In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics
is considered to be purely the result of the constructive mental
activity of humans rather than the discovery of fundamental principles
claimed to exist in an objective reality. That is, logic and mathematics
are not considered analytic activities wherein deep properties of
objective reality are revealed and applied, but are instead considered
the application of internally consistent methods used to realize more
complex mental constructs, regardless of their possible independent
existence in an objective reality.
Truth and proof
The
fundamental distinguishing characteristic of intuitionism is its
interpretation of what it means for a mathematical statement to be true.
In Brouwer's
original intuitionism, the truth of a mathematical statement is a
subjective claim: a mathematical statement corresponds to a mental
construction, and a mathematician can assert the truth of a statement
only by verifying the validity of that construction by intuition. The vagueness of the intuitionistic notion of truth often leads to misinterpretations about its meaning. Kleene
formally defined intuitionistic truth from a realist position, yet
Brouwer would likely reject this formalization as meaningless, given his
rejection of the realist/Platonist position. Intuitionistic truth
therefore remains somewhat ill-defined. However, because the
intuitionistic notion of truth is more restrictive than that of
classical mathematics, the intuitionist must reject some assumptions of
classical logic to ensure that everything they prove is in fact
intuitionistically true. This gives rise to intuitionistic logic.
To an intuitionist, the claim that an object with certain
properties exists is a claim that an object with those properties can be
constructed. Any mathematical object is considered to be a product of a
construction of a mind,
and therefore, the existence of an object is equivalent to the
possibility of its construction. This contrasts with the classical
approach, which states that the existence of an entity can be proved by
refuting its non-existence. For the intuitionist, this is not valid; the
refutation of the non-existence does not mean that it is possible to
find a construction for the putative object, as is required in order to
assert its existence. As such, intuitionism is a variety of mathematical constructivism; but it is not the only kind.
The interpretation of negation
is different in intuitionist logic than in classical logic. In
classical logic, the negation of a statement asserts that the statement
is false; to an intuitionist, it means the statement is refutable.
There is thus an asymmetry between a positive and negative statement in intuitionism. If a statement P is provable, then P certainly cannot be refutable. But even if it can be shown that P cannot be refuted, this does not constitute a proof of P. Thus P is a stronger statement than not-not-P.
Similarly, to assert that AorB holds, to an intuitionist, is to claim that either A or B can be proved. In particular, the law of excluded middle, "A or notA", is not accepted as a valid principle. For example, if A
is some mathematical statement that an intuitionist has not yet proved
or disproved, then that intuitionist will not assert the truth of "A or not A". However, the intuitionist will accept that "A and not A" cannot be true. Thus the connectives "and" and "or" of intuitionistic logic do not satisfy de Morgan's laws as they do in classical logic.
Intuitionistic logic substitutes constructability for abstract truth and is associated with a transition from the proof of model theory to abstract truth in modern mathematics.
The logical calculus preserves justification, rather than truth, across
transformations yielding derived propositions. It has been taken as
giving philosophical support to several schools of philosophy, most
notably the Anti-realism of Michael Dummett. Thus, contrary to the first impression its name might convey, and as realized in specific approaches and disciplines (e.g. Fuzzy Sets
and Systems), intuitionist mathematics is more rigorous than
conventionally founded mathematics, where, ironically, the foundational
elements which Intuitionism attempts to construct/refute/refound are
taken as intuitively given.
Infinity
Among the different formulations of intuitionism, there are several different positions on the meaning and reality of infinity.
The term potential infinity
refers to a mathematical procedure in which there is an unending series
of steps. After each step has been completed, there is always another
step to be performed. For example, consider the process of counting: 1, 2, 3, ...
The term actual infinity refers to a completed mathematical object which contains an infinite number of elements. An example is the set of natural numbers, N = {1, 2, ...}.
In Cantor's formulation of set theory, there are many different
infinite sets, some of which are larger than others. For example, the
set of all real numbers R is larger than N,
because any procedure that you attempt to use to put the natural
numbers into one-to-one correspondence with the real numbers will always
fail: there will always be an infinite number of real numbers "left
over". Any infinite set that can be placed in one-to-one correspondence
with the natural numbers is said to be "countable" or "denumerable".
Infinite sets larger than this are said to be "uncountable".
Modern constructive set theory includes the axiom of infinity from ZFC (or a revised version of this axiom) and the set N of natural numbers. Most modern constructive mathematicians accept the reality of countably infinite sets (however, see Alexander Esenin-Volpin for a counter-example).
Brouwer rejected the concept of actual infinity, but admitted the idea of potential infinity.
"According to Weyl 1946, 'Brouwer made it clear, as I think
beyond any doubt, that there is no evidence supporting the belief in the
existential character of the totality of all natural numbers ... the
sequence of numbers which grows beyond any stage already reached by
passing to the next number, is a manifold of possibilities open towards
infinity; it remains forever in the status of creation, but is not a
closed realm of things existing in themselves. That we blindly converted
one into the other is the true source of our difficulties, including
the antinomies – a source of more fundamental nature than Russell's
vicious circle principle indicated. Brouwer opened our eyes and made us
see how far classical mathematics, nourished by a belief in the
'absolute' that transcends all human possibilities of realization, goes
beyond such statements as can claim real meaning and truth founded on
evidence." (Kleene (1952): Introduction to Metamathematics, p. 48-49)
History
Intuitionism's history can be traced to two controversies in nineteenth century mathematics.
