Statement.

A choice function is a function "f", defined on a collection "X" of nonempty sets, such that for every set "A" in "X", "f"("A") is an element of "A". With this concept, the axiom can be stated: Formally, this may be expressed as follows:  Thus, the negation of the axiom of choice states that there exists a collection of nonempty sets that has no choice function.  Each choice function on a collection "X" of nonempty sets is an element of the Cartesian product of the sets in "X". This is not the most general situation of a Cartesian product of a family of sets, where a given set can occur more than once as a factor; however, one can focus on elements of such a product that select the same element every time a given set appears as factor, and such elements correspond to an element of the Cartesian product of all "distinct" sets in the family. The axiom of choice asserts the existence of such elements; it is therefore equivalent to:

Nomenclature ZF, AC, and ZFC.

In this article and other discussions of the Axiom of Choice the following abbreviations are common:

Variants.

There are many other equivalent statements of the axiom of choice. These are equivalent in the sense that, in the presence of other basic axioms of set theory, they imply the axiom of choice and are implied by it.  One variation avoids the use of choice functions by, in effect, replacing each choice function with its range. This guarantees for any partition of a set "X" the existence of a subset "C" of "X" containing exactly one element from each part of the partition.  Another equivalent axiom only considers collections "X" that are essentially powersets of other sets: Authors who use this formulation often speak of the "choice function on A", but be advised that this is a slightly different notion of choice function. Its domain is the powerset of "A" (with the empty set removed), and so makes sense for any set "A", whereas with the definition used elsewhere in this article, the domain of a choice function on a "collection of sets" is that collection, and so only makes sense for sets of sets. With this alternate notion of choice function, the axiom of choice can be compactly stated as which is equivalent to The negation of the axiom can thus be expressed as:

Restriction to finite sets.

The statement of the axiom of choice does not specify whether the collection of nonempty sets is finite or infinite, and thus implies that every finite collection of nonempty sets has a choice function. However, that particular case is a theorem of the Zermelo–Fraenkel set theory without the axiom of choice (ZF); it is easily proved by mathematical induction. In the even simpler case of a collection of "one" set, a choice function just corresponds to an element, so this instance of the axiom of choice says that every nonempty set has an element; this holds trivially. The axiom of choice can be seen as asserting the generalization of this property, already evident for finite collections, to arbitrary collections.

Usage.

Until the late 19th century, the axiom of choice was often used implicitly, although it had not yet been formally stated. For example, after having established that the set "X" contains only non-empty sets, a mathematician might have said "let "F(s)" be one of the members of "s" for all "s" in "X"" to define a function "F". In general, it is impossible to prove that "F" exists without the axiom of choice, but this seems to have gone unnoticed until Zermelo.  Not every situation requires the axiom of choice. For finite sets "X", the axiom of choice follows from the other axioms of set theory. In that case it is equivalent to saying that if we have several (a finite number of) boxes, each containing at least one item, then we can choose exactly one item from each box. Clearly we can do this: We start at the first box, choose an item; go to the second box, choose an item; and so on. The number of boxes is finite, so eventually our choice procedure comes to an end. The result is an explicit choice function: a function that takes the first box to the first element we chose, the second box to the second element we chose, and so on. (A formal proof for all finite sets would use the principle of mathematical induction to prove "for every natural number "k", every family of "k" nonempty sets has a choice function.") This method cannot, however, be used to show that every countable family of nonempty sets has a choice function, as is asserted by the axiom of countable choice. If the method is applied to an infinite sequence ("X" : "i"∈ω) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no "limiting" choice function can be constructed, in general, in ZF without the axiom of choice.

Examples.

The nature of the individual nonempty sets in the collection may make it possible to avoid the axiom of choice even for certain infinite collections. For example, suppose that each member of the collection "X" is a nonempty subset of the natural numbers. Every such subset has a smallest element, so to specify our choice function we can simply say that it maps each set to the least element of that set. This gives us a definite choice of an element from each set, and makes it unnecessary to apply the axiom of choice.  The difficulty appears when there is no natural choice of elements from each set. If we cannot make explicit choices, how do we know that our set exists? For example, suppose that "X" is the set of all non-empty subsets of the real numbers. First we might try to proceed as if "X" were finite. If we try to choose an element from each set, then, because "X" is infinite, our choice procedure will never come to an end, and consequently, we shall never be able to produce a choice function for all of "X". Next we might try specifying the least element from each set. But some subsets of the real numbers do not have least elements. For example, the open interval (0,1) does not have a least element: if "x" is in (0,1), then so is "x"/2, and "x"/2 is always strictly smaller than "x". So this attempt also fails.  Additionally, consider for instance the unit circle "S", and the action on "S" by a group "G" consisting of all rational rotations. Namely, these are rotations by angles which are rational multiples of "π". Here "G" is countable while "S" is uncountable. Hence "S" breaks up into uncountably many orbits under "G". Using the axiom of choice, we could pick a single point from each orbit, obtaining an uncountable subset "X" of "S" with the property that all of its translates by G are disjoint from "X". The set of those translates partitions the circle into a countable collection of disjoint sets, which are all pairwise congruent. Since "X" is not measurable for any rotation-invariant countably additive finite measure on "S", finding an algorithm to select a point in each orbit requires the axiom of choice. See non-measurable set for more details.  The reason that we are able to choose least elements from subsets of the natural numbers is the fact that the natural numbers are well-ordered: every nonempty subset of the natural numbers has a unique least element under the natural ordering. One might say, "Even though the usual ordering of the real numbers does not work, it may be possible to find a different ordering of the real numbers which is a well-ordering. Then our choice function can choose the least element of every set under our unusual ordering." The problem then becomes that of constructing a well-ordering, which turns out to require the axiom of choice for its existence; every set can be well-ordered if and only if the axiom of choice holds.

Criticism and acceptance.

A proof requiring the axiom of choice may establish the existence of an object without explicitly defining the object in the language of set theory. For example, while the axiom of choice implies that there is a well-ordering of the real numbers, there are models of set theory with the axiom of choice in which no well-ordering of the reals is definable. Similarly, although a subset of the real numbers that is not Lebesgue measurable can be proved to exist using the axiom of choice, it is consistent that no such set is definable.  The axiom of choice proves the existence of these intangibles (objects that are proved to exist, but which cannot be explicitly constructed), which may conflict with some philosophical principles. Because there is no canonical well-ordering of all sets, a construction that relies on a well-ordering may not produce a canonical result, even if a canonical result is desired (as is often the case in category theory). This has been used as an argument against the use of the axiom of choice.  Another argument against the axiom of choice is that it implies the existence of objects that may seem counterintuitive. One example is the Banach–Tarski paradox which says that it is possible to decompose the 3-dimensional solid unit ball into finitely many pieces and, using only rotations and translations, reassemble the pieces into two solid balls each with the same volume as the original. The pieces in this decomposition, constructed using the axiom of choice, are non-measurable sets.  Despite these seemingly paradoxical facts, most mathematicians accept the axiom of choice as a valid principle for proving new results in mathematics. The debate is interesting enough, however, that it is considered of note when a theorem in ZFC (ZF plus AC) is logically equivalent (with just the ZF axioms) to the axiom of choice, and mathematicians look for results that require the axiom of choice to be false, though this type of deduction is less common than the type which requires the axiom of choice to be true.  It is possible to prove many theorems using neither the axiom of choice nor its negation; such statements will be true in any model of ZF, regardless of the truth or falsity of the axiom of choice in that particular model. The restriction to ZF renders any claim that relies on either the axiom of choice or its negation unprovable. For example, the Banach–Tarski paradox is neither provable nor disprovable from ZF alone: it is impossible to construct the required decomposition of the unit ball in ZF, but also impossible to prove there is no such decomposition. Similarly, all the statements listed below which require choice or some weaker version thereof for their proof are unprovable in ZF, but since each is provable in ZF plus the axiom of choice, there are models of ZF in which each statement is true. Statements such as the Banach–Tarski paradox can be rephrased as conditional statements, for example, "If AC holds, then the decomposition in the Banach–Tarski paradox exists." Such conditional statements are provable in ZF when the original statements are provable from ZF and the axiom of choice.

In constructive mathematics.

