James Franklin | The University of New South Wales - Academia.edu

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James Franklin

The University of New South Wales, School of Mathematics and Statistics, Faculty Member

The University of New South Wales, School of Mathematics and Statistics, Faculty Member |

Phone: 61-2-93857093
Address: School of Mathematics and Statistics
UNSW
Sydney 2052
Australia

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Books

An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist vie... more An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.

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The Real Archbishop Mannix: From the Sources

Archbishop Mannix was Australia’s most famous churchman, its most famous Irishman, one of its gre... more Archbishop Mannix was Australia’s most famous churchman, its most famous Irishman, one of its great troublemakers. As Catholic Archbishop of Melbourne from the First World War to the Nineteen-Sixties, he was a tribal leader and political figure as much as a spiritual leader. A very public figure, equally loved and hated. But privately an enigma. The REAL Archbishop Mannix: from the sources, reveals Mannix through his own words, his own actions and the actions taken against him.” Arriving in San Francisco in June 1920, on his way to Rome to call on the Pope, Mannix wasted no time in making inflammatory remarks about the English. Addressing the Catholic summer school at Plattsburg, New York, he said, “There is no use mincing words-Ireland is ruled by an alien Government. England was your enemy; she is your enemy today; she will be your enemy for all time.” Following his arrest at sea on his way to Ireland, he said, “Since the Jutland battle, the British Navy has not scored a success comparable to the capture of the Archbishop of Melbourne, and not a single British sailor had lost his life. It has rendered the British Government the laughing stock of the world. I still claim the right to go to Ireland and intend to press the claim by any means in my power”. On a visit to the workers at Broken Hill in 1922, Mannix said, “Let the Church approve no social order … in which there is a great discrepancy between the luxury and wealth of a privileged few, and the wretchedness and material indigence of the many" and earlier, " The work before the Catholic Laborites is to capture the Labor machine.” He strongly held the view that, “When a man becomes a priest he does not cease to be a citizen, he has a right to his own opinions like other citizens.”

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Proof in Mathematics: An Introduction

This is a small (98 page) textbook designed to teach mathematics and computer science students th... more This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. Why do students take the instruction "prove" in examinations to mean "go to the next question"? Because they have not been shown the simple techniques of how to do it. Mathematicians meanwhile generate a mystique of proof, as if it requires an inborn and unteachable genius. True, creating research-level proofs does require talent; but reading and understanding the proof that the square of an even number is even is within the capacity of most mortals. Proof in Mathematics: an Introduction takes a straightforward, no nonsense approach to explaining the core technique of mathematics. "Mathematics teaches you to think" is often an empty marketing slogan. With this book, it can become a reality.

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The Science of Conjecture: Evidence and Probability Before Pascal

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Catholic Values and Australian Realities

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Corrupting the Youth: A History of Philosophy in Australia

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What Science Knows: And How It Knows It

To scientists, the tsunami of relativism, scepticism, and postmodernism that washed through the h... more To scientists, the tsunami of relativism, scepticism, and postmodernism that washed through the humanities in the twentieth century was all water off a duck’s back. Science remained committed to objectivity and continued to deliver remarkable discoveries and improvements in technology. In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. He begins with an account of the nature of evidence, where science imitates but extends commonsense and legal reasoning in basing conclusions solidly on inductive reasoning from facts. After a brief survey of the furniture of the world as science sees it–including causes, laws, dispositions and force fields as well as material things–Franklin reveals colorful examples of discoveries in the natural, mathematical, and social sciences and the reasons for believing them. He examines the limits of science, giving special attention both to mysteries that may be solved by science, such as the origin of life, and those that may in principle be beyond the reach of science, such as the meaning of ethics. What Science Knows will appeal to anyone who wants a sound, readable, and well-paced introduction to the intellectual edifice that is science. On the other hand, it will not please the enemies of science, whose willful misunderstandings of scientific method and the relation of evidence to conclusions Franklin mercilessly exposes.

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Papers

Discrete and Continuous: A Fundamental Dichotomy in Mathematics

The distinction between the discrete and the continuous lies at the heart of mathematics. Discret... more The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.

Views

Early Modern Mathematical Principles and Symmetry Arguments

The leaders of the Scientific Revolution (Galileo, Pascal, Huygens, Newton and others) were not B... more The leaders of the Scientific Revolution (Galileo, Pascal, Huygens, Newton and others) were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.

Views

Elliptical Orbits and the Aristotelian Scientific Revolution

The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its... more The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its applied mathematics pursued by new means the Aristotelian ideal of science as knowledge by insight into necessary causes. Newton’s derivation of Kepler’s elliptical planetary orbits from the inverse square law of gravity is a central example.

