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Transformations: Studies in the History of Science and Technology
Isaac Newton on Mathematical Certainty and Method (Transformations: Studies in the History of Science and Technology) by Niccol?2 Guicciardini
Historians of mathematics have devoted considerable attention to Isaac Newton's work on algebra, series, fluxions, quadratures, and geometry. In Isaac Newton on Mathematical Certainty and Method, Niccolò Guicciardini examines a critical aspect of Newton's work that has not been tightly connected to Newton's actual practice: his philosophy of mathematics.
Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the "common" and "new" analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns.
Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newtonon Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.
Transformations: Studies in the History of Science and Technology
Newton aimed to inject certainty into natural philosophy by deploying mathematical reasoning (titling his main work The Mathematical Principles of Natural Philosophy most probably to highlight a stark contrast to Descartes's Principles of Philosophy). To that end he paid concerted attention to method, particularly in relation to the issue of certainty, participating in contemporary debates on the subject and elaborating his own answers. Guicciardini shows how Newton carefully positioned himself against two giants in the "common" and "new" analysis, Descartes and Leibniz. Although his work was in many ways disconnected from the traditions of Greek geometry, Newton portrayed himself as antiquity's legitimate heir, thereby distancing himself from the moderns.
Guicciardini reconstructs Newton's own method by extracting it from his concrete practice and not solely by examining his broader statements about such matters. He examines the full range of Newton's works, from his early treatises on series and fluxions to the late writings, which were produced in direct opposition to Leibniz. The complex interactions between Newton's understanding of method and his mathematical work then reveal themselves through Guicciardini's careful analysis of selected examples. Isaac Newtonon Mathematical Certainty and Method uncovers what mathematics was for Newton, and what being a mathematician meant to him.
Transformations: Studies in the History of Science and Technology
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First published January 1, 2009
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April 23, 2023
Newton’s contribution to Physics is well known and needs no further explanation or description. His towering genius led some scholars to conclude that there was nothing left to discover in Physics; and part of the early resistance to Einstein’s twentieth century work was precisely the fact that it seemed to be querying aspects of Newton’s work.
Underlying Newton’s Physics is his use of Mathematics. Yet the Mathematics themselves, and Newton’s attitude to them, are rarely studied as a specific set of issues in themselves. It is that reason which prompts this scholarly book.
By the end of it, we can appreciate Newton’s disagreements with Descartes and Leibniz, but we also come to see that his mathematics was ‘messy.’ There was no big vision or overarching theory of mathematics. Instead there are a lot of ad hoc approaches, which work to varying degrees; and which Newton was committed to, with varying degrees of consistency.
We can see that aspects of Newton’s thinking, was shared by his contemporaries, such as his preference for Geometry over Algebra. But that was a short sighted traditional view, which failed to appreciate the power and versatility of algebra. The book doesn’t go into Newton’s mysticism and his (at times) almost fanatical quests for hidden ancient wisdom. Readers aware of that aspect of Newton’s thinking may well wonder whether his conservatism in Mathematics wasn’t part of a wider mindset which overvalued ancient authorities.
Newton fell out with many of his contemporaries because of his commitment to certainty. One of the developments in Enlightenment empiricism was a commitment to probability and a recognition of uncertainty in our knowledge and thought about the world. Newton initially rejected that view, convinced that mathematics provided certainty, and so its use in the analysis of empirical findings should enable scientific certainties. This was a view that he was fully committed to until near the end of his life, when he started to be more willing to recognise the uncertainties inherent to applications of mathematics to the physical reality of the world around him. What a shame that he spent so much energy in his younger years falling out with his contemporaries over what seems to have been his intellectual inability to appreciate the importance of uncertainties and probabilities.
Overall this is an interesting account of Newton’s intellectual development through his disagreements with leading figures of his day. Readers learn a lot about Newton’s mathematics, as well as the mathematics of Descartes and Leibniz. That is informative, but it is also challenging at times, especially for those who have not studied mathematics to higher levels. As the terminology and style of older forms of mathematics differs to its contemporary expression, readers with an expertise in modern mathematics may occasionally have to pause in order to appreciate older terminologies, in order to understand the formulas and diagrams which occasionally crop up in the book.
Underlying Newton’s Physics is his use of Mathematics. Yet the Mathematics themselves, and Newton’s attitude to them, are rarely studied as a specific set of issues in themselves. It is that reason which prompts this scholarly book.
By the end of it, we can appreciate Newton’s disagreements with Descartes and Leibniz, but we also come to see that his mathematics was ‘messy.’ There was no big vision or overarching theory of mathematics. Instead there are a lot of ad hoc approaches, which work to varying degrees; and which Newton was committed to, with varying degrees of consistency.
We can see that aspects of Newton’s thinking, was shared by his contemporaries, such as his preference for Geometry over Algebra. But that was a short sighted traditional view, which failed to appreciate the power and versatility of algebra. The book doesn’t go into Newton’s mysticism and his (at times) almost fanatical quests for hidden ancient wisdom. Readers aware of that aspect of Newton’s thinking may well wonder whether his conservatism in Mathematics wasn’t part of a wider mindset which overvalued ancient authorities.
Newton fell out with many of his contemporaries because of his commitment to certainty. One of the developments in Enlightenment empiricism was a commitment to probability and a recognition of uncertainty in our knowledge and thought about the world. Newton initially rejected that view, convinced that mathematics provided certainty, and so its use in the analysis of empirical findings should enable scientific certainties. This was a view that he was fully committed to until near the end of his life, when he started to be more willing to recognise the uncertainties inherent to applications of mathematics to the physical reality of the world around him. What a shame that he spent so much energy in his younger years falling out with his contemporaries over what seems to have been his intellectual inability to appreciate the importance of uncertainties and probabilities.
Overall this is an interesting account of Newton’s intellectual development through his disagreements with leading figures of his day. Readers learn a lot about Newton’s mathematics, as well as the mathematics of Descartes and Leibniz. That is informative, but it is also challenging at times, especially for those who have not studied mathematics to higher levels. As the terminology and style of older forms of mathematics differs to its contemporary expression, readers with an expertise in modern mathematics may occasionally have to pause in order to appreciate older terminologies, in order to understand the formulas and diagrams which occasionally crop up in the book.
Displaying 1 of 1 review