The second of these was Gottlob Frege's effort to reduce all of mathematics to a logical formulation via set theory and its derailing by a youthful Bertrand Russell, the discoverer of Russell's paradox.
Frege had planned a three volume definitive work, but just as the
second volume was going to press, Russell sent Frege a letter outlining
his paradox, which demonstrated that one of Frege's rules of
self-reference was self-contradictory. In an appendix to the second
volume, Frege acknowledged that one of the axioms of his system did in
fact lead to Russell's paradox.
Frege, the story goes, plunged into depression and did not
publish the third volume of his work as he had planned. For more see
Davis (2000) Chapters 3 and 4: Frege: From Breakthrough to Despair and Cantor: Detour through Infinity. See van Heijenoort for the original works and van Heijenoort's commentary.
These controversies are strongly linked as the logical methods
used by Cantor in proving his results in transfinite arithmetic are
essentially the same as those used by Russell in constructing his
paradox. Hence how one chooses to resolve Russell's paradox has direct
implications on the status accorded to Cantor's transfinite arithmetic.
In the early twentieth century L. E. J. Brouwer represented the intuitionist position and David Hilbert the formalist position—see van Heijenoort. Kurt Gödel offered opinions referred to as Platonist (see various sources re Gödel). Alan Turing considers:
"non-constructive systems of logic
with which not all the steps in a proof are mechanical, some being
intuitive". (Turing 1939, reprinted in Davis 2004, p. 210) Later, Stephen Cole Kleene brought forth a more rational consideration of intuitionism in his Introduction to Meta-mathematics (1952).
One of the bulbs with which Edison discovered thermionic emission. It consists of an evacuated glass light bulb containing a carbonfilament(hairpin shape), with an additional metal plate attached to wires emerging from the base. Electrons released by the filament were attracted to the plate when it had a positive voltage.
Thermionic emission is the liberation of electrons from an electrode by virtue of its temperature (releasing of energy supplied by heat). This occurs because the thermal energy given to the charge carrier overcomes the work function of the material. The charge carriers can be electrons or ions, and in older literature are sometimes referred to as thermions.
After emission, a charge that is equal in magnitude and opposite in
sign to the total charge emitted is initially left behind in the
emitting region. But if the emitter is connected to a battery, the
charge left behind is neutralized by charge supplied by the battery as
the emitted charge carriers move away from the emitter, and finally the
emitter will be in the same state as it was before emission.
The classical example of thermionic emission is that of electrons from a hot cathode into a vacuum (also known as thermal electron emission or the Edison effect) in a vacuum tube.
The hot cathode can be a metal filament, a coated metal filament, or a
separate structure of metal or carbides or borides of transition metals.
Vacuum emission from metals tends to become significant only for
temperatures over 1,000 K (730 °C; 1,340 °F).
This process is crucially important in the operation of a variety of electronic devices and can be used for electricity generation (such as thermionic converters and electrodynamic tethers) or cooling. The magnitude of the charge flow increases dramatically with increasing temperature.
The term 'thermionic emission' is now also used to refer to any
thermally-excited charge emission process, even when the charge is
emitted from one solid-state region into another.
History
The
Edison effect in a diode tube. A diode tube is connected in two
configurations; one has a flow of electrons and the other does not. (The
arrows represent electron current, not conventional current.)
Because the electron was not identified as a separate physical particle until the work of J. J. Thomson in 1897, the word "electron" was not used when discussing experiments that took place before this date.
The phenomenon was initially reported in 1853 by Edmond Becquerel. It was rediscovered in 1873 by Frederick Guthrie in Britain.
While doing work on charged objects, Guthrie discovered that a red-hot
iron sphere with a negative charge would lose its charge (by somehow
discharging it into air). He also found that this did not happen if the
sphere had a positive charge. Other early contributors included Johann Wilhelm Hittorf (1869–1883), Eugen Goldstein (1885), and Julius Elster and Hans Friedrich Geitel (1882–1889).
The effect was rediscovered again by Thomas Edison
on February 13, 1880, while he was trying to discover the reason for
breakage of lamp filaments and uneven blackening (darkest near the
positive terminal of the filament) of the bulbs in his incandescent lamps.
Edison built several experimental lamp bulbs with an extra wire,
metal plate, or foil inside the bulb that was separate from the filament
and thus could serve as an electrode. He connected a galvanometer,
a device used to measure current (the flow of charge), to the output of
the extra metal electrode. If the foil was put at a negative potential
relative to the filament, there was no measurable current between the
filament and the foil. When the foil was raised to a positive potential
relative to the filament, there could be a significant current between
the filament through the vacuum to the foil if the filament was heated
sufficiently (by its own external power source).
We now know that the filament was emitting electrons, which were
attracted to a positively charged foil, but not a negatively charged
one. This one-way current was called the Edison effect (although
the term is occasionally used to refer to thermionic emission itself).
