Exact sciences

{{short description|Sciences that admit of absolute precision in their results}}

{{About|a branch of science|the company of the same name|Exact Sciences (company)}}

File:Ulugh Beg's Astronomic Observatory.jpg's meridian arc for precise astronomical measurements (15th c.)]]

The exact sciences or quantitative sciences, sometimes called the exact mathematical sciences,{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | page = 43 | isbn = 9781139461092 }} are those sciences "which admit of absolute precision in their results"; especially the mathematical sciences.{{ Citation | title = Oxford English Dictionary, Online version | edition = 2nd | date = June 2016 | contribution = Exact, adj.¹ | publisher = Oxford University Press | place = Oxford }} Examples of the exact sciences are mathematics, optics, astronomy,{{Cite book |last1=Drake |first1=Stillman |url=https://www.jstor.org/stable/10.3138/j.ctvcj2wt5 |title=Essays on Galileo and the History and Philosophy of Science: Volume 1 |last2=Swerdlow |first2=N.M. |last3=Levere |first3=T.H. |date=1999 |publisher=University of Toronto Press |isbn=978-0-8020-7585-7 |jstor=10.3138/j.ctvcj2wt5 }} 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.{{Citation | last = Friedman | first = Michael | author-link = Michael Friedman (philosopher) | editor-last = Earman | editor-first = John | editor-link = John Earman | date = 1992 | title = Inference, Explanation, and Other Frustrations: Essays in the Philosophy of Science | contribution = Philosophy and the Exact Sciences: Logical Positivism as a Case Study | series = Pittsburgh series in philosophy and history of science | volume = 14 | page = 84 | publisher = University of California Press | place = Berkeley and Los Angeles | isbn = 9780520075771}} These sciences have been practiced in many cultures from antiquity{{Citation | last = Neugebauer | first = Otto | author-link = Otto Neugebauer | date = 1962 | title = The Exact Sciences in Antiquity | publisher = Harper & Bros. | place = New York | edition = 2nd, reprint | series = The Science Library }}{{Citation | last = Sarkar | first = Benoy Kumar | author-link = Benoy Kumar Sarkar | date = 1918 | title = Hindu Achievements in Exact Science: A Study in the History of Scientific Development | publisher = Longmans, Green and Company | isbn = 9780598626806 | place = London / New York | url = https://books.google.com/books?id=1CpRAAAAYAAJ }} to modern times.{{Citation | last1 = Harman | first1 = Peter M. | last2 = Shapiro | first2 = Alan E. | date = 2002 | title = The Investigation of Difficult Things: Essays on Newton and the History of the Exact Sciences in Honour of D.T. Whiteside | publisher = Cambridge University Press | place = Cambridge | isbn = 9780521892667 }}{{Citation | last = Pyenson | first = Lewis | date = 1993 | title = Cultural Imperialism and Exact Sciences Revisited | journal = Isis | volume = 84 | issue = 1 | pages = 103–108 | doi = 10.1086/356376| quote = [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. | jstor = 235556 | bibcode = 1993Isis...84..103P | s2cid = 144588820 }} 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.{{Cite book |last=Shapin |first=Steven |title=The Scientific Revolution |publisher=The University of Chicago Press |year=2018 |isbn=9780226398341 |edition=2nd |location=Chicago, IL |pages=46–47 |language=}}

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{{Cite book |last=Principe |first=Lawrence |title=The Scientific Revolution: A Very Short Introduction |publisher=Oxford University Press |year=2011 |isbn=9780199567416 |location=New York, NY |pages=27}} and considered the exact sciences to be the "more natural of the branches of mathematics."{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | pages = 42–43 | isbn = 9781139461092 }} Thomas Aquinas employed this distinction when he said that astronomy explains the spherical shape of the Earth{{Cite journal |last=Cormack |first=Lesley |date=1994 |title=Flat Earth or round sphere: misconceptions of the shape of the Earth and the fifteenth-century transformation of the world. |url=https://www.jstor.org/stable/44251730 |journal=Ecumene |volume=1 |issue=4 |page=365 |doi=10.1177/147447409400100404 |jstor=44251730 |url-access=subscription }} by mathematical reasoning while physics explains it by material causes.{{Citation | last = Aquinas | first = Thomas | author-link = Thomas Aquinas | title = Summa Theologica | at = Part I, Q. 1, Art. 1, Reply 2 | url = http://www.newadvent.org/summa/1001.htm#1 | access-date = 3 September 2016 | quote = 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. }} This distinction was widely, but not universally, accepted until the scientific revolution of the 17th century.{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | pages = 303–305 | isbn = 9781139461092 }} 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.{{Citation | last = Grant | first = Edward | author-link = Edward Grant | date = 2007 | title = A History of Natural Philosophy: From the Ancient World to the Nineteenth Century | publisher = Cambridge University Press | place = Cambridge | pages = 303, 312–313 | isbn = 9781139461092 }}