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Laws of form
Laws of form
by G. Spencer-Brown
Edition: Paperback
2 used & new from $31.99

5.0 out of 5 stars A THOUGHT-PROVOKING EXCURSION INTO MATHEMATICAL LOGIC, December 28, 2014
This review is from: Laws of form (Paperback)
George Spencer-Brown (born 1923) is a mathematician and logician, who has taught at Oxford, the University of London, the University of Western Australia, Stanford University, and the University of Maryland.

He wrote in the introductory section of this 1969 book, "The theme of this book is that a universe comes into being when a space is severed or falls apart... By tracing the way we represent such a severance, we can begin to reconstruct... the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance. The act is itself already remembered... as our first attempt to distinguish different things in a world where... the boundaries can be drawn anywhere we please.

"At this stage the universe cannot be distinguished from how we act upon it, and the world may seem like shifting sand beneath our feet... it becomes evident that the laws relating such forms are the same in any universe. It is this sameness... that lends such fascination to the study of mathematics. That mathematics... can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But ... Here the story is told from the beginning."

He states, "In the experiments above, imagine the circles to be forms and their circumferences to be the distinctions shaping the spaces of these forms. In this conception a distinction drawn in any space is a mark distinguishing the space. Equally and conversely, any mark in a space draws a distinction. We see now that the first distinction, the mark, and the observer are not only interchangeable, but, in the form, identical." (Pg. 76)

He says, "a proof can never be justified in the same way as a demonstration... In a proof we are dealing in terms which are outside of the calculus, and thus are not amenable to its instructions... The validity of a proof thus rests not in our common motivation by a set of instructions, but in our common experience of a state of affairs." (Pg. 93) He continues, "The fact that a proof is a way of making apparently obvious what was already latently so is of some mathematical interest... Thus we are not... seeking something that has ever been hidden..." (Pg. 95)

He suggests, "you will eventually construct the universe... as you know it now; but ... what you construct will not be all, for by the time you will have reached what now is, the universe will have expanded into a new order to contain what will then be... Thus the world, when ever it appears as a physical universe, must always seem to us, its representatives, to be playing a game of hide-and-seek with itself..." (Pg. 106)

Brown's book is, at one level, a serious contribution to mathematical logic. However, it must be acknowledged that many of his readers are only interested in the more esoteric, Eastern philosophy-flavored and "New Age" ideas that are also contained herein. In any case, his book is a fascinating "mind-expanding" journey, that will delight a wide variety of readers.


laws of Form
laws of Form
by G. Spencer-Brown
Edition: Mass Market Paperback

5.0 out of 5 stars A THOUGHT-PROVOKING EXCURSION INTO MATHEMATICAL LOGIC, December 28, 2014
George Spencer-Brown (born 1923) is a mathematician and logician, who has taught at Oxford, the University of London, the University of Western Australia, Stanford University, and the University of Maryland.

He wrote in the introductory section of this 1969 book, "The theme of this book is that a universe comes into being when a space is severed or falls apart... By tracing the way we represent such a severance, we can begin to reconstruct... the basic forms underlying linguistic, mathematical, physical, and biological science, and can begin to see how the familiar laws of our own experience follow inexorably from the original act of severance. The act is itself already remembered... as our first attempt to distinguish different things in a world where... the boundaries can be drawn anywhere we please.

"At this stage the universe cannot be distinguished from how we act upon it, and the world may seem like shifting sand beneath our feet... it becomes evident that the laws relating such forms are the same in any universe. It is this sameness... that lends such fascination to the study of mathematics. That mathematics... can lead us beyond ordinary existence, and can show us something of the structure in which all creation hangs together, is no new idea. But ... Here the story is told from the beginning."

He states, "In the experiments above, imagine the circles to be forms and their circumferences to be the distinctions shaping the spaces of these forms. In this conception a distinction drawn in any space is a mark distinguishing the space. Equally and conversely, any mark in a space draws a distinction. We see now that the first distinction, the mark, and the observer are not only interchangeable, but, in the form, identical." (Pg. 76)

He says, "a proof can never be justified in the same way as a demonstration... In a proof we are dealing in terms which are outside of the calculus, and thus are not amenable to its instructions... The validity of a proof thus rests not in our common motivation by a set of instructions, but in our common experience of a state of affairs." (Pg. 93) He continues, "The fact that a proof is a way of making apparently obvious what was already latently so is of some mathematical interest... Thus we are not... seeking something that has ever been hidden..." (Pg. 95)

He suggests, "you will eventually construct the universe... as you know it now; but ... what you construct will not be all, for by the time you will have reached what now is, the universe will have expanded into a new order to contain what will then be... Thus the world, when ever it appears as a physical universe, must always seem to us, its representatives, to be playing a game of hide-and-seek with itself..." (Pg. 106)

Brown's book is, at one level, a serious contribution to mathematical logic. However, it must be acknowledged that many of his readers are only interested in the more esoteric, Eastern philosophy-flavored and "New Age" ideas that are also contained herein. In any case, his book is a fascinating "mind-expanding" journey, that will delight a wide variety of readers.


