As I mentioned during our discussion last Saturday, I do not write on philosophy directly, because it is very tricky. So, I have been approaching the philosophy of mathematics quite indirectly, by first considering history, culture and identity. In view of this indirect approach, it seems to me that the best way to introduce my views on mathematics would be to show you some of my recent writings. I have enclosed two unfinished articles in this mail:

1. An essay titled, "Effective Philanthropy in India: a case study for contributing to the strengthening of the foundations of a developing nation". In this essay, I am making several observations about the relative strengths of the Western society and the Indian society, in their ability to support a life of mathematics. There are also several other discussions centered on mathematics.

2. Line-by-line commentary to the first few pages of Professor Amartya Sen's recent book, "The Argumentative Indian". In these comments, I touch on the mathematical nature of some ancient Indian literature, particularly, the Bhagavad Gita and the Vedas. I also make some observations about famous mathematicians like Andre Weil, Kurt Godel, G. H. Hardy and Srinivasan Ramanujan.

The first article is really a huge project, as you would realize immediately upon reading the abstract. My plan is to write about a hundred pages for this article. I have written six pages (in
12 font size) till now. But the main ideas are already mentioned in the parts I have managed to write so far -- a detailed abstract and the first few pages of an introduction. I have also included
a five page section called Resources, where further indications about some of the directions I intend to proceed are given in bulleted-points format.

The second article is nearly in its final form. There are twenty comments in all. I might come back on a later occasion to add comments to subsequent pages of Professor Amartya Sen's book. But, the twenty comments I have written so far are self-contained, and may be read as they are.



Now, I had originally had the opportunity to speak with you for a few minutes last Thursday (October 11). You had told me then that there are a lot of articles in recent published literature, on the philosophy of mathematics, that criticize Platonism. Moreover, we agreed that the main theme in the recent book, "Where Mathematics Comes From: How the Embodied Mind brings Mathematics into Being" by the Berkeley Linguist, Professor George Lakoff, and the Cognitive Psychologist, Professor Raphael Nunez, was a 'theory of the embodied mind' which had no place for Platonism. In addition, you told me that the Lakoff - Nunez theory needed a lot more empirical / scientific justification before they can claim that their 'conceptual metaphors' explained all of modern mathematics from a cognitive perspective.

Subsequently, on Saturday, I defended Platonism very strongly, and held that the main weakness of the Lakoff - Nunez theory is not that it lacked adequate justification, but that it tried to eliminate Platonism. In view of these discussions, I feel that I should make some points here to clarify what I believe Platonism to be. Again, this is because my view of Platonism is more unambiguous than what it is usually believed to be --

that it posits the existence of an 'ideal' world of ideas which a human being can inhabit, only occasionally, by way of much striving and thought.

1. Most of Plato's writings that have survived to the present day are in the form of dialogues. The participants in these dialogues, other than Socrates, are the young men of Athens who were rather unsophisticated and untrained in philosophical arguments. These dialogues were written in a simple language, meant to be understood by the common man, and are devoid of any nuanced and hairsplitting interpretations of philosophy. In the interest of full disclosure, I interject here to say that my own experience with Plato's dialogues has only been in the reading of Philebus, which Plato wrote as a result of a debate started by Eudoxus, the mathematician.

2. In view of the simplicity of the language of the dialogues, all of Plato's views on the philosophy of mathematics cannot be explained unambiguously by a narrow interpretation like the 'ideal world of ideas', mentioned in italics above. Interpretations of that type only became common in the Western world much later, as a result of religious theologies, which engaged in much nuanced interpretations of the original texts of the religions. Plato never really intended his dialogues to become theological doctrines, but rather, he intended them to provide basic material for common, every day discussions about philosophical matters. However, an unambiguous interpretation of Plato's views, sophisticated to any degree one wants, can be inferred quite accurately by relying on three factors -- (i) the spirit in which Plato wrote his dialogues and the principles he adhered by, (ii) the legacies he left behind, and (iii) the historical usefulness of views ascribed to Plato, in making progress on long-standing problems in mathematics -- all three of which we discuss below.

