"Vers toi je roule, baleine destructrice qui ne récolte que le néant, je suis aux prises avec toi jusqu’au dernier instant, du cœur de l’enfer je te frappe, au nom de la haine je crache contre toi mon dernier souffle. Sombrez tous cercueils, tous corbillards dans la mare commune puisque nuls ne peuvent êtres miens, que je sois déchiqueté et lié à toi en te chassant, baleine maudite ! C’est ainsi que je rends les armes !"
--la traduction est celle de Henriette Guex-Rolle
http://www.ebooksgratuits.com/html/melville_moby_dick.html
Showing posts with label philosophy. Show all posts
Showing posts with label philosophy. Show all posts
Sunday, May 15, 2011
Thursday, April 21, 2011
The Ancient Athenian Sophists (for an irreproachable legacy, be a philosopher, not a lawyer)
"From Wikipedia, the free encyclopedia
"In the second half of the 5th century BC, particularly at Athens, 'sophist' came to denote a class of mostly itinerant intellectuals who taught courses in various subjects, speculated about the nature of language and culture, and employed rhetoric to achieve their purposes, generally to persuade or convince others.... A few sophists claimed that they could find the answers to all questions. Most of these sophists are known today primarily through the writings of their opponents (specifically Plato and Aristotle), which makes it difficult to assemble an unbiased view of their practices and beliefs....
"Owing largely to the influence of Plato and Aristotle, philosophy came to be regarded as distinct from sophistry, the latter being regarded as specious and rhetorical, a practical discipline. Thus, by the time of the Roman Empire, a sophist was simply a teacher of rhetoric and a popular public speaker....
"The Sophists certainly were not directly responsible for Athenian democracy, but their cultural and psychological contributions played an important role in its growth. They contributed to the new democracy in part by espousing expertise in public deliberation, since this was the foundation of decision-making, which allowed and perhaps required a tolerance of the beliefs of others....
"In addition, Sophists had great impact on the early development of law, as the sophists were the first lawyers in the world. Their status as lawyers was a result of their extremely developed argumentation skills."
"In the second half of the 5th century BC, particularly at Athens, 'sophist' came to denote a class of mostly itinerant intellectuals who taught courses in various subjects, speculated about the nature of language and culture, and employed rhetoric to achieve their purposes, generally to persuade or convince others.... A few sophists claimed that they could find the answers to all questions. Most of these sophists are known today primarily through the writings of their opponents (specifically Plato and Aristotle), which makes it difficult to assemble an unbiased view of their practices and beliefs....
"Owing largely to the influence of Plato and Aristotle, philosophy came to be regarded as distinct from sophistry, the latter being regarded as specious and rhetorical, a practical discipline. Thus, by the time of the Roman Empire, a sophist was simply a teacher of rhetoric and a popular public speaker....
"The Sophists certainly were not directly responsible for Athenian democracy, but their cultural and psychological contributions played an important role in its growth. They contributed to the new democracy in part by espousing expertise in public deliberation, since this was the foundation of decision-making, which allowed and perhaps required a tolerance of the beliefs of others....
"In addition, Sophists had great impact on the early development of law, as the sophists were the first lawyers in the world. Their status as lawyers was a result of their extremely developed argumentation skills."
Tuesday, March 22, 2011
Straw Dogs --> Laozi's reference --> and elucidating commentary
"Heaven and Earth are heartless
treating creatures like straw dogs"
--Laozi, Tao Te Ching
"Heaven and Earth are not partial. They do not kill living things out of cruelty or give them birth out of kindness. We do the same when we make straw dogs to use in sacrifices. We dress them up and put them on the altar, but not because we love them. And when the ceremony is over, we throw them into the street, but not because we hate them."
--Su Ch'e, as quoted in Lao-tzu's Taoteching: with Selected Commentaries of the Past 2000 Years, translated by Red Pine
treating creatures like straw dogs"
--Laozi, Tao Te Ching
"Heaven and Earth are not partial. They do not kill living things out of cruelty or give them birth out of kindness. We do the same when we make straw dogs to use in sacrifices. We dress them up and put them on the altar, but not because we love them. And when the ceremony is over, we throw them into the street, but not because we hate them."
--Su Ch'e, as quoted in Lao-tzu's Taoteching: with Selected Commentaries of the Past 2000 Years, translated by Red Pine
Friday, December 03, 2010
Awesome Captured on Film: Orson Welles as Father Mapple in the 1956 movie *Moby Dick*
The sermon scene ends halfway through, and the following isn't worth watching, but this is the best-quality clip of Welles' performance on YouTube.
The set was reproduced from Melville's description, including the memorial plaques of the whalers lost at sea and the pulpit like a ship's prow.
"Delight is to him who against the proud commodores and gods of this earth, stands forth his own inexorable self...
"Yet this is nothing."
The set was reproduced from Melville's description, including the memorial plaques of the whalers lost at sea and the pulpit like a ship's prow.
