Editing Gottfried Wilhelm Leibniz (section)

==Science and engineering==
Leibniz's writings are currently discussed, not only for their anticipations and possible discoveries not yet recognized, but as ways of advancing present knowledge. Much of his writing on physics is included in Gerhardt's ''Mathematical Writings''.

===Physics===
{{See also|Dynamism (metaphysics)|Conatus#In Leibniz}}
Leibniz contributed a fair amount to the statics and dynamics emerging around him, often disagreeing with [[Descartes]] and [[Isaac Newton|Newton]]. He devised a new theory of [[Motion (physics)|motion]] ([[Dynamics (mechanics)|dynamics]]) based on [[kinetic energy]] and [[potential energy]], which posited space as relative, whereas Newton was thoroughly convinced that space was absolute. An important example of Leibniz's mature physical thinking is his ''Specimen Dynamicum'' of 1695.<ref>Ariew and Garber 117, Loemker §46, W II.5. On Leibniz and physics, see the chapter by Garber in Jolley (1995) and Wilson (1989).</ref>

Until the discovery of subatomic particles and the [[quantum mechanics]] governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated [[Albert Einstein]] by arguing, against Newton, that [[space]], time and motion are relative, not absolute: "As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions."<ref name="See H. G pp. 25"/>

Leibniz held a [[Relational theory|relational notion]] of space and time, against Newton's substantivalist views.<ref>Futch, Michael. ''Leibniz's Metaphysics of Time and Space''. New York: Springer, 2008.</ref><ref>Ray, Christopher. ''Time, Space and Philosophy''. London: Routledge, 1991.</ref><ref>Rickles, Dean. ''Symmetry, Structure and Spacetime''. Oxford: Elsevier, 2008.</ref> According to Newton's substantivalism, space and time are entities in their own right, existing independently of things. Leibniz's relationalism, in contrast, describes [[space and time]] as systems of relations that exist between objects. The rise of [[general relativity]] and subsequent work in the [[history of physics]] has put Leibniz's stance in a more favorable light.

One of Leibniz's projects was to recast Newton's theory as a [[Mechanical explanations of gravitation|vortex theory]].<ref name="Arthur p. 56">Arthur 2014, p. 56.</ref> However, his project went beyond vortex theory, since at its heart there was an attempt to explain one of the most difficult problems in physics, that of the origin of the [[Cohesion (chemistry)|cohesion of matter]].<ref name="Arthur p. 56"/>

The [[principle of sufficient reason]] has been invoked in recent [[cosmology]], and his [[identity of indiscernibles]] in quantum mechanics, a field some even credit him with having anticipated in some sense. In addition to his theories about the nature of reality, Leibniz's contributions to the development of calculus have also had a major impact on physics.

====The ''vis viva''====
Leibniz's ''[[vis viva]]'' (Latin for "living force") is {{math|{{var|m}}{{var|v}}{{sup|2}}}}, twice the modern [[kinetic energy]]. He realized that the total energy would be conserved in certain mechanical systems, so he considered it an innate motive characteristic of matter.<ref>See Ariew and Garber 155–86, Loemker §§53–55, W II.6–7a</ref> Here too his thinking gave rise to another regrettable nationalistic dispute. His ''vis viva'' was seen as rivaling the [[conservation of momentum]] championed by Newton in England and by [[Descartes]] and Voltaire in France; hence [[academic]]s in those countries tended to neglect Leibniz's idea. Leibniz knew of the validity of conservation of momentum. In reality, both energy and [[momentum]] are conserved (in [[closed systems]]), so both approaches are valid.

===Other natural science===
By proposing that the Earth has a molten core, he anticipated modern geology. In [[embryology]], he was a preformationist, but also proposed that organisms are the outcome of a combination of an infinite number of possible microstructures and of their powers. In the [[life sciences]] and [[paleontology]], he revealed an amazing transformist intuition, fueled by his study of comparative anatomy and fossils. One of his principal works on this subject, ''[[Protogaea]]'', unpublished in his lifetime, has recently been published in English for the first time. He worked out a primal [[organismic theory]].<ref>On Leibniz and biology, see Loemker (1969a: VIII).</ref> In medicine, he exhorted the physicians of his time—with some results—to ground their theories in detailed comparative observations and verified experiments, and to distinguish firmly scientific and metaphysical points of view.