As discussed above, in ZFC, the axiom of choice is able to provide "nonconstructive proofs" in which the existence of an object is proved although no explicit example is constructed. ZFC, however, is still formalized in classical logic. The axiom of choice has also been thoroughly studied in the context of constructive mathematics, where non-classical logic is employed. The status of the axiom of choice varies between different varieties of constructive mathematics.  In Martin-Löf type theory and higher-order Heyting arithmetic, the appropriate statement of the axiom of choice is (depending on approach) included as an axiom or provable as a theorem. Errett Bishop argued that the axiom of choice was constructively acceptable, saying  In constructive set theory, however, Diaconescu's theorem shows that the axiom of choice implies the law of excluded middle (unlike in Martin-Löf type theory, where it does not). Thus the axiom of choice is not generally available in constructive set theory. A cause for this difference is that the axiom of choice in type theory does not have the extensionality properties that the axiom of choice in constructive set theory does.  Some results in constructive set theory use the axiom of countable choice or the axiom of dependent choice, which do not imply the law of the excluded middle in constructive set theory. Although the axiom of countable choice in particular is commonly used in constructive mathematics, its use has also been questioned.

Independence.

In 1938, Kurt Gödel showed that the "negation" of the axiom of choice is not a theorem of ZF by constructing an inner model (the constructible universe) which satisfies ZFC and thus showing that ZFC is consistent if ZF itself is consistent. In 1963, Paul Cohen employed the technique of forcing, developed for this purpose, to show that, assuming ZF is consistent, the axiom of choice itself is not a theorem of ZF. He did this by constructing a much more complex model which satisfies ZF¬C (ZF with the negation of AC added as axiom) and thus showing that ZF¬C is consistent.  Together these results establish that the axiom of choice is logically independent of ZF. The assumption that ZF is consistent is harmless because adding another axiom to an already inconsistent system cannot make the situation worse. Because of independence, the decision whether to use the axiom of choice (or its negation) in a proof cannot be made by appeal to other axioms of set theory. The decision must be made on other grounds.  One argument given in favor of using the axiom of choice is that it is convenient to use it because it allows one to prove some simplifying propositions that otherwise could not be proved. Many theorems which are provable using choice are of an elegant general character: every ideal in a ring is contained in a maximal ideal, every vector space has a basis, and every product of compact spaces is compact. Without the axiom of choice, these theorems may not hold for mathematical objects of large cardinality.  The proof of the independence result also shows that a wide class of mathematical statements, including all statements that can be phrased in the language of Peano arithmetic, are provable in ZF if and only if they are provable in ZFC. Statements in this class include the statement that P = NP, the Riemann hypothesis, and many other unsolved mathematical problems. When one attempts to solve problems in this class, it makes no difference whether ZF or ZFC is employed if the only question is the existence of a proof. It is possible, however, that there is a shorter proof of a theorem from ZFC than from ZF.  The axiom of choice is not the only significant statement which is independent of ZF. For example, the generalized continuum hypothesis (GCH) is not only independent of ZF, but also independent of ZFC. However, ZF plus GCH implies AC, making GCH a strictly stronger claim than AC, even though they are both independent of ZF.

Stronger axioms.

The axiom of constructibility and the generalized continuum hypothesis each imply the axiom of choice and so are strictly stronger than it. In class theories such as Von Neumann–Bernays–Gödel set theory and Morse–Kelley set theory, there is an axiom called the axiom of global choice that is stronger than the axiom of choice for sets because it also applies to proper classes. The axiom of global choice follows from the axiom of limitation of size.

Equivalents.

There are important statements that, assuming the axioms of ZF but neither AC nor ¬AC, are equivalent to the axiom of choice. The most important among them are Zorn's lemma and the well-ordering theorem. In fact, Zermelo initially introduced the axiom of choice in order to formalize his proof of the well-ordering theorem.

Category theory.

There are several results in category theory which invoke the axiom of choice for their proof. These results might be weaker than, equivalent to, or stronger than the axiom of choice, depending on the strength of the technical foundations. For example, if one defines categories in terms of sets, that is, as sets of objects and morphisms (usually called a small category), or even locally small categories, whose hom-objects are sets, then there is no category of all sets, and so it is difficult for a category-theoretic formulation to apply to all sets. On the other hand, other foundational descriptions of category theory are considerably stronger, and an identical category-theoretic statement of choice may be stronger than the standard formulation, à la class theory, mentioned above.  Examples of category-theoretic statements which require choice include:

Weaker forms.

There are several weaker statements that are not equivalent to the axiom of choice, but are closely related. One example is the axiom of dependent choice (DC). A still weaker example is the axiom of countable choice (AC or CC), which states that a choice function exists for any countable set of nonempty sets. These axioms are sufficient for many proofs in elementary mathematical analysis, and are consistent with some principles, such as the Lebesgue measurability of all sets of reals, that are disprovable from the full axiom of choice.  Other choice axioms weaker than axiom of choice include the Boolean prime ideal theorem and the axiom of uniformization. The former is equivalent in ZF to the existence of an ultrafilter containing each given filter, proved by Tarski in 1930.

Results requiring AC (or weaker forms) but weaker than it.

One of the most interesting aspects of the axiom of choice is the large number of places in mathematics that it shows up. Here are some statements that require the axiom of choice in the sense that they are not provable from ZF but are provable from ZFC (ZF plus AC). Equivalently, these statements are true in all models of ZFC but false in some models of ZF.

Possibly equivalent implications of AC.

There are several historically important set-theoretic statements implied by AC whose equivalence to AC is open. The partition principle, which was formulated before AC itself, was cited by Zermelo as a justification for believing AC. In 1906 Russell declared PP to be equivalent, but whether the Partition Principle implies AC is still the oldest open problem in set theory, and the equivalences of the other statements are similarly hard old open problems. In every "known" model of ZF where choice fails, these statements fail too, but it is unknown if they can hold without choice.

Stronger forms of the negation of AC.

Now, consider stronger forms of the negation of AC. For example, if we abbreviate by BP the claim that every set of real numbers has the property of Baire, then BP is stronger than ¬AC, which asserts the nonexistence of any choice function on perhaps only a single set of nonempty sets. Strengthened negations may be compatible with weakened forms of AC. For example, ZF + DC + BP is consistent, if ZF is.  It is also consistent with ZF + DC that every set of reals is Lebesgue measurable; however, this consistency result, due to Robert M. Solovay, cannot be proved in ZFC itself, but requires a mild large cardinal assumption (the existence of an inaccessible cardinal). The much stronger axiom of determinacy, or AD, implies that every set of reals is Lebesgue measurable, has the property of Baire, and has the perfect set property (all three of these results are refuted by AC itself). ZF + DC + AD is consistent provided that a sufficiently strong large cardinal axiom is consistent (the existence of infinitely many Woodin cardinals).  Quine's system of axiomatic set theory, "New Foundations" (NF), takes its name from the title (“New Foundations for Mathematical Logic”) of the 1937 article which introduced it. In the NF axiomatic system, the axiom of choice can be disproved.

Statements consistent with the negation of AC.

There are models of Zermelo-Fraenkel set theory in which the axiom of choice is false. We shall abbreviate "Zermelo-Fraenkel set theory plus the negation of the axiom of choice" by ZF¬C. For certain models of ZF¬C, it is possible to prove the negation of some standard facts. Any model of ZF¬C is also a model of ZF, so for each of the following statements, there exists a model of ZF in which that statement is true. For each of the following statements, there is some model of ZF¬C where it is true:  For proofs, see.  Additionally, by imposing definability conditions on sets (in the sense of descriptive set theory) one can often prove restricted versions of the axiom of choice from axioms incompatible with general choice. This appears, for example, in the Moschovakis coding lemma.

Axiom of choice in type theory.

In type theory, a different kind of statement is known as the axiom of choice. This form begins with two types, σ and τ, and a relation "R" between objects of type σ and objects of type τ. The axiom of choice states that if for each "x" of type σ there exists a "y" of type τ such that "R"("x","y"), then there is a function "f" from objects of type σ to objects of type τ such that "R"("x","f"("x")) holds for all "x" of type σ: Unlike in set theory, the axiom of choice in type theory is typically stated as an axiom scheme, in which "R" varies over all formulas or over all formulas of a particular logical form.

Quotes.

This is a joke: although the three are all mathematically equivalent, many mathematicians find the axiom of choice to be intuitive, the well-ordering principle to be counterintuitive, and Zorn's lemma to be too complex for any intuition.  The observation here is that one can define a function to select from an infinite number of pairs of shoes by stating for example, to choose a left shoe. Without the axiom of choice, one cannot assert that such a function exists for pairs of socks, because left and right socks are (presumably) indistinguishable. Polish-American mathematician Jan Mycielski relates this anecdote in a 2006 article in the Notices of the AMS. This quote comes from the famous April Fools' Day article in the "computer recreations" column of the "Scientific American", April 1989.