He found that the current emitted by the hot filament increased rapidly
with increasing voltage, and filed a patent application for a
voltage-regulating device using the effect on November 15, 1883 (U.S.
patent 307,031,
the first US patent for an electronic device). He found that sufficient
current would pass through the device to operate a telegraph sounder.
This was exhibited at the International Electrical Exposition in Philadelphia in September 1884. William Preece,
a British scientist, took back with him several of the Edison effect
bulbs. He presented a paper on them in 1885, where he referred to
thermionic emission as the "Edison effect." The British physicist John Ambrose Fleming,
working for the British "Wireless Telegraphy" Company, discovered that
the Edison effect could be used to detect radio waves. Fleming went on
to develop the two-element vacuum tube known as the diode, which he patented on November 16, 1904.
The thermionic diode can also be configured as a device that
converts a heat difference to electric power directly without moving
parts (a thermionic converter, a type of heat engine).
Richardson's law
Following J. J. Thomson's identification of the electron in 1897, the British physicist Owen Willans Richardson began work on the topic that he later called "thermionic emission". He received a Nobel Prize in Physics in 1928 "for his work on the thermionic phenomenon and especially for the discovery of the law named after him".
From band theory, there are one or two electrons per atom
in a solid that are free to move from atom to atom. This is sometimes
collectively referred to as a "sea of electrons". Their velocities
follow a statistical distribution, rather than being uniform, and
occasionally an electron will have enough velocity to exit the metal
without being pulled back in. The minimum amount of energy needed for an
electron to leave a surface is called the work function. The work function is characteristic of the material and for most metals is on the order of several electronvolts.
Thermionic currents can be increased by decreasing the work function.
This often-desired goal can be achieved by applying various oxide
coatings to the wire.
In 1901 Richardson
published the results of his experiments: the current from a heated
wire seemed to depend exponentially on the temperature of the wire with a
mathematical form similar to the Arrhenius equation. Later, he proposed that the emission law should have the mathematical form
In the period 1911 to 1930, as physical understanding of the
behaviour of electrons in metals increased, various theoretical
expressions (based on different physical assumptions) were put forward
for AG, by Richardson, Saul Dushman, Ralph H. Fowler, Arnold Sommerfeld and Lothar Wolfgang Nordheim. Over 60 years later, there is still no consensus among interested theoreticians as to the exact expression of AG, but there is agreement that AG must be written in the form
where λR is a material-specific correction factor that is typically of order 0.5, and A0 is a universal constant given by
where m and are the mass and charge of an electron, respectively, and h is Planck's constant.
In fact, by about 1930 there was agreement that, due to the wave-like nature of electrons, some proportion rav
of the outgoing electrons would be reflected as they reached the
emitter surface, so the emission current density would be reduced, and λR would have the value (1-rav). Thus, one sometimes sees the thermionic emission equation written in the form
.
However, a modern theoretical treatment by Modinos assumes that the band-structure of the emitting material must also be taken into account. This would introduce a second correction factor λB into λR, giving . Experimental values for the "generalized" coefficient AG are generally of the order of magnitude of A0, but do differ significantly as between different emitting materials, and can differ as between different crystallographic faces
of the same material. At least qualitatively, these experimental
differences can be explained as due to differences in the value of λR.
Considerable confusion exists in the literature of this area because: (1) many sources do not distinguish between AG and A0, but just use the symbol A
(and sometimes the name "Richardson constant") indiscriminately; (2)
equations with and without the correction factor here denoted by λR
are both given the same name; and (3) a variety of names exist for
these equations, including "Richardson equation", "Dushman's equation",
"Richardson–Dushman equation" and "Richardson–Laue–Dushman equation". In
the literature, the elementary equation is sometimes given in
circumstances where the generalized equation would be more appropriate,
and this in itself can cause confusion. To avoid misunderstandings, the
meaning of any "A-like" symbol should always be explicitly defined in
terms of the more fundamental quantities involved.
Because of the exponential function, the current increases rapidly with temperature when kT is less than W. (For essentially every material, melting occurs well before kT = W.)
The thermionic emission law has been recently revised for 2D materials in various models.
In electron emission devices, especially electron guns,
the thermionic electron emitter will be biased negative relative to its
surroundings. This creates an electric field of magnitude E at the emitter surface. Without the field, the surface barrier seen by an escaping Fermi-level electron has height W equal to the local work-function. The electric field lowers the surface barrier by an amount ΔW, and increases the emission current. This is known as the Schottky effect (named for Walter H. Schottky) or field enhanced thermionic emission. It can be modeled by a simple modification of the Richardson equation, by replacing W by (W − ΔW). This gives the equation
where ε0 is the electric constant (also, formerly, called the vacuum permittivity).
Electron emission that takes place in the field-and-temperature-regime where this modified equation applies is often called Schottky emission. This equation is relatively accurate for electric field strengths lower than about 108 V m−1. For electric field strengths higher than 108 V m−1, so-called Fowler-Nordheim (FN) tunneling
begins to contribute significant emission current. In this regime, the
combined effects of field-enhanced thermionic and field emission can be
modeled by the Murphy-Good equation for thermo-field (T-F) emission.