The Structure Of Scientific Revolutions - Second Edition, Enlarged
The Structure Of Scientific Revolutions - Second Edition, Enlarged
by Thomas S. Kuhn
Edition: Paperback
2 used & new from $2.54

5.0 out of 5 stars THE BOOK THAT REINTRODUCED THE WORD "PARADIGM" TO THE WORLD, December 28, 2014
Thomas Samuel Kuhn (1922-1996) was an American physicist, historian, and philosopher of science, who taught at Harvard, UC Berkeley, and MIT. He wrote other books such as The Road since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, The Essential Tension: Selected Studies in Scientific Tradition and Change, etc.

He wrote in the Preface to the original 1962 edition, “The essay that follows is the first full published report on a project originally conceived almost fifteen years ago… an experimental college course treating physical science for the non-scientist provided my first exposure to the history of science… that exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science…” (Pg. v) He continues, “[In} 1958-1959 … I was able to give undivided attention to the problems discussed below… I was struck by the number and extent of the overt disagreements between social scientists about the nature of legitimate scientific problems and methods… Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called ‘paradigms.’ These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.” (Pg. viii)

He observes, “Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time.” (Pg. 4) He asserts, “a new theory… is seldom or never just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man and never overnight.” (Pg. 7)

He begins to make one of his major points about works to Aristotle, Ptolemy, Newton, Lavosier, Lyell, etc.: “these and many other works served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners. They were able to do so because they shared two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve.” (Pg. 10)

He elaborates, “The study of paradigms… is that mainly prepares the student for membership in the particular scientific community with which he will later practice. Because he there joins men who learned the bases of their field from the same concrete models, his subsequent practice will seldom evoke overt disagreement over fundamentals. Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, i.e., for the genesis and continuation of a particular research tradition.” (Pg. 10-11)

He explains, “To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it is confronted.” (Pg. 17-18) He continues, “Paradigms gain their status because they are more successful than their competitors in solving a few problems that the group of practitioners has come to recognize as acute. To be more successful is not, however, to be either completely successful with a single problem or notably successful with any large number. The success of a paradigm… is at the start largely a promise of success discoverable in selected and still incomplete examples. Normal science consists in the actualization of that promise… by increasing the extent of the match between those facts and the paradigm’s predictions, and by further actualization of the paradigm itself.” (Pg. 23-24)

He elaborates, “normal science … ensures the relaxation of the restrictions that bond research whenever the paradigm from which they derive ceases to function effectively. At that point scientists begin to behave differently, and the nature of their research problems changes.” (Pg. 24) He suggests, “a novel theory emerged only after a pronounced failure in the normal problem-solving activity. Furthermore… that breakdown and the proliferation of theories that is its sign occurred no more than a decade or two before the new theory’s enunciation. The novel theory seems a direct response to crisis.” (Pg. 74-75) He adds, “The significance of crises is the indication they provide that an occasion for retooling has arrived.” (Pg. 76)

He summarizes, “when confronted by even severe and prolonged anomalies…they may begin to lose faith and then to consider alternatives, [but] they do not renounce the paradigm that has led them into crisis. They do not… treat anomalies as counter-instances … once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternate candidate is available to take its place.” (Pg. 77)

He admits, “The man who embraces a new paradigm at an early stage must often do so in defiance of the evidence provided by problem-solving. He must, that is, have faith that the new paradigm will succeed with the many large problems that confront it, knowing only that the older paradigm has failed with a few. A decision of that kind can only be made on faith.” (Pg. 158)

The influence of this book has (unfortunately, in some cases) extended far beyond the “philosophy of science” boundaries that it originally appeared within. It is “must reading” for not only students of the philosophy of science, but of contemporary Western culture in general.