"Delight is to him who against the proud commodores and gods of this earth, stands forth his own inexorable self...
"Yet this is nothing."
Monday, November 29, 2010
uninterpenetratingly: the comprehensive cosmic horror of Moby-Dick
“How dost thou know that some entire, living, thinking thing may not be invisibly and uninterpenetratingly standing precisely where thou now standest; aye, and standing there in thy spite?”
--Herman Melville, Moby-Dick; or, The Whale
--Herman Melville, Moby-Dick; or, The Whale
Friday, October 01, 2010
"enormous moral energy": Bataille on de Sade
"We know what men are with their particular circumstances and limitations. We know in advance that generally speaking they cannot fail to judge de Sade and his writings in the same way.
"Lack of understanding is in the order of things; it is that of mankind in general; it comes from their lack of strength and their feeling of being threatened.
"The criticisms that de Sade defied were well founded. He was not against the fool and the hypocrite as much as against the decent man, the normal man in all of us, so to speak. He was less concerned to convince than to challenge.
"Certain minds are fired by the thought of turning the most securely established values topsy-turvy. They are thus able to say gaily that the most subversive man who ever lived--the Marquis de Sade--was also the man who rendered the greatest service to humanity. Nothing to their mind be more certain; we shiver at the thought of death and pain (even the death and pain of other people), tragic or unspeakable events cut us to the quick, but that which inspires us with terror is like the sun, no less glorious if we turn our weak eyes away from its blaze.
"Like the sun at least in being intolerable to the naked eye, the figure of de Sade fascinated and terrified his contemporaries: was not the very idea that the monster was alive revolting? In our day and age, however, an apologist for his ideas is never taken seriously, and no one thinks them at all significant.... That would not matter if only de Sade's ideas did not lose their essential value: namely, that of being incompatible with the ideas of reasonable beings.
"De Sade asserted these unacceptable values in book after book. Life, he maintained, was the pursuit of pleasure, and the degree of pleasure was in direct ratio to the destruction of life. In other words, life reached its highest intensity in a monstrous denial of its own principle.
"Such a strange doctrine could obviously not be generally accepted, nor even generally propounded, unless it were glossed over, deprived of significance and reduced to a trivial piece of pyrotechnics. Obviously, if it were taken seriously, no society could accept it for a single instant. Indeed, those people who used to rate de Sade as a scoundrel responded better to his intentions than his admirers do in our own day: de Sade provokes indignation and protest, otherwise the paradox of pleasure would be nothing but a poetic fancy.
"In one way it is easier to be be receptive to de Sade's eroticism than to the religious demands of old. No-one today could deny that impulses connecting sexuality and the desire to hurt and to kill do exist. Hence the so-called sadistic instincts enable the ordinary man to account for certain acts of cruelty, while religious impulses are explained away as aberrations. By describing these instincts in masterly fashion then, de Sade has contributed to man's slow-growing awareness of himself--in philosophical terminology 'consciousness of self'; The expression 'sadistic', in universal use, is in itself clear proof of his contribution.
"The cruelty of de Sade's heroes should not be wholeheartedly abominated. It is a denial of the principles on which humanity is founded. We are bound to reject something that would end in the ruin of all our works. If instinct urges us to destroy the very thing we are building, we must condemn those instincts and defend ourselves from them. But there remains this question. Is our being ineluctably the negation as well as the affirmation of its own princple?
"One cannot fail to observe mankind's double nature throughout its career. There are two extremes. At one end, existence is basically orderly and decent. Work, concern for the children, kindness and honesty rule men's dealings with their fellows. At the other, violence rages pitilessly. In certain circumstances the same men practise pillage and arson, murder, violence and torture. Excess contrasts with reason.
"These extremes are called civilisation and barbarism. But the use of these words is misleading, for they imply that there are barbarians on the one hand and civilised men on the other.
"Common language will not express violence. It treats it as a guilty and importunate thing and disallows it by denying it any function or any excuse. If violence does occur, and occur it will, it is explained by a mistake somewhere, just as men of backward civilisations think that death can only happen if someone makes it by magic or otherwise. Violence in advanced societies and death in backward ones are not just given, like a storm or a flood; they can only be the result of something going wrong.
"But silence cannot do away with things that language cannot state. Violence is as stubbornly there just as much as death, and if language cheats to conceal universal annihilation, the placid work of time, language alone suffers, not time and not violence.
"Useless and dangerous violence cannot be abolished by irrational refusals to have any truck with it, any more than the irrational refusals to treat with death can eliminate that.
"The characters of de Sade's novels do not speak to man in general, as literature does even in the apparent discretion of the private journal. If they speak at all it is to someone of their own kind. De Sade's twisted libertines talk to each other. But they indulge in long speeches to show they are right.... What they insist upon is the overriding value of violence, excesses, crimes and tortures. In this way they fall short of the profound silence peculiar to violence, for violence never declares either its own existence or its right to exist; it simply exists.