===Psychology===
Psychology had been a central interest of Leibniz.<ref>L. E. Loemker: ''Introduction to Philosophical papers and letters: A selection.'' Gottfried W. Leibniz (transl. and ed., by Leroy E. Loemker). Dordrecht: Riedel (2nd ed. 1969).</ref><ref>T. Verhave: ''Contributions to the history of psychology: III. G. W. Leibniz (1646–1716)''. ''On the Association of Ideas and Learning''. ''Psychological Report'', 1967, Vol. 20, 11–116.</ref> He appears to be an "underappreciated pioneer of psychology"<ref>R. E. Fancher & H. Schmidt: Gottfried Wilhelm Leibniz: ''Underappreciated pioneer of psychology''. In: G. A. Kimble & M. Wertheimer (Eds.). ''Portraits of pioneers in psychology'', Vol. V. American Psychological Association, Washington, DC, 2003, pp. 1–17.</ref> He wrote on topics which are now regarded as fields of psychology: [[attention]] and [[consciousness]], [[memory]], [[learning]] ([[Association (psychology)|association]]), [[motivation]] (the act of "striving"), emergent [[individuality]], the general dynamics of development ([[evolutionary psychology]]). His discussions in the ''New Essays'' and ''Monadology'' often rely on everyday observations such as the behaviour of a dog or the noise of the sea, and he develops intuitive analogies (the synchronous running of clocks or the balance spring of a clock). He also devised postulates and principles that apply to psychology: the continuum of the unnoticed ''petites perceptions'' to the distinct, self-aware [[apperception]], and [[psychophysical parallelism]] from the point of view of causality and of purpose: "Souls act according to the laws of final causes, through aspirations, ends and means. Bodies act according to the laws of efficient causes, i.e. the laws of motion. And these two realms, that of efficient causes and that of final causes, harmonize with one another."<ref>{{cite book |last=Leibniz |first=G. W. |orig-year=1714/1720 |title=The Principles of Philosophy known as Monadology |translator=Jonathan Bennett |year=2007 |url=http://www.earlymoderntexts.com/authors/leibniz |page=11}}</ref> This idea refers to the mind-body problem, stating that the mind and brain do not act upon each other, but act alongside each other separately but in harmony.<ref>Larry M. Jorgensen, The Principle of Continuity and Leibniz's Theory of Consciousness.</ref> Leibniz, however, did not use the term ''psychologia''.<ref>The German scholar Johann Thomas Freigius was the first to use this Latin term 1574 in print: ''Quaestiones logicae et ethicae'', Basel, Henricpetri.</ref>
Leibniz's epistemological position—against [[John Locke]] and English [[empiricism]] ([[sensualism]])—was made clear: "Nihil est in intellectu quod non fuerit in sensu, nisi intellectu ipse." – "Nothing is in the intellect that was not first in the senses, except the intellect itself."<ref>Leibniz, Nouveaux essais, 1765, Livre II, Des Idées, Chapitre 1, § 6. ''New Essays on Human Understanding'' Book 2. p. 36; transl. by Jonathan Bennett, 2009.</ref> Principles that are not present in sensory impressions can be recognised in human perception and consciousness: logical inferences, categories of thought, the principle of [[causality]] and the principle of purpose ([[teleology]]).