The Structure of Scientific Revolutions-2nd Ed. Enlarged
The Structure of Scientific Revolutions-2nd Ed. Enlarged
by Thomas Kuhn
Edition: Paperback
6 used & new from $24.95

5.0 out of 5 stars THE BOOK THAT REINTRODUCED THE WORD "PARADIGM" TO THE WORLD, December 28, 2014
Thomas Samuel Kuhn (1922-1996) was an American physicist, historian, and philosopher of science, who taught at Harvard, UC Berkeley, and MIT. He wrote other books such as The Road since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, The Essential Tension: Selected Studies in Scientific Tradition and Change, etc.

He wrote in the Preface to the original 1962 edition, “The essay that follows is the first full published report on a project originally conceived almost fifteen years ago… an experimental college course treating physical science for the non-scientist provided my first exposure to the history of science… that exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science…” (Pg. v) He continues, “[In} 1958-1959 … I was able to give undivided attention to the problems discussed below… I was struck by the number and extent of the overt disagreements between social scientists about the nature of legitimate scientific problems and methods… Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called ‘paradigms.’ These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.” (Pg. viii)

He observes, “Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time.” (Pg. 4) He asserts, “a new theory… is seldom or never just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man and never overnight.” (Pg. 7)

He begins to make one of his major points about works to Aristotle, Ptolemy, Newton, Lavosier, Lyell, etc.: “these and many other works served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners. They were able to do so because they shared two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve.” (Pg. 10)

He elaborates, “The study of paradigms… is that mainly prepares the student for membership in the particular scientific community with which he will later practice. Because he there joins men who learned the bases of their field from the same concrete models, his subsequent practice will seldom evoke overt disagreement over fundamentals. Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, i.e., for the genesis and continuation of a particular research tradition.” (Pg. 10-11)

He explains, “To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it is confronted.” (Pg. 17-18) He continues, “Paradigms gain their status because they are more successful than their competitors in solving a few problems that the group of practitioners has come to recognize as acute. To be more successful is not, however, to be either completely successful with a single problem or notably successful with any large number. The success of a paradigm… is at the start largely a promise of success discoverable in selected and still incomplete examples. Normal science consists in the actualization of that promise… by increasing the extent of the match between those facts and the paradigm’s predictions, and by further actualization of the paradigm itself.” (Pg. 23-24)

He elaborates, “normal science … ensures the relaxation of the restrictions that bond research whenever the paradigm from which they derive ceases to function effectively. At that point scientists begin to behave differently, and the nature of their research problems changes.” (Pg. 24) He suggests, “a novel theory emerged only after a pronounced failure in the normal problem-solving activity. Furthermore… that breakdown and the proliferation of theories that is its sign occurred no more than a decade or two before the new theory’s enunciation. The novel theory seems a direct response to crisis.” (Pg. 74-75) He adds, “The significance of crises is the indication they provide that an occasion for retooling has arrived.” (Pg. 76)

He summarizes, “when confronted by even severe and prolonged anomalies…they may begin to lose faith and then to consider alternatives, [but] they do not renounce the paradigm that has led them into crisis. They do not… treat anomalies as counter-instances … once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternate candidate is available to take its place.” (Pg. 77)

He admits, “The man who embraces a new paradigm at an early stage must often do so in defiance of the evidence provided by problem-solving. He must, that is, have faith that the new paradigm will succeed with the many large problems that confront it, knowing only that the older paradigm has failed with a few. A decision of that kind can only be made on faith.” (Pg. 158)

The influence of this book has (unfortunately, in some cases) extended far beyond the “philosophy of science” boundaries that it originally appeared within. It is “must reading” for not only students of the philosophy of science, but of contemporary Western culture in general.


The Structure of Scientific Revolutions by Kuhn, Thomas S. Published by University of Chicago Press 2nd (second) edition (1970) Paperback
The Structure of Scientific Revolutions by Kuhn, Thomas S. Published by University of Chicago Press 2nd (second) edition (1970) Paperback
5 used & new from $4.58

5.0 out of 5 stars THE BOOK THAT REINTRODUCED THE WORD "PARADIGM" TO THE WORLD, December 28, 2014
Thomas Samuel Kuhn (1922-1996) was an American physicist, historian, and philosopher of science, who taught at Harvard, UC Berkeley, and MIT. He wrote other books such as The Road since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, The Essential Tension: Selected Studies in Scientific Tradition and Change, etc.