At even higher fields, FN tunneling becomes the dominant electron
emission mechanism, and the emitter operates in the so-called "cold field electron emission (CFE)" regime.
Thermionic emission can also be enhanced by interaction with other forms of excitation such as light. For example, excited Cs-vapours in thermionic converters form clusters of Cs-Rydberg matter which yield a decrease of collector emitting work function from 1.5 eV to 1.0–0.7 eV. Due to long-lived nature of Rydberg matter this low work function remains low which essentially increases the low-temperature converter's efficiency.
Photon-enhanced thermionic emission
Photon-enhanced thermionic emission (PETE) is a process developed by scientists at Stanford University
that harnesses both the light and heat of the sun to generate
electricity and increases the efficiency of solar power production by
more than twice the current levels. The device developed for the process
reaches peak efficiency above 200 °C, while most silicon solar cells become inert after reaching 100 °C. Such devices work best in parabolic dish collectors, which reach temperatures up to 800 °C. Although the team used a gallium nitride semiconductor in its proof-of-concept device, it claims that the use of gallium arsenide can increase the device's efficiency to 55–60 percent, nearly triple that of existing systems, and 12–17 percent more than existing 43 percent multi-junction solar cells.
The frontispiece of Hobbes's Leviathan shows a body formed of multitudinous citizens, surmounted by a king's head.
The body politic is a polity—such as a city, realm, or state—considered metaphorically as a physical body. Historically, the sovereign
is typically portrayed as the body's head, and the analogy may also be
extended to other anatomical parts, as in political readings of Aesop's fable of "The Belly and the Members". The image originates in ancient Greek philosophy, beginning in the 6th century BC, and was later extended in Roman philosophy. Following the high and late medieval revival of the Byzantine Corpus Juris Civilis in Latin Europe, the "body politic" took on a jurisprudential significance by being identified with the legal theory of the corporation, gaining salience in political thought from the 13th century on. In English law the image of the body politic developed into the theory of the king's two bodies and the Crown as corporation sole.
The metaphor was elaborated further from the Renaissance on, as medical knowledge based on Galen was challenged by thinkers such as William Harvey. Analogies were drawn between supposed causes of disease and disorder and their equivalents in the political field, viewed as plagues or infections that might be remedied with purges and nostrums. The 17th century writings of Thomas Hobbes
developed the image of the body politic into a modern theory of the
state as an artificial person. Parallel terms deriving from the Latin corpus politicum exist in other European languages.
Etymology
The term body politic derives from Medieval Latincorpus politicum, which itself developed from corpus mysticum, originally designating the Catholic Church as the mystical body of Christ but extended to politics from the 11th century on in the form corpus reipublicae (mysticum), "(mystical) body of the commonwealth". Parallel terms exist in other European languages, such as Italian corpo politico, Polish ciało polityczne, and German Staatskörper ("state body"). An equivalent early modern French term is corps-état; contemporary French uses corps politique.
History
A visualization of the body politic metaphor in a 14th-century French manuscript.
The king is head. Next, the seneschals, bailiffs, and provosts and
other judges are compared to eyes and ears. The counsellors and wise men
are linked to the heart. As defenders of the commonwealth, the knights
are the hands. Because of their constant voyages, the merchants are
associated with the legs. Finally, laborers, who work close to the earth
and support the body, are its feet.
Classical philosophy
The Western concept of the "body politic", originally meaning a human society considered as a collective body, originated in classical Greek and Roman philosophy. The general metaphor emerged in the 6th century BC, with the Athenian statesman Solon and the poet Theognis describing cities (poleis) in biological terms as "pregnant" or "wounded". Plato's Republic provided one of its most influential formulations. The term itself, however—in Ancient Greek, τῆς πόλεως σῶμα, tēs poleōs sōma, "the body of the state"—appears as such for the first time in the late 4th century Athenian orators Dinarch and Hypereides at the beginning of the Hellenistic era. In these early formulations, the anatomical
detail of the body politic was relatively limited: Greek thinkers
typically confined themselves to distinguishing the ruler as head of the
body, and comparing political stasis, that is, crises of the state, to biological disease.
The image of the body politic occupied a central place in the political thought of the Roman Republic,
and the Romans were the first to develop the anatomy of the "body" in
full detail, endowing it with nerves, "blood, breath, limbs, and
organs". In its origins, the concept was particularly connected to a politicised version of Aesop's fable of "The Belly and the Members", told in relation to the first secessio plebis, the temporary departure of the plebeian order from Rome in 495–93 BC. On the account of the Roman historian Livy, a senator
explained the situation to the plebeians by a metaphor: the various
members of the Roman body had become angry that the "stomach", the patricians,
consumed their labours while providing nothing in return. However, upon
their secession, they became feeble and realised that the stomach's
digestion had provided them vital energy. Convinced by this story, the
plebeians returned to Rome, and the Roman body was made whole and
functional. This legend formed a paradigm for "nearly all surviving
republican discourse of the body politic".
