Exact sciences

The exact sciences or quantitative sciences, sometimes called the exact mathematical sciences,^[1] are those sciences "which admit of absolute precision in their results"; especially the mathematical sciences.^[2] Examples of the exact sciences are mathematics, optics, astronomy,^[3] and physics, which many philosophers from René Descartes, Gottfried Leibniz, and Immanuel Kant to the logical positivists took as paradigms of rational and objective knowledge.^[4] These sciences have been practiced in many cultures from antiquity^[5]^[6] to modern times.^[7]^[8] Given their ties to mathematics, the exact sciences are characterized by accurate quantitative expression, precise predictions and/or rigorous methods of testing hypotheses involving quantifiable predictions and measurements.^[9]

The distinction between the quantitative exact sciences and those sciences that deal with the causes of things is due to Aristotle, who distinguished mathematics from natural philosophy^[10] and considered the exact sciences to be the "more natural of the branches of mathematics."^[11] Thomas Aquinas employed this distinction when he said that astronomy explains the spherical shape of the Earth^[12] by mathematical reasoning while physics explains it by material causes.^[13] This distinction was widely, but not universally, accepted until the Scientific Revolution of the 17th century.^[14] Edward Grant has proposed that a fundamental change leading to the new sciences was the unification of the exact sciences and physics by Johannes Kepler, Isaac Newton, and others, which resulted in a quantitative investigation of the physical causes of natural phenomena.^[15]

References

^ Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, p. 43, ISBN 9781139461092
^ "Exact, adj.¹", Oxford English Dictionary, Online version (2nd ed.), Oxford: Oxford University Press, June 2016
^ Drake, Stillman; Swerdlow, N.M.; Levere, T.H. (1999). Essays on Galileo and the History and Philosophy of Science: Volume 1. University of Toronto Press. ISBN 978-0-8020-7585-7. JSTOR 10.3138/j.ctvcj2wt5.
^ Friedman, Michael (1992), "Philosophy and the Exact Sciences: Logical Positivism as a Case Study", in Earman, John (ed.), Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science, Pittsburgh series in philosophy and history of science, vol. 14, Berkeley and Los Angeles: University of California Press, p. 84, ISBN 9780520075771
^ Neugebauer, Otto (1962), The Exact Sciences in Antiquity, The Science Library (2nd, reprint ed.), New York: Harper & Bros.
^ Sarkar, Benoy Kumar (1918), Hindu Achievements in Exact Science: A Study in the History of Scientific Development, London / New York: Longmans, Green and Company, ISBN 9780598626806 {{citation}}: ISBN / Date incompatibility (help)
^ Harman, Peter M.; Shapiro, Alan E. (2002), The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences in Honour of D.T. Whiteside, Cambridge: Cambridge University Press, ISBN 9780521892667
^ Pyenson, Lewis (1993), "Cultural Imperialism and Exact Sciences Revisited", Isis, 84 (1): 103–108, Bibcode:1993Isis...84..103P, doi:10.1086/356376, JSTOR 235556, S2CID 144588820, [M]any of the exact sciences... between Claudius Ptolemy and Tycho Brahe were in a common register, whether studied in the diverse parts of the Islamic world, in India, in Christian Europe, in China, or apparently in Mesoamerica.
^ Shapin, Steven (2018). The Scientific Revolution (2nd ed.). Chicago, IL: The University of Chicago Press. pp. 46–47. ISBN 9780226398341.
^ Principe, Lawrence (2011). The Scientific Revolution: A Very Short Introduction. New York, NY: Oxford University Press. p. 27. ISBN 9780199567416.
^ Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, pp. 42–43, ISBN 9781139461092
^ Cormack, Lesley (1994). "Flat Earth or round sphere: misconceptions of the shape of the Earth and the fifteenth-century transformation of the world". Ecumene. 1 (4): 365. doi:10.1177/147447409400100404. JSTOR 44251730.
^ Aquinas, Thomas, Summa Theologica, Part I, Q. 1, Art. 1, Reply 2, retrieved 3 September 2016, For the astronomer and the physicist both may prove the same conclusion: that the earth, for instance, is round: the astronomer by means of mathematics (i.e. abstracting from matter), but the physicist by means of matter itself.
^ Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, pp. 303–305, ISBN 9781139461092
^ Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, pp. 303, 312–313, ISBN 9781139461092

[Grant_43-1] Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, p. 43, ISBN 9781139461092

[2] "Exact, adj.¹", Oxford English Dictionary, Online version (2nd ed.), Oxford: Oxford University Press, June 2016

[3] Drake, Stillman; Swerdlow, N.M.; Levere, T.H. (1999). Essays on Galileo and the History and Philosophy of Science: Volume 1. University of Toronto Press. ISBN 978-0-8020-7585-7. JSTOR 10.3138/j.ctvcj2wt5.

[4] Friedman, Michael (1992), "Philosophy and the Exact Sciences: Logical Positivism as a Case Study", in Earman, John (ed.), Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science, Pittsburgh series in philosophy and history of science, vol. 14, Berkeley and Los Angeles: University of California Press, p. 84, ISBN 9780520075771

[5] Neugebauer, Otto (1962), The Exact Sciences in Antiquity, The Science Library (2nd, reprint ed.), New York: Harper & Bros.

[6] Sarkar, Benoy Kumar (1918), Hindu Achievements in Exact Science: A Study in the History of Scientific Development, London / New York: Longmans, Green and Company, ISBN 9780598626806 {{citation}}: ISBN / Date incompatibility (help)

[7] Harman, Peter M.; Shapiro, Alan E. (2002), The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences in Honour of D.T. Whiteside, Cambridge: Cambridge University Press, ISBN 9780521892667

[8] Pyenson, Lewis (1993), "Cultural Imperialism and Exact Sciences Revisited", Isis, 84 (1): 103–108, Bibcode:1993Isis...84..103P, doi:10.1086/356376, JSTOR 235556, S2CID 144588820, [M]any of the exact sciences... between Claudius Ptolemy and Tycho Brahe were in a common register, whether studied in the diverse parts of the Islamic world, in India, in Christian Europe, in China, or apparently in Mesoamerica.

[9] Shapin, Steven (2018). The Scientific Revolution (2nd ed.). Chicago, IL: The University of Chicago Press. pp. 46–47. ISBN 9780226398341.

[10] Principe, Lawrence (2011). The Scientific Revolution: A Very Short Introduction. New York, NY: Oxford University Press. p. 27. ISBN 9780199567416.

[Grant_42-11] Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, pp. 42–43, ISBN 9781139461092

[12] Cormack, Lesley (1994). "Flat Earth or round sphere: misconceptions of the shape of the Earth and the fifteenth-century transformation of the world". Ecumene. 1 (4): 365. doi:10.1177/147447409400100404. JSTOR 44251730.

[13] Aquinas, Thomas, Summa Theologica, Part I, Q. 1, Art. 1, Reply 2, retrieved 3 September 2016, For the astronomer and the physicist both may prove the same conclusion: that the earth, for instance, is round: the astronomer by means of mathematics (i.e. abstracting from matter), but the physicist by means of matter itself.

[Grant_303-14] Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, pp. 303–305, ISBN 9781139461092

[Grant_312-15] Grant, Edward (2007), A History of Natural Philosophy: From the Ancient World to the Nineteenth Century, Cambridge: Cambridge University Press, pp. 303, 312–313, ISBN 9781139461092

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Exact sciences

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