He wrote in the Preface to the original 1962 edition, “The essay that follows is the first full published report on a project originally conceived almost fifteen years ago… an experimental college course treating physical science for the non-scientist provided my first exposure to the history of science… that exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science…” (Pg. v) He continues, “[In} 1958-1959 … I was able to give undivided attention to the problems discussed below… I was struck by the number and extent of the overt disagreements between social scientists about the nature of legitimate scientific problems and methods… Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called ‘paradigms.’ These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.” (Pg. viii)

He observes, “Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time.” (Pg. 4) He asserts, “a new theory… is seldom or never just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man and never overnight.” (Pg. 7)

He begins to make one of his major points about works to Aristotle, Ptolemy, Newton, Lavosier, Lyell, etc.: “these and many other works served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners. They were able to do so because they shared two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve.” (Pg. 10)

He elaborates, “The study of paradigms… is that mainly prepares the student for membership in the particular scientific community with which he will later practice. Because he there joins men who learned the bases of their field from the same concrete models, his subsequent practice will seldom evoke overt disagreement over fundamentals. Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, i.e., for the genesis and continuation of a particular research tradition.” (Pg. 10-11)

He explains, “To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it is confronted.” (Pg. 17-18) He continues, “Paradigms gain their status because they are more successful than their competitors in solving a few problems that the group of practitioners has come to recognize as acute. To be more successful is not, however, to be either completely successful with a single problem or notably successful with any large number. The success of a paradigm… is at the start largely a promise of success discoverable in selected and still incomplete examples. Normal science consists in the actualization of that promise… by increasing the extent of the match between those facts and the paradigm’s predictions, and by further actualization of the paradigm itself.” (Pg. 23-24)

He elaborates, “normal science … ensures the relaxation of the restrictions that bond research whenever the paradigm from which they derive ceases to function effectively. At that point scientists begin to behave differently, and the nature of their research problems changes.” (Pg. 24) He suggests, “a novel theory emerged only after a pronounced failure in the normal problem-solving activity. Furthermore… that breakdown and the proliferation of theories that is its sign occurred no more than a decade or two before the new theory’s enunciation. The novel theory seems a direct response to crisis.” (Pg. 74-75) He adds, “The significance of crises is the indication they provide that an occasion for retooling has arrived.” (Pg. 76)

He summarizes, “when confronted by even severe and prolonged anomalies…they may begin to lose faith and then to consider alternatives, [but] they do not renounce the paradigm that has led them into crisis. They do not… treat anomalies as counter-instances … once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternate candidate is available to take its place.” (Pg. 77)

He admits, “The man who embraces a new paradigm at an early stage must often do so in defiance of the evidence provided by problem-solving. He must, that is, have faith that the new paradigm will succeed with the many large problems that confront it, knowing only that the older paradigm has failed with a few. A decision of that kind can only be made on faith.” (Pg. 158)

The influence of this book has (unfortunately, in some cases) extended far beyond the “philosophy of science” boundaries that it originally appeared within. It is “must reading” for not only students of the philosophy of science, but of contemporary Western culture in general.


The Structure of Scientific Revolutions, Volume II, Number 2 (Second Edition, Enlarged)
The Structure of Scientific Revolutions, Volume II, Number 2 (Second Edition, Enlarged)
by Thomas, S.; Thomas S. Kuhn (Author) Kuhn
Edition: Paperback
46 used & new from $1.63

5.0 out of 5 stars THE BOOK THAT REINTRODUCED THE WORD "PARADIGM" TO THE WORLD, December 28, 2014
Thomas Samuel Kuhn (1922-1996) was an American physicist, historian, and philosopher of science, who taught at Harvard, UC Berkeley, and MIT. He wrote other books such as The Road since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, The Essential Tension: Selected Studies in Scientific Tradition and Change, etc.

He wrote in the Preface to the original 1962 edition, “The essay that follows is the first full published report on a project originally conceived almost fifteen years ago… an experimental college course treating physical science for the non-scientist provided my first exposure to the history of science… that exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science…” (Pg. v) He continues, “[In} 1958-1959 … I was able to give undivided attention to the problems discussed below… I was struck by the number and extent of the overt disagreements between social scientists about the nature of legitimate scientific problems and methods… Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called ‘paradigms.’ These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.” (Pg. viii)

He observes, “Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time.” (Pg. 4) He asserts, “a new theory… is seldom or never just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man and never overnight.” (Pg. 7)

He begins to make one of his major points about works to Aristotle, Ptolemy, Newton, Lavosier, Lyell, etc.: “these and many other works served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners. They were able to do so because they shared two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve.” (Pg. 10)

He elaborates, “The study of paradigms… is that mainly prepares the student for membership in the particular scientific community with which he will later practice. Because he there joins men who learned the bases of their field from the same concrete models, his subsequent practice will seldom evoke overt disagreement over fundamentals. Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, i.e., for the genesis and continuation of a particular research tradition.” (Pg. 10-11)