3. An important legacy of Plato for the modern world has been the university as a place of higher education and research. This is particularly relevant for the pure mathematician, because the modern university has been the main source of employment for pure mathematicians, whereas applied mathematicians, engineers, scientists and computer professionals have successfully found career employment elsewhere. To be sure, research in mathematics has also benefited from the efforts of technical societies, national academies, multi-disciplinary centers, institutes of advanced study, R & D labs, private corporations and software companies. In fact, during the middle-ages, royal patronage of scientific academies in Europe was a major reason that made new mathematical discoveries possible. But, for sheer longevity, Plato's legacy is unrivaled. The academy that Plato set up survived for nearly nine hundred years, before it was closed down by the Roman Emperor Justinian I in 529 AD, as a possible threat to Christianity. Much of the modern university system is modeled after Plato's academy (except that his academy did not issue academic degrees). However, I have to mention a disclaimer here. It would be a big mistake to ascribe everything that happens in the modern university to the legacy of Plato. The university system was heavily subjected to later influences like the Church and the Roman Empire. So, the functioning of the modern university is determined, not just by a quest for knowledge and wisdom, as Plato would have liked, but also by subtle influences of power and money.

4. Another important legacy of Plato to the modern mathematician has been the thesis advisor - graduate student relationship. The sense of respect and admiration in which Plato held Socrates in all his dialogues, written over the course of over forty years, has been the enduring source of inspiration for the way research is to be conducted by the advisor - student duo. Again, this is particularly important to the student of pure mathematics. For doctoral students in other disciplines, the necessity for a physical infrastructure - e.g. computers, laboratories - and attending conferences and seminars to keep abreast of latest developments may be equally important as interacting with the thesis advisor.

5. The particular relevance of Plato's views to the working mathematician of today can be traced back to Sir Isaac Newton's writing of the Principia Mathematica. Just before Newton's time, mathematics was dominated by Rene Descartes. In the Cartesian world view, theorems and proofs (in the spirit of Euclid's high school geometry) did not matter when it came to advanced studies. What mattered were ideas and perceptions. It was with this view that Descartes introduced the Cartesian axes. In one stroke, he had managed to bring together numbers, pictures, motion and measurements -- all the main concerns of mathematics then. This view could be characterized as cognitive existentialism (Cogito Ergo Sum), and it placed much emphasis on geometric intuition (via the Cartesian axes) and empirical evidence (via the Scientific method). Newton in his early years was often engaged in claims and counter-claims with other scholars of the day who were active in the same areas he worked in. However, the publication of the Principia Mathematica in 1686 settled, once and for all, the supreme dominance of Newton's intellect. Every one of his strongest critics, from all over Europe, conceded that Newton's mind existed in a different world -- the Platonic world of ideas. The level of clarity in the exposition, and the complete mastery of the mathematical principles in applying them to physical problems were unprecedented. The Principia Mathematica installed Platonism as the highest ideal of mathematical investigation, sidelining the Cartesian world view, as far as mathematics was concerned, for the next 300 years. We mention here that Newton was also an early pioneer of the school of thought named Formalism, and he was perhaps the greatest intuitionist the world has ever known.

6. The narrow interpretation of Platonism mentioned in italics above completely overlooks some other important aspects of Platonism. The sense of respectful adoration that society bestows on its great thinkers is in the belief that the thinkers are roaming in the Platonic world with no care or worry about the physical world. Also, associated with Platonism is a strong sense of romance and fascination with the subject that is being investigated. Platonism shares such romantic traits with Intuitionism, though the emphasis in Platonism is less on the human element and more on the objects of study than in Intuitionism. Moreover, in Platonism, there is no sense of urgency, as clearly exists in Formalism, for example. Progress happens at its own pace. It is beauty, clarity, depth and finality that one is looking for. For this reason, when a Platonist finally manages to establish a result after a lot of hard work, it comes as a blessing. In fact, under Platonism, engaging in the work itself is therapeutic in a way that the other approaches could not be. In the words of Karl Weierstrass, "The mathematician who is not also something of a poet will never be a complete mathematician".