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that "a Cartesian product of a collection of non-empty sets is non-empty". Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin, even if the collection is infinite. Formally, it states that for every indexed family formula_1 of nonempty sets there exists an indexed family formula_2 of elements such that formula_3 for every formula_4. The axiom of choice was formulated in 1904 by Ernst Zermelo in order to formalize his proof of the well-ordering theorem.

Das Auswahlaxiom ist ein Axiom der Zermelo-Fraenkel-Mengenlehre. Es wurde erstmals von Ernst Zermelo 1904 formuliert. Das Auswahlaxiom besagt, dass zu jeder Menge von nichtleeren Mengen eine Auswahlfunktion existiert, also eine Funktion, die jeder dieser nichtleeren Mengen ein Element derselben zuordnet und somit „auswählt“. Für endliche Mengen kann man das auch ohne dieses Axiom folgern, daher ist das Auswahlaxiom nur für unendliche Mengen interessant.


Etymology.

The word "zwetschge", plural "zwetschgen", is from the German. Variants of the word include: "Quetsch(e)" (Lorraine, Alsace, Luxembourg, and regionally in Germany); "Zwetschke" (regionally in Austria); and "Zwetsche" (regionally in Germany). These names, like "damson", are thought ultimately to derive from postulated Vulgar Latin *"davascena", altered from "damascena", meaning "of Damascus", reflexes of which appear mainly in Franco-Provençal, e.g. "daveigne" (Jura), "dav(d)gna" (Franche-Comté).  Another explanation says that the German word "zwetschge" originates from the Czech word "švestka" of same meaning. The Czech word originates from Latin "sebestena", as in "prunus sebestena" (mentioned by Mattioli). May be also related to Sebaste.

Description.

The zwetschge tree is often found in "streuobstwiesen". It grows to 6–10 m in height; older trees have spreading branches. The bark is brownish. The leaf is simple, 4–10 cm long, alternate, petiolate, crenulate, and elliptic. The blossom appears in April and May in the Northern Hemisphere, before or with foliation, and is white, greenish-white, or yellowish-green on two or three downy pedicels. The fruit is a freestone drupe. It is less round than other plums, its ends are more pointed and the groove is less pronounced.

Uses.

The red-brown wood is used in fine cabinetry.  The fruit, which ripens in August and September in the Northern Hemisphere, is a popular seasonal table fruit.  Zwetschgen hold their form well at oven temperatures and are much used in baking, for example in tarts such as "quetschentaart" and "zwetschgenkuchen". Zwetschgen are the sole ingredient in the traditional "powidl" jam of Austria and the Czech Republic, and the main ingredient in "schmootsch", a similar but spiced jam from Silesia. Fermented zwetschgen are distilled to make eaux de vie: "zwetschgenwasser" or "zwetsch" (in Austria, Germany, and Switzerland), "zwetschgeler" (in South Tyrol, Italy), and "quetsch" (in Alsace, France). Carlsbad plums are a candied zwetschgen confection named after Carlsbad (now Karlovy Vary) in the Czech Republic. "Szilvás gombóc" and "zwetschkenknödel" are potato dumplings with a zwetschgen filling in Hungary and Austria respectively, served as a sweet main course or as a dessert. At Christmas markets in Germany, for example the Christkindlesmarkt in Nuremberg, a "zwetschgenmännla" ("little zwetschge man") or "zwetschgenweibla" ("little zwetschge woman"), with a walnut head, a body of dried figs, and limbs of dried zwetschgen, is a popular treat.

Varieties.

More than a hundred varieties of zwetschge are grown in Central Europe. Examples include Cacaks Beste, Elena, Hauszwetschge, and Ortenauer.

The zwetschge (; "Prunus domestica" subsp. "domestica") is a fruit-bearing tree, or its fruit. It is a subspecies of the plum "Prunus domestica". The freestone fruit is similar to, but distinct from, the clingstone damson ("Prunus domestica" subsp. "insititia") and is especially popular in Central Europe.

Die Echte Zwetschge ("Prunus domestica" subsp. "domestica") ist eine Unterart der Pflaume ("Prunus domestica"). Sie wird in Europa, Westasien, Nordamerika sowie Nord- und Südafrika als Obstbaum angebaut.


Origins.

The ballad derives its name from medieval Scottish dance songs or "ballares" (L: "ballare", to dance), from which 'ballet' is also derived, as did the alternative rival form that became the French ballade. As a narrative song, their theme and function may originate from Scandinavian and Germanic traditions of storytelling that can be seen in poems such as "Beowulf". Musically they were influenced by the Minnelieder of the Minnesang tradition. The earliest example of a recognizable ballad in form in England is "Judas" in a 13th-century manuscript.

Ballad form.

Ballads were originally written to accompany dances, and so were composed in couplets with refrains in alternate lines. These refrains would have been sung by the dancers in time with the dance. Most northern and west European ballads are written in ballad stanzas or quatrains (four-line stanzas) of alternating lines of iambic (an unstressed followed by a stressed syllable) tetrameter (eight syllables) and iambic trimeter (six syllables), known as ballad meter. Usually, only the second and fourth line of a quatrain are rhymed (in the scheme a, b, c, b), which has been taken to suggest that, originally, ballads consisted of couplets (two lines) of rhymed verse, each of 14 syllables. This can be seen in this stanza from "Lord Thomas and Fair Annet":  The horse | fair Ann | et rode | upon | He amb | led like | the wind |, With sil | ver he | was shod | before, With burn | ing gold | behind |.  There is considerable variation on this pattern in almost every respect, including length, number of lines and rhyming scheme, making the strict definition of a ballad extremely difficult. In southern and eastern Europe, and in countries that derive their tradition from them, ballad structure differs significantly, like Spanish "romanceros", which are octosyllabic and use consonance rather than rhyme.  Ballads usually are heavily influenced by the regions in which they originate and use the common dialect of the people. Scotland's ballads in particular, both in theme and language, are strongly characterised by their distinctive tradition, even exhibiting some pre-Christian influences in the inclusion of supernatural elements such as travel to the Fairy Kingdom in the Scots ballad "Tam Lin". The ballads do not have any known author or correct version; instead, having been passed down mainly by oral tradition since the Middle Ages, there are many variations of each. The ballads remained an oral tradition until the increased interest in folk songs in the 18th century led collectors such as Bishop Thomas Percy (1729–1811) to publish volumes of popular ballads.  In all traditions most ballads are narrative in nature, with a self-contained story, often concise, and rely on imagery, rather than description, which can be tragic, historical, romantic or comic. Themes concerning rural laborers and their sexuality are common, and there are many ballads based on the Robin Hood legend. Another common feature of ballads is repetition, sometimes of fourth lines in succeeding stanzas, as a refrain, sometimes of third and fourth lines of a stanza and sometimes of entire stanzas.

Composition.

Scholars of ballads have been divided into "communalists", such as Johann Gottfried Herder (1744–1803) and the Brothers Grimm, who argue that ballads are originally communal compositions, and "individualists" such as Cecil Sharp, who assert that there was one single original author. Communalists tend to see more recent, particularly printed, broadside ballads of known authorship as a debased form of the genre, while individualists see variants as corruptions of an original text. More recently scholars have pointed to the interchange of oral and written forms of the ballad.

Transmission.

The transmission of ballads comprises a key stage in their re-composition. In romantic terms this process is often dramatized as a narrative of degeneration away from the pure 'folk memory' or 'immemorial tradition'. In the introduction to "Minstrelsy of the Scottish Border" (1802) the romantic poet and historical novelist Walter Scott argued a need to'remove obvious corruptions' in order to attempt to restore a supposed original. For Scott, the process of multiple recitations 'incurs the risk of impertinent interpolations from the conceit of one rehearser, unintelligible blunders from the stupidity of another, and omissions equally to be regretted, from the want of memory of a third.' Similarly, John Robert Moore noted 'a natural tendency to oblivescence'.

Classification.

European Ballads have been generally classified into three major groups: traditional, broadside and literary. In America a distinction is drawn between ballads that are versions of European, particularly British and Irish songs, and 'Native American ballads', developed without reference to earlier songs. A further development was the evolution of the blues ballad, which mixed the genre with Afro-American music. For the late 19th century the music publishing industry found a market for what are often termed sentimental ballads, and these are the origin of the modern use of the term 'ballad' to mean a slow love song.

Traditional ballads.

