Isaac Newton, Robert Simson and Adam Smith

Ackerberg-Hastings A.

In the eighteenth and nineteenth centuries, three understandings of the terms “analysis” and “synthesis” were particularly influential with the creators and readers of elementary geometry textbooks in Western Europe and North America: as perceived contrasts in styles of mathematical practice in Great Britain and France; as contemporary appeals to ancient methods of proof; and as approaches to mathematics education. One widely used textbook arose from the attempt by University of Glasgow mathematics professor Robert Simson to restore Euclid’s text, which appeared in 1756 as The Elements of Euclid, in simultaneous English and Latin versions. This essay explores what we can learn about the book’s preparation, content, and reception by examining the volume through the lenses of analysis and synthesis.

Wickman M.

Orenstein D.

When the University of Toronto hosted the International Mathematical Congress (IMC) in August 1924, the prime organizer, University of Toronto mathematician John Charles Fields (1863–1932) insisted the papers cover a wide range of mathematical topics: algebra, analysis, astronomy, engineering, statistics, and history and philosophy of mathematics. Section VI of the Congress covered History, Philosophy and Didactics of Mathematics. There were in total 13 papers in the published proceedings: seven full Communications and six Abstracts. Five were historical, six philosophical and only two pedagogical. In Section VI the American algebraist G. A. Miller looked at “The History of Several Mathematical Concepts” including “the unknown” and “permutations”, going back to the ancient Egyptians and Greeks. Miller also presented in Toronto on algebra, looking at commutativity in Abelian subgroups. The great Italian logician Giuseppe Peano, who had also presented in Zurich in 1897 at the IMC and then in Cambridge in 1912, spoke in simplified Latin “De Aequalitate”, On Equality. The Swiss educator Henri Fehr contributed to the pedagogical programmes at four other IMCs (1904, 1908, 1912 and 1932), focusing in Toronto on the university’s preparation of high school mathematics teachers. Florian Cajori, the great American historian of mathematics, discussed mathematical notation in two different papers: its history in geometry and a programme for its improvement. This paper examines the role of both History and Philosophy of Mathematics at the Toronto IMC.

Montes L.

While Newton's influence on Adam Smith has been widely acknowledged, there is scant research on the actual nature of this influence. This paper sums up a line of investigation delving into this issue. After a short introduction, it is argued that Newton's methodology is more complex than a merely positivistic interpretation. Then the context of Newton's influence during the turn of the seventeenth century and the eighteenth century is assessed. It will be suggested that a British (and particularly Scottish) interpretation of Newton diverges from the French reading of his legacy. The final section analyses Smith's understanding of Newton, arguing that the father of economics was a sophisticated interpreter. The intellectual context of what the Scottish Enlightenment made of Newton, and how he was interpreted, may have played a major role in explaining how Smith understood Newton's legacy. Copyright The Author 2008. Published by Oxford University Press on behalf of the Cambridge Political Economy Society. All rights reserved., Oxford University Press.

Schliesser E.

In this essay, I construct an epistemology for Adam Smith from some of his lesser known writings, especially ‘The History of Astronomy’ (‘Astronomy’), collected in his posthumous Essays on Philosop...

Evensky J.

Adam Smith is the best known among economists for his book, The Wealth of Nations, often viewed as the keystone of modern economic thought. For many he has become associated with a quasi-libertarian laissez-faire philosophy. Others, often heterodox economists and social philosophers, on the contrary, focus on Smith's Theory of Moral Sentiments, and explore his moral theory. There has been a long debate about the relationship or lack thereof between these, his two great works. This work treats these dimensions of Smith's work as elements in a seamless moral philosophical vision, demonstrating the integrated nature of these works and Smith's other writings. This book weaves Smith into a constructive critique of modern economic analysis (engaging along the way the work of Nobel Laureates Gary Becker, Amarty Sen, Douglass North, and James Buchanan) and builds bridges between that discourse and the other social sciences.

Montes L.