He explains, “To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it is confronted.” (Pg. 17-18) He continues, “Paradigms gain their status because they are more successful than their competitors in solving a few problems that the group of practitioners has come to recognize as acute. To be more successful is not, however, to be either completely successful with a single problem or notably successful with any large number. The success of a paradigm… is at the start largely a promise of success discoverable in selected and still incomplete examples. Normal science consists in the actualization of that promise… by increasing the extent of the match between those facts and the paradigm’s predictions, and by further actualization of the paradigm itself.” (Pg. 23-24)

He elaborates, “normal science … ensures the relaxation of the restrictions that bond research whenever the paradigm from which they derive ceases to function effectively. At that point scientists begin to behave differently, and the nature of their research problems changes.” (Pg. 24) He suggests, “a novel theory emerged only after a pronounced failure in the normal problem-solving activity. Furthermore… that breakdown and the proliferation of theories that is its sign occurred no more than a decade or two before the new theory’s enunciation. The novel theory seems a direct response to crisis.” (Pg. 74-75) He adds, “The significance of crises is the indication they provide that an occasion for retooling has arrived.” (Pg. 76)

He summarizes, “when confronted by even severe and prolonged anomalies…they may begin to lose faith and then to consider alternatives, [but] they do not renounce the paradigm that has led them into crisis. They do not… treat anomalies as counter-instances … once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternate candidate is available to take its place.” (Pg. 77)

He admits, “The man who embraces a new paradigm at an early stage must often do so in defiance of the evidence provided by problem-solving. He must, that is, have faith that the new paradigm will succeed with the many large problems that confront it, knowing only that the older paradigm has failed with a few. A decision of that kind can only be made on faith.” (Pg. 158)

The influence of this book has (unfortunately, in some cases) extended far beyond the “philosophy of science” boundaries that it originally appeared within. It is “must reading” for not only students of the philosophy of science, but of contemporary Western culture in general.


The Structure of Scientific Revolutions
The Structure of Scientific Revolutions
by Thomas S. Kuhn
Edition: Paperback
360 used & new from $0.01

5.0 out of 5 stars THE BOOK THAT REINTRODUCED THE WORD "PARADIGM" TO THE WORLD, December 28, 2014
Thomas Samuel Kuhn (1922-1996) was an American physicist, historian, and philosopher of science, who taught at Harvard, UC Berkeley, and MIT. He wrote other books such as The Road since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, The Essential Tension: Selected Studies in Scientific Tradition and Change, etc.

He wrote in the Preface to the original 1962 edition, “The essay that follows is the first full published report on a project originally conceived almost fifteen years ago… an experimental college course treating physical science for the non-scientist provided my first exposure to the history of science… that exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science…” (Pg. v) He continues, “[In} 1958-1959 … I was able to give undivided attention to the problems discussed below… I was struck by the number and extent of the overt disagreements between social scientists about the nature of legitimate scientific problems and methods… Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called ‘paradigms.’ These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners.” (Pg. viii)

He observes, “Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time.” (Pg. 4) He asserts, “a new theory… is seldom or never just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man and never overnight.” (Pg. 7)

He begins to make one of his major points about works to Aristotle, Ptolemy, Newton, Lavosier, Lyell, etc.: “these and many other works served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners. They were able to do so because they shared two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve.” (Pg. 10)

He elaborates, “The study of paradigms… is that mainly prepares the student for membership in the particular scientific community with which he will later practice. Because he there joins men who learned the bases of their field from the same concrete models, his subsequent practice will seldom evoke overt disagreement over fundamentals. Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, i.e., for the genesis and continuation of a particular research tradition.” (Pg. 10-11)

He explains, “To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it is confronted.” (Pg. 17-18) He continues, “Paradigms gain their status because they are more successful than their competitors in solving a few problems that the group of practitioners has come to recognize as acute. To be more successful is not, however, to be either completely successful with a single problem or notably successful with any large number. The success of a paradigm… is at the start largely a promise of success discoverable in selected and still incomplete examples. Normal science consists in the actualization of that promise… by increasing the extent of the match between those facts and the paradigm’s predictions, and by further actualization of the paradigm itself.” (Pg. 23-24)

He elaborates, “normal science … ensures the relaxation of the restrictions that bond research whenever the paradigm from which they derive ceases to function effectively. At that point scientists begin to behave differently, and the nature of their research problems changes.” (Pg. 24) He suggests, “a novel theory emerged only after a pronounced failure in the normal problem-solving activity. Furthermore… that breakdown and the proliferation of theories that is its sign occurred no more than a decade or two before the new theory’s enunciation. The novel theory seems a direct response to crisis.” (Pg. 74-75) He adds, “The significance of crises is the indication they provide that an occasion for retooling has arrived.” (Pg. 76)