Late republican orators developed the image further, comparing
attacks on Roman institutions to mutilations of the republic's body.
During the First Triumvirate in 59 BC, Cicero described the Roman state as "dying of a new sort of disease". Lucan's Pharsalia, written in the early imperial era in the 60s AD, abounded in this kind of imagery. Depicting the dictatorSulla
as a surgeon out of control who had butchered the Roman body politic in
the process of cutting out its putrefied limbs, Lucan used vivid
organic language to portray the decline of the Roman Republic as a
literal process of decay, its seas and rivers becoming choked with blood
and gore.
Medieval usage
The metaphor of the body politic remained in use after the fall of the Western Roman Empire. The Neoplatonist Islamic philosopher al-Farabi, known in the West as Alpharabius, discussed the image in his work The Perfect State
(c. 940), stating, "The excellent city resembles the perfect and
healthy body, all of whose limbs cooperate to make the life of the
animal perfect". John of Salisbury gave it a definitive Latin high medieval form in his Policraticus
around 1159: the king was the body's head; the priest was the soul; the
councillors were the heart; the eyes, ears, and tongue were the
magistrates of the law; one hand, the army, held a weapon; the other,
without a weapon, was the realm's justice. The body's feet were the
common people. Each member of the body had its vocation, and each was beholden to work in harmony for the benefit of the whole body.
In the Late Middle Ages, the concept of the corporation, a legal person made up of a group of real individuals, gave the idea of a body politic judicial significance. The corporation had emerged in imperial Roman law under the name universitas, and a formulation of the concept attributed to Ulpian was collected in the 6th century Digest of Justinian I during the early Byzantine era. The Digest, along with the other parts of Justinian's Corpus Juris Civilis, became the bedrock of medieval civil law upon its recovery and annotation by the glossators beginning in the 11th century. It remained for the glossators' 13th century successors, the commentators—especially Baldus de Ubaldis—to develop the idea of the corporation as a persona ficta, a fictive person, and apply the concept to human societies as a whole.
The imperial eagle in Dante's Paradiso, depicted by Giovanni di Paolo in the 1440s
Where his jurist predecessor Bartolus of Saxoferrato
conceived the corporation in essentially legal terms, Baldus expressly
connected the corporation theory to the ancient, biological and
political concept of the body politic. For Baldus, not only was man, in Aristotelian terms, a "political animal", but the whole populus, the body of the people, formed a type of political animal in itself: a populus "has government as part of [its] existence, just as every animal is ruled by its own spirit and soul". Baldus equated the body politic with the respublica,
the state or realm, stating that it "cannot die, and for this reason it
is said that it has no heir, because it always lives on in itself". From here, the image of the body politic became prominent in the medieval imagination. In Canto XVIII of his Paradiso, for instance, Dante,
writing in the early 14th century, presents the Roman Empire as a
corporate body in the form of an imperial eagle, its body made of souls. The French court writer Christine de Pizan discussed the concept at length in her Book of the Body Politic (1407).
The idea of the body politic, rendered in legal terms through corporation theory, also drew natural comparison to the theological concept of the church as a corpus mysticum, the mystical body of Christ. The concept of the people as a corpus mysticum also featured in Baldus, and the idea that the realm of France was a corpus mysticum formed an important part of late medieval French jurisprudence. Jean de Terrevermeille [fr],
around 1418–19, described the French laws of succession as established
by the "whole civic or mystical body of the realm", and the Parlement of Paris in 1489 proclaimed itself a "mystical body" composed of both ecclesiastics and laymen, representing the "body of the king".
From at least the 14th century, the doctrine developed that the French
kings were mystically married to the body politic; at the coronation of Henry II in 1547, he was said to have "solemnly married his realm". The English jurist John Fortescue also invoked the "mystical body" in his De Laudibus Legum Angliae
(c. 1470): just as a physical body is "held together by the nerves",
the mystical body of the realm is held together by the law, and
Just as the physical body grows out
of the embryo, regulated by one head, so does there issue from the
people the kingdom, which exists as a corpus mysticum governed by one man as head.
The king's body politic
In England
In Tudor and Stuart England, the concept of the body politic was given a peculiar additional significance through the idea of the king's two bodies, the doctrine discussed by the German-American medievalist Ernst Kantorowicz in his eponymous work.
This legal doctrine held that the monarch had two bodies: the physical
"king body natural" and the immortal "King body politic". Upon the
"demise" of an individual king, his body natural fell away, but the body
politic lived on. This was an indigenous development of English law without a precise equivalent in the rest of Europe. Extending the identification of the body politic as a corporation, English jurists argued that the Crown was a "corporation sole":
a corporation made up of one body politic that was at the same time the
body of the realm and its parliamentary estates, and also the body of
the royal dignity itself—two concepts of the body politic that were
conflated and fused.
Elizabethan jurists held that the immaturity of Edward VI's body natural was expunged by his body politic.
