Albert Einstein &
Alfred North Whitehead
https://www.yumpu.com/user/t.gmail25341
Edwin Arthur Burtt:
The Metaphysical Foundations of Modern Science
http://semiconductorfilms.com/art/magnetic-movie/
Embedded Files
Edwin Arthur Burtt:
Edwin Arthur Burtt:
The Metaphysical Foundation of Modern Physical Science.
The Metaphysical Foundation of Modern Physical Science.
Kegan Paul, Trench, Trubner & Co., LTD. London. 1925
Kegan Paul, Trench, Trubner & Co., LTD. London. 1925
Quotations
Quotations
Chapter I. Introduction
Chapter I. Introduction
“Knowledge was not a problem for the ruling philosophy of the Middle Ages; that the whole world which man’s mind seeks to unterstand is intelligible to it was explicitly taken for granted. That people subsequently came to consider knowledge a problem implies that they had been led to accept certain different beliefs about the nature of man and about the things which he tries to understand.”.(p.2)
“Knowledge was not a problem for the ruling philosophy of the Middle Ages; that the whole world which man’s mind seeks to unterstand is intelligible to it was explicitly taken for granted. That people subsequently came to consider knowledge a problem implies that they had been led to accept certain different beliefs about the nature of man and about the things which he tries to understand.”.(p.2)
“And that the modern mind clearly has such a picture, as clearly as any previous age that one might wish to select, it will not take us long to see”.(p.3)
“And that the modern mind clearly has such a picture, as clearly as any previous age that one might wish to select, it will not take us long to see”.(p.3)
“For the dominant trend in medieval thought, man occupied a more significant and determinative place in the universe than the realm of physical nature, while for the main current of modern thought, nature holds a more independent, more determinative, and more permanent place than man.”(..) “For the Middle Ages man was in every sense the centre of the universe. The whole world of nature was believed to be teleologically subordinate to him and his eternal destiny”.(p.4)
“For the dominant trend in medieval thought, man occupied a more significant and determinative place in the universe than the realm of physical nature, while for the main current of modern thought, nature holds a more independent, more determinative, and more permanent place than man.”(..) “For the Middle Ages man was in every sense the centre of the universe. The whole world of nature was believed to be teleologically subordinate to him and his eternal destiny”.(p.4)
“This view underlay medieval physics. The entire world of nature was held not only to exist for man’s sake, but to be likewise immediately present and fully intelligible to his mind. Hence the categories in terms of which it was interpreted were not those of time, space, mass, energy, and the like; but substance, essence, matter, form, quality, quantity – categories developed in the attempt to throw into scientific form the facts and relations observed in man’s unaided sense-experience of the world and the main uses which he made it serve”.(p. 4-5).
“This view underlay medieval physics. The entire world of nature was held not only to exist for man’s sake, but to be likewise immediately present and fully intelligible to his mind. Hence the categories in terms of which it was interpreted were not those of time, space, mass, energy, and the like; but substance, essence, matter, form, quality, quantity – categories developed in the attempt to throw into scientific form the facts and relations observed in man’s unaided sense-experience of the world and the main uses which he made it serve”.(p. 4-5).
“And, of course, that which was real about objects was that which could be immediately perceived about them by human senses”.(p. 5)
“And, of course, that which was real about objects was that which could be immediately perceived about them by human senses”.(p. 5)
“an explanation in terms of the relation of things to human purpose was accounted just as real as and often more important than an explanation in terms of efficient causality, which expressed their relations to each other. Rain fell because it nourished man’s crops as truly as because it was expelled from the clouds”.(p. 5)
“an explanation in terms of the relation of things to human purpose was accounted just as real as and often more important than an explanation in terms of efficient causality, which expressed their relations to each other. Rain fell because it nourished man’s crops as truly as because it was expelled from the clouds”.(p. 5)
“The whole universe was a small, finite place, and it was man’s place. He occupied the centre; his good was the controlling end of the natural creation”.(p. 6)
“The whole universe was a small, finite place, and it was man’s place. He occupied the centre; his good was the controlling end of the natural creation”.(p. 6)
“The world of nature existed that it might be known and enjoyed by man. Man in turn existed that he might “know God and enjoy him forever”.(7)
“The world of nature existed that it might be known and enjoyed by man. Man in turn existed that he might “know God and enjoy him forever”.(7)
“Berkeley, Hume, Kant, Fichte, Hegel, James, Bergson – all are united in one earnest attempt, the attempt to reinstate man with his high spiritual claims in a place of importance in the cosmic scheme. The constant renewal of these attempts and their constant failure widely and thoroughly to convince men, reveals how powerful a grip the view they were attacking was winning over people’s mind’s”.(p.11)
“Berkeley, Hume, Kant, Fichte, Hegel, James, Bergson – all are united in one earnest attempt, the attempt to reinstate man with his high spiritual claims in a place of importance in the cosmic scheme. The constant renewal of these attempts and their constant failure widely and thoroughly to convince men, reveals how powerful a grip the view they were attacking was winning over people’s mind’s”.(p.11)
“Insted of treating things in terms of substance, accident, and causality, essence and idea, matter and form, potentiality, and actuality, we now treat them in terms of forces, motions, and laws, changes of mass in space and time, and the like”.(...) “In particular it is difficult for the modern mind, accustomed to think so largely in terms of space and time, to realize how unimportant these entities were for scholastic science”.(...) “Insted of spatial connections of things, men were seeking their logical connexions; instead of the onward march of time, men thought of the eternal passage of potentiality into actuality”.(p. 13)
“Insted of treating things in terms of substance, accident, and causality, essence and idea, matter and form, potentiality, and actuality, we now treat them in terms of forces, motions, and laws, changes of mass in space and time, and the like”.(...) “In particular it is difficult for the modern mind, accustomed to think so largely in terms of space and time, to realize how unimportant these entities were for scholastic science”.(...) “Insted of spatial connections of things, men were seeking their logical connexions; instead of the onward march of time, men thought of the eternal passage of potentiality into actuality”.(p. 13)
“It might be that under cover of this change of ideas modern philosophy had accepted uncritically certain important presuppositions, either in the form of meanings carried by these new terms or in the forms of doctrines about man and his knowledge subtly insinuated (eindringen) with them – presuppositions which by their own nature negatived a successful attempt to reanalyse, through their means, man’s true relation to his environing world”.(14)
“It might be that under cover of this change of ideas modern philosophy had accepted uncritically certain important presuppositions, either in the form of meanings carried by these new terms or in the forms of doctrines about man and his knowledge subtly insinuated (eindringen) with them – presuppositions which by their own nature negatived a successful attempt to reanalyse, through their means, man’s true relation to his environing world”.(14)
“We inevitably see our limited problem in terms of inherited notions which ought themselves to form part of a larger problem. The continued uncritical use in the writings of these men of traditional ideas like that of ‘the external world’, the dichotomy assumed between the world of the physicist and the world of sense, the physiological and psychological postulates taken for granted, as, for example, the distiction between sensation and act of sensing, are a few illustrations of what is meant”.(p. 15)
“We inevitably see our limited problem in terms of inherited notions which ought themselves to form part of a larger problem. The continued uncritical use in the writings of these men of traditional ideas like that of ‘the external world’, the dichotomy assumed between the world of the physicist and the world of sense, the physiological and psychological postulates taken for granted, as, for example, the distiction between sensation and act of sensing, are a few illustrations of what is meant”.(p. 15)
“We must grasp the essential contrast between the whole modern world-view and that of previous thought, and use that clearly conceived contrast as a guiding clue (Anhaltspunkt, Schlüssel) to pick out for criticism and evaluation, in the light of their historical development, every one of our significant modern presuppositions. An analysis of this scope (Gebiet) and to this purpose has nowhere appeared”.(p. 16)
“We must grasp the essential contrast between the whole modern world-view and that of previous thought, and use that clearly conceived contrast as a guiding clue (Anhaltspunkt, Schlüssel) to pick out for criticism and evaluation, in the light of their historical development, every one of our significant modern presuppositions. An analysis of this scope (Gebiet) and to this purpose has nowhere appeared”.(p. 16)
“But the whole magnificient movement of modern science is essentially of a piece; (...) especially the all-important postulate that valid explanations must always be in terms of small, elementary units in regularly changing relations”.(17)
“But the whole magnificient movement of modern science is essentially of a piece; (...) especially the all-important postulate that valid explanations must always be in terms of small, elementary units in regularly changing relations”.(17)
“philosophy came to take science, in the main, for granted, and another way to put our central theme is, did not the problems to which philosophers now devoted themselves arise directly out of that uncritical acceptence?”(p. 17)
“philosophy came to take science, in the main, for granted, and another way to put our central theme is, did not the problems to which philosophers now devoted themselves arise directly out of that uncritical acceptence?”(p. 17)
“So far as objects were masses, moving in space and time under the impress of forces as he (Newton) has defined them, their behaviour was now, as a result of his labours, fully explicable in terms of exact mathematics”.(p. 20)
“So far as objects were masses, moving in space and time under the impress of forces as he (Newton) has defined them, their behaviour was now, as a result of his labours, fully explicable in terms of exact mathematics”.(p. 20)
“Of course, these men do not accept Newton as gospel truth – they all criticize some of his conceptions, espacially force and space – but none of them subjects the whole system of categories which had come to its clearest expression in the great Principia to a critical analysis”.(p. 22)
“Of course, these men do not accept Newton as gospel truth – they all criticize some of his conceptions, espacially force and space – but none of them subjects the whole system of categories which had come to its clearest expression in the great Principia to a critical analysis”.(p. 22)
Chapter II. Copernicus and Kepler
Chapter II. Copernicus and Kepler
“Contemporary empiricists, had they lived in the sixteenth century, would have been first to scoff out of court the new philosophy of the universe”.(25).