Leibniz found his most important interpreter in [[Wilhelm Wundt]], founder of psychology as a discipline. Wundt used the "… nisi intellectu ipse" quotation 1862 on the title page of his ''Beiträge zur Theorie der Sinneswahrnehmung'' (Contributions on the Theory of Sensory Perception) and published a detailed and aspiring monograph on Leibniz.<ref>Wundt: ''Leibniz zu seinem zweihundertjährigen Todestag, 14. November 1916.'' Alfred Kröner Verlag, Leipzig 1917.</ref> Wundt shaped the term [[apperception]], introduced by Leibniz, into an experimental psychologically based apperception psychology that included neuropsychological modelling – an excellent example of how a concept created by a great philosopher could stimulate a psychological research program. One principle in the thinking of Leibniz played a fundamental role: "the principle of equality of separate but corresponding viewpoints." Wundt characterized this style of thought ([[perspectivism]]) in a way that also applied for him—viewpoints that "supplement one another, while also being able to appear as opposites that only resolve themselves when considered more deeply."<ref>Wundt (1917), p. 117.</ref><ref>{{cite web |url=https://psydok.psycharchives.de/jspui/bitstream/20.500.11780/3772/1/The%20influence%20of%20Gottfried%20Wilhelm%20Leibniz%20on%20the%20Psychology%2C%20Philosophy%2C%20and%20Ethics%20of%20Wilhelm%20Wundt.pdf |last=Fahrenberg |first=Jochen |date=2017 |title=The influence of Gottfried Wilhelm Leibniz on the Psychology, philosophy, and Ethics of Wilhelm Wundt |access-date=28 June 2022}}</ref>
Much of Leibniz's work went on to have a great impact on the field of psychology.<ref>D. Brett King, Wayne Viney and William Woody. ''A History of Psychology: Ideas and Context'' (2009), 150–153.</ref> Leibniz thought that there are many petites perceptions, or small perceptions of which we perceive but of which we are unaware. He believed that by the principle that phenomena found in nature were continuous by default, it was likely that the transition between conscious and unconscious states had intermediary steps.<ref>Nicholls and Leibscher ''Thinking the Unconscious: Nineteenth-Century German Thought'' (2010), 6.</ref> For this to be true, there must also be a portion of the mind of which we are unaware at any given time. His theory regarding consciousness in relation to the principle of continuity can be seen as an early theory regarding the [[stages of sleep]]. In this way, Leibniz's theory of perception can be viewed as one of many theories leading up to the idea of the [[The unconscious|unconscious]]. Leibniz was a direct influence on [[Ernst Platner]], who is credited with originally coining the term Unbewußtseyn (unconscious).<ref>Nicholls and Leibscher (2010).</ref> Additionally, the idea of [[subliminal stimuli]] can be traced back to his theory of small perceptions.<ref>King et al. (2009), 150–153.</ref> Leibniz's ideas regarding music and tonal perception went on to influence the laboratory studies of Wilhelm Wundt.<ref>{{cite journal | last1 = Klempe | first1 = SH | year = 2011 | title = The role of tone sensation and musical stimuli in early experimental psychology | journal = Journal of the History of the Behavioral Sciences | volume = 47 | issue = 2| pages = 187–199 | doi = 10.1002/jhbs.20495 | pmid = 21462196 }}</ref>

===Social science===
{{Unreferenced section|date=September 2021}}
In public health, he advocated establishing a medical administrative authority, with powers over [[epidemiology]] and [[veterinary medicine]]. He worked to set up a coherent medical training program, oriented towards public health and preventive measures. In economic policy, he proposed tax reforms and a national insurance program, and discussed the [[balance of trade]]. He even proposed something akin to what much later emerged as [[game theory]]. In sociology he laid the ground for [[communication theory]].