Views

An Aristotelian Realist Philosophy of Mathematics: Mathematics as the Science of Quantity and Structure

An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist vie... more An Aristotelian Philosophy of Mathematics breaks the impasse between Platonist and nominalist views of mathematics. Neither a study of abstract objects nor a mere language or logic, mathematics is a science of real aspects of the world as much as biology is. For the first time, a philosophy of mathematics puts applied mathematics at the centre. Quantitative aspects of the world such as ratios of heights, and structural ones such as symmetry and continuity, are parts of the physical world and are objects of mathematics. Though some mathematical structures such as infinities may be too big to be realized in fact, all of them are capable of being realized. Informed by the author's background in both philosophy and mathematics, but keeping to simple examples, the book shows how infant perception of patterns is extended by visualization and proof to the vast edifice of modern pure and applied mathematical knowledge.

Views

The Real Archbishop Mannix: From the Sources

Archbishop Mannix was Australia’s most famous churchman, its most famous Irishman, one of its gre... more Archbishop Mannix was Australia’s most famous churchman, its most famous Irishman, one of its great troublemakers. As Catholic Archbishop of Melbourne from the First World War to the Nineteen-Sixties, he was a tribal leader and political figure as much as a spiritual leader. A very public figure, equally loved and hated. But privately an enigma. The REAL Archbishop Mannix: from the sources, reveals Mannix through his own words, his own actions and the actions taken against him.” Arriving in San Francisco in June 1920, on his way to Rome to call on the Pope, Mannix wasted no time in making inflammatory remarks about the English. Addressing the Catholic summer school at Plattsburg, New York, he said, “There is no use mincing words-Ireland is ruled by an alien Government. England was your enemy; she is your enemy today; she will be your enemy for all time.” Following his arrest at sea on his way to Ireland, he said, “Since the Jutland battle, the British Navy has not scored a success comparable to the capture of the Archbishop of Melbourne, and not a single British sailor had lost his life. It has rendered the British Government the laughing stock of the world. I still claim the right to go to Ireland and intend to press the claim by any means in my power”. On a visit to the workers at Broken Hill in 1922, Mannix said, “Let the Church approve no social order … in which there is a great discrepancy between the luxury and wealth of a privileged few, and the wretchedness and material indigence of the many" and earlier, " The work before the Catholic Laborites is to capture the Labor machine.” He strongly held the view that, “When a man becomes a priest he does not cease to be a citizen, he has a right to his own opinions like other citizens.”

Views

Proof in Mathematics: An Introduction

This is a small (98 page) textbook designed to teach mathematics and computer science students th... more This is a small (98 page) textbook designed to teach mathematics and computer science students the basics of how to read and construct proofs. Why do students take the instruction "prove" in examinations to mean "go to the next question"? Because they have not been shown the simple techniques of how to do it. Mathematicians meanwhile generate a mystique of proof, as if it requires an inborn and unteachable genius. True, creating research-level proofs does require talent; but reading and understanding the proof that the square of an even number is even is within the capacity of most mortals. Proof in Mathematics: an Introduction takes a straightforward, no nonsense approach to explaining the core technique of mathematics. "Mathematics teaches you to think" is often an empty marketing slogan. With this book, it can become a reality.

Views

The Science of Conjecture: Evidence and Probability Before Pascal

Views

Catholic Values and Australian Realities

Views

Corrupting the Youth: A History of Philosophy in Australia

Views

What Science Knows: And How It Knows It

To scientists, the tsunami of relativism, scepticism, and postmodernism that washed through the h... more To scientists, the tsunami of relativism, scepticism, and postmodernism that washed through the humanities in the twentieth century was all water off a duck’s back. Science remained committed to objectivity and continued to deliver remarkable discoveries and improvements in technology. In What Science Knows, the Australian philosopher and mathematician James Franklin explains in captivating and straightforward prose how science works its magic. He begins with an account of the nature of evidence, where science imitates but extends commonsense and legal reasoning in basing conclusions solidly on inductive reasoning from facts. After a brief survey of the furniture of the world as science sees it–including causes, laws, dispositions and force fields as well as material things–Franklin reveals colorful examples of discoveries in the natural, mathematical, and social sciences and the reasons for believing them. He examines the limits of science, giving special attention both to mysteries that may be solved by science, such as the origin of life, and those that may in principle be beyond the reach of science, such as the meaning of ethics. What Science Knows will appeal to anyone who wants a sound, readable, and well-paced introduction to the intellectual edifice that is science. On the other hand, it will not please the enemies of science, whose willful misunderstandings of scientific method and the relation of evidence to conclusions Franklin mercilessly exposes.