“Contemporary empiricists, had they lived in the sixteenth century, would have been first to scoff out of court the new philosophy of the universe”.(25).
“For to oppose to these profoundly serious objections he (Copernicus) could plead only that his conception threw the facts of astronomy into a simpler and more harmonious mathematical order”.(26)
“For to oppose to these profoundly serious objections he (Copernicus) could plead only that his conception threw the facts of astronomy into a simpler and more harmonious mathematical order”.(26)
“He who is not a mathematician according to my principles must not read me”.
“He who is not a mathematician according to my principles must not read me”.
“Oh, students, study mathematics, and do not build without a foundation”.(p. 30-31,
“Oh, students, study mathematics, and do not build without a foundation”.(p. 30-31,
Leonardo da Vinci, 1452-1519)
Leonardo da Vinci, 1452-1519)
“During the next century, that marked by the appeearance of Copernicus’ epochmaking book, the geometrical method in mechanics and the other mathematico-physical sciences was assumed by all important thinkers”.(p. 31)
“During the next century, that marked by the appeearance of Copernicus’ epochmaking book, the geometrical method in mechanics and the other mathematico-physical sciences was assumed by all important thinkers”.(p. 31)
“Our current conception of mathematics as an ideal science, of geometry in particular as dealing with an ideal space, rather than the actual space in which the universe is set, was a notion quite unformulated before Hobbes, and not taken seriously till the middle of the eighteenth century, though it was dimly felt after by a few Aristotelian opponents of Copernicus”.(p. 33)
“Our current conception of mathematics as an ideal science, of geometry in particular as dealing with an ideal space, rather than the actual space in which the universe is set, was a notion quite unformulated before Hobbes, and not taken seriously till the middle of the eighteenth century, though it was dimly felt after by a few Aristotelian opponents of Copernicus”.(p. 33)
“men readily felt, therefore, that whatever was true in geometry must be necessarily and fully true of astronomy”.(p. 34)
“men readily felt, therefore, that whatever was true in geometry must be necessarily and fully true of astronomy”.(p. 34)
(Ptolemy-Copernicus) “As far as atronomy is mathematics, both are true, because both represent the facts, but one is simpler an more harmonious than the other”.(p. 37)
(Ptolemy-Copernicus) “As far as atronomy is mathematics, both are true, because both represent the facts, but one is simpler an more harmonious than the other”.(p. 37)
“And it is not surprising that for the sixty years that elapsed before Copernicus’ theory was confirmed in more empirical fashion, practically all those who ventured to stand with him were accomplished mathematicians, whose thinking was thoroughly in line with the mathematical advances of the day”.(p. 39).
“And it is not surprising that for the sixty years that elapsed before Copernicus’ theory was confirmed in more empirical fashion, practically all those who ventured to stand with him were accomplished mathematicians, whose thinking was thoroughly in line with the mathematical advances of the day”.(p. 39).
“but is the universe as a whole, including our earth, fundamentally mathematical in its structure? Just because this shift of the point of reference gives a simpler geometrical expression for the facts, is it legitimate to make it? To admit this point is to overthrow the whole Aristotelian physics and cosmology”.(p. 40)
“but is the universe as a whole, including our earth, fundamentally mathematical in its structure? Just because this shift of the point of reference gives a simpler geometrical expression for the facts, is it legitimate to make it? To admit this point is to overthrow the whole Aristotelian physics and cosmology”.(p. 40)
“the philosophy of Plato. The world is an infinite harmony, in which all things have their mathematical proportions. Hence “knowledge is always measurement”, “number is the first model of things in the mind of the Creator”; in a word, all certain knowledge that is possible for man must be mathematical knowledge”.(p. 42)
“the philosophy of Plato. The world is an infinite harmony, in which all things have their mathematical proportions. Hence “knowledge is always measurement”, “number is the first model of things in the mind of the Creator”; in a word, all certain knowledge that is possible for man must be mathematical knowledge”.(p. 42)
(Copernicus) “He had himself become convinced that the whole universe was made of numbers, hence whatever was mathematically true was really or astronomically true. Our earth was no exception – it, too, was essentially geometrical in nature – therefore the principle of relativity of mathematical values applied to man’s domain just as to any other part of the astronomical realm. The transformation to the new world-view, for him, was nothing but a mathematical reduction, under the encouragement of the renewed Platonism of the day, of a complex geometrical labyrinth into a beatifully simple and harmonious system”.(p. 44)
(Copernicus) “He had himself become convinced that the whole universe was made of numbers, hence whatever was mathematically true was really or astronomically true. Our earth was no exception – it, too, was essentially geometrical in nature – therefore the principle of relativity of mathematical values applied to man’s domain just as to any other part of the astronomical realm. The transformation to the new world-view, for him, was nothing but a mathematical reduction, under the encouragement of the renewed Platonism of the day, of a complex geometrical labyrinth into a beatifully simple and harmonious system”.(p. 44)
(Kepler) “A true hypothesis is one which binds together rationally (i.e., for him mathematically) things which had before been held distinct”.(p. 45)
(Kepler) “A true hypothesis is one which binds together rationally (i.e., for him mathematically) things which had before been held distinct”.(p. 45)
“But the connexion between Kepler, the sun-worshipper, and Kepler, the seeker of exact mathematical knowledge of astronomical nature, is very close”.(p. 49)
“But the connexion between Kepler, the sun-worshipper, and Kepler, the seeker of exact mathematical knowledge of astronomical nature, is very close”.(p. 49)
“First and centrally, he means that he has reached a new conception of causality, that is, he thinks of the underlying mathematical harmony discoverable in the observed facts as the cause of the latter, the reason, as he usually puts it, why they are as they are. This notion of causality is substancially the Aristotelian formal cause reinterpreted in terms of exact mathematics”.(p. 53)
“First and centrally, he means that he has reached a new conception of causality, that is, he thinks of the underlying mathematical harmony discoverable in the observed facts as the cause of the latter, the reason, as he usually puts it, why they are as they are. This notion of causality is substancially the Aristotelian formal cause reinterpreted in terms of exact mathematics”.(p. 53)
“A true hypothesis is always a more inclusive conception, binding together facts which hitherto been regarded as distinct; it reveals a mathematical order and harmony where before there had been unexplained diversity. And it is important to remember that this more inclusive mathematical order is something discovered in the facts themselves”.(...) in fact, it is just these ideas that made Kepler so impatient with certain wellmeaning Aristotelian friends who advised him to treat his own and Copernicus’ discoveries as mathematical hypothesis merely, not necessarily true of the real world. Such hypotheses as these, Kepler maintained, are precisely what give us the true picture of the real world, and the world thus revealed is a bigger and far more beautiful realm than man’s reason had ever before entered”.(p. 54-55)
“A true hypothesis is always a more inclusive conception, binding together facts which hitherto been regarded as distinct; it reveals a mathematical order and harmony where before there had been unexplained diversity. And it is important to remember that this more inclusive mathematical order is something discovered in the facts themselves”.(...) in fact, it is just these ideas that made Kepler so impatient with certain wellmeaning Aristotelian friends who advised him to treat his own and Copernicus’ discoveries as mathematical hypothesis merely, not necessarily true of the real world. Such hypotheses as these, Kepler maintained, are precisely what give us the true picture of the real world, and the world thus revealed is a bigger and far more beautiful realm than man’s reason had ever before entered”.(p. 54-55)
“Knowledge as it is immediately offered the mind through the senses is abscure, confused, contradictory, and hence untrustworthy; only those features of the world in terms of which we can get certain and consistent knowledge open before us what is indubitably and permanently real. Other qualities are not real qualities of things, but only signs of them”.(...) The real world is a world of quantitative characteristics only; its differences are differences of number alone”.(p. 56)
“Knowledge as it is immediately offered the mind through the senses is abscure, confused, contradictory, and hence untrustworthy; only those features of the world in terms of which we can get certain and consistent knowledge open before us what is indubitably and permanently real. Other qualities are not real qualities of things, but only signs of them”.(...) The real world is a world of quantitative characteristics only; its differences are differences of number alone”.(p. 56)