===Technology===
In 1906, Garland published a volume of Leibniz's writings bearing on his many practical inventions and engineering work. To date, few of these writings have been translated into English. Nevertheless, it is well understood that Leibniz was a serious inventor, engineer, and applied scientist, with great respect for practical life. Following the motto ''theoria cum praxi'', he urged that theory be combined with practical application, and thus has been claimed as the father of [[applied science]]. He designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc. With [[Denis Papin]], he created a [[steam engine]]. He even proposed a method for desalinating water. From 1680 to 1685, he struggled to overcome the chronic flooding that afflicted the ducal silver mines in the [[Harz Mountains]], but did not succeed.<ref>Aiton (1985), 107–114, 136</ref>

===={{anchor|Information technology}}Computation====
Leibniz may have been the first computer scientist and information theorist.<ref>Davis (2000) discusses Leibniz's prophetic role in the emergence of calculating machines and of formal languages.</ref> Early in life, he documented the [[binary numeral system]] ([[radix|base]] 2), then revisited that system throughout his career.<ref>See Couturat (1901): 473–478.</ref> While Leibniz was examining other cultures to compare his metaphysical views, he encountered an ancient Chinese book ''[[I Ching]]''. Leibniz interpreted a diagram which showed yin and yang and corresponded it to a zero and one.<ref>{{Cite journal |jstor = 1399337|title = Leibniz' Binary System and Shao Yong's "Yijing"|journal = Philosophy East and West|volume = 46|issue = 1|pages = 59–90|last1 = Ryan|first1 = James A.|year = 1996|doi = 10.2307/1399337}}</ref> More information can be found in the [[#Sinophology|Sinophology]] section. Leibniz had similarities with [[Juan Caramuel y Lobkowitz]] and [[Thomas Harriot]], who independently developed the binary system, as he was familiar with their works on the binary system.<ref>{{Cite journal|last1=Ares|first1=J.|last2=Lara|first2=J.|last3=Lizcano|first3=D.|last4=Martínez|first4=M.|date=2017|title=Who Discovered the Binary System and Arithmetic?|journal=Science and Engineering Ethics|volume=24|issue=1|pages=173–188|pmid=28281152|doi=10.1007/s11948-017-9890-6|s2cid=35486997|hdl=20.500.12226/69|hdl-access=free}}</ref> Juan Caramuel y Lobkowitz worked extensively on logarithms including logarithms with base 2.<ref>{{cite journal|last1=Navarro-Loidi|first1=Juan|title=The Introductions of Logarithms into Spain|journal=Historia Mathematica|date=May 2008|volume=35|issue=2|pages=83–101|doi=10.1016/j.hm.2007.09.002|doi-access=free}}</ref> Thomas Harriot's manuscripts contained a table of binary numbers and their notation, which demonstrated that any number could be written on a base 2 system.<ref>{{cite journal|last1=Booth|first1=Michael|title=Thomas Harriot's Translations|journal=The Yale Journal of Criticism|date=2003|volume=16|issue=2|pages=345–361|issn=0893-5378|doi=10.1353/yale.2003.0013|s2cid=161603159}}</ref> Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set.<ref>{{cite journal|last1=Lande|first1=Daniel|title=Development of the Binary Number System and the Foundations of Computer Science|journal=The Mathematics Enthusiast|pages=513–540}}</ref> He anticipated [[Lagrange polynomial|Lagrangian interpolation]] and [[algorithmic information theory]]. His [[calculus ratiocinator]] anticipated aspects of the [[universal Turing machine]]. In 1961, [[Norbert Wiener]] suggested that Leibniz should be considered the patron saint of [[cybernetics]].<ref>Wiener, N., ''Cybernetics'' (2nd edition with revisions and two additional chapters), The MIT Press and Wiley, New York, 1961, p. 12.</ref> Wiener is quoted with "Indeed, the general idea of a computing machine is nothing but a mechanization of Leibniz's Calculus Ratiocinator."<ref>{{cite journal |last1=Wiener |first1=Norbert |title=Time, Communication, and the Nervous System |journal=Annals of the New York Academy of Sciences |date=1948 |volume=50 |issue=4 Teleological |pages=197–220 |doi=10.1111/j.1749-6632.1948.tb39853.x |pmid=18886381 |bibcode=1948NYASA..50..197W |s2cid=28452205 |url=https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/j.1749-6632.1948.tb39853.x |language=en |access-date=23 July 2021 |archive-date=23 July 2021 |archive-url=https://web.archive.org/web/20210723233238/https://nyaspubs.onlinelibrary.wiley.com/doi/abs/10.1111/j.1749-6632.1948.tb39853.x |url-status=dead }}</ref>

