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Oxidation state

In chemistry, the oxidation state, or oxidation number, is the hypothetical charge of an atom if all of its bonds to other atoms were fully ionic. It describes the degree of oxidation (loss of electrons) of an atom in a chemical compound. Conceptually, the oxidation state may be positive, negative or zero. While fully ionic bonds are not found in nature, many bonds exhibit strong ionicity, making oxidation state a useful predictor of charge.

The oxidation state of an atom does not represent the "real" charge on that atom, or any other actual atomic property. This is particularly true of high oxidation states, where the ionization energy required to produce a multiply positive ion is far greater than the energies available in chemical reactions. Additionally, the oxidation states of atoms in a given compound may vary depending on the choice of electronegativity scale used in their calculation. Thus, the oxidation state of an atom in a compound is purely a formalism. It is nevertheless important in understanding the nomenclature conventions of inorganic compounds. Also, several observations regarding chemical reactions may be explained at a basic level in terms of oxidation states.

Oxidation states are typically represented by integers which may be positive, zero, or negative. In some cases, the average oxidation state of an element is a fraction, such as $8⁄3$ for iron in magnetite Fe3O4 (see below). The highest known oxidation state is reported to be +9, displayed by iridium in the tetroxoiridium(IX) cation (IrO4+). It is predicted that even a +10 oxidation state may be achieved by platinum in tetroxoplatinum(X), PtO4(2+). The lowest oxidation state is −5, as for boron in Al3BC and gallium in pentamagnesium digallide (Mg5Ga2).

In inorganic nomenclature, the oxidation state is represented by a Roman numeral placed after the element name inside parentheses or as a superscript after the element symbol, e.g. Iron(III) oxide.

The term oxidation was first used by Antoine Lavoisier to signify the reaction of a substance with oxygen. Much later, it was realized that the substance, upon being oxidized, loses electrons, and the meaning was extended to include other reactions in which electrons are lost, regardless of whether oxygen was involved. The increase in the oxidation state of an atom, through a chemical reaction, is known as oxidation; a decrease in oxidation state is known as a reduction. Such reactions involve the formal transfer of electrons: a net gain in electrons being a reduction, and a net loss of electrons being oxidation. For pure elements, the oxidation state is zero.

IUPAC definition
IUPAC has published a "Comprehensive definition of oxidation state (IUPAC Recommendations 2016)". It is a distillation of an IUPAC technical report "Toward a comprehensive definition of oxidation state" from 2014. The current IUPAC Gold Book definition of oxidation state is:

"The oxidation state of an atom is the charge of this atom after ionic approximation of its heteronuclear bonds."

and the term oxidation number is nearly synonymous.

The ionic approximation means extrapolating bonds to ionic. Several criteria were considered for the ionic approximation:

 * 1) Extrapolation of the bond's polarity; 1. from the electronegativity difference,

2. from the dipole moment, and

3. from quantum‐chemical calculations of charges.
 * 1) Assignment of electrons according to the atom's contribution to the bonding Molecular orbital (MO) or the electron's allegiance in a LCAO–MO model.

In a bond between two different elements, the bond's electrons are assigned to its main atomic contributor typically of higher electronegativity; in a bond between two atoms of the same element, the electrons are divided equally. This is because most electronegativity scales depend on the atom's bonding state, which makes the assignment of the oxidation state a somewhat circular argument. For example, some scales may turn out unusual oxidation states, such as −6 for platinum in PtH4(2-), for Pauling and Mulliken scales. The dipole moments would, sometimes, also turn out abnormal oxidation numbers, such as in CO and NO, which are oriented with their positive end towards oxygen. Therefore, this leaves the atom's contribution to the bonding MO, the atomic-orbital energy, and from quantum-chemical calculations of charges, as the only viable criteria with cogent values for ionic approximation. However, for a simple estimate for the ionic approximation, we can use Allen electronegativities, as only that electronegativity scale is truly independent of the oxidation state, as it relates to the average valence‐electron energy of the free atom:

Determination
While introductory levels of chemistry teaching use postulated oxidation states, the IUPAC recommendation and the Gold Book entry list two entirely general algorithms for the calculation of the oxidation states of elements in chemical compounds.

Simple approach without bonding considerations
Introductory chemistry uses postulates: the oxidation state for an element in a chemical formula is calculated from the overall charge and postulated oxidation states for all the other atoms.

A simple example is based on two postulates,

 * 1) OS = +1 for hydrogen
 * 2) OS = −2 for oxygen

where OS stands for oxidation state. This approach yields correct oxidation states in oxides and hydroxides of any single element, and in acids such as sulfuric acid (H2SO4) or dichromic acid (H2Cr2O7). Its coverage can be extended either by a list of exceptions or by assigning priority to the postulates. The latter works for hydrogen peroxide (H2O2) where the priority of rule 1 leaves both oxygens with oxidation state −1.