"These disquisitions upon violence which keep interrupting the accounts of infamous cruelties that make up de Sade's books do not belong to the violent characters into whose mouths they are put. If such people had really lived, they would probably have lived in silence. These are de Sade's own ideas, and he uses this means to address other people.
"A paradox underlies his behaviour. De Sade speaks, but he is the mouthpiece of a silent life, of utter and inevitably speechless solitude. The solitary man for whom he speaks pays not the slightest heed to his fellows; in his loneliness he is a sovereign being, never called to account, never needing to justify himself to anyone.... All this calls for enormous moral energy, but such energy is in fact the point at issue.
"The solitary man proceeds step by step towards total negation: denial of other people first, and then by some monstrous logic denial of himself.
"It may be that de Sade's language is not common parlance, not addressed to all comers, but intended for those rare spirits capable of attaining to superhuman solitude in the very bosom of humanity.
"The man who speaks has nevertheless broken out of the solitude to which his condemnation of other people has condemned him.
"This monstrous anomaly hardly seems to correspond with the intentions of a man who, as he spoke, forgot the solitude to which he was condemning himself more unreservedly than other people had done, for he was betraying this solitude. Normal men, standing for common necessity, obviously could not understand him. His plea could not have any meaning, so that this enormous work taught solitude in solitude; a century and a half passed before its message was spread.
"Misunderstanding and revulsion from the generality of mankind are the only results worth of de Sade's ideas.
"De Sade's philosophy is not to be classed as madness. It is simply an excess, an excess to make our heads reel, but the excess of our own extravagance. We cannot ignore this without ignoring our own nature--and it is our nature that makes us tremble with fear.
"For the sake of greater satisfaction de Sade strove to infuse violence with the orderly calm of awareness.
"De Sade's writings, and this is their peculiar value, tend to bring men back to an awareness of something they have almost completely turned their backs on, looking for loop-holes and postponing the moment for coming to terms.
"They bring to man's thinking on the subject of violence the slow pace and the spirit of observation that characterise the conscious intelligence.
"In this way we reach a violence possessing the calmness of reason.
"The fact is that what de Sade was trying to bring to the surface of the conscious mind was precisely the thing that revolted the mind.
"It is only today we realise that without de Sade's cruelty we should never have penetrated with such ease the once inaccessible domain where the most painful truths lay hidden.
"And if today the average man has a profound insight into what transgression means for him, de Sade was the one who made ready the path. Now the average man knows that he must become aware of the things which repel him most violently--those things which repel us most violently are part of our own nature."
--Georges Bataille, "De Sade and the normal man" in L'Erotisme (Death and Sensuality: A Study of Eroticism and the Taboo), 1957
"Lack of understanding is in the order of things; it is that of mankind in general; it comes from their lack of strength and their feeling of being threatened.
"The criticisms that de Sade defied were well founded. He was not against the fool and the hypocrite as much as against the decent man, the normal man in all of us, so to speak. He was less concerned to convince than to challenge.
"Certain minds are fired by the thought of turning the most securely established values topsy-turvy. They are thus able to say gaily that the most subversive man who ever lived--the Marquis de Sade--was also the man who rendered the greatest service to humanity. Nothing to their mind be more certain; we shiver at the thought of death and pain (even the death and pain of other people), tragic or unspeakable events cut us to the quick, but that which inspires us with terror is like the sun, no less glorious if we turn our weak eyes away from its blaze.
"Like the sun at least in being intolerable to the naked eye, the figure of de Sade fascinated and terrified his contemporaries: was not the very idea that the monster was alive revolting? In our day and age, however, an apologist for his ideas is never taken seriously, and no one thinks them at all significant.... That would not matter if only de Sade's ideas did not lose their essential value: namely, that of being incompatible with the ideas of reasonable beings.
"De Sade asserted these unacceptable values in book after book. Life, he maintained, was the pursuit of pleasure, and the degree of pleasure was in direct ratio to the destruction of life. In other words, life reached its highest intensity in a monstrous denial of its own principle.
"Such a strange doctrine could obviously not be generally accepted, nor even generally propounded, unless it were glossed over, deprived of significance and reduced to a trivial piece of pyrotechnics. Obviously, if it were taken seriously, no society could accept it for a single instant. Indeed, those people who used to rate de Sade as a scoundrel responded better to his intentions than his admirers do in our own day: de Sade provokes indignation and protest, otherwise the paradox of pleasure would be nothing but a poetic fancy.
"In one way it is easier to be be receptive to de Sade's eroticism than to the religious demands of old. No-one today could deny that impulses connecting sexuality and the desire to hurt and to kill do exist. Hence the so-called sadistic instincts enable the ordinary man to account for certain acts of cruelty, while religious impulses are explained away as aberrations. By describing these instincts in masterly fashion then, de Sade has contributed to man's slow-growing awareness of himself--in philosophical terminology 'consciousness of self'; The expression 'sadistic', in universal use, is in itself clear proof of his contribution.