The traditional, classical or popular (meaning of the people) ballad has been seen as beginning with the wandering minstrels of late medieval Europe. From the end of the 15th century there are printed ballads that suggest a rich tradition of popular music. A reference in William Langland's "Piers Plowman" indicates that ballads about Robin Hood were being sung from at least the late 14th century and the oldest detailed material is Wynkyn de Worde's collection of Robin Hood ballads printed about 1495.  Early collections of English ballads were made by Samuel Pepys (1633–1703) and in the Roxburghe Ballads collected by Robert Harley, (1661–1724), which paralleled the work in Scotland by Walter Scott and Robert Burns. Inspired by his reading as a teenager of "Reliques of Ancient English Poetry" by Thomas Percy, Scott began collecting ballads while he attended Edinburgh University in the 1790s. He published his research from 1802 to 1803 in a three-volume work, "Minstrelsy of the Scottish Border". Burns collaborated with James Johnson on the multi-volume "Scots Musical Museum", a miscellany of folk songs and poetry with original work by Burns. Around the same time, he worked with George Thompson on "A Select Collection of Original Scottish Airs for the Voice".  Both Northern English and Southern Scots shared in the identified tradition of Border ballads, particularly evinced by the cross-border narrative in versions of "The Ballad of Chevy Chase" sometimes associated with the Lancashire-born sixteenth-century minstrel Richard Sheale.  It has been suggested that the increasing interest in traditional popular ballads during the eighteenth century was prompted by social issues such as the enclosure movement as many of the ballads deal with themes concerning rural laborers. James Davey has suggested that the common themes of sailing and naval battles may also have prompted the use (at least in England) of popular ballads as naval recruitment tools.  Key work on the traditional ballad was undertaken in the late 19th century in Denmark by Svend Grundtvig and for England and Scotland by the Harvard professor Francis James Child. They attempted to record and classify all the known ballads and variants in their chosen regions. Since Child died before writing a commentary on his work it is uncertain exactly how and why he differentiated the 305 ballads printed that would be published as "The English and Scottish Popular Ballads". There have been many different and contradictory attempts to classify traditional ballads by theme, but commonly identified types are the religious, supernatural, tragic, love ballads, historic, legendary and humorous. The traditional form and content of the ballad were modified to form the basis for twenty-three bawdy pornographic ballads that appeared in the underground Victorian magazine "The Pearl", which ran for eighteen issues between 1879 and 1880. Unlike the traditional ballad, these obscene ballads aggressively mocked sentimental nostalgia and local lore.

Broadsides.

Broadside ballads (also known as 'broadsheet','stall', 'vulgar' or 'come all ye' ballads) were a product of the development of cheap print in the 16th century. They were generally printed on one side of a medium to large sheet of poor quality paper. In the first half of the 17th century, they were printed in black-letter or gothic type and included multiple, eye-catching illustrations, a popular tune title, as well as an alluring poem. By the 18th century, they were printed in white letter or roman type and often without much decoration (as well as tune title). These later sheets could include many individual songs, which would be cut apart and sold individually as "slip songs." Alternatively, they might be folded to make small cheap books or "chapbooks" which often drew on ballad stories. They were produced in huge numbers, with over 400,000 being sold in England annually by the 1660s. Tessa Watt estimates the number of copies sold may have been in the millions. Many were sold by travelling chapmen in city streets or at fairs. The subject matter varied from what has been defined as the traditional ballad, although many traditional ballads were printed as broadsides. Among the topics were love, marriage, religion, drinking-songs, legends, and early journalism, which included disasters, political events and signs, wonders and prodigies.

Literary ballads.

Literary or lyrical ballads grew out of an increasing interest in the ballad form among social elites and intellectuals, particularly in the Romantic movement from the later 18th century. Respected literary figures Robert Burns and Walter Scott in Scotland collected and wrote their own ballads. Similarly in England William Wordsworth and Samuel Taylor Coleridge produced a collection of "Lyrical Ballads" in 1798 that included Coleridge's "The Rime of the Ancient Mariner". Wordsworth, Coleridge, and Keats were attracted to the simple and natural style of these folk ballads and tried to imitate it. At the same time in Germany Goethe cooperated with Schiller on a series of ballads, some of which were later set to music by Schubert. Later important examples of the poetic form included Rudyard Kipling's "Barrack-Room Ballads" (1892-6) and Oscar Wilde's "The Ballad of Reading Gaol" (1897).

Ballad operas.

In the 18th century ballad operas developed as a form of English stage entertainment, partly in opposition to the Italian domination of the London operatic scene. It consisted of racy and often satirical spoken (English) dialogue, interspersed with songs that are deliberately kept very short to minimize disruptions to the flow of the story. Rather than the more aristocratic themes and music of the Italian opera, the ballad operas were set to the music of popular folk songs and dealt with lower-class characters. Subject matter involved the lower, often criminal, orders, and typically showed a suspension (or inversion) of the high moral values of the Italian opera of the period. The first, most important and successful was "The Beggar's Opera" of 1728, with a libretto by John Gay and music arranged by John Christopher Pepusch, both of whom probably influenced by Parisian vaudeville and the burlesques and musical plays of Thomas d'Urfey (1653–1723), a number of whose collected ballads they used in their work. Gay produced further works in this style, including a sequel under the title "Polly". Henry Fielding, Colley Cibber, Arne, Dibdin, Arnold, Shield, Jackson of Exeter, Hook and many others produced ballad operas that enjoyed great popularity. Ballad opera was attempted in America and Prussia. Later it moved into a more pastoral form, like Isaac Bickerstaffe's "Love in a Village" (1763) and Shield's "Rosina" (1781), using more original music that imitated, rather than reproduced, existing ballads. Although the form declined in popularity towards the end of the 18th century its influence can be seen in light operas like that of Gilbert and Sullivan's early works like "The Sorcerer" as well as in the modern musical. In the 20th century, one of the most influential plays, Kurt Weill and Bertolt Brecht's (1928) "The Threepenny Opera" was a reworking of "The Beggar's Opera", setting a similar story with the same characters, and containing much of the same satirical bite, but only using one tune from the original. The term ballad opera has also been used to describe musicals using folk music, such as "The Martins and the Coys" in 1944, and Peter Bellamy's "The Transports" in 1977. The satiric elements of ballad opera can be seen in some modern musicals such as "Chicago" and "Cabaret".

Beyond Europe.

American ballads.

Some 300 ballads sung in North America have been identified as having origins in British traditional or broadside ballads. Examples include 'The Streets of Laredo', which was found in Britain and Ireland as 'The Unfortunate Rake'; however, a further 400 have been identified as originating in America, including among the best known, 'The Ballad of Davy Crockett' and 'Jesse James'. They became an increasing area of interest for scholars in the 19th century and most were recorded or catalogued by George Malcolm Laws, although some have since been found to have British origins and additional songs have since been collected. They are usually considered closest in form to British broadside ballads and in terms of style are largely indistinguishable, however, they demonstrate a particular concern with occupations, journalistic style and often lack the ribaldry of British broadside ballads.

Blues ballads.

The blues ballad has been seen as a fusion of Anglo-American and Afro-American styles of music from the 19th century. Blues ballads tend to deal with active protagonists, often anti-heroes, resisting adversity and authority, but frequently lacking a strong narrative and emphasising character instead. They were often accompanied by banjo and guitar which followed the blues musical format. The most famous blues ballads include those about John Henry and Casey Jones.

Bush ballads.

The ballad was taken to Australia by early settlers from Britain and Ireland and gained particular foothold in the rural outback. The rhyming songs, poems and tales written in the form of ballads often relate to the itinerant and rebellious spirit of Australia in The Bush, and the authors and performers are often referred to as bush bards. The 19th century was the golden age of bush ballads. Several collectors have catalogued the songs including John Meredith whose recording in the 1950s became the basis of the collection in the National Library of Australia. The songs tell personal stories of life in the wide open country of Australia. Typical subjects include mining, raising and droving cattle, sheep shearing, wanderings, war stories, the 1891 Australian shearers' strike, class conflicts between the landless working class and the squatters (landowners), and outlaws such as Ned Kelly, as well as love interests and more modern fare such as trucking. The most famous bush ballad is "Waltzing Matilda", which has been called "the unofficial national anthem of Australia".

Sentimental ballads.

Sentimental ballads, sometimes called "tear-jerkers" or "drawing-room ballads" owing to their popularity with the middle classes, had their origins in the early "Tin Pan Alley" music industry of the later 19th century. They were generally sentimental, narrative, strophic songs published separately or as part of an opera (descendants perhaps of broadside ballads, but with printed music, and usually newly composed). Such songs include "Little Rosewood Casket" (1870), "After the Ball" (1892) and "Danny Boy". The association with sentimentality led to the term "ballad" being used for slow love songs from the 1950s onwards. Modern variations include "jazz ballads", "pop ballads", ""rock ballads", "R&B ballads" and "power ballads".