“The changeable, surface qualities which do not fit into this underlying harmony are on a lower level of reality; they do not so truly exist”.(p. 57-58)
“The changeable, surface qualities which do not fit into this underlying harmony are on a lower level of reality; they do not so truly exist”.(p. 57-58)
Chapter III. Galileo
Chapter III. Galileo
“Others before him had asked why heavy bodies fall; now, the homogeneity of the earth with the heavenly bodies having suggested that terrestrial motion is a proper subject for exact methematical study, we have the further question raised: how do they fall? with the expectation that the answer will be given in mathematical terms”.(p. 62)
“Others before him had asked why heavy bodies fall; now, the homogeneity of the earth with the heavenly bodies having suggested that terrestrial motion is a proper subject for exact methematical study, we have the further question raised: how do they fall? with the expectation that the answer will be given in mathematical terms”.(p. 62)
“Philosophy is written in that great book which ever lies before our eyes – I mean the universe – but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth”.(64)
“Philosophy is written in that great book which ever lies before our eyes – I mean the universe – but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth”.(64)
“In other words, logic is the instrument of criticism, mathematics that of discovery”.(p. 65)
“In other words, logic is the instrument of criticism, mathematics that of discovery”.(p. 65)
“This passage introduces us to Galileo’s conception of the proper way of combining the mathematical and the experimental methods in science. With it in mind, let us study his other expressions on this point”.(p. 67)
“This passage introduces us to Galileo’s conception of the proper way of combining the mathematical and the experimental methods in science. With it in mind, let us study his other expressions on this point”.(p. 67)
“But the world of the senses is not its own explanation; as it stands it is an unsolved cipher, a book written in a strange language, which is to be interpreted or explained in terms of the alphabet of that language”.(p. 68)
“But the world of the senses is not its own explanation; as it stands it is an unsolved cipher, a book written in a strange language, which is to be interpreted or explained in terms of the alphabet of that language”.(p. 68)
“On the one hand we cannot deny that it is the senses which offer us the world to be explained; on the other we are equally certain that they do not give us the rational order which alone supplies the desired explanation”.(p. 69)
“On the one hand we cannot deny that it is the senses which offer us the world to be explained; on the other we are equally certain that they do not give us the rational order which alone supplies the desired explanation”.(p. 69)
“God has made the world an immutable mathematical system, permitting by the mathematical method an absolute certainty of scientific knowledge”.(p. 72)
“God has made the world an immutable mathematical system, permitting by the mathematical method an absolute certainty of scientific knowledge”.(p. 72)
“Galileo makes the clear distinction between that in the world which is absolute, objective, immutable, and mathematical; and that which is relative, subjective, fluctuating, and sensible. The former is the realm of knowledge, divine and human; the latter is the realm of opinion and illusion”.(p. 73)
“Galileo makes the clear distinction between that in the world which is absolute, objective, immutable, and mathematical; and that which is relative, subjective, fluctuating, and sensible. The former is the realm of knowledge, divine and human; the latter is the realm of opinion and illusion”.(p. 73)
“The confused and untrustworthy elements in the sense picture of nature are somehow the effect of the senses themselves”. (...) The secondary qualities are declared to be effects on the senses of the primary qualities which are alone real in nature”.(p. 74)
“The confused and untrustworthy elements in the sense picture of nature are somehow the effect of the senses themselves”. (...) The secondary qualities are declared to be effects on the senses of the primary qualities which are alone real in nature”.(p. 74)
“Till the time of Galileo it had always been taken for granted that man and nature were both integral parts of a larger whole, in which man’s place was the more fundamental. Whatever distinctions might be made between being and non-being, between primary and secondary, man was regarded as fundamentally allied with the positive and the primary. In the philosophies of Plato and Aristotle this is obvious enough; the remark holds true none the less for the ancient materialists. Man’s soul for Democritus was composed of the very finest and most mobile fire-atoms, which statement at once allied it to the most active and causal elements in the outside world. Indeed, to all important ancient and medieval thinkers, man was a genuine microcosm; in him was exemplified such a union of things primary and secondary as truly typified their relations in the vast macrocosm, whether the real and primary be regarded as ideas or as some material substance. Now, in the course of translating this distinction of primary and secondary into terms suited to the new mathematical interpretation of nature, we have the first stage in the reading of man quite out of the real and primary realm. Obviously man was not a subject suited to mathematical study. His performances could not be treated by the quantitative method, exept in the most meagre fashion. His was a life of colours and sounds, of pleasures, of griefs, of passionated loves, of ambitions, and strivings. Hence the real world must be the world outside of man; the world of astronomy and the world of resting and moving terrestrial objects. The only thing in common between man and the real world was his ability to discover it, a fact which, being necessarily presupposed, was easily neglected, and did not in any case suffice to exalt him to a parity of reality and causal efficiency with that which he was able to know. Quite naturally enough, along with this exaltation of the external world as more primary and more real, went an attribution to it of greater dgnity and value”.(p. 78-79)
“Till the time of Galileo it had always been taken for granted that man and nature were both integral parts of a larger whole, in which man’s place was the more fundamental. Whatever distinctions might be made between being and non-being, between primary and secondary, man was regarded as fundamentally allied with the positive and the primary. In the philosophies of Plato and Aristotle this is obvious enough; the remark holds true none the less for the ancient materialists. Man’s soul for Democritus was composed of the very finest and most mobile fire-atoms, which statement at once allied it to the most active and causal elements in the outside world. Indeed, to all important ancient and medieval thinkers, man was a genuine microcosm; in him was exemplified such a union of things primary and secondary as truly typified their relations in the vast macrocosm, whether the real and primary be regarded as ideas or as some material substance. Now, in the course of translating this distinction of primary and secondary into terms suited to the new mathematical interpretation of nature, we have the first stage in the reading of man quite out of the real and primary realm. Obviously man was not a subject suited to mathematical study. His performances could not be treated by the quantitative method, exept in the most meagre fashion. His was a life of colours and sounds, of pleasures, of griefs, of passionated loves, of ambitions, and strivings. Hence the real world must be the world outside of man; the world of astronomy and the world of resting and moving terrestrial objects. The only thing in common between man and the real world was his ability to discover it, a fact which, being necessarily presupposed, was easily neglected, and did not in any case suffice to exalt him to a parity of reality and causal efficiency with that which he was able to know. Quite naturally enough, along with this exaltation of the external world as more primary and more real, went an attribution to it of greater dgnity and value”.(p. 78-79)
“Man begins to appear for the first time in the history of thought as an irrelevant spectator and insignificant effect of the great mathematical system which is the substance of reality”.(p. 80)
“Man begins to appear for the first time in the history of thought as an irrelevant spectator and insignificant effect of the great mathematical system which is the substance of reality”.(p. 80)
“The why of motion had been the object of study and the study had proceeded in qualitative and substantive terms; with Galileo now it is the how of motion that becomes the object of analysis, and that by the method of exact mathematics”.(p. 81)
“The why of motion had been the object of study and the study had proceeded in qualitative and substantive terms; with Galileo now it is the how of motion that becomes the object of analysis, and that by the method of exact mathematics”.(p. 81)
“The real world is the world of bodies in mathematically reducible motions, and this means that the real world is a world of bodies moving in space and time”.(p. 83)
“The real world is the world of bodies in mathematically reducible motions, and this means that the real world is a world of bodies moving in space and time”.(p. 83)
“The real world is simply a succession of atomic motions in mathematical continuity”.(p. 90)
“The real world is simply a succession of atomic motions in mathematical continuity”.(p. 90)
“In more popular parlance, we have the postulate of the conservation of energy, energy being always revealed in the form of motion. The conception of the world as a perfect machine is thus rendered inevitable”.(p. 92)