"The cruelty of de Sade's heroes should not be wholeheartedly abominated. It is a denial of the principles on which humanity is founded. We are bound to reject something that would end in the ruin of all our works. If instinct urges us to destroy the very thing we are building, we must condemn those instincts and defend ourselves from them. But there remains this question. Is our being ineluctably the negation as well as the affirmation of its own princple?
"One cannot fail to observe mankind's double nature throughout its career. There are two extremes. At one end, existence is basically orderly and decent. Work, concern for the children, kindness and honesty rule men's dealings with their fellows. At the other, violence rages pitilessly. In certain circumstances the same men practise pillage and arson, murder, violence and torture. Excess contrasts with reason.
"These extremes are called civilisation and barbarism. But the use of these words is misleading, for they imply that there are barbarians on the one hand and civilised men on the other.
"Common language will not express violence. It treats it as a guilty and importunate thing and disallows it by denying it any function or any excuse. If violence does occur, and occur it will, it is explained by a mistake somewhere, just as men of backward civilisations think that death can only happen if someone makes it by magic or otherwise. Violence in advanced societies and death in backward ones are not just given, like a storm or a flood; they can only be the result of something going wrong.
"But silence cannot do away with things that language cannot state. Violence is as stubbornly there just as much as death, and if language cheats to conceal universal annihilation, the placid work of time, language alone suffers, not time and not violence.
"Useless and dangerous violence cannot be abolished by irrational refusals to have any truck with it, any more than the irrational refusals to treat with death can eliminate that.
"The characters of de Sade's novels do not speak to man in general, as literature does even in the apparent discretion of the private journal. If they speak at all it is to someone of their own kind. De Sade's twisted libertines talk to each other. But they indulge in long speeches to show they are right.... What they insist upon is the overriding value of violence, excesses, crimes and tortures. In this way they fall short of the profound silence peculiar to violence, for violence never declares either its own existence or its right to exist; it simply exists.
"These disquisitions upon violence which keep interrupting the accounts of infamous cruelties that make up de Sade's books do not belong to the violent characters into whose mouths they are put. If such people had really lived, they would probably have lived in silence. These are de Sade's own ideas, and he uses this means to address other people.
"A paradox underlies his behaviour. De Sade speaks, but he is the mouthpiece of a silent life, of utter and inevitably speechless solitude. The solitary man for whom he speaks pays not the slightest heed to his fellows; in his loneliness he is a sovereign being, never called to account, never needing to justify himself to anyone.... All this calls for enormous moral energy, but such energy is in fact the point at issue.
"The solitary man proceeds step by step towards total negation: denial of other people first, and then by some monstrous logic denial of himself.
"It may be that de Sade's language is not common parlance, not addressed to all comers, but intended for those rare spirits capable of attaining to superhuman solitude in the very bosom of humanity.
"The man who speaks has nevertheless broken out of the solitude to which his condemnation of other people has condemned him.
"This monstrous anomaly hardly seems to correspond with the intentions of a man who, as he spoke, forgot the solitude to which he was condemning himself more unreservedly than other people had done, for he was betraying this solitude. Normal men, standing for common necessity, obviously could not understand him. His plea could not have any meaning, so that this enormous work taught solitude in solitude; a century and a half passed before its message was spread.
"Misunderstanding and revulsion from the generality of mankind are the only results worth of de Sade's ideas.
"De Sade's philosophy is not to be classed as madness. It is simply an excess, an excess to make our heads reel, but the excess of our own extravagance. We cannot ignore this without ignoring our own nature--and it is our nature that makes us tremble with fear.
"For the sake of greater satisfaction de Sade strove to infuse violence with the orderly calm of awareness.
"De Sade's writings, and this is their peculiar value, tend to bring men back to an awareness of something they have almost completely turned their backs on, looking for loop-holes and postponing the moment for coming to terms.
"They bring to man's thinking on the subject of violence the slow pace and the spirit of observation that characterise the conscious intelligence.
"In this way we reach a violence possessing the calmness of reason.
"The fact is that what de Sade was trying to bring to the surface of the conscious mind was precisely the thing that revolted the mind.
"It is only today we realise that without de Sade's cruelty we should never have penetrated with such ease the once inaccessible domain where the most painful truths lay hidden.
"And if today the average man has a profound insight into what transgression means for him, de Sade was the one who made ready the path. Now the average man knows that he must become aware of the things which repel him most violently--those things which repel us most violently are part of our own nature."