A ballad is a form of verse, often a narrative set to music. Ballads derive from the medieval French "chanson balladée" or "ballade", which were originally "dance songs". Ballads were particularly characteristic of the popular poetry and song of Britain and Ireland from the later medieval period until the 19th century. They were widely used across Europe, and later in Australia, North Africa, North America and South America. Ballads are often 13 lines with an ABABBCBC form, consisting of couplets (two lines) of rhymed verse, each of 14 syllables. Another common form is ABAB or ABCB repeated, in alternating 8 and 6 syllable lines.

Das Wort Ballade entstammt der okzitanischen Sprache der südfranzösischen mittelalterlichen Trobadordichtung. Es bezeichnete ursprünglich eine Gattung des Tanzliedes. In der deutschsprachigen Literatur wird seit dem 18. Jahrhundert ein mehrstrophiges, erzählendes Gedicht als Ballade bezeichnet.


Synonyms.

"Tone quality" and "tone color" are synonyms for "timbre", as well as the ""texture" attributed to a single instrument". However, the word texture can also refer to the type of music, such as multiple, interweaving melody lines versus a singable melody accompanied by subordinate chords. Hermann von Helmholtz used the German "Klangfarbe" ("tone color"), and John Tyndall proposed an English translation, "clangtint", but both terms were disapproved of by Alexander Ellis, who also discredits "register" and "color" for their pre-existing English meanings. The sound of a musical instrument may be described with words such as "bright", "dark", "warm", "harsh", and other terms. There are also colors of noise, such as pink and white. In visual representations of sound, timbre corresponds to the shape of the image, while loudness corresponds to brightness; pitch corresponds to the y-shift of the spectrogram.

ASA definition.

The Acoustical Society of America (ASA) Acoustical Terminology definition 12.09 of timbre describes it as "that attribute of auditory sensation which enables a listener to judge that two nonidentical sounds, similarly presented and having the same loudness and pitch, are dissimilar", adding, "Timbre depends primarily upon the frequency spectrum, although it also depends upon the sound pressure and the temporal characteristics of the sound".

Attributes.

Timbre has been called "...the psychoacoustician's multidimensional waste-basket category for everything that cannot be labeled pitch or loudness." (; "cf." and ).  Many commentators have attempted to decompose timbre into component attributes. For example, J. F. Schouten (1968, 42) describes the "elusive attributes of timbre" as "determined by at least five major acoustic parameters", which Robert finds, "scaled to the concerns of much contemporary music":  An example of a tonal sound is a musical sound that has a definite pitch, such as pressing a key on a piano; a sound with a noiselike character would be white noise, the sound similar to that produced when a radio is not tuned to a station.  See also Psychoacoustic evidence below.

Harmonics.

The richness of a sound or note a musical instrument produces is sometimes described in terms of a sum of a number of distinct frequencies. The lowest frequency is called the "fundamental frequency", and the pitch it produces is used to name the note, but the fundamental frequency is not always the dominant frequency. The dominant frequency is the frequency that is most heard, and it is always a multiple of the fundamental frequency. For example, the dominant frequency for the transverse flute is double the fundamental frequency. Other significant frequencies are called overtones of the fundamental frequency, which may include harmonics and partials. Harmonics are whole number multiples of the fundamental frequency, such as ×2, ×3, ×4, etc. Partials are other overtones. There are also sometimes subharmonics at whole number "divisions" of the fundamental frequency. Most instruments produce harmonic sounds, but many instruments produce partials and inharmonic tones, such as cymbals and other indefinite-pitched instruments.  When the tuning note in an orchestra or concert band is played, the sound is a combination of 440 Hz, 880 Hz, 1320 Hz, 1760 Hz and so on. Each instrument in the orchestra or concert band produces a different combination of these frequencies, as well as harmonics and overtones. The sound waves of the different frequencies overlap and combine, and the balance of these amplitudes is a major factor in the characteristic sound of each instrument.  William Sethares wrote that just intonation and the western equal tempered scale are related to the harmonic spectra/timbre of many western instruments in an analogous way that the inharmonic timbre of the Thai renat (a xylophone-like instrument) is related to the seven-tone near-equal tempered pelog scale in which they are tuned. Similarly, the inharmonic spectra of Balinese metallophones combined with harmonic instruments such as the stringed rebab or the voice, are related to the five-note near-equal tempered slendro scale commonly found in Indonesian gamelan music.

Envelope.

The timbre of a sound is also greatly affected by the following aspects of its "envelope": attack time and characteristics, decay, sustain, release (ADSR envelope) and transients. Thus these are all common controls on professional synthesizers. For instance, if one takes away the attack from the sound of a piano or trumpet, it becomes more difficult to identify the sound correctly, since the sound of the hammer hitting the strings or the first blast of the player's lips on the trumpet mouthpiece are highly characteristic of those instruments. The envelope is the overall amplitude structure of a sound, so called because the sound just "fits" inside its envelope: what this means should be clear from a time-domain display of almost any interesting sound, zoomed out enough that the entire waveform is visible.

In music history.

Instrumental timbre played an increasing role in the practice of orchestration during the eighteenth and nineteenth centuries. Berlioz and Wagner made significant contributions to its development during the nineteenth century. For example, Wagner’s “Sleep motif” from Act 3 of his opera "Die Walküre", features a descending chromatic scale that passes through a gamut of orchestral timbres. First the woodwind (flute, followed by oboe), then the massed sound of strings with the violins carrying the melody, and finally the brass (French horns).Debussy, who composed during the last decades of the nineteenth and the first decades of the twentieth centuries, has been credited with elevating further the role of timbre: "To a marked degree the music of Debussy elevates timbre to an unprecedented structural status; already in "Prélude à l'après-midi d'un faune" the "color" of flute and harp functions referentially".  Mahler’s approach to orchestration illustrates the increasing role of differentiated timbres in music of the early twentieth century. Norman describes the following passage from the Scherzo movement of his Sixth Symphony, as "a seven-bar link to the trio consisting of an extension in diminuendo of the repeated As... though now rising in a succession of piled octaves which moreover leap-frog with Cs added to the As. The lower octaves then drop away and only the Cs remain so as to dovetail with the first oboe phrase of the trio." During these bars, Mahler passes the repeated notes through a gamut of instrumental colors, mixed and single: starting with horns and pizzicato strings, progressing through trumpet, clarinet, flute, piccolo and finally, oboe: See also Klangfarbenmelodie.  In rock music from the late 1960s to the 2000s, the timbre of specific sounds is important to a song. For example, in heavy metal music, the sonic impact of the heavily amplified, heavily distorted power chord played on electric guitar through very loud guitar amplifiers and rows of speaker cabinets is an essential part of the style's musical identity. You could not take the heavily amplified electric guitar part and substitute it with the same notes played on a grand piano or pipe organ.

Psychoacoustic evidence.

Often, listeners can identify an instrument, even at different pitches and loudness, in different environments, and with different players. In the case of the clarinet, acoustic analysis shows waveforms irregular enough to suggest three instruments rather than one. David suggests that this implies that "[C]ertain strong regularities in the acoustic waveform of the above instruments must exist which are invariant with respect to the above variables." However, Robert Erickson argues that there are few regularities and they do not explain our "...powers of recognition and identification." He suggests borrowing the concept of subjective constancy from studies of vision and visual perception.  Psychoacoustic experiments from the 1960s onwards tried to elucidate the nature of timbre. One method involves playing pairs of sounds to listeners, then using a multidimensional scaling algorithm to aggregate their dissimilarity judgments into a timbre space. The most consistent outcomes from such experiments are that brightness or spectral energy distribution, and the "bite", or rate and synchronicity and rise time, of the attack are important factors.

Tristimulus timbre model.

The concept of tristimulus originates in the world of color, describing the way three primary colors can be mixed together to create a given color. By analogy, the musical tristimulus measures the mixture of harmonics in a given sound, grouped into three sections. It is basically a proposal of reducing a huge number of sound partials, that can amount to dozens or hundreds in some cases, down to only three values. The first tristimulus measures the relative weight of the first harmonic; the second tristimulus measures the relative weight of the second, third, and fourth harmonics taken together; and the third tristimulus measures the relative weight of all the remaining harmonics (;, ): More evidences, studies and applications would be needed regarding this type of representation, in order to validate it.

Brightness.

The term "brightness" is also used in discussions of sound timbres, in a rough analogy with visual brightness. Timbre researchers consider brightness to be one of the perceptually strongest distinctions between sounds, and formalize it acoustically as an indication of the amount of high-frequency content in a sound, using a measure such as the spectral centroid.