He summarizes, “when confronted by even severe and prolonged anomalies…they may begin to lose faith and then to consider alternatives, [but] they do not renounce the paradigm that has led them into crisis. They do not… treat anomalies as counter-instances … once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternate candidate is available to take its place.” (Pg. 77)

He admits, “The man who embraces a new paradigm at an early stage must often do so in defiance of the evidence provided by problem-solving. He must, that is, have faith that the new paradigm will succeed with the many large problems that confront it, knowing only that the older paradigm has failed with a few. A decision of that kind can only be made on faith.” (Pg. 158)

The influence of this book has (unfortunately, in some cases) extended far beyond the “philosophy of science” boundaries that it originally appeared within. It is “must reading” for not only students of the philosophy of science, but of contemporary Western culture in general.


The Structure of Scientific Revolutions, second edition, enlarged
The Structure of Scientific Revolutions, second edition, enlarged
by Thomas Kuhn
Edition: Hardcover
8 used & new from $69.94

5.0 out of 5 stars THE BOOK THAT REINTRODUCED THE WORD "PARADIGM" TO THE WORLD, December 28, 2014
Thomas Samuel Kuhn (1922-1996) was an American physicist, historian, and philosopher of science, who taught at Harvard, UC Berkeley, and MIT. He wrote other books such as The Road since Structure: Philosophical Essays, 1970-1993, with an Autobiographical Interview, The Copernican Revolution: Planetary Astronomy in the Development of Western Thought, The Essential Tension: Selected Studies in Scientific Tradition and Change, etc.

He wrote in the Preface to the original 1962 edition, "The essay that follows is the first full published report on a project originally conceived almost fifteen years ago... an experimental college course treating physical science for the non-scientist provided my first exposure to the history of science... that exposure to out-of-date scientific theory and practice radically undermined some of my basic conceptions about the nature of science..." (Pg. v) He continues, "[In} 1958-1959 ... I was able to give undivided attention to the problems discussed below... I was struck by the number and extent of the overt disagreements between social scientists about the nature of legitimate scientific problems and methods... Attempting to discover the source of that difference led me to recognize the role in scientific research of what I have since called `paradigms.' These I take to be universally recognized scientific achievements that for a time provide model problems and solutions to a community of practitioners." (Pg. viii)

He observes, "Observation and experience can and must drastically restrict the range of admissible scientific belief, else there would be no science. But they cannot alone determine a particular body of such belief. An apparently arbitrary element, compounded of personal and historical accident, is always a formative ingredient of the beliefs espoused by a given scientific community at a given time." (Pg. 4) He asserts, "a new theory... is seldom or never just an increment to what is already known. Its assimilation requires the reconstruction of prior theory and the re-evaluation of prior fact, an intrinsically revolutionary process that is seldom completed by a single man and never overnight." (Pg. 7)

He begins to make one of his major points about works to Aristotle, Ptolemy, Newton, Lavosier, Lyell, etc.: "these and many other works served for a time implicitly to define the legitimate problems and methods of a research field for succeeding generations of practitioners. They were able to do so because they shared two essential characteristics. Their achievement was sufficiently unprecedented to attract an enduring group of adherents away from competing modes of scientific activity. Simultaneously, it was sufficiently open-ended to leave all sorts of problems for the redefined group of practitioners to resolve." (Pg. 10)

He elaborates, "The study of paradigms... is that mainly prepares the student for membership in the particular scientific community with which he will later practice. Because he there joins men who learned the bases of their field from the same concrete models, his subsequent practice will seldom evoke overt disagreement over fundamentals. Men whose research is based on shared paradigms are committed to the same rules and standards for scientific practice. That commitment and the apparent consensus it produces are prerequisites for normal science, i.e., for the genesis and continuation of a particular research tradition." (Pg. 10-11)

He explains, "To be accepted as a paradigm, a theory must seem better than its competitors, but it need not, and in fact never does, explain all the facts with which it is confronted." (Pg. 17-18) He continues, "Paradigms gain their status because they are more successful than their competitors in solving a few problems that the group of practitioners has come to recognize as acute. To be more successful is not, however, to be either completely successful with a single problem or notably successful with any large number. The success of a paradigm... is at the start largely a promise of success discoverable in selected and still incomplete examples. Normal science consists in the actualization of that promise... by increasing the extent of the match between those facts and the paradigm's predictions, and by further actualization of the paradigm itself." (Pg. 23-24)