“In more popular parlance, we have the postulate of the conservation of energy, energy being always revealed in the form of motion. The conception of the world as a perfect machine is thus rendered inevitable”.(p. 92)
“But what , now, is the nature of these ultimate forces which reveal themselves in the vast system of motions constituting the real world? Can we find Galileo attempting to answer this question, much of the medieval metaphysics which has now been deported may be able to re-enter. But here is the last evidence of Galileo’s revolutionary greatness. In an age when uncontrolled speculation was the order of the day we find a man with sufficient self-restraint to leave certain ultimate questions unsolved, as beyond the realm of positive science”.(p. 93)
“But what , now, is the nature of these ultimate forces which reveal themselves in the vast system of motions constituting the real world? Can we find Galileo attempting to answer this question, much of the medieval metaphysics which has now been deported may be able to re-enter. But here is the last evidence of Galileo’s revolutionary greatness. In an age when uncontrolled speculation was the order of the day we find a man with sufficient self-restraint to leave certain ultimate questions unsolved, as beyond the realm of positive science”.(p. 93)
“According to Galileo, we know nothing about the inner nature or essence of force, we only know its quantitative effects in terms of motion”.(p. 93)
“According to Galileo, we know nothing about the inner nature or essence of force, we only know its quantitative effects in terms of motion”.(p. 93)
“The natural world was portrayed as a vast, self-contained mathematical machine, consisting of motions of matter in space and time, and man with his purposes, feelings, and secondary qualities was shoved apart as an unimportant spectator and semi-real effect of the great mathematical drama outside. In view of this manifold and radical performances Galileo must be regarded as one of the massive intellects of all time”(p. 95)
“The natural world was portrayed as a vast, self-contained mathematical machine, consisting of motions of matter in space and time, and man with his purposes, feelings, and secondary qualities was shoved apart as an unimportant spectator and semi-real effect of the great mathematical drama outside. In view of this manifold and radical performances Galileo must be regarded as one of the massive intellects of all time”(p. 95)
Chapter IV. Descartes
Chapter IV. Descartes
“If we can get rid of all other qualities, or reduce them to these, it is clear that mathematics must be the sole and adequate key to unlock the truths of nature”.(p. 97-98)
“If we can get rid of all other qualities, or reduce them to these, it is clear that mathematics must be the sole and adequate key to unlock the truths of nature”.(p. 97-98)
“This does not mean that the objects of mathematics are imaginary entities without existence in the physical world”.(p. 98)
“This does not mean that the objects of mathematics are imaginary entities without existence in the physical world”.(p. 98)
“Descartes is at pains carefully to illustrate his thesis that exact knowledge in any science is always mathematical knowledge”.(p. 99)
“Descartes is at pains carefully to illustrate his thesis that exact knowledge in any science is always mathematical knowledge”.(p. 99)
“Physics, as something different from mathematics, merely determines whether certain parts of mathematics are founded on anything real or not”.(p. 99)
“Physics, as something different from mathematics, merely determines whether certain parts of mathematics are founded on anything real or not”.(p. 99)
“It might be taken for granted that all exact science is mathematical – that science as a whole is simply a larger mathematics, new concepts being added from time to time in terms of which more qualities of the phenomena become mathematically reducible”.(p. 101)
“It might be taken for granted that all exact science is mathematical – that science as a whole is simply a larger mathematics, new concepts being added from time to time in terms of which more qualities of the phenomena become mathematically reducible”.(p. 101)
“There is no spontaneity at any point”.(...) “all happens in accordance with the regularity, precision, inevitability, of a smoothly running machine”.(p. 103)
“There is no spontaneity at any point”.(...) “all happens in accordance with the regularity, precision, inevitability, of a smoothly running machine”.(p. 103)
(The Platonic-Aristotelian-Christian view:) “God had created the world of physical existence, for the purpose that in man, the highest natural end, the whole process might find its way back to God. Now God is relegated to the position of first cause of motion, the happenings of the universe then continuing in aeternum as incidents in the regular revolutions of a great mathematical machine”.(...) “The world is pictured concretely as material rather than spiritual, as mechanical rather than teleological. The stage is set for the likening of it, in Boyle, Locke, and Leibniz, to a big clock once wound up by the Creator, and since kept in orderly motion by nothing more than his ‘general concourse’”.(p. 105)
(The Platonic-Aristotelian-Christian view:) “God had created the world of physical existence, for the purpose that in man, the highest natural end, the whole process might find its way back to God. Now God is relegated to the position of first cause of motion, the happenings of the universe then continuing in aeternum as incidents in the regular revolutions of a great mathematical machine”.(...) “The world is pictured concretely as material rather than spiritual, as mechanical rather than teleological. The stage is set for the likening of it, in Boyle, Locke, and Leibniz, to a big clock once wound up by the Creator, and since kept in orderly motion by nothing more than his ‘general concourse’”.(p. 105)
“the sensible world is a vague and confused something”.(...) Why, now, are we sure that the primary, geometrical qualities inhere in objects as they really are, while the secondary qualities do not”? (...) “Descartes’ own justification for this claim is that these qualities are more permanent than the others”. (...) “But we might ask, are not colour and resistance equally constant properties of bodies? Objects change in colour, to be sure, and there are varying degrees of resistance, but does one meet bodies totally without colour or resistance? The fact is and this is of central importance for our whole study, Descartes’ real criterion is not permanence but the possibility of mathematical handling”.(p. 109-110)
“the sensible world is a vague and confused something”.(...) Why, now, are we sure that the primary, geometrical qualities inhere in objects as they really are, while the secondary qualities do not”? (...) “Descartes’ own justification for this claim is that these qualities are more permanent than the others”. (...) “But we might ask, are not colour and resistance equally constant properties of bodies? Objects change in colour, to be sure, and there are varying degrees of resistance, but does one meet bodies totally without colour or resistance? The fact is and this is of central importance for our whole study, Descartes’ real criterion is not permanence but the possibility of mathematical handling”.(p. 109-110)
“Hence the secondary qualities, when considered as belonging to the objects, like the primary, inevitably appear to his mind obscure and confused; they are not a clear field for mathematical operations”.(p. 110)
“Hence the secondary qualities, when considered as belonging to the objects, like the primary, inevitably appear to his mind obscure and confused; they are not a clear field for mathematical operations”.(p. 110)
“Such, then, is Descartes’ famous dualism – one world consisting of a huge, mathematical machine, extended in space; and another world consisting of unextended, thinking spirits. And whatever is not mathematical or depends at all on the activity of thinking substance, especially the so-called secondary qualities, belongs with the latter”.(p. 113)
“Such, then, is Descartes’ famous dualism – one world consisting of a huge, mathematical machine, extended in space; and another world consisting of unextended, thinking spirits. And whatever is not mathematical or depends at all on the activity of thinking substance, especially the so-called secondary qualities, belongs with the latter”.(p. 113)
“Of course, the problem of knowledge was not solved by this interpretation of Cartesian position, but rather tremendously accentuated. How is it possible for such a mind to know anything about such a world?”(p. 115)
“Of course, the problem of knowledge was not solved by this interpretation of Cartesian position, but rather tremendously accentuated. How is it possible for such a mind to know anything about such a world?”(p. 115)
“Now the world is an infinite and monotonous mathematical machine. Not only is his high place in a cosmic teleology lost, but all these things which were the very substance of the physical world to the scholastic – the things that made it alive and lovely and spiritual – are lumped together and crowded into the small fluctuating and temporary positions of extension which we call human nervous and circulatory systems”.(p. 116).
“Now the world is an infinite and monotonous mathematical machine. Not only is his high place in a cosmic teleology lost, but all these things which were the very substance of the physical world to the scholastic – the things that made it alive and lovely and spiritual – are lumped together and crowded into the small fluctuating and temporary positions of extension which we call human nervous and circulatory systems”.(p. 116).