Views

Discrete and Continuous: A Fundamental Dichotomy in Mathematics

The distinction between the discrete and the continuous lies at the heart of mathematics. Discret... more The distinction between the discrete and the continuous lies at the heart of mathematics. Discrete mathematics (arithmetic, algebra, combinatorics, graph theory, cryptography, logic) has a set of concepts, techniques, and application areas largely distinct from continuous mathematics (traditional geometry, calculus, most of functional analysis, differential equations, topology). The interaction between the two – for example in computer models of continuous systems such as fluid flow – is a central issue in the applicable mathematics of the last hundred years. This article explains the distinction and why it has proved to be one of the great organizing themes of mathematics.

Views

Early Modern Mathematical Principles and Symmetry Arguments

The leaders of the Scientific Revolution (Galileo, Pascal, Huygens, Newton and others) were not B... more The leaders of the Scientific Revolution (Galileo, Pascal, Huygens, Newton and others) were not Baconian in temperament, in trying to build up theories from data. Their project was that same as in Aristotle's Posterior Analytics: they hoped to find necessary principles that would show why the observations must be as they are. Their use of mathematics to do so expanded the Aristotelian project beyond the qualitative methods used by Aristotle and the scholastics. In many cases they succeeded.

Views

Elliptical Orbits and the Aristotelian Scientific Revolution

The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its... more The Scientific Revolution was far from the anti-Aristotelian movement traditionally pictured. Its applied mathematics pursued by new means the Aristotelian ideal of science as knowledge by insight into necessary causes. Newton’s derivation of Kepler’s elliptical planetary orbits from the inverse square law of gravity is a central example.

Views

Catholic missions to Aboriginal Australia: an evaluation of their overall effect

The paper gives an overview of the Catholic Church's missionary efforts to the Aborigines of nort... more The paper gives an overview of the Catholic Church's missionary efforts to the Aborigines of northern and western Australia up to 1970. It aims to understand the interaction of missions with native culture and the resulting hybrid culture created on the missions. It describes the differing points of view of missionaries and the generations who grew up on the missions. It is argued that the culture created on the missions by the joint efforts of missionaries and local peoples was by and large a positive phase in Australian black history, between the violence of pre-contact times and the dysfunctionality of recent decades. Criticisms of the missions are addressed, such as those arising from their opposition to aspects of native culture and from their involvement in child removals.

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Pre-history of probability

Oxford Handbook of Probability and Philosophy, 2016

It has been common to begin histories of probability with the calculations of Fermat and Pascal ... more It has been common to begin histories of probability with the calculations of Fermat and Pascal on games of chance in 1654. Those calculations were the first substantial mathematical results on stochastic phenomena, which, according to a frequentist philosophy of probability, are the true subject-matter of the field. But there is great philosophical interest in studying earlier ideas. That is because we see a struggle to understand a range of basic concepts about probability and uncertain evidence, before the straightjacket of a single formalization was imposed. There is still much to learn from seeing how the problems now studied with the aid of probability theory were dealt with in “bare hands” fashion before that formalization was available.

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Homomorphisms between Verma modules in characteristic p

Journal of Algebra, 1988

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Logical probability and the strength of mathematical conjectures

In pure mathematics, unproved conjectures differ in their strength. Some are well-supported by ev... more In pure mathematics, unproved conjectures differ in their strength. Some are well-supported by evidence and regarded as "almost proved", others are weak. Since there is nothing to the relation of pure mathematical propositions but logic, this supports the theory of logical probability (a.k.a. non-deductive logic) - the view of Keynes and Jaynes that (one fundamental kind of) probability is a sort of pure logic; a degree of partial implication. Examples from mathematics are given and conclusions drawn about the nature of logical probability.

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Gerald Ridsdale, Pedophile Priest, In His Own Words

Gerald Ridsdale, Australia's worst pedophile priest, told his story to the Royal Commission on In... more

Views

Divine proportions: Rational trigonometry to universal geometry

The Mathematical Intelligencer, 2006

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On the Reality of the Continuum Discussion Note: A Reply to Ormell, ‘Russell's Moment of Candour’, Philosophy

by James Franklin and Anne Newstead

Philosophy, 2008

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The Sydney School: Mathematics, the Science of Structure

The "Sydney School" defends an Aristotelian realist philosophy of mathematics. Contrary to Platon... more

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The Restraint Project: Temperance and Self-Control in Australia

by James Franklin and Catherine Legg

The virtue of temperance and self-control has had a low profile since the 1960s. But it is a nece... more The virtue of temperance and self-control has had a low profile since the 1960s. But it is a necessary part of being a whole person who can take ethical action and live a healthy and coherent life. The project looks at the history of self-control in Australia and the present need for it in areas such as health, anti-drug campaigns and indigenous violence.

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Australian Database of Indigenous Violence

Keeps track of news items on the high level of violence in Australian indigenous communities.

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