In 1671, Leibniz began to invent a machine that could execute all four arithmetic operations, gradually improving it over a number of years. This "[[stepped reckoner]]" attracted fair attention and was the basis of his election to the [[Royal Society]] in 1673. A number of such machines were made during his years in [[Hanover]] by a craftsman working under his supervision. They were not an unambiguous success because they did not fully mechanize the [[Carry (arithmetic)|carry operation]]. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.<ref>Couturat (1901), 115</ref> Leibniz also devised a (now reproduced) cipher machine, recovered by [[Nicholas Rescher]] in 2010.<ref>See N. Rescher, ''Leibniz and Cryptography'' (Pittsburgh, University Library Systems, University of Pittsburgh, 2012).</ref> In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph".<ref>[http://amatterofmind.org/Pierres_PDFs/TRANSLATIONS/4._GOTTFRIED_LEIBNIZ_SELECTIONS_FROM_ACTA_ERUDITORUM.pdf "The discoveries of principle of the calculus in Acta Eruditorum"] (commentary, pp. 60–61), translated by Pierre Beaudry, amatterofmind.org, Leesburg, Va., September 2000. (pdf)</ref>

Leibniz was groping towards hardware and software concepts worked out much later by [[Charles Babbage]] and [[Ada Lovelace]]. In 1679, while mulling over his binary arithmetic, Leibniz imagined a machine in which binary numbers were represented by marbles, governed by a rudimentary sort of punched cards.<ref>{{cite web|url=http://www.edge.org/discourse/schirrmacher_eurotech.html|title=The Reality Club: Wake Up Call for Europe Tech|website=www.edge.org|access-date=11 January 2006|archive-date=28 December 2005|archive-url=https://web.archive.org/web/20051228133959/http://www.edge.org/discourse/schirrmacher_eurotech.html|url-status=dead}}</ref><ref>{{cite book|last1=Agarwal|first1=Ravi P|last2=Sen|first2=Syamal K|title=Creators of Mathematical and Computational Sciences|date=2014|publisher=Springer, Cham|isbn=978-3-319-10870-4|page=28}}</ref> Modern electronic digital computers replace Leibniz's marbles moving by gravity with shift registers, voltage gradients, and pulses of electrons, but otherwise they run roughly as Leibniz envisioned in 1679.