The development of the doctrine of the king's two bodies can be traced in the Reports of Edmund Plowden. In the 1561 Case of the Duchy of Lancaster, which concerned whether an earlier gift of land made by Edward VI
could be voided on account of his "nonage", that is, his immaturity,
the judges held that it could not: the king's "Body politic, which is
annexed to his Body natural, takes away the Imbecility of his Body
natural". The king's body politic, then, "that cannot be seen or handled", annexes the body natural and "wipes away" all its defects. What was more, the body politic rendered the king immortal as an individual: as the judges in the case Hill v. Grange
argued in 1556, once the king had made an act, "he as King never dies,
but the King, in which Name it has Relation to him, does ever
continue"—thus, they held, Henry VIII was still "alive", a decade after his physical death.
The doctrine of the two bodies could serve to limit the powers of the real king. When Edward Coke, Chief Justice of the Common Pleas
at the time, reported the way in which judges had differentiated the
bodies in 1608, he noted that it was the "natural body" of the king that
was created by God—the "politic body", by contrast, was "framed by the
policy of man". In the Case of Prohibitions of the same year, Coke denied the king "in his own person" any right to administer justice or order arrests. Finally, in its declaration of 27 May 1642 shortly before the start of the English Civil War, Parliament drew on the theory to invoke the powers of the body politic of Charles I against his body natural, stating:
What they [Parliament] do herein,
hath the Stamp of Royal Authority, although His Majesty seduced by evil
Counsel, do in His own Person, oppose, or interrupt the same. For the
King's Supreme Power, and Royal Pleasure, is exercised and declared in
this High Court of Law, and Council, after a more eminent and obligatory
manner, than it can be by any personal Act or Resolution of His Own.
The 18th century jurist William Blackstone, in Book I of his Commentaries on the Laws of England (1765), summarised the doctrine of the king's body politic as it subsequently developed after the Restoration: the king "in his political capacity" manifests "absolute perfection"; he can "do no wrong", nor even is he capable of "thinking
wrong"; he can have no defect, and is never in law "a minor or under
age". Indeed, Blackstone says, if an heir to the throne should accede
while "attainted of treason or felony", his assumption of the crown
"would purge the attainder ipso facto". The king manifests "absolute immortality": "Henry, Edward, or George may die; but the king survives them all". Soon after the appearance of the Commentaries, however, Jeremy Bentham mounted an extensive attack on Blackstone which the historian Quentin Skinner describes as "almost lethal" to the theory: legal fictions like the body politic, Bentham argued, were conducive to royal absolutism
and should be entirely avoided in law. Bentham's position dominated
later British legal thinking, and though aspects of the theory of the
body politic would survive in subsequent jurisprudence, the idea of the
Crown as a corporation sole was widely critiqued.
In the late 19th century, Frederic William Maitland
revived the legal discourse of the king's two bodies, arguing that the
concept of the Crown as corporation sole had originated from the
amalgamation of medieval civil law with the law of church property.
He proposed, in contrast, to view the Crown as an ordinary corporation
aggregate, that is, a corporation of many people, with a view to
describing the legal personhood of the state.
In France
A related but contrasting concept in France was the doctrine termed by Sarah Hanley the king's one body, summarised by Jean Bodin in his own 1576 pronouncement that "the king never dies".
Rather than distinguishing the immortal body politic from the mortal
body natural of the king, as in the English theory, the French doctrine
conflated the two, arguing that the Salic law
had established a single king body politic and natural that constantly
regenerated through the biological reproduction of the royal line. The body politic, on this account, was biological and necessarily male, and 15th century French jurists such as Jean Juvénal des Ursins
argued on this basis for the exclusion of female heirs to the
crown—since, they argued, the king of France was a "virile office". In the ancien régime,
the king's heir was held to assimilate the body politic of the old king
in a physical "transfer of corporeality" upon his accession.
Aside from the doctrine of the king's two bodies, the conventional
image of the whole of the realm as a body politic had also remained in
use in Stuart England: James I compared the office of the king to "the office of the head towards the body". Upon the outbreak of the English Civil War in 1642, however, parliamentarians such as William Bridge
put forward the argument that the "ruling power" belonged originally to
"the whole people or body politicke", who could revoke it from the
monarch. The execution of Charles I in 1649 made necessary a radical revision of the whole concept. In 1651, Thomas Hobbes's Leviathan
made a decisive contribution to this effect, reviving the concept while
endowing it with new features. Against the parliamentarians, Hobbes
maintained that sovereignty was absolute and the head could certainly
not be "of lesse power" than the body of the people; against the royal
absolutists, however, he developed the idea of a social contract,
emphasising that the body politic—Leviathan, the "mortal god"—was
fictional and artificial rather than natural, derived from an original
decision by the people to constitute a sovereign.
Hobbes's theory of the body politic exercised an important
influence on subsequent political thinkers, who both repeated and
modified it. Republican partisans of the Commonwealth presented alternative figurations of the metaphor in defence of the parliamentarian model. James Harrington, in his 1656 Commonwealth of Oceana,
argued that "the delivery of a Model Government ... is no less than
political Anatomy"; it must "imbrace all those Muscles, Nerves, Arterys
and Bones, which are necessary to any Function of a well order'd
Commonwealth". Invoking William Harvey's recent discovery of the circulatory system, Harrington presented the body politic as a dynamic system of political circulation, comparing his ideal bicameral legislature, for example, to the ventricles of the human heart. In contrast to Hobbes, the "head" was once more dependent on the people: the execution of the law must follow the law itself, so that "Leviathan may see, that the hand or sword that executeth the Law is in it, and not above it". In Germany, Samuel von Pufendorf
recapitulated Hobbes's explanation of the origin of the state as a
social contract, but extended his notion of personhood to argue that the
state must be a specifically moral person with a rational nature, and
not simply coercive power.