7. Some scholars of the Renaissance period might view Newton's contribution to the revival of Platonism, as only one part of a mass awakening, spanning several centuries during the Renaissance enlightenment, to the teachings of Plato. We recall here that it was Aristotle who was the dominant philosopher throughout the first millennium. In any case, after Newton, the standards of mathematical scholarship were predominantly focused on Platonic ideals. This state of affairs was further sanctioned by the mathematical developments in the late Renaissance period -- e.g., the discovery of the imaginary number, the proof of the unsolvability of the general quintic polynomial by radicals, and the development of projective geometry. Humanity had gone through generations and generations of thinking about mathematics. Whole civilizations had developed, decayed and disappeared over the course of millenniums. But, in all that time, nobody had thought of the imaginary number. This was the clearest indication that there was indeed something called a Platonic world that was quite different from the physical world. The development of projective geometry is important here for two reasons. Firstly, Blaise Pascal, one of its founders, was the prime example of the human striving for higher knowledge. He made his mark equally in religious theology as well as in mathematics, his Pensees being considered 'the most eloquent book in French prose' by Will Durant. Secondly, the Renaissance painters and artists with their lifestyles revolving around the laid-back, romantic side of Platonism, were intimately involved in using projective geometry in their works. Next, the string of unsolvability results established in this period -- e.g., the impossibility of trisecting an angle, doubling the cube and squaring the circle using only compass and straight-edge, the Abel-Ruffini theorem on polynomials of degree five or higher -- were developments that would be hard to explain solely through a theory of embodied mind for mathematics.

8. In 1854, Bernhard Riemann gave his Habilitation lecture, "On the Hypotheses which lie at the Foundations of Geometry". The topic of the lecture was chosen by Carl Gustav Gauss. In this celebrated address, Riemann stated, "the propositions of geometry cannot be derived from general notions of magnitude, but the properties which distinguish space from other conceivable triply extended magnitudes are only to be deduced from experience". This was wisdom gained from centuries of effort by mathematicians on the independence of the parallel postulate from the first four axioms of Euclid. Clearly, the symbolic manipulation skills of the Formalist or the cognitive skills of the Intuitionist do not account for the techniques and the approaches that were needed for tackling problems of such scale. Platonism alone gave a credible account of the nature and the kind of mathematical reality that mathematicians needed to be concerned with, in order to be able to make progress with such problems that remained unsolved for millennia. Throughout the nineteenth century, pre-occupation with the shape of physical space led frequently to one of the central debates among mathematicians -- whether mathematical reality existed outside of us, or inside. After a lot of deliberations, debates and discussions, a consensus emerged in the twentieth century. By 1940, G. H. Hardy was able to say in his famous essay, 'A Mathematician's Apology', "I believe mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our 'creations', are simply our notes of our observations."

I hope that the eight observations given above show convincingly that Platonism will always be an indispensable philosophical disposition among mathematicians. However, it is true that Formalism began to occupy center-stage among mathematicians in the twentieth century, under the influence of David Hilbert. Swearing a poetic sensibility in the spirit of Weierstrass today would do little to advance the cause of a young mathematician towards his academic tenure. But, it would be a mistake to think modern mathematics has left Platonism behind. In fact, Formalism can be seen as an adaptation of Platonism for the busy, competitive, cosmopolitan lifestyle.

At present, I am trying to understand how the pre-occupation with the building of an empire among the social classes of the late nineteenth century Europe could have motivated a Formalist world view among mathematicians. The socio-political problems that occupied the intellectuals in Europe during the nineteenth century, were very much the concerns of an empire. The second Nobel Prize in Literature was awarded in 1902 to Theodore Mommsen, "the greatest living master of the art of historical writing, with special reference to his monumental work, A history of Rome". Of course, Formalism is founded on the age old debate on form versus function, and hence may be a natural human instinct. This particular project of mine, towards understanding the roots of Formalism, is still work in progress, and is far from final form.

During our discussions last Saturday, a gentleman named Dr. Michael Kelly joined us. He had made two comments. The first was that when I mentioned that the Lakoff - Nunez team can explain the imaginary number I, using their conceptual metaphors, Dr. Kelly asked what
about 2*I, 3*I, and so on. I suppose his point is that there are an infinite number of Platonic objects in mathematics, and they would have to explain each one cognitively. This is really quite
a nuanced interpretation of Platonism for which I would refer the gentleman to my point (1) above on Platonism. The second comment was made when I mentioned that since the Lakoff - Nunez book went against Platonism, it is going to run into serious trouble with a lot of mathematicians. Dr. Kelly said something to the effect that there are whole departments working on the meaning of Platonism, and if there was a consensus against it, surely their book could go against it. My answer is to refer the gentleman to point (2) above on Platonism.