--Georges Bataille, "De Sade and the normal man" in L'Erotisme (Death and Sensuality: A Study of Eroticism and the Taboo), 1957
Saturday, August 14, 2010
shared between ourselves and death
"We do not suddenly fall on death, but advance towards it by slight degrees; we die every day. For every day a little of our life is taken from us; even when we are growing, our life is on the wane. We lose our childhood, then our boyhood, and then our youth. Counting even yesterday, all past time is lost time; the very day which we are now spending is shared between ourselves and death. It is not the last drop that empties the water-clock, but all that which previously has flowed out; similarly, the final hour when we cease to exist does not of itself bring death; it merely of itself completes the death-process. We reach death at that moment, but we have been a long time on the way."
--Lucius Annaeus Seneca, Ad Lucilium epistulae morales, ca. 65 CE, translated by Richard M. Gummere
--Lucius Annaeus Seneca, Ad Lucilium epistulae morales, ca. 65 CE, translated by Richard M. Gummere
Tuesday, August 10, 2010
Coastline Paradox
"From Wikipedia, the free encyclopedia
"The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal-like properties of coastlines.
"The measured length of a coastline depends on the scale of measurement: the smaller the increment of measurement, the longer the measured length becomes. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and smaller, there is no obvious limit to the size of the smallest feature that should not be measured around, and hence no single well-defined perimeter to the landmass.
"Over a wide range of measurement scales, down to the atomic, coastlines show a degree of self-similarity, and as the measurement scale is made smaller and smaller, the measured length continues to increase, tending towards infinity.
"An example of the coastline paradox. If the coastline of Great Britain is measured using fractal units 100 km long, then the length of the coastline is approximately 2800 km. With 50 km units, the total length is approximately 3400 km (600 km longer)."
"The coastline paradox is the counterintuitive observation that the coastline of a landmass does not have a well-defined length. This results from the fractal-like properties of coastlines.
"The measured length of a coastline depends on the scale of measurement: the smaller the increment of measurement, the longer the measured length becomes. Since a landmass has features at all scales, from hundreds of kilometers in size to tiny fractions of a millimeter and smaller, there is no obvious limit to the size of the smallest feature that should not be measured around, and hence no single well-defined perimeter to the landmass.
"Over a wide range of measurement scales, down to the atomic, coastlines show a degree of self-similarity, and as the measurement scale is made smaller and smaller, the measured length continues to increase, tending towards infinity.
Wednesday, August 04, 2010
a grandeur, and unnecessary duplicates
“Seat thyself sultanically among the moons of Saturn, and take high abstracted man alone; and he seems a wonder, a grandeur, and a woe. But from the same point, take mankind in mass, and for the most part, they seem a mob of unnecessary duplicates, both contemporary and hereditary.”
--Herman Melville, Moby-Dick; or, The Whale
--Herman Melville, Moby-Dick; or, The Whale
Wednesday, June 30, 2010
Gödel and the Grundlagenkrise der Mathematik (and Knowledgelessness)
“From Wikipedia, the free encyclopedia
“Since the time of Pythagoras, mathematicians have wondered about the nature of mathematical truth, the ontology of mathematical entities and the reasons for the validity of proof and, more generally, mathematical knowledge. From the Enlightenment until the middle of the 19th century, the prevailing scientific ideology saw mathematics as the only way of reaching a truth that is final, absolute and totally independent of the human mind's capacity to understand it. The basic notions of mathematics were thought to reflect essential properties of the cosmos and the theorems to be the truths of a higher reality.... Yet, in the 19th century this traditional belief was undermined in the minds of some people and eventually led to a serious foundational crisis in mathematics. The first of the discoveries which caused the loss of faith, dating from the time of the Renaissance, was that of the imaginary numbers (i.e. those involving the square root of minus one)....
“The foundational crisis of mathematics (in German: Grundlagenkrise der Mathematik) was the early 20th century's term for the search for proper foundations of mathematics.
“After several schools of the philosophy of mathematics ran into difficulties one after the other in the 20th century, the assumption that mathematics had any foundation that could be stated within mathematics itself began to be heavily challenged.
“One attempt after another to provide unassailable foundations for mathematics was found to suffer from various paradoxes (such as Russell's paradox) and to be inconsistent: an undesirable situation in which every mathematical statement that can be formulated in a proposed system (such as 2 + 2 = 5) can also be proved in the system.
“Various schools of thought on the right approach to the foundations of mathematics were fiercely opposing each other. The leading school was that of the formalist approach, of which David Hilbert was the foremost proponent, culminating in what is known as Hilbert's program, which thought to ground mathematics on a small basis of a logical system proved sound by metamathematical finitistic means. The main opponent was the intuitionist school, led by L. E. J. Brouwer, which resolutely discarded formalism as a meaningless game with symbols. The fight was acrimonious. In 1920 Hilbert succeeded in having Brouwer, whom he considered a threat to mathematics, removed from the editorial board of Mathematische Annalen, the leading mathematical journal of the time.