In music, timbre (, ), also known as tone color or tone quality (from psychoacoustics), is the perceived sound quality of a musical note, sound or tone. Timbre distinguishes different types of sound production, such as choir voices and musical instruments, such as string instruments, wind instruments, and percussion instruments. It also enables listeners to distinguish different instruments in the same category (e.g., an oboe and a clarinet, both woodwind instruments).

Die Klangfarbe (auch das Timbre) ist in der Musik einer der Parameter des einzelnen Tons. Sie wird bestimmt durch dessen Klangspektrum, also das spezifische Gemisch aus Grund- oder 1. Partialton, Obertönen und Rauschanteilen sowie durch den zeitlichen Verlauf dieses Spektrums, die Lautstärke und weitere Parameter.


Etymology.

The name is derived from the word Perseidai (Greek : Περσείδαι), the sons of Perseus in Greek mythology.

Characteristics.

The stream of debris is called the Perseid cloud and stretches along the orbit of the comet Swift–Tuttle. The cloud consists of particles ejected by the comet as it travels on its 133-year orbit. Most of the particles have been part of the cloud for around a thousand years. However, there is also a relatively young filament of dust in the stream that was pulled off the comet in 1865, which can give an early mini-peak the day before the maximum shower. The dimensions of the cloud in the vicinity of the Earth are estimated to be approximately 0.1 astronomical units (AU) across and 0.8 AU along the latter's orbit, spread out by annual interactions with the Earth's gravity.  The shower is visible from mid-July each year, with the peak in activity between 9 and 14 August, depending on the particular location of the stream. During the peak, the rate of meteors reaches 60 or more per hour. They can be seen all across the sky; however, because of the shower's radiant in the constellation of Perseus, the Perseids are primarily visible in the Northern Hemisphere. As with many meteor showers the visible rate is greatest in the pre-dawn hours, since more meteoroids are scooped up by the side of the Earth moving forward into the stream, corresponding to local times between midnight and noon, as can be seen in the accompanying diagram. While many meteors arrive between dawn and noon, they are usually not visible due to daylight. Some can also be seen before midnight, often grazing the Earth's atmosphere to produce long bright trails and sometimes fireballs. Most Perseids burn up in the atmosphere while at heights above.

Historical observations and associations.

Some Catholics refer to the Perseids as the "tears of Saint Lawrence", suspended in the sky but returning to earth once a year on August 10, the canonical date of that saint's martyrdom in 258 AD. The saint is said to have been burned alive on a gridiron, and this tradition is almost certainly the origin of the Mediterranean folk legend that the shooting stars are the sparks of that fire and that during the night of August 9–10 its cooled embers appear in the ground under plants, and which are known as the "coal of Saint Lawrence". The transition in favor of the Catholic saint and his feast day on August 10 and away from pagan gods and their festivals, known as Christianization, was facilitated by the phonetic assonance of the Latin name Laurentius with Larentia.  In 1835, Adolphe Quetelet identified the shower as emanating from the constellation Perseus. In 1866, after the perihelion passage of Swift-Tuttle in 1862, the Italian astronomer Giovanni Virginio Schiaparelli discovered the link between meteor showers and comets. The finding is contained in an exchange of letters with Angelo Secchi.

In popular culture.

In his song "Rocky Mountain High", American singer-songwriter John Denver refers to his experience watching the Perseid meteor shower during a family camping trip in the mountains near Aspen, Colorado, with the chorus lyric, "I've seen it raining fire in the sky."  In the popular Japanese band Sandaime J Soul Brothers's song "R.Y.U.S.E.I" (Meteor), they describe the Perseid meteor as falling like an evening rain shower – its shooting stars like raindrops pulling their tails behind them.  In the song “RPG,” by Japanese band Sekai no Owari, the narrator mentions watching the Perseid meteor shower on the night something “precious to them fell apart.”  In his novel Against the Day, American novelist Thomas Pynchon refers to the Perseid meteor showers being watched by three characters west of the Dolores Valley after playing a game of tarot.

The Perseids are a prolific meteor shower associated with the comet Swift–Tuttle. The meteors are called the Perseids because the point from which they appear to hail (called the radiant) lies in the constellation Perseus.

Die Perseiden [] (Laurentiustränen, "Tränen des Laurentius") sind ein jährlich in der ersten Augusthälfte wiederkehrender Meteorstrom, der in den Tagen um den 12. August ein deutliches Maximum an Sternschnuppen aufweist. Oft erreichen sie als sogenannte Feuerkugeln sogar Venushelligkeit. Der Radiant, der scheinbare Ursprung dieses Stroms, liegt im namensgebenden Sternbild Perseus, nahe der Grenze zur Kassiopeia.


Definitions.

Docetism is broadly defined as any teaching that claims that Jesus' body was either absent or illusory. The term 'docetic' is rather nebulous. Two varieties were widely known. In one version, as in Marcionism, Christ was so divine that he could not have been human, since God lacked a material body, which therefore could not physically suffer. Jesus only "appeared" to be a flesh-and-blood man; his body was a phantasm. Other groups who were accused of docetism held that Jesus was a man in the flesh, but Christ was a separate entity who entered Jesus's body in the form of a dove at his baptism, empowered him to perform miracles, and abandoned him upon his death on the cross.

Christology and theological implications.

Docetism's origin within Christianity is obscure. Ernst Käsemann controversially defined the Christology of St John’s Gospel as "naïve docetism" in 1968. The ensuing debate reached an impasse as awareness grew that the very term "docetism", like "gnosticism", was difficult to define within the religio-historical framework of the debate. It has occasionally been argued that its origins were in heterodox Judaism or Oriental and Grecian philosophies. The alleged connection with Jewish Christianity would have reflected Jewish Christian concerns with the inviolability of (Jewish) monotheism. Docetic opinions seem to have circulated from very early times, 1 John 4:2 appearing explicitly to reject them. Some 1stcentury Christian groups developed docetic interpretations partly as a way to make Christian teachings more acceptable to pagan ways of thinking about divinity.  In his critique of the theology of Clement of Alexandria, Photius in his Myriobiblon held that Clement's views reflected a quasi-docetic view of the nature of Christ, writing that "[Clement] hallucinates that the Word was not incarnate but "only seems to be"." (ὀνειροπολεῖ καὶ μὴ σαρκωθῆναι τὸν λόγον ἀλλὰ "δόξαι".) In Clement's time, some disputes contended over whether Christ assumed the "psychic" flesh of mankind as heirs to Adam, or the "spiritual" flesh of the resurrection. Docetism largely died out during the first millennium AD.  The opponents against whom Ignatius of Antioch inveighs are often taken to be Monophysite docetists. In his letter to the Smyrnaeans, 7:1, written around 110AD, he writes: While these characteristics fit a Monophysite framework, a slight majority of scholars consider that Ignatius was waging a polemic on two distinct fronts, one Jewish, the other docetic; a minority holds that he was concerned with a group that commingled Judaism and docetism. Others, however, doubt that there was actual docetism threatening the churches, arguing that he was merely criticizing Christians who lived Jewishly or that his critical remarks were directed at an Ebionite or Cerinthian possessionist Christology, according to which Christ was a heavenly spirit that temporarily possessed Jesus.

Islam and docetism.

Some commentators have attempted to make a connection between Islam and Docetism using the following Quranic verse:  Some scholars accept that Islam was influenced by Manichaeism (Docetism) in this view. However the general consensus is that Manichaeism was not prevalent in Mecca in the 6th and 7th centuries, when Islam developed.

Docetism and Christ myth theory.

Since Arthur Drews published his "The Christ Myth" ("Die Christusmythe") in 1909, occasional connections have been drawn between docetist theories and the modern idea that Christ was a myth. Shailer Mathews called Drews' theory a "modern docetism". Frederick Cornwallis Conybeare thought any connection to be based on a misunderstanding of docetism. The idea recurred in classicist Michael Grant's 1977 review of the evidence for Jesus, who compared modern scepticism about a historical Jesus to the ancient docetic idea that Jesus only "seemed" to come into the world "in the flesh". Modern theories did away with "seeming".

In the history of Christianity, docetism (from the "dokeĩn" "to seem", "dókēsis" "apparition, phantom") is the heterodox doctrine that the phenomenon of Jesus, his historical and bodily existence, and above all the human form of Jesus, was mere semblance without any true reality. Broadly it is taken as the belief that Jesus only seemed to be human, and that his human form was an illusion.

Der Doketismus (griechisch δοκεῖν "dokein" „scheinen“) ist eine Lehre, der die Auffassung zugrunde liegt, dass die Materie niedrig und böse sei, und die Christus nur einen Scheinleib zuerkennt. So sei Jesus aus doketischer Sicht Gott geblieben, weil seine physische Existenz sein Wesen nicht berührt habe, er also nur zum Schein gelitten habe und gestorben sei. Das Menschsein und die Geschichtlichkeit Christi werden damit im Doketismus aufgegeben oder zumindest eingeschränkt.