He elaborates, "normal science ... ensures the relaxation of the restrictions that bond research whenever the paradigm from which they derive ceases to function effectively. At that point scientists begin to behave differently, and the nature of their research problems changes." (Pg. 24) He suggests, "a novel theory emerged only after a pronounced failure in the normal problem-solving activity. Furthermore... that breakdown and the proliferation of theories that is its sign occurred no more than a decade or two before the new theory's enunciation. The novel theory seems a direct response to crisis." (Pg. 74-75) He adds, "The significance of crises is the indication they provide that an occasion for retooling has arrived." (Pg. 76)

He summarizes, "when confronted by even severe and prolonged anomalies...they may begin to lose faith and then to consider alternatives, [but] they do not renounce the paradigm that has led them into crisis. They do not... treat anomalies as counter-instances ... once it has achieved the status of paradigm, a scientific theory is declared invalid only if an alternate candidate is available to take its place." (Pg. 77)

He admits, "The man who embraces a new paradigm at an early stage must often do so in defiance of the evidence provided by problem-solving. He must, that is, have faith that the new paradigm will succeed with the many large problems that confront it, knowing only that the older paradigm has failed with a few. A decision of that kind can only be made on faith." (Pg. 158)

The influence of this book has (unfortunately, in some cases) extended far beyond the "philosophy of science" boundaries that it originally appeared within. It is "must reading" for not only students of the philosophy of science, but of contemporary Western culture in general.


Mathematics, Science and Epistemology: Volume 2, Philosophical Papers (Philosophical Papers (Cambridge))
Mathematics, Science and Epistemology: Volume 2, Philosophical Papers (Philosophical Papers (Cambridge))
by Imre Lakatos
Edition: Paperback
Price: $53.36
47 used & new from $6.00

5.0 out of 5 stars ONE OF THE GREATEST PHILOSOPHERS OF SCIENCE & MATHEMATICS OF THE 20TH CENTURY, December 28, 2014
Imre Lakatos (1922-1974) was a Hungarian philosopher of mathematics and science; the companion volume to this book is The Methodology of Scientific Research Programmes: Volume 1: Philosophical Papers.

The Editor's Introduction states, "When Imre Lakatos died in 1974, many friends and colleagues expressed the hope that his unpublished papers would be made available. Some were also interested in seeing his contributions to journals and conference proceedings collected together in a book... we have prepared two volumes of selected papers which we hope will meet these demands. None of the papers published here for the first time was regarded by Lakatos as entirely satisfactory..." Volume 2 contains papers on the philosophy of mathematics, as well as some essays on contemporary philosophers on political and educational matters.

He explains, "The Frege-Russell approach aimed to deduce all mathematical truths---with the help of ingenious defintions---from indubitably true logical axioms. It turned out that some of the logical ... axioms were not only not indubitably true but not even consistent. It turned out that the sophisticated second ... axioms---devised to avoid the known paradoxes---even if true, were not indubitably true (and not even indubitably consistent), and that the crucial evidence for them was that classical mathematics might be EXPLAINED---but certainly not PROVED---by them." (Pg. 30)

He states, "So we cannot prove in science; the most we can do, if we are anti-inductive empiricists, is to disprove. If, however, we extend our critical attitude to the facts too... we can allow only tentative recognition to basic statements. The Popperian epistemological zipfastener, unlike the zipfastener of logical positivism, is unsuitable even for infallible disproof. It cannot prove and it can disprove only tentatively. As to the heuristic zipfastener, this may start from a reasoned fact... may move upwards through a deductive passage, and then make an inductive jump to the Theory of Gravitation; and then turn back along a purely deductive path, erase the former fact... and so on. There are no absolutely hard, stubborn, perfectly reasoned facts." (Pg. 90)

He observes, "But if we start from a proposition P and draw consequences from it rather than try to look for premises from which it follows, then what we objectively do is TEST rather than PROVE. Thus in analysis we test---Popperianwise---a conjecture; but if we FAIL to refute it, we may succeed in turning it first into a proof and then into a mathematical research programme." (Pg. 95-96)

He argues, "According to the demarcationist one theory is better than another if it satisfies certain objective criteria. According to the elitist one theory is better than another if the scientific élite prefers it. But then it is vital to know who belongs to the scientific élite. While élitists claim that no universal criteria for appraising scientific achievements are possible they may admit the possibility of universal criteria for deciding whether persons or communities belong to the elite." (Pg. 112-113)

He asserts, "where corroborations of two theories are incomparable, so are their reliabilities... We can only judge the reliability of eliminated theories from the vantage point of our present theories... we cannot give even a fallible absolute estimate of Einstein's theory itself before it, in turn, is superseded by another theory. Thus we cannot grade our best available theories for reliability even tentatively, for they are our ultimate standards of the moment. Only God could give us a correct, detailed estimate of the absolute reliability of ALL theories by checking them against HIS blueprint of the universe." (Pg. 185)

Though far less well-known than Popper or Thomas Kuhn, Lakatos was one of the most important philosophers of science and mathematics of the 20th century, and his writings are "must reading" for anyone studying the philosophy of science.