In the 18th century, Hobbes's theory of the state as an
artificial body politic gained wide acceptance both in Britain and
continental Europe. Thomas Pownall, later the British governor of Massachusetts and a proponent of American liberty, drew on Hobbes's theory in his 1752 Principles of Polity to argue that "the whole Body politic" should be conceived as "one Person"; states were "distinct Persons and independent". At around the same time, the Swiss jurist Emer de Vattel
pronounced that "states are bodies politic", "moral persons" with their
own "understanding and ... will", a statement that would become
accepted international law.
The tension between organic understandings of the body politic
and theories emphasizing its artificial character formed a theme in
English political debates in this period. Writing in 1780, during the American Revolutionary War, the British reformist John Cartwright
emphasised the artificial and immortal character of the body politic in
order to refute the use of biological analogies in conservative
rhetoric. Arguing that it was better conceived as a machine operating by the "due action and re-action of the ... springs of the constitution" than a human body, he termed "the body
politic" a "careless figurative expression": "It is not corporeal ...
not formed from the dust of the earth. It is purely intellectual; and
its life-spring is truth."
Modern law
The English term "body politic" is sometimes used in modern legal contexts to describe a type of legal person, typically the state itself or an entity connected to it. A body politic is a type of taxable legal person in British law, for example, and likewise a class of legal person in Indian law. In the United States, a municipal corporation is considered a body politic, as opposed to a private body corporate. The U.S. Supreme Court affirmed the theory of the state as an artificial body politic in the 1851 case Cotton v. United States,
declaring that "every sovereign State is of necessity a body politic,
or artificial person, and as such capable of making contracts and
holding property, both real and personal", and differentiated the United
States' powers as a sovereign from its rights as a body politic.
Organicism is the philosophical position that states that the universe and its various parts (including human societies) ought to be considered alive and naturally ordered, much like a living organism. Vital to the position is the idea that organicistic elements are not dormant "things" per se
but rather dynamic components in a comprehensive system that is, as a
whole, everchanging. Organicism is related to but remains distinct from holism
insofar as it prefigures holism; while the latter concept is applied
more broadly to universal part-whole interconnections such as in
anthropology and sociology, the former is traditionally applied only in
philosophy and biology. Furthermore, organicism is incongruous with reductionism because of organicism's consideration of "both bottom-up and top-down causation." Regarded as a fundamental tenet in natural philosophy, organicism has remained a vital current in modern thought, alongside both reductionism and mechanism, that has guided scientific inquiry since the early 17th century.
Though there remains dissent among scientific historians concerning organicism's pregeneration, most scholars agree on Ancient Athens as its birthplace. Surfacing in Athenian writing in the 4th-century BC, Plato
was among the first philosophers to consider the universe an
intelligent living (almost sentient) being, which he posits in his Philebus and Timaeus. At the turn of the 18th-century, Immanuel Kant
championed a revival of organicisitic thought by stressing, in his
written works, "the inter-relatedness of the organism and its parts[,]
and the circular causality" inherent to the inextricable entanglement of
the greater whole.
Organicism flourished for a period during the German romanticism intellectual movement and was a position considered by Friedrich Wilhelm Joseph Schelling to be an important principle in the burgeoning field of biological studies. Within contemporary biology, organicism stresses the organization (particularly the self-organizing properties) rather than the composition (the reduction into biological components) of organisms. John Scott Haldane
was the first modern biologist to use the term to expand his
philosophical stance in 1917; other 20th-century academics and
professionals, such as Theodor Adorno and Albert Dalcq, have followed in Haldane's wake.
The French zoologist Yves Delage, in his seminal text L'Hérédité Et Les Grands Problèmes de la Biologie Générale, described organicism thus:
[L]ife,
the form of the body, the properties and characters of its diverse
parts, as resulting from the reciprocal play or struggle of all its
elements, cells, fibres, tissues, organs, which act the one on the
other, modify one the other, allot among them each its place and part,
and lead all together to the final result, giving thus the appearance of
a consensus, or a pre-established harmony, where in reality there is
nothing but the result of independent phenomena.
In philosophy
Organicism as a doctrine rejects mechanism and reductionism
(doctrines that claim that the smallest parts by themselves explain the
behavior of larger organized systems of which they are a part).
However, organicism also rejects vitalism, the doctrine that there is a vital force different from physical forces that accounts for living things. As Fritjof Capra
puts it, both schools, organicism and vitalism, were born from the
quest for getting rid of the Cartesian picture of reality, a view that
has been claimed to be the most destructive paradigm nowadays, from
science to politics.