Biography.

Born into one of Jerusalem's elite families, Josephus introduces himself in Greek as" Iōsēpos" (Ιώσηπος), son of Matthias, an ethnic Jewish priest. He was the second-born son of Matthias. His older full-blooded brother was also called Matthias. Their mother was an aristocratic woman who descended from the royal and formerly ruling Hasmonean dynasty. Josephus's paternal grandparents were Josephus and his wife—an unnamed Hebrew noblewoman, distant relatives of each other and direct descendants of Simon Psellus. Josephus's family was wealthy. He descended through his father from the priestly order of the Jehoiarib, which was the first of the 24 orders of priests in the Temple in Jerusalem. Josephus was a descendant of the high priest Jonathon. He was raised in Jerusalem and educated alongside his brother.  In his mid twenties, he traveled to negotiate with Emperor Nero for the release of 12 Jewish priests. Upon his return to Jerusalem, at the outbreak of the First Jewish–Roman War, Josephus was appointed the military governor of Galilee. His arrival in Galilee, however, was fraught with internal division: the inhabitants of Sepphoris and Tiberias opting to maintain peace with the Romans; the people of Sepphoris enlisting the help of the Roman army to protect their city, whilst the people of Tiberias appealing to King Agrippa's forces to protect them from the insurgents. Josephus also contended with John of Gischala who had also set his sight over the control of Galilee. Like Josephus, John had amassed to himself a large band of supporters from Gischala (Gush Halab) and Gabara, including the support of the Sanhedrin in Jerusalem. Meanwhile, Josephus fortified several towns and villages in Lower Galilee, among which were Tiberias, Bersabe, Selamin, Japha, and Tarichaea, in anticipation of a Roman onslaught. In Upper Galilee, he fortified the towns of Jamnith, Seph, Mero, and Achabare, among other places. Josephus, with the Galileans under his command, managed to bring both Sepphoris and Tiberias into subjection, but was eventually forced to relinquish his hold on Sepphoris by the arrival of Roman forces under Placidus the tribune and later by Vespasian himself. Josephus first engaged the Roman army at a village called Garis, where he launched an attack against Sepphoris a second time, before being repulsed. At length, he resisted the Roman army in its siege of Yodfat (Jotapata) until it fell to the Roman army in the lunar month of Tammuz, in the thirteenth year of Nero's reign.  After the Jewish garrison of Yodfat fell under siege, the Romans invaded, killing thousands; the survivors committed suicide. According to Josephus, he was trapped in a cave with 40 of his companions in July 67 CE. The Romans (commanded by Flavius Vespasian and his son Titus, both subsequently Roman emperors) asked the group to surrender, but they refused. Josephus suggested a method of collective suicide; they drew lots and killed each other, one by one, counting to every third person. Two men were left who surrendered to the Roman forces and became prisoners. In 69 CE, Josephus was released. According to his account, he acted as a negotiator with the defenders during the Siege of Jerusalem in 70 CE, during which time his parents were held as hostages by Simon bar Giora.  While being confined at Yodfat (Jotapata), Josephus claimed to have experienced a divine revelation that later led to his speech predicting Vespasian would become emperor. After the prediction came true, he was released by Vespasian, who considered his gift of prophecy to be divine. Josephus wrote that his revelation had taught him three things: that God, the creator of the Jewish people, had decided to "punish" them; that "fortune" had been given to the Romans; and that God had chosen him "to announce the things that are to come". To many Jews, such claims were simply self-serving.  In 71 CE, he went to Rome in the entourage of Titus, becoming a Roman citizen and client of the ruling Flavian dynasty (hence he is often referred to as Flavius Josephus). In addition to Roman citizenship, he was granted accommodation in conquered Judaea and a pension. While in Rome and under Flavian patronage, Josephus wrote all of his known works. Although he uses "Josephus", he appears to have taken the Roman praenomen Titus and nomen Flavius from his patrons.  Vespasian arranged for Josephus to marry a captured Jewish woman, whom he later divorced. About 71 CE, Josephus married an Alexandrian Jewish woman as his third wife. They had three sons, of whom only Flavius Hyrcanus survived childhood. Josephus later divorced his third wife. Around 75 CE, he married his fourth wife, a Greek Jewish woman from Crete, who was a member of a distinguished family. They had a happy married life and two sons, Flavius Justus and Flavius Simonides Agrippa.  Josephus's life story remains ambiguous. He was described by Harris in 1985 as a law-observant Jew who believed in the compatibility of Judaism and Graeco-Roman thought, commonly referred to as Hellenistic Judaism. Before the 19th century, the scholar Nitsa Ben-Ari notes that his work was banned as those of a traitor, whose work was not to be studied or translated into Hebrew. His critics were never satisfied as to why he failed to commit suicide in Galilee, and after his capture, accepted the patronage of Romans.  The historian E. Mary Smallwood writes critically of Josephus: [Josephus] was conceited, not only about his own learning, but also about the opinions held of him as commander both by the Galileans and by the Romans; he was guilty of shocking duplicity at Jotapata, saving himself by sacrifice of his companions; he was too naive to see how he stood condemned out of his own mouth for his conduct, and yet no words were too harsh when he was blackening his opponents; and after landing, however involuntarily, in the Roman camp, he turned his captivity to his own advantage, and benefited for the rest of his days from his change of side.  Author Joseph Raymond calls Josephus "the Jewish Benedict Arnold" for betraying his own troops at Jotapata.

Scholarship and impact on history.

The works of Josephus provide crucial information about the First Jewish-Roman War and also represent important literary source material for understanding the context of the Dead Sea Scrolls and late Temple Judaism.  Josephan scholarship in the 19th and early 20th centuries took an interest in Josephus's relationship to the sect of the Pharisees. It consistently portrayed him as a member of the sect and as a traitor to the Jewish nation—a view which became known as the classical concept of Josephus. In the mid-20th century a new generation of scholars challenged this view and formulated the modern concept of Josephus. They consider him a Pharisee but restore his reputation in part as patriot and a historian of some standing. In his 1991 book, Steve Mason argued that Josephus was not a Pharisee but an orthodox Aristocrat-Priest who became associated with the philosophical school of the Pharisees as a matter of deference, and not by willing association.

Impact on history and archaeology.

The works of Josephus include useful material for historians about individuals, groups, customs, and geographical places. Josephus mentions that in his day there were 240 towns and villages scattered across Upper and Lower Galilee, some of which he names. A few of the Jewish customs named by him include the practice of hanging a curtain of fine-linen at the entrance to one's house, and the Jewish custom to partake of a Sabbath-day's meal around the sixth-hour of the day (at noon). He notes also that it was permissible for Jewish men to marry many wives (polygamy). His writings provide a significant, extra-Biblical account of the post-Exilic period of the Maccabees, the Hasmonean dynasty, and the rise of Herod the Great. He describes the Sadducees, Jewish High Priests of the time, Pharisees and Essenes, the Herodian Temple, Quirinius' census and the Zealots, and such figures as Pontius Pilate, Herod the Great, Agrippa I and Agrippa II, John the Baptist, James the brother of Jesus, and Jesus (found only in the Slavonic version of the "Jewish War"). Josephus represents an important source for studies of immediate post-Temple Judaism and the context of early Christianity.  A careful reading of Josephus's writings and years of excavation allowed Ehud Netzer, an archaeologist from Hebrew University, to discover what he considered to be the location of Herod's Tomb, after searching for 35 years. It was above aqueducts and pools, at a flattened desert site, halfway up the hill to the Herodium, 12 km south of Jerusalem—as described in Josephus's writings. In October 2013, archaeologists Joseph Patrich and Benjamin Arubas challenged the identification of the tomb as that of Herod. According to Patrich and Arubas, the tomb is too modest to be Herod's and has several unlikely features. Roi Porat, who replaced Netzer as excavation leader after the latter's death, stood by the identification.  Josephus's writings provide the first-known source for many stories considered as Biblical history, despite not being found in the Bible or related material. These include Ishmael as the founder of the Arabs, the connection of "Semites", "Hamites" and "Japhetites" to the classical nations of the world, and the story of the Siege of Masada.

Manuscripts, textual criticism, and editions.