Chapter V. Seventeenth-century English Philosophy.
Chapter V. Seventeenth-century English Philosophy.
Inasmuch as images are always of particular objects, we find Hobbes quite in line with the strong nominalistic tendency of the later Middle Ages, vigorous especially in England, which regarded individual things as the only real existences”.(p. 120)
Inasmuch as images are always of particular objects, we find Hobbes quite in line with the strong nominalistic tendency of the later Middle Ages, vigorous especially in England, which regarded individual things as the only real existences”.(p. 120)
(Hobbes) “Whence (woher) it is evident that essence in so far as it is distinguished from existence, is nothing else than a union of names by means of the verb is. And thus essence without existence is a fiction of our mind”.(p. 121)
(Hobbes) “Whence (woher) it is evident that essence in so far as it is distinguished from existence, is nothing else than a union of names by means of the verb is. And thus essence without existence is a fiction of our mind”.(p. 121)
(Hobbes) “For light and colour, and heat and sound, and other qualities which are commonly called sensible, are not objects, but phantasms in the sentients”.(p. 123)
(Hobbes) “For light and colour, and heat and sound, and other qualities which are commonly called sensible, are not objects, but phantasms in the sentients”.(p. 123)
“From now on it is a settled assumption (beständige Voraussetzung) for modern thought in practically every field, that to explain anything is to reduce it to its elementary parts, whose relations, where temporal in character (Beschaffenheit), are conceived in terms of efficient causality solely (lediglich)”.(p. 127)
“From now on it is a settled assumption (beständige Voraussetzung) for modern thought in practically every field, that to explain anything is to reduce it to its elementary parts, whose relations, where temporal in character (Beschaffenheit), are conceived in terms of efficient causality solely (lediglich)”.(p. 127)
More lists no fewer than twenty attributes which can be applied both to God and to space: each is “one, simple, immobile, eternal, perfect, independent, existing by itself, subsisting through itself, incorruptible, necessary, immense, uncreated, uncircumscribed, incomprehensible, omnipresent, incorporeal, permeating and embracing all things, essential being, actual being, pure actuality”.(p. 140) “eins, einfach, unbeweglich, ewig, perfekt, unabhängig, aus sich selbst heraus existierend, durch sich selbst bestehend, unverfälscht, notwendig, unermesslich, unerschaffen, unbegreiflich, allgegenwärtig, körperlos, alle Dinge durchdringend und umfassend, wesentliches Sein, wirkliches Sein, reine Wirklichkeit”.
More lists no fewer than twenty attributes which can be applied both to God and to space: each is “one, simple, immobile, eternal, perfect, independent, existing by itself, subsisting through itself, incorruptible, necessary, immense, uncreated, uncircumscribed, incomprehensible, omnipresent, incorporeal, permeating and embracing all things, essential being, actual being, pure actuality”.(p. 140) “eins, einfach, unbeweglich, ewig, perfekt, unabhängig, aus sich selbst heraus existierend, durch sich selbst bestehend, unverfälscht, notwendig, unermesslich, unerschaffen, unbegreiflich, allgegenwärtig, körperlos, alle Dinge durchdringend und umfassend, wesentliches Sein, wirkliches Sein, reine Wirklichkeit”.
A mechanical world alone would inevitably fly into pieces, by the unhampered (ungehinderte) operation of the laws of motion“.(p. 141-142).
A mechanical world alone would inevitably fly into pieces, by the unhampered (ungehinderte) operation of the laws of motion“.(p. 141-142).
“After a few preliminary remarks on the history of mathematics, Barrow observes that the object of the science is quantity, which may be considered either in its pure form, as in geometry and arithmetic, or in its mixed form, united with non-mathematical qualities”.(p. 145)
“After a few preliminary remarks on the history of mathematics, Barrow observes that the object of the science is quantity, which may be considered either in its pure form, as in geometry and arithmetic, or in its mixed form, united with non-mathematical qualities”.(p. 145)
“Thus physics, so far as it is a science, is wholly mathematical, likewise all of mathematics is applied in physics, hence we may say that the two sciences are co-extensive (ausgedehnt) and equal”.(p. 145)
“Thus physics, so far as it is a science, is wholly mathematical, likewise all of mathematics is applied in physics, hence we may say that the two sciences are co-extensive (ausgedehnt) and equal”.(p. 145)
“Mathematics is fundmentally, Barrow observes, a science of measurement”.(p.)
“Mathematics is fundmentally, Barrow observes, a science of measurement”.(p.)
“Just as space had ceased to appear accidental to abjects and relative to magnitudes, and became a vast infinite substance existing in its own right (except for its relation to God) so time ceased to be regarded merely as the measure of motion, and became a mysterious something ultimately of religious significance, but quite independent of motion, in fact mesured now by it, flowing on from everlasting to everlasting in its even mathematical course. From being a realm of sunstances in qualitative and teleological relations the world of nature had definitely become a realm of
“Just as space had ceased to appear accidental to abjects and relative to magnitudes, and became a vast infinite substance existing in its own right (except for its relation to God) so time ceased to be regarded merely as the measure of motion, and became a mysterious something ultimately of religious significance, but quite independent of motion, in fact mesured now by it, flowing on from everlasting to everlasting in its even mathematical course. From being a realm of sunstances in qualitative and teleological relations the world of nature had definitely become a realm of
bodies moving mechanically in space and time”.(p. 154)
bodies moving mechanically in space and time”.(p. 154)
Chapter VI. Gilbert and Boyle.
Chapter VI. Gilbert and Boyle.
“Now Gilbert, like the other fathers of modern science, was not content simply to note and formulate the results of his experiments; he sought ultimate explanations of the phenomena”.(p. 157)
“Now Gilbert, like the other fathers of modern science, was not content simply to note and formulate the results of his experiments; he sought ultimate explanations of the phenomena”.(p. 157)
Boyle: mathematical and mechanical principles are the “alphabet in which God wrote the world”. (p. 166)
Boyle: mathematical and mechanical principles are the “alphabet in which God wrote the world”. (p. 166)
“form (the scholastic essential qualities)” (p. 169)
“form (the scholastic essential qualities)” (p. 169)
(Boyle) “But for him the appeal to a mysterious entity is no genuine explanation; to explain a phenomenon is to deduce (ableiten) it from something else in nature more known than the thing to be explained. Substancial forms and other covers for our ignorance, like ‘nature’, are therefore no explanations, they just are as unique as the things to be explained”.(p. 170)
(Boyle) “But for him the appeal to a mysterious entity is no genuine explanation; to explain a phenomenon is to deduce (ableiten) it from something else in nature more known than the thing to be explained. Substancial forms and other covers for our ignorance, like ‘nature’, are therefore no explanations, they just are as unique as the things to be explained”.(p. 170)
Boyle “points out that an answer to the ultimate why of anything is no substitute for an answer to the immeditae how”. (...) “He must be a very dull inquirer who, demanding an account of the phenomena of a watch, shall rest satisfied with being told, that it is an engin made by a watchmaker”.(...) “A total axplanation of things is not the object of experimental science”.(p. 171)
Boyle “points out that an answer to the ultimate why of anything is no substitute for an answer to the immeditae how”. (...) “He must be a very dull inquirer who, demanding an account of the phenomena of a watch, shall rest satisfied with being told, that it is an engin made by a watchmaker”.(...) “A total axplanation of things is not the object of experimental science”.(p. 171)
“Galileo and Descartes had been eager to banish man from the mathematical world of nature into a secondary and unreal realm – to be sure Descartes had maintained the independence of thinking substance – but the whole effect of his work, like that of Galileo, was to make man’s place and importance seem very meagre, secondary, dependent. The real world was the mathematical and mechanical realm of extention and motion, man being put a puny appendage (winziger Anhang) and irrelevant spectator”.(p. 173
“Galileo and Descartes had been eager to banish man from the mathematical world of nature into a secondary and unreal realm – to be sure Descartes had maintained the independence of thinking substance – but the whole effect of his work, like that of Galileo, was to make man’s place and importance seem very meagre, secondary, dependent. The real world was the mathematical and mechanical realm of extention and motion, man being put a puny appendage (winziger Anhang) and irrelevant spectator”.(p. 173
“I am by these considerations disposed to think the soul of man a nobler and more valuable being, than the whole corporeal world”. Some touches of the medieval teleological hierarchy [‘haiera:cki] (Hierarchie, Rangordnung) are thus reaffirmend in Boyle, against the prevailing current”.(p. 176)
“I am by these considerations disposed to think the soul of man a nobler and more valuable being, than the whole corporeal world”. Some touches of the medieval teleological hierarchy [‘haiera:cki] (Hierarchie, Rangordnung) are thus reaffirmend in Boyle, against the prevailing current”.(p. 176)
