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
Leibniz contributed a fair amount to the statics and dynamics emerging around him, often disagreeing with Descartes and Newton. He devised a new theory of motion (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.[131]
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."[77]
Leibniz held a relationist notion of space and time, against Newton's substantivalist views.[132][133][134] According to Newton's substantivalism, space and time are entities in their own right, existing independently of things. Leibniz's relationism, 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 vortex theory.[135] 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 of matter.[135]
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 mv2, 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.[136] 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 academics 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.[137] 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.[138][139] He appears to be an "underappreciated pioneer of psychology"[140] He wrote on topics which are now regarded as fields of psychology: attention and consciousness, memory, learning (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."[141] 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.[142] Leibniz, however, did not use the term psychologia.[143] 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."[144] 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.[145] 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."[146][147] Much of Leibniz's work went on to have a great impact on the field of psychology.[148] 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.[149] 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 unconscious. Leibniz was a direct influence on Ernst Platner, who is credited with originally coining the term Unbewußtseyn (unconscious).[150] Additionally, the idea of subliminal stimuli can be traced back to his theory of small perceptions.[151] Leibniz's ideas regarding music and tonal perception went on to influence the laboratory studies of Wilhelm Wundt.[152]
Social science
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.[153]
Computation
Leibniz may have been the first computer scientist and information theorist.[154] Early in life, he documented the binary numeral system (base 2), then revisited that system throughout his career.[155] 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.[156] More information can be found in the 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.[157] Juan Caramuel y Lobkowitz worked extensively on logarithms including logarithms with base 2.[158] 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.[159] Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set.[160] He anticipated 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.[161] Wiener is quoted with "Indeed, the general idea of a computing machine is nothing but a mechanization of Leibniz's Calculus Ratiocinator."[162]
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 operation. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.[163] Leibniz also devised a (now reproduced) cipher machine, recovered by Nicholas Rescher in 2010.[164] In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph".[165]
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.[166][167] 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.[168] 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".[169] 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 Bibliotheca Augusta at Wolfenbüttel. It was an extensive library with at least 25,946 printed volumes.[169] 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.[170] Leibniz, for example, proposed the following classification system in the Otivm Hanoveranvm Sive Miscellanea (1737):[170][171]
- 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 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 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.
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), 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 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 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.[172]