For many years, the works of Josephus were largely known in Europe only in an imperfect Latin translation from the original Greek. Only in 1544 did a version of the standard Greek text become available in French, edited by the Dutch humanist Arnoldus Arlenius. The first English translation, by Thomas Lodge, appeared in 1602, with subsequent editions appearing throughout the 17th century. The 1544 Greek edition formed the basis of the 1732 English translation by William Whiston, which achieved enormous popularity in the English-speaking world. It was often the book—after the Bible—that Christians most frequently owned. A cross-reference apparatus for Whiston's version of Josephus and the biblical canon also exists. Whiston claimed that certain works by Josephus had a similar style to the Epistles of St Paul.  Later editions of the Greek text include that of Benedikt Niese, who made a detailed examination of all the available manuscripts, mainly from France and Spain. Henry St. John Thackeray used Niese's version for the Loeb Classical Library edition widely used today.  The standard "editio maior" of the various Greek manuscripts is that of Benedictus Niese, published 1885–95. The text of "Antiquities" is damaged in some places. In the "Life", Niese follows mainly manuscript P, but refers also to AMW and R. Henry St. John Thackeray for the Loeb Classical Library has a Greek text also mainly dependent on P. André Pelletier edited a new Greek text for his translation of "Life". The ongoing Münsteraner Josephus-Ausgabe of Münster University will provide a new critical apparatus. There also exist late Old Slavonic translations of the Greek, but these contain a large number of Christian interpolations.

Josephus's audience.

Scholars debate about Josephus's intended audience. For example, "Antiquities of the Jews" could be written for Jews—"a few scholars from Laqueur onward have suggested that Josephus must have written primarily for fellow-Jews (if also secondarily for Gentiles). The most common motive suggested is repentance: in later life he felt so badly about the traitorous "War" that he needed to demonstrate... his loyalty to Jewish history, law and culture." However, Josephus's "countless incidental remarks explaining basic Judean language, customs and laws... assume a Gentile audience. He does not expect his first hearers to know anything about the laws or Judean origins." The issue of who would read this multi-volume work is unresolved. Other possible motives for writing "Antiquities" could be to dispel the misrepresentation of Jewish origins or as an apologetic to Greek cities of the Diaspora in order to protect Jews and to Roman authorities to garner their support for the Jews facing persecution. Neither motive explains why the proposed Gentile audience would read this large body of material.

Historiography and Josephus.

In the Preface to "Jewish Wars", Josephus criticizes historians who misrepresent the events of the Jewish–Roman War, writing that "they have a mind to demonstrate the greatness of the Romans, while they still diminish and lessen the actions of the Jews." Josephus states that his intention is to correct this method but that he "will not go to the other extreme... [and] will prosecute the actions of both parties with accuracy." Josephus suggests his method will not be wholly objective by saying he will be unable to contain his lamentations in transcribing these events; to illustrate this will have little effect on his historiography, Josephus suggests, "But if any one be inflexible in his censures of me, let him attribute the facts themselves to the historical part, and the lamentations to the writer himself only."  His preface to "Antiquities" offers his opinion early on, saying, "Upon the whole, a man that will peruse this history, may principally learn from it, that all events succeed well, even to an incredible degree, and the reward of felicity is proposed by God." After inserting this attitude, Josephus contradicts himself: "I shall accurately describe what is contained in our records, in the order of time that belongs to them... without adding any thing to what is therein contained, or taking away any thing therefrom." He notes the difference between history and philosophy by saying, "[T]hose that read my book may wonder how it comes to pass, that my discourse, which promises an account of laws and historical facts, contains so much of philosophy."  In both works, Josephus emphasizes that accuracy is crucial to historiography. Louis H. Feldman notes that in "Wars", Josephus commits himself to critical historiography, but in "Antiquities", Josephus shifts to rhetorical historiography, which was the norm of his time. Feldman notes further that it is significant that Josephus called his later work "Antiquities" (literally, archaeology) rather than history; in the Hellenistic period, archaeology meant either "history from the origins or archaic history." Thus, his title implies a Jewish peoples' history from their origins until the time he wrote. This distinction is significant to Feldman, because "in ancient times, historians were expected to write in chronological order," while "antiquarians wrote in a systematic order, proceeding topically and logically" and included all relevant material for their subject. Antiquarians moved beyond political history to include institutions and religious and private life. Josephus does offer this wider perspective in "Antiquities".  To compare his historiography with another ancient historian, consider Dionysius of Halicarnassus. Feldman lists these similarities: "Dionysius in praising Rome and Josephus in praising Jews adopt same pattern; both often moralize and psychologize and stress piety and role of divine providence; and the parallels between... Dionysius's account of deaths of Aeneas and Romulus and Josephus's description of the death of Moses are striking."

Works.

The works of Josephus are major sources of our understanding of Jewish life and history during the first century.

"The Jewish War".

His first work in Rome was an account of the Jewish War, addressed to certain "upper barbarians"—usually thought to be the Jewish community in Mesopotamia—in his "paternal tongue" ("War" I.3), arguably the Western Aramaic language. In 78 CE he finished a seven-volume account in Greek known as the "Jewish War" (Latin "Bellum Judaicum" or "De Bello Judaico"). It starts with the period of the Maccabees and concludes with accounts of the fall of Jerusalem, and the succeeding fall of the fortresses of Herodion, Macharont and Masada and the Roman victory celebrations in Rome, the mopping-up operations, Roman military operations elsewhere in the empire and the uprising in Cyrene. Together with the account in his "Life" of some of the same events, it also provides the reader with an overview of Josephus's own part in the events since his return to Jerusalem from a brief visit to Rome in the early 60s ("Life" 13–17).  In the wake of the suppression of the Jewish revolt, Josephus would have witnessed the marches of Titus's triumphant legions leading their Jewish captives, and carrying treasures from the despoiled Temple in Jerusalem. It was against this background that Josephus wrote his "War", claiming to be countering anti-Judean accounts. He disputes the claim that the Jews served a defeated God and were naturally hostile to Roman civilization. Rather, he blames the Jewish War on what he calls "unrepresentative and over-zealous fanatics" among the Jews, who led the masses away from their traditional aristocratic leaders (like himself), with disastrous results. Josephus also blames some of the Roman governors of Judea, representing them as corrupt and incompetent administrators. According to Josephus, the traditional Jew was, should be, and can be a loyal and peace-loving citizen. Jews can, and historically have, accepted Rome's hegemony precisely because their faith declares that God himself gives empires their power.

"Jewish Antiquities".

The next work by Josephus is his twenty-one volume "Antiquities of the Jews", completed during the last year of the reign of the Emperor Flavius Domitian, around 93 or 94 CE. In expounding Jewish history, law and custom, he is entering into many philosophical debates current in Rome at that time. Again he offers an "apologia" for the antiquity and universal significance of the Jewish people. Josephus claims to be writing this history because he "saw that others perverted the truth of those actions in their writings," those writings being the history of the Jews. In terms of some of his sources for the project, Josephus says that he drew from and "interpreted out of the Hebrew Scriptures" and that he was an eyewitness to the wars between the Jews and the Romans, which were earlier recounted in "Jewish Wars".  He outlines Jewish history beginning with the creation, as passed down through Jewish historical tradition. Abraham taught science to the Egyptians, who, in turn, taught the Greeks. Moses set up a senatorial priestly aristocracy, which, like that of Rome, resisted monarchy. The great figures of the Tanakh are presented as ideal philosopher-leaders. He includes an autobiographical appendix defending his conduct at the end of the war when he cooperated with the Roman forces.  Louis H. Feldman outlines the difference between calling this work "Antiquities of the Jews" instead of "History of the Jews". Although Josephus says that he describes the events contained in "Antiquities" "in the order of time that belongs to them," Feldman argues that Josephus "aimed to organize [his] material systematically rather than chronologically" and had a scope that "ranged far beyond mere political history to political institutions, religious and private life."

"Against Apion".

Josephus's "Against Apion" is a two-volume defence of Judaism as classical religion and philosophy, stressing its antiquity, as opposed to what Josephus claimed was the relatively more recent tradition of the Greeks. Some anti-Judaic allegations ascribed by Josephus to the Greek writer Apion and myths accredited to Manetho are also addressed.

Titus Flavius Josephus (; ; 37 – 100), born Yosef ben Matityahu (, "Yosef ben Matityahu"; ), was a first-century Romano-Jewish historian who was born in Jerusalem—then part of Roman Judea—to a father of priestly descent and a mother who claimed royal ancestry.

Flavius Josephus (; geboren 37 oder 38 in Jerusalem als Joseph ben Mathitjahu ha Kohen,, „Josephos, Sohn des Matthias“; gestorben nach 100 vermutlich in Rom) war ein römisch-jüdischer Geschichtsschreiber. Er verfasste seine Werke in griechischer Sprache, zum Teil aber zunächst in seiner aramäischen Muttersprache.