“We might well ask, as we examine the metaphysics of the age – with its prevalent conception of the soul located within the body, where it is affected by the primary motions coming to the various senses and promulgated (verbreiten) to its seat in the brain – how any certain knowledge at all is possible of the real corporeal world outside, with which the soul is never in contact?” (p. 178)
“We might well ask, as we examine the metaphysics of the age – with its prevalent conception of the soul located within the body, where it is affected by the primary motions coming to the various senses and promulgated (verbreiten) to its seat in the brain – how any certain knowledge at all is possible of the real corporeal world outside, with which the soul is never in contact?” (p. 178)
Boyle’s positivism: “Since the reach of human knowledge is so small in comparison with the totality of being, it is ridiculous to attempt (versuchen) the projection of great systems; better to have a little knowledge which is certain because based on experiment, and is growing, though alsways incomplete and fragmentary, than to construct large speculative hypotheses of the universe”.(p. 180)
Boyle’s positivism: “Since the reach of human knowledge is so small in comparison with the totality of being, it is ridiculous to attempt (versuchen) the projection of great systems; better to have a little knowledge which is certain because based on experiment, and is growing, though alsways incomplete and fragmentary, than to construct large speculative hypotheses of the universe”.(p. 180)
(I) Summary of the Pre-Newtonian Development
(I) Summary of the Pre-Newtonian Development
Copernicus dared (wagte) to attribute to the earth a diurnal (täglich) motion on its axis and an annual motion around the sun, because of the greater mathematical simplicity of the atronomical system thus attained, a venture, whose metaphysical implications he could accept because of the widespread revival in his day of the Platonic-Pythagorean conception of the universe, and which was suggested to his mind by the preceding (vorausgehenden) developments in the science of mathematics. Kepler, moved by the beauty and harmony of this orderly system of the universe and by the satisfaction it accorded his adolescent deification (jugendlichen Vergötterung) of the sun, devoted himself to the search for additional geometrical harmonies among the exact data compiled by Tycho Brahe, conceiving the harmonious relations thus laid bare as the cause of the visible phenomena and likewise as the ultimately real and primary characteristics of things. Galileo was led by the thought of the motion of the earth and its mathematical treatment in astronomy to see if the motions of small parts of its crust (Kruste) might not be mathematically reducible, an attempt whose successful issue crowned him as the founder of a new science and led him in his efforts to see the fuller bearings (Erträge) of what he had accomplished to further metaphysical interferences (Eingriffe). The scholastic substances and causes, in terms of which the fact of motion and its ultimate why had been accounted (erklärt) for teleologically, were swept away in favour of the notion that bodies are composed of indestructible atoms, equipped with none but mathematical qualities, and move in an infinite homogeneous space and time in terms of which the actual process of motion could be formulated mathematically. Intoxicated by his success and supported by the onrushing Phytagorean tide, Galileo conceived the whole physical universe as a world of extension, figure, motion, and weight; all other qualities which we suppose to exist in rerum natura really have no place there but are due to the confusion and deceitfulness
Copernicus dared (wagte) to attribute to the earth a diurnal (täglich) motion on its axis and an annual motion around the sun, because of the greater mathematical simplicity of the atronomical system thus attained, a venture, whose metaphysical implications he could accept because of the widespread revival in his day of the Platonic-Pythagorean conception of the universe, and which was suggested to his mind by the preceding (vorausgehenden) developments in the science of mathematics. Kepler, moved by the beauty and harmony of this orderly system of the universe and by the satisfaction it accorded his adolescent deification (jugendlichen Vergötterung) of the sun, devoted himself to the search for additional geometrical harmonies among the exact data compiled by Tycho Brahe, conceiving the harmonious relations thus laid bare as the cause of the visible phenomena and likewise as the ultimately real and primary characteristics of things. Galileo was led by the thought of the motion of the earth and its mathematical treatment in astronomy to see if the motions of small parts of its crust (Kruste) might not be mathematically reducible, an attempt whose successful issue crowned him as the founder of a new science and led him in his efforts to see the fuller bearings (Erträge) of what he had accomplished to further metaphysical interferences (Eingriffe). The scholastic substances and causes, in terms of which the fact of motion and its ultimate why had been accounted (erklärt) for teleologically, were swept away in favour of the notion that bodies are composed of indestructible atoms, equipped with none but mathematical qualities, and move in an infinite homogeneous space and time in terms of which the actual process of motion could be formulated mathematically. Intoxicated by his success and supported by the onrushing Phytagorean tide, Galileo conceived the whole physical universe as a world of extension, figure, motion, and weight; all other qualities which we suppose to exist in rerum natura really have no place there but are due to the confusion and deceitfulness
(Täuschung) of our senses. The real world is mathematical, and an appropriate positive conception of causality is presented; all immediate causality is lodged in quantitatively reducibly motions of its atomic elements, hence only by mathematics can we arrive at true knowledge of that world. In so far, in fact, as we cannot attain mathematical knowledge it is better to confess our ignorance and proceed by tentative steps towards a fuller future science than to propound (vorschlagen) hasty speculations for grounded truths. In Descartes the early conviction that mathematics is the key to unlock the secrets of nature was powerfully strengthened by a mystic experience and directed by his pristine (vormaliger) invention, that of analytical geometry. Could not the whole of nature be reduced to an exclusively geometrical system? On this hypothesis Descartes constructed the first modern mechanical cosmology. But what about the non – geometrical qualities? Some, those with which Galileo had been struggling, Descartes hid in the vagueness of the ether; others, encouraged by Galileo’s example and led by his metaphysical propensities (Neigungen), he banished out of the realm of space and made into modes of thought, another substance totally different from extension and existing independently of it. “When any one tells us that he sees colour in a body or feels pain in one of his limps, this is exactly the same as if he said that he there saw or felt something, of the nature of which he was entirely ignorant, or that he did not know what he saw or felt”.(Descartes) But these totally different substances are in obvious and important relations. How is this to be accounted for? (Wie ist das zu erklären?) Descartes found himself quite unable to answer this overwhelming difficulty without speaking of the res cogitans (mind) as though it were after all confined (beschränkt) to an exeedingly (extraordinarily) meagre location within the body”.(p. 197-198)
(Täuschung) of our senses. The real world is mathematical, and an appropriate positive conception of causality is presented; all immediate causality is lodged in quantitatively reducibly motions of its atomic elements, hence only by mathematics can we arrive at true knowledge of that world. In so far, in fact, as we cannot attain mathematical knowledge it is better to confess our ignorance and proceed by tentative steps towards a fuller future science than to propound (vorschlagen) hasty speculations for grounded truths. In Descartes the early conviction that mathematics is the key to unlock the secrets of nature was powerfully strengthened by a mystic experience and directed by his pristine (vormaliger) invention, that of analytical geometry. Could not the whole of nature be reduced to an exclusively geometrical system? On this hypothesis Descartes constructed the first modern mechanical cosmology. But what about the non – geometrical qualities? Some, those with which Galileo had been struggling, Descartes hid in the vagueness of the ether; others, encouraged by Galileo’s example and led by his metaphysical propensities (Neigungen), he banished out of the realm of space and made into modes of thought, another substance totally different from extension and existing independently of it. “When any one tells us that he sees colour in a body or feels pain in one of his limps, this is exactly the same as if he said that he there saw or felt something, of the nature of which he was entirely ignorant, or that he did not know what he saw or felt”.(Descartes) But these totally different substances are in obvious and important relations. How is this to be accounted for? (Wie ist das zu erklären?) Descartes found himself quite unable to answer this overwhelming difficulty without speaking of the res cogitans (mind) as though it were after all confined (beschränkt) to an exeedingly (extraordinarily) meagre location within the body”.(p. 197-198)
Chapter VII. The metaphysics of Newton.
Chapter VII. The metaphysics of Newton.