“Gödel's incompleteness theorems, proved in 1931, showed that essential aspects of Hilbert's program could not be attained. In Gödel's first result he showed how to construct, for any sufficiently powerful and consistent recursively axiomatizable system -- such as necessary to axiomatize the elementary theory of arithmetic on the (infinite) set of natural numbers -- a statement that can be shown to be true, but that does not follow from the rules of the system. It thus became clear that the notion of mathematical truth can not be reduced to a purely formal system as envisaged in Hilbert's program. In a next result Gödel showed that such a system was not powerful enough for proving its own consistency, let alone that a simpler system could do the job. This dealt a final blow to the heart of Hilbert's program, the hope that consistency could be established by finitistic means... Meanwhile, the intuitionistic school had not attracted many adherents among working mathematicians, due to difficulties of constructive mathematics.
“In a sense, the crisis has not been resolved, but faded away: most mathematicians either do not work from axiomatic systems, or if they do, do not doubt the consistency of ZFC (the Zermelo–Fraenkel set theory with the axiom of choice), generally their preferred axiomatic system....
“It may or may not be the case that there is a fundamental limit to what humans can understand about numbers (i.e., there may be true number-theoretical principles which cannot be perceived as being true by any human), but Gödel's theorem does not tell us which of these is the case, and we have no way of knowing.”
“Since the time of Pythagoras, mathematicians have wondered about the nature of mathematical truth, the ontology of mathematical entities and the reasons for the validity of proof and, more generally, mathematical knowledge. From the Enlightenment until the middle of the 19th century, the prevailing scientific ideology saw mathematics as the only way of reaching a truth that is final, absolute and totally independent of the human mind's capacity to understand it. The basic notions of mathematics were thought to reflect essential properties of the cosmos and the theorems to be the truths of a higher reality.... Yet, in the 19th century this traditional belief was undermined in the minds of some people and eventually led to a serious foundational crisis in mathematics. The first of the discoveries which caused the loss of faith, dating from the time of the Renaissance, was that of the imaginary numbers (i.e. those involving the square root of minus one)....
“The foundational crisis of mathematics (in German: Grundlagenkrise der Mathematik) was the early 20th century's term for the search for proper foundations of mathematics.
“After several schools of the philosophy of mathematics ran into difficulties one after the other in the 20th century, the assumption that mathematics had any foundation that could be stated within mathematics itself began to be heavily challenged.
“One attempt after another to provide unassailable foundations for mathematics was found to suffer from various paradoxes (such as Russell's paradox) and to be inconsistent: an undesirable situation in which every mathematical statement that can be formulated in a proposed system (such as 2 + 2 = 5) can also be proved in the system.
“Various schools of thought on the right approach to the foundations of mathematics were fiercely opposing each other. The leading school was that of the formalist approach, of which David Hilbert was the foremost proponent, culminating in what is known as Hilbert's program, which thought to ground mathematics on a small basis of a logical system proved sound by metamathematical finitistic means. The main opponent was the intuitionist school, led by L. E. J. Brouwer, which resolutely discarded formalism as a meaningless game with symbols. The fight was acrimonious. In 1920 Hilbert succeeded in having Brouwer, whom he considered a threat to mathematics, removed from the editorial board of Mathematische Annalen, the leading mathematical journal of the time.
“Gödel's incompleteness theorems, proved in 1931, showed that essential aspects of Hilbert's program could not be attained. In Gödel's first result he showed how to construct, for any sufficiently powerful and consistent recursively axiomatizable system -- such as necessary to axiomatize the elementary theory of arithmetic on the (infinite) set of natural numbers -- a statement that can be shown to be true, but that does not follow from the rules of the system. It thus became clear that the notion of mathematical truth can not be reduced to a purely formal system as envisaged in Hilbert's program. In a next result Gödel showed that such a system was not powerful enough for proving its own consistency, let alone that a simpler system could do the job. This dealt a final blow to the heart of Hilbert's program, the hope that consistency could be established by finitistic means... Meanwhile, the intuitionistic school had not attracted many adherents among working mathematicians, due to difficulties of constructive mathematics.
“In a sense, the crisis has not been resolved, but faded away: most mathematicians either do not work from axiomatic systems, or if they do, do not doubt the consistency of ZFC (the Zermelo–Fraenkel set theory with the axiom of choice), generally their preferred axiomatic system....
“It may or may not be the case that there is a fundamental limit to what humans can understand about numbers (i.e., there may be true number-theoretical principles which cannot be perceived as being true by any human), but Gödel's theorem does not tell us which of these is the case, and we have no way of knowing.”
Friday, June 04, 2010
heard of him; but don't believe in him at all
“Come aboard, come aboard!” cried the gay Bachelor's commander, lifting a glass and a bottle in the air.
“Hast seen the White Whale?” gritted Ahab in reply.
“No; only heard of him; but don't believe in him at all,” said the other good-humoredly.
--Herman Melville, Moby-Dick; or, The Whale
“Hast seen the White Whale?” gritted Ahab in reply.