I have several other comments to make about the Lakoff - Nunez book. Last Thursday, you had mentioned that Professor George Lakoff's work has become quite political, the title of his latest book being, 'Don't think of the elephant:...' Well, mathematics is in a crisis now. In the nineteenth century, mathematics occupied a pre-eminent position among the scientists and the thinkers. To mention just one example, fifty years before Albert Einstein developed his special theory of relativity, Riemann had already built the mathematical infrastructure required for it, by defining the Riemannian manifold. However, over the course of the twentieth century, an interesting combination of psychology, linguistics, anthropology, evolution, genetics, medicine and ecology (all seen from a computational perspective) has taken over the intellectual center-stage of the modern society. In fact, the most important discoveries are happening elsewhere, and mathematics is simply trying to imitate the exciting developments in these other areas. I am sure that the Lakoff - Nunez team sees this clearly. According to them, the game is already over. They don't believe they need to make any more justifications. They have nothing to learn from mathematicians. They say explicitly in their book:

"But mathematics by itself does not and cannot empirically study human ideas; human cognition is simply not its subject matter. It is up to cognitive science and the neurosciences to do what mathematics itself cannot do -- namely, apply the science of mind to human mathematical ideas. That is the purpose of this book."

Professor Lakoff has moved onto politics, perhaps hoping to make a bigger impact there. It appears that the Lakoff - Nunez team see themselves as philosophers, as intellectual heirs of Rene Descartes. Since philosophers have always concerned themselves with the political situation of the day, they probably are not embarrassed by becoming politically active.

On the other hand, the Cartesian world view, building on the Aristotlean world view, has continued to be the dominant tradition in the biological sciences and the experimental sciences. Descriptive prose and pictures are the major medium of communication. In these disciplines, the level of certainty provided by experimental verification allows the researchers to forego any historical concerns, if and when necessary. In fact, the same situation also applies in some other natural sciences, like Physics and Chemistry. As a result, existing theories in these disciplines have been replaced many times by newer and simpler theories that explain the experimental
results better. Examples are (i) Newton's work on chemistry which was later relegated to alchemy, (ii) the theory of the ancient Greeks that matter is made of fire, water, earth, air and ether would not have any subscribers today.

The Lakoff - Nunez team's strategy of quickly explaining the cognitive foundations of a given discipline and then moving on to another discipline would work well in such areas where history can be consigned to the trash bin without much trouble. However, in mathematics that strategy would not work. History matters quite a lot here, since history is usually the best guarantee against the false proofs and missteps. And, it is Platonism that has often shown the way forward during crucial periods in the history of mathematics.

The Lakoff - Nunez book also criticizes modern mathematicians that they use highly abstract language which is socially exclusive, and that mathematicians greatly emphasize formal manipulation of symbols and ignore the perception of new ideas. Rene Descartes said that in transcendental matters, one must be transcendentally clear. To their credit, the Lakoff - Nunez team has followed that example quite sincerely in the writing of the book. The book is really clear and is easy to read.

What makes the Lakoff - Nunez book tick is that most of the material has been worked out thoroughly over many centuries. Aristotle, Rene Descartes, Charles Darwin, Sigmund Freud and Noam Chomsky have all left their deep impressions on the material dealt with in this book. But, one would not get that impression upon reading this book. One would think that the Lakoff - Nunez team invented it all by themselves. In fact, the material in the first few chapters explains how humans understand arithmetic by extending on their biological capabilities for counting numbers. This material is nearly the same as found in Tobias Dantzig's book, which Albert Einstein recommended highly, and was written more than seventy five years ago.

I hope that you enjoyed reading the arguments I have made in this letter. I have printed out the pages of this correspondence and mailed them to you at my own cost. Moreover, I drafted this correspondence outside of office work. This correspondence does not involve my current employer, (-employer's name edited out-) in any way, except that (i) I met you in the (-employer's name edited out-) Conference last week, and (ii) I store my writings in my office computer. I request that this letter, and the enclosed articles, be treated as a private correspondence that does not involve (-employer's name edited out-).

I would really appreciate an opportunity to work with you on this subject of identifying future directions for doing research in mathematics. Please let me know about your opinions. Thank you very much, Sir.

Sincerely,
T. V. Selvakumaran