“In scientific discovery and formulation Newton was a marvellous genious; as a philosopher he was uncritical, scetchy inconsistent, even second-rate”.(p. 203)
“In scientific discovery and formulation Newton was a marvellous genious; as a philosopher he was uncritical, scetchy inconsistent, even second-rate”.(p. 203)
“Thus, for Newton, careful experimentation must occur at the beginning and end of every important scientific step, because it is always the sensible facts that we are seeking to comprehend; but the comprehension, so far as it is exact, must be expressed in the mathematical language”.(p. 218)
“Thus, for Newton, careful experimentation must occur at the beginning and end of every important scientific step, because it is always the sensible facts that we are seeking to comprehend; but the comprehension, so far as it is exact, must be expressed in the mathematical language”.(p. 218)
“The ultimate nature of gravity is unknown; it is not necessary for science that it be known, for science seeks to understand how it acts, not what it is. For Newton, then, science was composed of laws stating ( festsetzen) the mathematical behaviour of nature solely – laws clearly deducible from phenomena and exactly verifiable in phenomena – everything further is to be swept out of science, which thus becomes a body of absolutely certain truth about the doings of the physical world”.(...) “Science is the exact mathematical formulation of the process of the natural world”.(p. 223)
“The ultimate nature of gravity is unknown; it is not necessary for science that it be known, for science seeks to understand how it acts, not what it is. For Newton, then, science was composed of laws stating ( festsetzen) the mathematical behaviour of nature solely – laws clearly deducible from phenomena and exactly verifiable in phenomena – everything further is to be swept out of science, which thus becomes a body of absolutely certain truth about the doings of the physical world”.(...) “Science is the exact mathematical formulation of the process of the natural world”.(p. 223)
“Newton, we are told, was the first great positivist”.(...) “With his work the era of great speculative systems ended, and a new day of exactitude and promise for man’s intellectual conquest of nature dawned. How, then, speak of him as a metaphysician”?(...) “The only way to avoid becoming a metaphysician is to say nothing”.(p. 223-224)
“Newton, we are told, was the first great positivist”.(...) “With his work the era of great speculative systems ended, and a new day of exactitude and promise for man’s intellectual conquest of nature dawned. How, then, speak of him as a metaphysician”?(...) “The only way to avoid becoming a metaphysician is to say nothing”.(p. 223-224)
“Now the history of mind reveals pretty clearly that the thinker who decries (tadelt) metaphysics will actually hold metaphysical notions of three main types. For one thing, he will share the ideas of his age on ultimate questions. (...) In the second place, if he be a manengaged in any important inquiry, he must have a method, and he will be under a strong and constant temptation to make a metaphysics out of his method. (...) Finally since human nature demands metaphysics for its full intellectual satisfaction, no great mind can wholly avoid playing with ultimate questions”.(p. 226)
“Now the history of mind reveals pretty clearly that the thinker who decries (tadelt) metaphysics will actually hold metaphysical notions of three main types. For one thing, he will share the ideas of his age on ultimate questions. (...) In the second place, if he be a manengaged in any important inquiry, he must have a method, and he will be under a strong and constant temptation to make a metaphysics out of his method. (...) Finally since human nature demands metaphysics for its full intellectual satisfaction, no great mind can wholly avoid playing with ultimate questions”.(p. 226)
“But inasmuch as the positive mind has failed to school itself in careful metaphysical thinking, its ventures (Wagnisse) at such points will be apt (voraussichtlich) to appear pitiful, inadequate, or even fantastic. Each of these three types is exemplified in Newton. His general conception of the physical world and of man’s relation to it, including the revolutionary doctrine of causality and the Cartesian dualism in its final ambiguous outcome (which were the two central features of the new ontology) with their somewhat less central corollaries (natürliche Folgen, Ergebnisse) about the nature and process of sensation, primary and secondary qualities, the imprisoned seat and petty powers of the human soul, was taken over without examination as an assured result of the victorious movement whose greatest champion he was destined to become”.(p. 226-227)
“But inasmuch as the positive mind has failed to school itself in careful metaphysical thinking, its ventures (Wagnisse) at such points will be apt (voraussichtlich) to appear pitiful, inadequate, or even fantastic. Each of these three types is exemplified in Newton. His general conception of the physical world and of man’s relation to it, including the revolutionary doctrine of causality and the Cartesian dualism in its final ambiguous outcome (which were the two central features of the new ontology) with their somewhat less central corollaries (natürliche Folgen, Ergebnisse) about the nature and process of sensation, primary and secondary qualities, the imprisoned seat and petty powers of the human soul, was taken over without examination as an assured result of the victorious movement whose greatest champion he was destined to become”.(p. 226-227)
“For Newton too the world of matter was a world possessing mathematical characteristics fundamentally. It was composed ultimately of absolutely hard, indestructible particles, equipped with the same characteristics which had now become familiar under the head of primary qualities, with the exception that Newton’s discovery and exact definition of a new exact-mathematical quality of bodies, the vis inertiae ( that property of matter that is proportional to its mass), induced (veranlasste) him to join it to the list. All changes in nature are to be regarded as separations, associations, and motions of these permanent atoms”.(p. 228)
“For Newton too the world of matter was a world possessing mathematical characteristics fundamentally. It was composed ultimately of absolutely hard, indestructible particles, equipped with the same characteristics which had now become familiar under the head of primary qualities, with the exception that Newton’s discovery and exact definition of a new exact-mathematical quality of bodies, the vis inertiae ( that property of matter that is proportional to its mass), induced (veranlasste) him to join it to the list. All changes in nature are to be regarded as separations, associations, and motions of these permanent atoms”.(p. 228)
“When we come from these quotations to Newton’s clearest statements on the doctrine of primary and secondary qualities, we are prepared for no appreciable divergence from the doctrine as it had been handed on to him by his metaphysical forrunners”.(p. 232)
“When we come from these quotations to Newton’s clearest statements on the doctrine of primary and secondary qualities, we are prepared for no appreciable divergence from the doctrine as it had been handed on to him by his metaphysical forrunners”.(p. 232)
Newton: “light pruduceth in our minds the phantasms (Phantasma, Trugbild, Hirngespinst) of colours...”(p. 232). Newton: “For the rays to speak properly are not coloured. In them there is nothing else than a certain power and disposition to stir up (anregen) a sensation of this or that colour. For as sound in a bell or a musical string or other sounding body, is nothing but a trembling motion, and in the air nothing but that motion propagated from the object, and in the sensorium (the whole sensory apparatus in the body) ‘tis a sense of that motion under the form of sound; so colours in the object are nothing but a disposition to reflect this or that sort of rays more copiously than the rest; in the rays they are nothing but their disposition to propagate this or that motion into the sensorium, and in the sensorium they are sensations of those motions under the forms of colours”.(p. 233)
Newton: “light pruduceth in our minds the phantasms (Phantasma, Trugbild, Hirngespinst) of colours...”(p. 232). Newton: “For the rays to speak properly are not coloured. In them there is nothing else than a certain power and disposition to stir up (anregen) a sensation of this or that colour. For as sound in a bell or a musical string or other sounding body, is nothing but a trembling motion, and in the air nothing but that motion propagated from the object, and in the sensorium (the whole sensory apparatus in the body) ‘tis a sense of that motion under the form of sound; so colours in the object are nothing but a disposition to reflect this or that sort of rays more copiously than the rest; in the rays they are nothing but their disposition to propagate this or that motion into the sensorium, and in the sensorium they are sensations of those motions under the forms of colours”.(p. 233)
Burtt: “Here the current doctrine of secondary qualities is clearly proclaimed. They have no real existence outside of human brains, save as a disposition of the bodies or the rays to reflect or propagate certain motions. Outside, nothing but the particles of matter, equipped with the qualities which have become mathematically handled, moving in certain ways”.(p. 233-234)
Burtt: “Here the current doctrine of secondary qualities is clearly proclaimed. They have no real existence outside of human brains, save as a disposition of the bodies or the rays to reflect or propagate certain motions. Outside, nothing but the particles of matter, equipped with the qualities which have become mathematically handled, moving in certain ways”.(p. 233-234)
“The world that people had thought themselves living in – a world rich with colour and sound, redolent with fragrance, filled with gladness, love and beauty, speaking everywhere of purposive harmony and creative ideals – was crowded now into minute corners in the brain of scattered (vereinzelte) organic beings. The really important world outside was a world hard, cold, colourless, silent, and dead; a world of quantity, a world of mathematically computable (berechenbare) motions in mechanical regularity. The world of qualities as immediately perceived by man became just a curious and quite minor effect of that infinite machine beyond. In Newton the Cartesian metaphysics, ambiguously (zweideutig) interpreted and stripped (entblöst) of its distinctive claim for serious philosophical consideration, finally overthrew Aristotelianism and became the predominant world – view of modern times”.(p. 236-237)
