Editing Science (section)

=== Formal ===
[[Formal science]] is an area of study that generates knowledge using [[formal system]]s.<ref>{{cite web |url=https://my.wlu.edu/the-sciences-at-wandl/formal-sciences |title=Formal Sciences: Washington and Lee University |website=Washington and Lee University |access-date=14 May 2021 |quote=A "formal science" is an area of study that uses formal systems to generate knowledge such as in Mathematics and Computer Science. Formal sciences are important subjects because all of quantitative science depends on them. |archive-date=14 May 2021 |archive-url=https://web.archive.org/web/20210514125428/https://my.wlu.edu/the-sciences-at-wandl/formal-sciences |url-status=live}}</ref><ref name="Löwe2002"/><ref name="Rucker2019"/> A formal system is an [[abstract structure]] used for inferring [[theorem]]s from [[axiom]]s according to a set of rules.<ref>{{Cite encyclopedia |title=Formal system |url=https://www.britannica.com/topic/formal-system |access-date=30 May 2022 |encyclopedia=Encyclopædia Britannica |archive-date=29 April 2008 |archive-url=https://web.archive.org/web/20080429174130/http://www.britannica.com/eb/article-9034889/formal-system |url-status=live}}</ref> It includes mathematics,<ref>{{cite book |last=Tomalin |first=Marcus |year=2006 |title=Linguistics and the Formal Sciences}}</ref><ref>{{Cite journal |title=The Formal Sciences: Their Scope, Their Foundations, and Their Unity |journal=Synthese |volume=133 |pages=5–11 |doi=10.1023/a:1020887832028 |year=2002 |last1=Löwe |first1=Benedikt |issue=1/2 |s2cid=9272212}}</ref> [[systems theory]], and [[theoretical computer science]]. The formal sciences share similarities with the other two branches by relying on objective, careful, and systematic study of an area of knowledge. They are, however, different from the empirical sciences as they rely exclusively on deductive reasoning, without the need for empirical evidence, to verify their abstract concepts.<ref name="Fetzer2013"/><ref>{{cite book |first=Thompson |last=Bill |title=The Nature of Statistical Evidence |chapter=2.4 Formal Science and Applied Mathematics |publisher=Springer |series=Lecture Notes in Statistics |volume=189 |year=2007 |page=15}}</ref><ref name="Popper2002" /> The formal sciences are therefore ''[[a priori]]'' disciplines and because of this, there is disagreement on whether they constitute a science.<ref name="Kluwer"/><ref>{{cite book |last1=Bunge |first1=Mario |title=Philosophy of Science: Volume 1, From Problem to Theory |year=1998 |publisher=Routledge |isbn=978-0-7658-0413-6 |edition=revised |volume=1 |location=New York |pages=3–50 |chapter=The Scientific Approach}}</ref> Nevertheless, the formal sciences play an important role in the empirical sciences. [[Calculus]], for example, was initially invented to understand [[motion]] in physics.<ref>{{Cite book |last1=Mujumdar |first1=Anshu Gupta |last2=Singh |first2=Tejinder |year=2016 |chapter=Cognitive science and the connection between physics and mathematics |title=Trick or Truth?: The Mysterious Connection Between Physics and Mathematics |editor-first1=Anthony |editor-last1=Aguirre |editor-first2=Brendan |editor-last2=Foster |series=The Frontiers Collection |pages=201–218 |location=Switzerland |publisher=Springer |isbn=978-3-319-27494-2}}</ref> Natural and social sciences that rely heavily on mathematical applications include [[mathematical physics]],<ref>{{cite web |title=About the Journal |url=http://jmp.aip.org/jmp/staff.jsp |url-status=dead |archive-url=https://web.archive.org/web/20061003233339/http://jmp.aip.org/jmp/staff.jsp |archive-date=3 October 2006 |access-date=3 October 2006 |website=[[Journal of Mathematical Physics]]}}</ref> [[mathematical chemistry|chemistry]],<ref>{{cite book |last=Restrepo |first=G. |chapter=Mathematical chemistry, a new discipline |title=Essays in the philosophy of chemistry |editor-last1=Scerri |editor-first1=E. |editor-last2=Fisher |editor-first2=G. |publisher=Oxford University Press |location=New York |year=2016 |pages=332–351 |isbn=978-0-19-049459-9 |url=https://global.oup.com/academic/product/essays-in-the-philosophy-of-chemistry-9780190494599?cc=de&lang=en& |archive-date=10 June 2021 |access-date=31 May 2022 |archive-url=https://web.archive.org/web/20210610130352/https://global.oup.com/academic/product/essays-in-the-philosophy-of-chemistry-9780190494599?cc=de&lang=en& |url-status=live }}</ref> [[mathematical biology|biology]],<ref>{{Cite web |title=What is mathematical biology |publisher=Centre for Mathematical Biology, University of Bath |url=http://www.bath.ac.uk/cmb/mathBiology/ |url-status=dead |archive-url=https://web.archive.org/web/20180923070442/http://www.bath.ac.uk/cmb/mathBiology/ |archive-date=23 September 2018 |access-date=7 June 2018}}</ref> [[mathematical finance|finance]],<ref>{{cite magazine |last=Johnson |first=Tim |date=1 September 2009 |title=What is financial mathematics? |url=https://plus.maths.org/content/what-financial-mathematics |access-date=1 March 2021 |magazine=+Plus Magazine |archive-date=8 April 2022 |archive-url=https://web.archive.org/web/20220408231344/https://plus.maths.org/content/what-financial-mathematics |url-status=live}}</ref> and [[mathematical economics|economics]].<ref>{{cite book |last=Varian |first=Hal |author-link=Hal Varian |year=1997 |chapter=What Use Is Economic Theory? |editor-last1=D'Autume |editor-first1=A. |editor-last2=Cartelier |editor-first2=J. |title=Is Economics Becoming a Hard Science? |publisher=Edward Elgar}} [http://www.sims.berkeley.edu/~hal/Papers/theory.pdf Pre-publication]. {{Webarchive|url=https://web.archive.org/web/20060625062619/http://www.sims.berkeley.edu/~hal/Papers/theory.pdf |date=25 June 2006 }}. Retrieved 1 April 2008.</ref>