''Natura non facit saltus''

Alexander Baumgarten Alexander Gottlieb Baumgarten (; ; 17 July 1714 – 27 MayJan LekschasBaumgarten Family'' 1762) was a German philosopher. He was a brother to theologian Siegmund Jakob Baumgarten (1706–1757). Biography Baumgarten was born in Berlin as the ...

, ''Metaphysics: A Critical Translation with Kant's Elucidations'', Translated and Edited by Courtney D. Fugate and John Hymers, Bloomsbury, 2013, "Preface of the Third Edition (1750)"
p. 79 n. d
" aumgartenmust also have in mind Leibniz's "''natura non facit saltus'' ature does not make leaps ( NE IV, 16)." Also see Gottfried Wilhelm Leibniz, ''

Nouveaux essais sur l'entendement humain ''New Essays on Human Understanding'' (french: Nouveaux essais sur l'entendement humain) is a chapter-by-chapter rebuttal by Gottfried Leibniz of John Locke's major work ''An Essay Concerning Human Understanding''. It is one of only two full-lengt ...

'', 1704, p. 5

/ref> (

Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...

for "nature does not make jumps") has been an important principle of

natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior throu ...

. It appears as an axiom in the works of

Gottfried Leibniz Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mathem ...

( ''New Essays'', IV, 16: ''"la nature ne fait jamais des sauts"'', "nature does not make jumps"), one of the inventors of the

infinitesimal calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithm ...

(see

Law of Continuity The law of continuity is a heuristic principle introduced by Gottfried Leibniz based on earlier work by Nicholas of Cusa and Johannes Kepler. It is the principle that "whatever succeeds for the finite, also succeeds for the infinite". Kepler used ...

). It is also an essential element of

Charles Darwin Charles Robert Darwin ( ; 12 February 1809 – 19 April 1882) was an English naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all species of life have descended fr ...

's treatment of natural selection in his ''

Origin of Species ''On the Origin of Species'' (or, more completely, ''On the Origin of Species by Means of Natural Selection, or the Preservation of Favoured Races in the Struggle for Life''),The book's full original title was ''On the Origin of Species by Me ...

''. The Latin translation comes from

Linnaeus Carl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his ennoblement in 1761 as Carl von Linné Blunt (2004), p. 171. (), was a Swedish botanist, zoologist, taxonomist, and physician who formalised binomial nomenclature, the ...

' ''

Philosophia Botanica ''Philosophia Botanica'' ("Botanical Philosophy", ed. 1, Stockholm & Amsterdam, 1751.) was published by the Swedish naturalist and physician Carl Linnaeus (1707–1778) who greatly influenced the development of botanical taxonomy and systematics ...

''.

Overview

The principle expresses the idea that natural things and properties change gradually, rather than suddenly. In a mathematical context, this allows one to assume that the solutions of the governing equations are

continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...

, and also does not preclude their being

differentiable In mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its ...

(differentiability implies continuity). Modern day

quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...

is sometimes seen as violating the principle, with its idea of a

quantum leap ''Quantum Leap'' is an American science fiction television series, created by Donald P. Bellisario, that premiered on NBC and aired for five seasons, from March 26, 1989, to May 5, 1993. The series stars Scott Bakula as Dr. Sam Beckett, a physi ...

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger (, ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was a Nobel Prize-winning Austrian physicist with Irish citizenship who developed a number of fundamental results in quantum theory ...

in his objections to quantum jumps supported the principle, and initially developed his

wave mechanics Wave mechanics may refer to: * the mechanics of waves * the ''wave equation'' in quantum physics, see Schrödinger equation See also * Quantum mechanics * Wave equation The (two-way) wave equation is a second-order linear partial different ...

in order to remove these jumps. In the biological context, the principle was used by

and others to defend the evolutionary postulate that all species develop from earlier species through gradual and minute changes rather than through the sudden emergence of new forms. In botany in particular, the

Antoine-Laurent de Jussieu Antoine-Laurent de Lavoisier ( , ; ; 26 August 17438 May 1794),
CNRS (

evolutionary biology Evolutionary biology is the subfield of biology that studies the evolutionary processes (natural selection, common descent, speciation) that produced the diversity of life on Earth. It is also defined as the study of the history of life fo ...

has terminology suggesting both continuous change, such as

genetic drift Genetic drift, also known as allelic drift or the Wright effect, is the change in the frequency of an existing gene variant (allele) in a population due to random chance. Genetic drift may cause gene variants to disappear completely and there ...

, and discontinuous variation, such as

mutation In biology, a mutation is an alteration in the nucleic acid sequence of the genome of an organism, virus, or extrachromosomal DNA. Viral genomes contain either DNA or RNA. Mutations result from errors during DNA or viral replication, mi ...

. However, as the basic structure of DNA is discrete, nature is now widely understood to make jumps at the biological level, if only on a very small scale.

Variant forms

The principle is also variously referred to as: *''Natura in operationibus suis non facit saltum'' (transl.: "Nature in its operations doesn't make a (any) jump") — 1613 appearance of a similar expression.Texlog.de
/ref> *''Natura non faciat saltus, nec ab extremo ad extremum transeat nisi per medium'' (transl.: "Nature may not make jumps, nor may it pass from extreme to extreme except by way of a mean.") — John Ray (1682). *''Natura non saltum facit'' (literally, "Nature does not make a jump") is a variant form, sometimes attributed to Gottfried Leibniz. ''Natura non facit saltum'' is also the epigraph of

Alfred Marshall Alfred Marshall (26 July 1842 – 13 July 1924) was an English economist, and was one of the most influential economists of his time. His book '' Principles of Economics'' (1890) was the dominant economic textbook in England for many years. I ...

's 1890 ''Principles of Economics''. He most likely borrowed the phrase from Darwin's ''The Origin of Species''. An admirer of

Herbert Spencer Herbert Spencer (27 April 1820 – 8 December 1903) was an English philosopher, psychologist, biologist, anthropologist, and sociologist famous for his hypothesis of social Darwinism. Spencer originated the expression "survival of the fittest" ...

, Marshall intended the epigraph both to proclaim his adherence to evolutionary thought and to justify his use of

differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...

as an analytical tool—a use seen in all the seminal thinkers of

neoclassical economics Neoclassical economics is an approach to economics in which the production, consumption and valuation (pricing) of goods and services are observed as driven by the supply and demand model. According to this line of thought, the value of a good ...

. The spelling variation (''saltus'' vs. ''saltum'') displays a mere numeral difference; because the Latin noun ''

saltus Saltus may refer to: People *Edgar Saltus (1855–1921), American writer known for his highly refined prose style *Francis Saltus Saltus (1849–1889), American poet *Thomas Saltus Lubbock (1817–1862), Texas Ranger and soldier in the Confederat ...

'', meaning "leap", belongs to the 4th declension; so its singular accusative is ''saltum'' (leap), while the plural is ''saltus'' (leaps). *''Die Natur macht keine Sprünge'' —

German German(s) may refer to: * Germany (of or related to) **Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ger ...

translation of the phrase.

References

{{reflist, 2 Latin philosophical phrases Natural philosophy