“The world that people had thought themselves living in – a world rich with colour and sound, redolent with fragrance, filled with gladness, love and beauty, speaking everywhere of purposive harmony and creative ideals – was crowded now into minute corners in the brain of scattered (vereinzelte) organic beings. The really important world outside was a world hard, cold, colourless, silent, and dead; a world of quantity, a world of mathematically computable (berechenbare) motions in mechanical regularity. The world of qualities as immediately perceived by man became just a curious and quite minor effect of that infinite machine beyond. In Newton the Cartesian metaphysics, ambiguously (zweideutig) interpreted and stripped (entblöst) of its distinctive claim for serious philosophical consideration, finally overthrew Aristotelianism and became the predominant world – view of modern times”.(p. 236-237)
“Since Newton nature come to be thought of by the modern mind as essentially a realm of masses, moving according to mathematical laws in space and time, under the influence of definite and dependable forces”.(p. 237)
“Since Newton nature come to be thought of by the modern mind as essentially a realm of masses, moving according to mathematical laws in space and time, under the influence of definite and dependable forces”.(p. 237)
“with, too, the early discovery that all the basic units of mechanics could be defined in units of mass, space and time, it was a simple enough metaphysical advance of the kind with which we are now surely familiar enough, from the statement that bodies are masses, to the assumption (Übernahme) that bodies are nothing but masses, and that all residual phenomena can be explained by factors external to the bodies themselves. Thus Newton, quite in opposition to certain presumtions fundamental in his own thinking, appeared to succeding generations in the light of a hearty upholder of the full mechanical conception of physical nature. The idea of mass had been incorporated into the Cartesian geometrical machine”.(p. 243)
“We can argue from effect to cause but not from caus to effect; the cause is entirely unknown and hypothetical until the effect appears”.(p. 251)
“The fact is, the idea of time thrust upon the world by modern scienceis a mixture of two peculiar (sonderbaren) conceptions. On the one hand, time is conceived as a homogeneous mathematical continuum, extending from the infinite past to the infinite future. Being one and entire, its whole extent is somehow present at once; it is neccessarily bound together and all subject to knowledge. The laws of motion, together with the doctrine of the constancy of energy, inevitably result in this picture of the whole sweep (Spielraum, Schwung) of time as a realm mathematically determinate in terms of an adequate present knowledge. But carry this conception to the limit, and does not time quite disappear as anything ultimately different from space? Once the Platonic year is discovered, everything hat can happen as a present event. Accordingly there is another element in the conception of time, which accords more congenially (geistesverwandt, passend) nominalistic predilections (Vorlieben) of some of the later medievelists and most of the early British scientist. Time is a succsession of discrete parts, or moments, no two of which are present simontaneously, and hence nothing exists or is present except the moment now. But the moment now is constantly passing into the past, and a future moment is becoming now. Hence from this point of view time simmers down till it is contracted into a methematical limit between the past and the future. Obviously, this limit can be described as flowing equably in time, but it is hardly time itself. Motion is inexplicable in terms of such a conception; any given motion will occupy more time than a sheer limit between what has gone by and what is yet to come. How combine these two elements into a single, mathematically usable idea, that shall, moreover, find some justification in actual experience? Newton does so by ingeniously (aufrichtig, schlicht) applying to time as an infinite continuum language that propperly applies only to this moving limit; hence the ‘equable flow’ (gleichförmige Fluss), in which description he hardly does more than follow his predesessor Barrow. The basic difficulty here, as pointed out in the chapter on Galileo, is that the scientific notion of time has almoust entirely lost touch with duration as immediately experienced. Until a closer relation is gained, it is probable that science will never reach a very
satisfactory description of time”.(p. 261-262)
Newton: “That gravity should be innate, inherent, and essential to matter, so that one body may act upon another, at a distance through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed (befördert) from one to another, is to me so great an absurdity, that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent acting constantly according to certain laws; but whether this agent be material or immaterial, I have left to the consideration of my readers”.(p. 265-266)
“The ultimate nature of anything he rather consistently denied knowledge of”.(p. 280)
Newton “You sometimes speak of gravity as essential and inherent to matter. Pray do not ascribe that notion to me; for the cause of gravity is what I do not know, and therefore would take more time to consider it”.(p. 287, preface to the second edition of the Pricipia)
“Space, time, and mass became regarded as permanent and indestructible constituents of the infinite world-order, while the notion of the ether continued to assume unpredictable shapes (Formen) and remains in the scientific thought of to-day a relic of ancient animism still playing havoc (Verwüstung) with poor man’s attempts to think straight about his world”.(p. 296)
“Newton’s doctrine is a most interesting and historically important transitional stage between the miraculous providentialism (Vorsehung) of earlier religious philosophy and the later tendency to identify the Deity with the sheer fact of rational order and harmony”.(p. 296)
“Whereever was taught as truth the universal formula of gravitation, there was also insinuated (eingebracht) as a nimbus (Heiligenschein, Regenwolke) of surrounding belief that man is but the puny and local spectator, nay irrelevant product of an infinite selfmoving engine, which existed eternally before him and will be eternally after him, enshrining (einschließen) the rigour (Strenge) of mathematical relationships while banishing into impotence all ideal imaginations; an engine which consists of raw masses wandering to no purpose in an undiscoverable time and space, and is in general wholly devoid of any qualities that might spell satisfaction for the major interests of human nature, save solely the central aim of the mathematical physicist”.(p. 299)
Chapter VIII. Conclusion.
We have observed that the heart of the new scientific metaphysics is to be found in the ascription of ultimate reality and causal efficacy to the world of mathematics, which world is identified with the realm of material bodies moving in space and time.
Expressed somewhat more fully, three essential points are to be distinguished in the transformation which issued in the victory of this metaphysical view; there is a change in the prevailing conception (1) of reality, (2) of causality, and (3) of the human mind.
First, the real world in which man lives is no longer regarded as a world of substances possessed of as many ultimate qualities as can experienced in them, but has become a world of atoms (now electrons), equipped with none but mathematical characteristics and moving according to laws fully statable (feststellbar) in mathematical form.
Second, explanations in terms of forms and final causes of events, both in this world and in the less independent realm of mind, have been definitely set aside in favour of explanations in terms of their simplest elements, the latter related temporally as efficient causes, and being mechanically treatable motions of bodies wherever it is possible to regard them. In connexion with this aspect of the change, God ceased to be regarded as a Supreme Final Cause, and, where still beleived in, became the First Efficient Cause of the world. Man likewise lost his high place over against nature which had been his as a part of the earlier teleological hierarchy, and his mind came to be described as a combination of sensations (now reactions) instead of in terms of the scholastic faculties.
Third, the attempt by philosophers of science in the light of these two changes to re-describe the relation of the human mind to nature, expressed itself in the popular form of the Cartesian dualism, with its doctrine of primary and secudary qualities, its location of the mind in a corner of the brain, and its account of the mechanical genesis of sensation and idea.
These changes have conditioned practically the whole of modern exact thinking”.(p. 300-3001)
“has the time not arrived for us to stop swallowing gullibly (leichtgläubig) this metaphysical substructure of the scientific movement and subject is to a thorough, critical examination”?
(p. 304)
“The fact is, there is simply no science possible of the realm of sensible phenomena unless the trustworthiness of our immediate perception of spacial directions and relations be taken for granted”.(p. 312-313)
“Mind appears to be an irreducible something that can know the world of extended matter, love ardently its order and beauty, and transform it continually in the light of a still more attractive and commanding good”.(p. 318)
“These founders of the philosophy of science were mathematical pragmatists, of a rather extreme type. They were absorbed in the mathematical study of nature. Metaphysics they tended more and more to avoid, so far as they could avoid it; so far as not, it became an instrument for their future mathematical conquest of the world”.(p. 325)
“There did remain of course, for these men, as we have seen, the terrible problem of knowledge. If the spacio-temporal realm is insulated from mind, how can mind possibly know it”?(p. 326)
Page updated
Google Sites
Report abuse