“No; only heard of him; but don't believe in him at all,” said the other good-humoredly.
--Herman Melville, Moby-Dick; or, The Whale
Thursday, May 20, 2010
Risk and Peril
"This Book explains the Universe....
"Each one of us has an universe of his own....
"The object that you see is never the same as the one that I see ; we infer that it is the same because your experience tallies with mine on so many points that the actual differences of our observation are negligible. For instance, if a friend is walking between us, you see only his left side, I his right ; but we agree that it is the same man, although we may differ not only as to what we may see of his body but as to what we know of his qualitites. This conviction of identity grows stronger as we see him more often and get to know him better. Yet all the time neither of us can know anything of him at all beyond the total impression made on our respective minds....
"The study of this Book is forbidden. It is wise to destroy this copy after the first reading.
"Whosoever disregards this does so at his own risk and peril."
--Aleister Crowley, The Book of the Law, 1938
"Each one of us has an universe of his own....
"The object that you see is never the same as the one that I see ; we infer that it is the same because your experience tallies with mine on so many points that the actual differences of our observation are negligible. For instance, if a friend is walking between us, you see only his left side, I his right ; but we agree that it is the same man, although we may differ not only as to what we may see of his body but as to what we know of his qualitites. This conviction of identity grows stronger as we see him more often and get to know him better. Yet all the time neither of us can know anything of him at all beyond the total impression made on our respective minds....
"The study of this Book is forbidden. It is wise to destroy this copy after the first reading.
"Whosoever disregards this does so at his own risk and peril."
--Aleister Crowley, The Book of the Law, 1938
Friday, May 14, 2010
Yes, per logical consistency, and in denial of self-righteous fiction
"The conditions of combat place human beings under unbearable and extraordinary circumstances of stress that can and have provoked decent and good men to perform terrible acts. Is it just for those judging these acts to place standards on combat behavior that they cannot say with any confidence that they could meet themselves, if placed under the same conditions?
"The United States walked right into this one when it launched the first international war crimes trial at Nuremberg after World War II. Nobody doubted that what the Nazis had done to Jews and others during the war was monstrous, but subjecting it to official and legal condemnation under the category of 'war crimes' was, and remains, problematical. The tribunal at Nuremberg would not accept 'following orders' as a defense, but neither does the US military permit soldiers to pass their own moral judgements on which orders they will obey.
"Ultimately, the importance of officially condemning the atrocities of the Holocaust was determined to be more important than consistency. What the Nazis did could not stand unpunished, even though, in truth, there were bound to be actions by American soldiers in future wars that could be called war crimes under the Nuremberg definition. There were such actions during W.W. II: should the crew of the Enola Gay have refused to drop the atom bomb?"
--Ethics Scoreboard, "The Housewife and the Marine," 2004 November 22
"The United States walked right into this one when it launched the first international war crimes trial at Nuremberg after World War II. Nobody doubted that what the Nazis had done to Jews and others during the war was monstrous, but subjecting it to official and legal condemnation under the category of 'war crimes' was, and remains, problematical. The tribunal at Nuremberg would not accept 'following orders' as a defense, but neither does the US military permit soldiers to pass their own moral judgements on which orders they will obey.
"Ultimately, the importance of officially condemning the atrocities of the Holocaust was determined to be more important than consistency. What the Nazis did could not stand unpunished, even though, in truth, there were bound to be actions by American soldiers in future wars that could be called war crimes under the Nuremberg definition. There were such actions during W.W. II: should the crew of the Enola Gay have refused to drop the atom bomb?"
--Ethics Scoreboard, "The Housewife and the Marine," 2004 November 22
Sunday, May 02, 2010
in the great loneliness
"The only true wisdom lives far from mankind, out in the great loneliness."
--Igjugarjuk, as quoted by Joseph Campbell in The Power of Myth, 1988
--Igjugarjuk, as quoted by Joseph Campbell in The Power of Myth, 1988
Of all this fiery life
"Of all this fiery life of thine, what will at length remain but one little heap of ashes!"
--Herman Melville, Moby-Dick; or, The Whale
--Herman Melville, Moby-Dick; or, The Whale
Friday, April 30, 2010
Alfred Korzybski Koan
"From Wikipedia, the free encyclopedia
"One day, Korzybski was giving a lecture to a group of students, and he suddenly interrupted the lesson in order to retrieve a packet of biscuits, wrapped in white paper, from his briefcase. He muttered that he just had to eat something, and he asked the students in the front row if they would also like a biscuit. A few students took a biscuit. 'Nice biscuit, don't you think,' said Korzybski, while he took a second one. The students were chewing vigorously. Then he tore the white paper from the biscuits, in order to reveal the original packaging. On it was a big picture of a dog's head and the words 'Dog Cookies.' The students looked at the package, and were shocked. Two of them wanted to throw up, put their hands in front of their mouths, and ran out of the lecture hall to the toilet. 'You see, ladies and gentlemen,' Korzybski remarked, 'I have just demonstrated that people don't just eat food, but also words, and that the taste of the former is often outdone by the taste of the latter.' Apparently his prank aimed to illustrate how some human suffering originates from the confusion or conflation of linguistic representations of reality and reality itself."