===Librarian===
Later in Leibniz's career (after the death of von Boyneburg), Leibniz moved to Paris and accepted a position as a librarian in the Hanoverian court of Johann Friedrich, Duke of Brunswick-Luneburg.<ref>{{Cite web|url=https://www.britannica.com/biography/Gottfried-Wilhelm-Leibniz|title=Gottfried Wilhelm Leibniz {{!}} Biography & Facts|website=Encyclopedia Britannica|access-date=2019-02-18}}</ref> Leibniz's predecessor, Tobias Fleischer, had already created a cataloging system for the Duke's library but it was a clumsy attempt. At this library, Leibniz focused more on advancing the library than on the cataloging. For instance, within a month of taking the new position, he developed a comprehensive plan to expand the library. He was one of the first to consider developing a core collection for a library and felt "that a library for display and ostentation is a luxury and indeed superfluous, but a well-stocked and organized library is important and useful for all areas of human endeavor and is to be regarded on the same level as schools and churches".<ref name=":0">{{cite journal |last=Schulte-Albert |first=H. |date=April 1971 |title=Gottfried Wilhelm Leibniz and Library Classification |journal=The Journal of Library History |volume=6 |number=2 |pages=133–152 |jstor=25540286 |url=https://www.jstor.org/stable/25540286}}</ref> Leibniz lacked the funds to develop the library in this manner. After working at this library, by the end of 1690 Leibniz was appointed as privy-councilor and librarian of the [[Herzog August Library|Bibliotheca Augusta]] at Wolfenbüttel. It was an extensive library with at least 25,946 printed volumes.<ref name=":0" /> At this library, Leibniz sought to improve the catalog. He was not allowed to make complete changes to the existing closed catalog, but was allowed to improve upon it so he started on that task immediately. He created an alphabetical author catalog and had also created other cataloging methods that were not implemented. While serving as librarian of the ducal libraries in [[Hanover]] and [[Wolfenbüttel]], Leibniz effectively became one of the founders of [[library science]]. Seemingly, Leibniz paid a good deal of attention to the classification of subject matter, favoring a well-balanced library covering a host of numerous subjects and interests.<ref name=":1">{{Cite journal |last=Schulte-Albert |first=H. G. |date=1971 |title=Gottfried Wilhelm Leibniz and Library Classification |url=https://www.jstor.org/stable/25540286 |journal=The Journal of Library History |volume=6 |issue=2 |pages=133–152|jstor=25540286 }}</ref> Leibniz, for example, proposed the following classification system in the ''Otivm Hanoveranvm Sive Miscellanea'' (1737):<ref name=":1" /><ref>{{Cite book |url=http://digitale.bibliothek.uni-halle.de/vd18/5254469 |title=Otivm Hanoveranvm Sive Miscellanea Ex ore & schedis Illustris Viri, piæ memoriæ, Godofr. Gvilielmi Leibnitii ... / Quondam notata & descripta, Cum ipsi in collendis & excerpendis rebus ad Historiam Brunsvicensem pertinentibus operam navaret, Joachimvs Fridericvs Fellervs, Secretarius Ducalis Saxo-Vinariensis. Additæ sunt coronidis loco Epistolæ Gallicæ amœbeæ Leibnitii & Pellissonii de Tolerantia Religionum & de controversiis quibusdam Theologicis ... |date=1737 |language=en |access-date=21 March 2022 |archive-date=20 June 2023 |archive-url=https://web.archive.org/web/20230620193634/https://digitale.bibliothek.uni-halle.de/vd18/5254469 |url-status=dead }}</ref>

* Theology
* Jurisprudence
* Medicine
* Intellectual Philosophy
* Philosophy of the Imagination or Mathematics
* Philosophy of Sensible Things or Physics
* Philology or Language
* Civil History
* Literary History and Libraries
* General and Miscellaneous

He also designed a book [[library classification|indexing system]] in ignorance of the only other such system then extant, that of the [[Bodleian Library]] at [[Oxford University]]. He also called on publishers to distribute abstracts of all new titles they produced each year, in a standard form that would facilitate indexing. He hoped that this abstracting project would eventually include everything printed from his day back to [[Johannes Gutenberg|Gutenberg]]. Neither proposal met with success at the time, but something like them became standard practice among English language publishers during the 20th century, under the aegis of the [[Library of Congress]] and the [[British Library]].{{Citation needed|date=January 2024}}

He called for the creation of an [[empirical]] [[database]] as a way to further all sciences. His ''[[characteristica universalis]]'', [[calculus ratiocinator]], and a "community of minds"—intended, among other things, to bring political and religious unity to Europe—can be seen as distant unwitting anticipations of artificial languages (e.g., [[Esperanto]] and its rivals), [[Mathematical logic|symbolic logic]], even the [[World Wide Web]].

===Advocate of scientific societies===
Leibniz emphasized that research was a collaborative endeavor. Hence he warmly advocated the formation of national scientific societies along the lines of the [[Royal Society|British Royal Society]] and the French Académie Royale des Sciences. More specifically, in his correspondence and travels he urged the creation of such societies in Dresden, [[Saint Petersburg]], Vienna, and Berlin. Only one such project came to fruition; in 1700, the [[Prussian Academy of Sciences|Berlin Academy of Sciences]] was created. Leibniz drew up its first statutes, and served as its first President for the remainder of his life. That Academy evolved into the German Academy of Sciences, the publisher of the ongoing critical edition of his works.<ref>On Leibniz's projects for scientific societies, see Couturat (1901), App. IV.</ref>