A number of biologists in the early to mid-twentieth century
embraced organicism. They wished to reject earlier vitalisms but also to
stress that whole organism biology was not fully explainable by atomic
mechanism. The larger organization of an organic system has features
that must be taken into account to explain its behavior.
Scott Gilbert and Sahotra Sarkar distinguish organicism from
holism to avoid what they see as the vitalistic or spiritualistic
connotations of holism. Val Dusek notes that holism contains a continuum
of degrees of the top-down control of organization, ranging from monism
(the doctrine that the only complete object is the whole universe, or
that there is only one entity, the universe) to organicism, which allows
relatively more independence of the parts from the whole, despite the
whole being more than the sum of the parts, and/or the whole exerting
some control on the behavior of the parts.
Still more independence is present in relational holism. This
doctrine does not assert top-down control of the whole over its parts,
but does claim that the relations of the parts are essential to
explanation of behavior of the system. Aristotle and early modern
philosophers and scientists tended to describe reality as made of
substances and their qualities, and to neglect relations. Gottfried Wilhelm Leibniz
showed the bizarre conclusions to which a doctrine of the non-existence
of relations led. Twentieth century philosophy has been characterized
by the introduction of and emphasis on the importance of relations,
whether in symbolic logic, in phenomenology, or in metaphysics.
William Wimsatt
has suggested that the number of terms in the relations considered
distinguishes reductionism from holism. Reductionistic explanations
claim that two or at most three term relations are sufficient to account
for the system's behavior. At the other extreme the system could be
considered as a single ten to the twenty-sixth term relation, for
instance.
Organicism has also been used to characterize notions put forth by
various late 19th-century social scientists who considered human society
to be analogous to an organism, and individual humans to be analogous
to the cells of an organism. This sort of organicist sociology was
articulated by Alfred Espinas, Paul von Lilienfeld, Jacques Novicow, Albert Schäffle, Herbert Spencer, and René Worms, among others.
Thomas Hobbes arguably put forward a form of organicism. In the Leviathan,
he argued that the state is like a secular God whose constituents
(individual people) make up a larger organism. However, the body of the
Leviathan is composed of many human faces (all looking outwards from the
body), and these faces do not symbolize different organs of a complex
organism but the individual people who themselves have consented to the
social contract, and thereby ceded their power to the Leviathan. That
the Leviathan is more like a constructed machine than like a literal
organism is perfectly in line with Hobbes' elementaristic individualism
and mechanical materialism.
Some forms of organicism have intellectually and politically
controversial, or suspect, associations. "Holism" in terms of the
doctrine that the whole is more than the sum of its parts, often used
synonymously with organicism, or as a broader category under which
organicism falls, has been co-opted in recent decades by proponents of "holistic medicine" and New Age thought.[citation needed]Dialectical materialism in the Soviet Union also made appeals to an holistic and organicist approach, stemming from Hegel via Karl Marx's co-worker Friedrich Engels, again giving a controversial political association to organicism. Adolf Hitler himself along with other members of the National Socialist German Workers' Party (German: Nationalsozialistische Deutsche Arbeiterpartei, NSDAP) in the Weimar Republic
(1918–1933) were greatly influenced by several 19th- and early
20th-century thinkers and proponents of philosophical, onto-epistemic,
and theoretical perspectives on ecological anthropology, scientific racism, holistic science, and organicism regarding the constitution of complex systems and theorization of organic-racial societies. In particular, one of the most significant ideological influences on the Nazis was the 19th-century German nationalist philosopher Johann Gottlieb Fichte,
whose works had served as an inspiration to Hitler and other Nazi Party
members, and whose ideas were implemented among the philosophical and
ideological foundations of Nazi-oriented Völkisch nationalism.
In
breathing entities, cells, the smallest unit of life, were first
observed in the 17th century, when the multifaceted equipment microscope
was conceived. Before that period, the individual organisms were
studied as a whole in a field known as organismic biology; that area of
research remains an important component of the biological sciences. Further, as Capra
puts it, during the early 1900s, the quantum researchers struggled with
the same paradigm shift from "the parts to the whole" that culminated
into the scholars of organismic biology.
In biology organicism considers that the observable structures of
life, its overall form and the properties and characteristics of its
component parts are a result of the reciprocal play of all the
components on each other. Examples of 20th century biologists who were organicists are Ross Harrison, Paul Weiss, and Joseph Needham. Donna Haraway discusses them in her first book Crystals, Fabrics, and Fields. John Scott Haldane (father of J. B. S. Haldane), William Emerson Ritter, Edward Stuart Russell, Joseph Henry Woodger, Ludwig von Bertalanffy, and Ralph Stayner Lillie are other early twentieth century organicists. Robert Rosen,
founder of "Relational Biology" provided a comprehensive mathematical
and category-theoretic treatment of irreducible causal relations he
believed to be responsible for life.
In ecology, "organicism" and "organicistic" (or "organismic") are used to designate theories which conceptualize populations, especially, ecological communities or ecosystems, according to the model of the individual organism. As such, "organicism" is sometimes used interchangeably with "holism," although there are versions of holism that are not organicistic/organismic but individualistic.
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