The Methodology of Scientific Research Programmes: Volume 1: Philosophical Papers (Philosophical Papers (Cambridge))
The Methodology of Scientific Research Programmes: Volume 1: Philosophical Papers (Philosophical Papers (Cambridge))
by Imre Lakatos
Edition: Paperback
Price: $55.49
44 used & new from $27.95

5.0 out of 5 stars ONE OF THE GREATEST PHILOSOPHERS OF SCIENCE OF THE 20TH CENTURY, December 28, 2014
Imre Lakatos (1922-1974) was a Hungarian philosopher of mathematics and science; the companion volume to this book is Mathematics, Science and Epistemology: Volume 2, Philosophical Papers.

The Editor’s Introduction states, “When Imre Lakatos died in 1974, many friends and colleagues expressed the hope that his unpublished papers would be made available. Some were also interested in seeing his contributions to journals and conference proceedings collected together in a book… we have prepared two volumes of selected papers which we hope will meet these demands. None of the papers published here for the first time was regarded by Lakatos as entirely satisfactory… Volume 1 is a collection of Lakatos’s best known articles developing the methodology of scientific research programmes…”

He rejects “dogmatic falsificationism” [e.g., Karl Popper]: “For the truth-value of the ‘observational’ propositions cannot be indubitably decided: no factual proposition can ever be proved from an experiment. Propositions can only be derived from other propositions, they cannot be derived from facts; one cannot prove statements from experiences… This is one of the basic points of elementary logic, but one which is understood by relatively few people even today.” (Pg. 15-16)

He then explains “scientific/progressive” explanations: “If we put forward a theory to resolve a contradiction between a previous theory and a counterexample in such a way that the new theory, instead of offering a content-increasing (scientific) explanation, only offers a content-decreasing (linguistic) explanation, the contradiction is resolved in a merely semantical, unscientific way. A given fact is established scientifically only if a new fact is also explained with it. Sophisticated falsificationism thus shifts the problem of how to appraise theories to the problem of how to appraise series of theories. Not an isolated theory, but only a series of theories can be said to be scientific or unscientific: to apply the term ‘scientific’ to one single theory is a category mistake.” (Pg. 34)

He observes, “It is very difficult to defeat a research programme supported by talented, imaginative scientists. Alternatively, stubborn defenders of the defeated programme may offer ad hoc explanations of the experiments or a shrewd ad hoc ‘reduction’ of the victorious programme to the defeated one. But such efforts we should reject as unscientific. Our considerations explain why crucial experiments are seen to be crucial only decades later.” (Pg. 72)

He states, “The direction of science is determined primarily by human creative imagination and not by the universe of facts which surrounds us. Creative imagination is likely to find corroborating novel evidence even for the most ‘absurd’ programme, if the search has sufficient drive. This look-out for new confirming evidence is perfectly permissible. Scientists dream up phantasies and then pursue a highly selective hunt for new facts which fit these phantasies. This process may be described as ‘science creating its own universe’… A brilliant school of scholars (backed by a rich society to finance a few well-planned tests) might succeed in pushing any fantastic programme ahead, or, alternatively, if so inclined, in overthrowing any arbitrarily chosen pillar of ‘established knowledge.’” (Pg. 99-100)

He argues, “The methodology of research programmes… must be supplemented by empirical-external history. No rationality theory will ever solve problems like why Mendelian genetics disappeared in Soviet Russia in the 1950s, or why certain schools of research into genetic racial differences or into the economics of foreign aid came into disrepute in the Anglo-Saxon countries in the 1960s. Moreover, to explain different speeds of development of different research programmes we may need to invoke external history. Rational reconstruction of science … cannot be comprehensive since human beings are not COMPLETELY rational animals; and even when they act rationally they may have a false theory of their own rational actions.” (Pg. 114)

Though far less well-known than Popper or Thomas Kuhn, Lakatos was one of the most important philosophers of science of the 20th century, and his writings are “must reading” for anyone studying the philosophy of science.


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