There is general consensus that in economics Adam Smith is, in the words of Jevons, the ‘father of the science’. In this setting it has regularly been argued that neoclassical and modern mainstream economics carry through the methodological impetus brought into the discipline by Smith. Moreover, economists conventionally take it for granted that Smith applied Newton’s method to political economy. Because Newton’s method is thought to be similar to that of modern mainstream economics, the association of Smith with Newton is taken to further bolster the claim that modern mainstream economics continues the Smithian tradition. Support for this commonly accepted view is gathered from Smith’s panegyric attitude to Newton’s conception of philosophy. This shared conviction among economists underpins some interpretations of the ‘invisible hand’ and of the intention behind the controversial chapter 7 of Book I of the WN, baptising Smith as a forerunner, if not the founder, of theories of general economic equilibrium (e.g. Robbins, 1962 [1932]; Schumpeter, 1994 [1954]; Arrow-Hahn, 1971; Jaffe, 1977; Hollander, 1973, 1987; Samuelson, 1977, 1992). As an offspring of the same tradition Walras, the architect of the ‘equilibrium system’, has been set alongside Newton, the discoverer of the ‘world system’ (Samuelson, 1952, p. 61).

Guicciardini N.

Isaac Newton's Principia is considered one of the masterpieces in the history of science. The mathematical methods employed by Newton in the Principia stimulated much debate among his contemporaries, especially Leibniz, Huygens, Bernoulli and Euler, who debated their merits and drawbacks. Among the questions they asked were: How should natural philosophy be mathematized?; Is it legitimate to use uninterpreted symbols?; Is it possible to depart from the established Archimedean or Galilean/Huygenian tradition of geometrizing nature?; What is the value of elegance and conciseness?; What is the relation between Newton's geometrical methods and the calculus? This book explains how Newton addressed these issues, taking into consideration the values that directed the research of Newton and his contemporaries. This book will be of interest to researchers and advanced students in departments of history of science, philosophy of science, physics, mathematics and astronomy.

Blaug M.

This book is an examination of the nature of economic explanation. The opening chapters introduce current thinking in the philosophy of science and review the literature on methodology. Professor Blaug then turns to the troublesome question of the logical status of welfare economics, giving the reader an understanding of the outstanding issues in the methodology of economics. This is followed by a series of case studies of leading economic controversies, which shows how controversies in economics may be illuminated by paying attention to questions of methodology. A final chapter draws the strands together and gives the author's view of what is wrong with modern economics. This book is a revised and updated edition of a classic work on the methodology of economics, in which Professor Blaug develops his discussion of the latest developments in macroeconomics, general equilibrium theory and international trade theory. A new section on the rationality postulate is also added.

Smith A.

Heilbroner R.L.

Smith A., Smith A.R., Smith A., Smith A.

Smith A.

Hollander S.

Gibson G.A.

The centre of interest now shifts from St Andrews and Edinburgh to Glasgow. The troubles that afflicted Scotland during the 17th Century bore heavily on Glasgow University and more particularly on the position of Mathematics in the University; but in 1691 a distinct Professorship of Mathematics was founded, and from that date the old system of Regents disappeared from Glasgow so far as Mathematics was concerned. The first occupant of the Chair was George Sinclair, who is now chiefly remembered by the controversy in which James Gregory held up Sinclair's Treatise Ars nova et magna to ridicule. It is not fair however to take Gregory's pamphlet as a final estimate of Sinclair's contributions to science; Sinclair laid himself open to attack, but he rendered great service to the mining industry of Scotland and deserves the gratitude of posterity in spite of his many eccentricities. His contributions to mathematics however are of no importance, but during his tenure of the Chair the number of students grew rapidly and the new professorship made a good start.

Kurz H.D.

Abstract The paper examines evolutionary elements in Adam Smith’s social theory, connecting them to an earlier contribution to natural history by George-Louis Leclerc, Comte de Buffon. It then compares Smith’s analysis with those of Karl Marx and Joseph Schumpeter, who were fascinated by Darwinian evolutionary biology. This comparison demonstrates that while developing evolutionary approaches to the social sciences suitable for their respective subject matter, Marx and Schumpeter drew heavily on Smith’s insights. All three authors aimed to unveil the forces shaping the “process of civilization”, or society’s “law of motion,” along with its associated hazards. They pondered whether this process inherently led to rising living standards, along with “equality, liberty, and justice”, and whether it could derail, ending in a tailspin.