"One day, Korzybski was giving a lecture to a group of students, and he suddenly interrupted the lesson in order to retrieve a packet of biscuits, wrapped in white paper, from his briefcase. He muttered that he just had to eat something, and he asked the students in the front row if they would also like a biscuit. A few students took a biscuit. 'Nice biscuit, don't you think,' said Korzybski, while he took a second one. The students were chewing vigorously. Then he tore the white paper from the biscuits, in order to reveal the original packaging. On it was a big picture of a dog's head and the words 'Dog Cookies.' The students looked at the package, and were shocked. Two of them wanted to throw up, put their hands in front of their mouths, and ran out of the lecture hall to the toilet. 'You see, ladies and gentlemen,' Korzybski remarked, 'I have just demonstrated that people don't just eat food, but also words, and that the taste of the former is often outdone by the taste of the latter.' Apparently his prank aimed to illustrate how some human suffering originates from the confusion or conflation of linguistic representations of reality and reality itself."
Monday, April 26, 2010
Dharma Bums VIIII
"In bed at night, warm and happy in my bag on the good bunk, I'd see my table and my clothes in the moonlight and feel, 'Poor Raymond boy, his day is so sorrowful and worried, his reasons are so ephemeral, it's such a haunted and pitiful thing to have to live' and on this I'd go to sleep like a lamb."
--Jack Kerouac, The Dharma Bums, 1958
--Jack Kerouac, The Dharma Bums, 1958
E-Prime
"From Wikipedia, the free encyclopedia
"E-Prime (short for English-Prime) is a form of the English language in which the verb to be in all its forms does not exist. E-Prime therefore uses alternate means to express most statements which use the passive voice, thus encouraging writers and speakers to clearly state an action's agent.
"Some people use E-Prime as a mental discipline to filter speech and translate the speech of others. For example, the sentence 'the movie was good' could translate into E-Prime as 'I liked the movie' or as 'the movie made me laugh'. The E-Prime versions communicate the speaker's experience rather than judgment, making it harder for the writer or reader to confuse opinion with fact."
"E-Prime (short for English-Prime) is a form of the English language in which the verb to be in all its forms does not exist. E-Prime therefore uses alternate means to express most statements which use the passive voice, thus encouraging writers and speakers to clearly state an action's agent.
"Some people use E-Prime as a mental discipline to filter speech and translate the speech of others. For example, the sentence 'the movie was good' could translate into E-Prime as 'I liked the movie' or as 'the movie made me laugh'. The E-Prime versions communicate the speaker's experience rather than judgment, making it harder for the writer or reader to confuse opinion with fact."
Friday, April 23, 2010
World War I and H.P. Lovecraft
"At the beginning of the twentieth century, belief in the rational suffered a massive blow on the charnel fields of the First World War. Here were the rational, modern, capitalist powers, expressing their supposedly rational interests with an eruption of mechanized human butchery unprecedented in history. The scale of the psychic and cultural trauma of the First World War is vast—perhaps even 'undescribable.' The war smashed apart the complacencies of 'rationality' and uncovered the irrationality at the heart of the modern world with a savagery that eclipsed any fantasist's nightmares. How, then, could the genre known as fantasy present anything that could compare with such horror? Certainly, its stock of werewolves and effete vampires were utterly inadequate to the task....
"Traditionally, genre horror is concerned with the irruption of dreadful forces into a comforting status quo—one which the protagonists frantically scrabble to preserve. By contrast, Lovecraft's horror is not one of intrusion but of realization. The world has always been implacably bleak; the horror lies in our acknowledging that fact."
--China Mieville, introduction to At the Mountains of Madness by H.P. Lovecraft, 2005
"Traditionally, genre horror is concerned with the irruption of dreadful forces into a comforting status quo—one which the protagonists frantically scrabble to preserve. By contrast, Lovecraft's horror is not one of intrusion but of realization. The world has always been implacably bleak; the horror lies in our acknowledging that fact."
--China Mieville, introduction to At the Mountains of Madness by H.P. Lovecraft, 2005
Sunday, April 18, 2010
gloomy contemplation
“Many Americans have never seen a corpse, and those who have probably encountered only the travesty of a beautiful death concocted in the mortician's beauty parlor. Nor is the prevailing present-day lifestyle in the United States and large parts of the Western world, set by egotistical, hyperactive people obsessed with amassing money and luxury goods, conducive to gloomy contemplation of death...”
--Jan Bondeson, Buried Alive: The Terrifying History of Our Most Primal Fear, 2001
--Jan Bondeson, Buried Alive: The Terrifying History of Our Most Primal Fear, 2001
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