Additional postulates and their ranking may expand the range of compounds to fit a textbook's scope. As an example, one postulatory algorithm from many possible; in a sequence of decreasing priority:

 * 1) An element in a free form has OS = 0.
 * 2) In a compound or ion, the sum of the oxidation states equals the total charge of the compound or ion.
 * 3) Fluorine in compounds has OS = −1; this extends to chlorine and bromine only when not bonded to a lighter halogen, oxygen or nitrogen.
 * 4) Group 1 and group 2 metals in compounds have OS = +1 and +2, respectively.
 * 5) Hydrogen has OS = +1 but adopts −1 when bonded as a hydride to metals or metalloids.
 * 6) Oxygen in compounds has OS = −2 but only when not bonded to oxygen (e.g. in peroxides) or fluorine.

This set of postulates covers oxidation states of fluorides, chlorides, bromides, oxides, hydroxides, and hydrides of any single element. It covers all oxoacids of any central atom (and all their fluoro-, chloro-, and bromo-relatives), as well as salts of such acids with group 1 and 2 metals. It also covers iodides, sulfides, and similar simple salts of these metals.

Algorithm of assigning bonds
This algorithm is performed on a Lewis structure (a diagram that shows all valence electrons). Oxidation state equals the charge of an atom after each of its heteronuclear bonds has been assigned to the more electronegative partner of the bond (except when that partner is a reversibly bonded Lewis-acid ligand) and homonuclear bonds have been divided equally:

 * 1oxstate.svg

where each "—" represents an electron pair (either shared between two atoms or solely on one atom), and "OS" is the oxidation state as a numerical variable.

After the electrons have been assigned according to the vertical red lines on the formula, the total number of valence electrons that now "belong" to each atom is subtracted from the number $N$ of valence electrons of the neutral atom (such as 5 for nitrogen in group 15) to yield that atom's oxidation state.

This example shows the importance of describing the bonding. Its summary formula, HNO3, corresponds to two structural isomers; the peroxynitrous acid in the above figure and the more stable nitric acid. With the formula HNO3, the simple approach without bonding considerations yields −2 for all three oxygens and +5 for nitrogen, which is correct for nitric acid. For the peroxynitrous acid, however, both oxygens in the O–O bond have OS = −1, and the nitrogen has OS = +3, which requires a structure to understand.

Organic compounds are treated in a similar manner; exemplified here on functional groups occurring in between methane (CH4) and carbon dioxide (CO2):

 * 3oxstate.svg

Analogously for transition-metal compounds; CrO(O2)2 on the left has a total of 36 valence electrons (18 pairs to be distributed), and hexacarbonylchromium (Cr(CO)6) on the right has 66 valence electrons (33 pairs):

 * 2oxstate.svg

A key step is drawing the Lewis structure of the molecule (neutral, cationic, anionic): Atom symbols are arranged so that pairs of atoms can be joined by single two-electron bonds as in the molecule (a sort of "skeletal" structure), and the remaining valence electrons are distributed such that sp atoms obtain an octet (duet for hydrogen) with a priority that increases in proportion with electronegativity. In some cases, this leads to alternative formulae that differ in bond orders (the full set of which is called the resonance formulas). Consider the sulfate anion (SO4(2-)) with 32 valence electrons; 24 from oxygens, 6 from sulfur, 2 of the anion charge obtained from the implied cation. The bond orders to the terminal oxygens do not affect the oxidation state so long as the oxygens have octets. Already the skeletal structure, top left, yields the correct oxidation states, as does the Lewis structure, top right (one of the resonance formulas):

 * 7oxstate.svg

The bond-order formula at the bottom is closest to the reality of four equivalent oxygens each having a total bond order of 2. That total includes the bond of order $1⁄2$ to the implied cation and follows the 8 − N rule requiring that the main-group atom's bond-order total equals 8 − N valence electrons of the neutral atom, enforced with a priority that proportionately increases with electronegativity.

This algorithm works equally for molecular cations composed of several atoms. An example is the ammonium cation of 8 valence electrons (5 from nitrogen, 4 from hydrogens, minus 1 electron for the cation's positive charge):

 * 5oxstate.svg

Drawing Lewis structures with electron pairs as dashes emphasizes the essential equivalence of bond pairs and lone pairs when counting electrons and moving bonds onto atoms. Structures drawn with electron dot pairs are of course identical in every way:

 * 4oxstate.svg

The algorithm's caveat
The algorithm contains a caveat, which concerns rare cases of transition-metal complexes with a type of ligand that is reversibly bonded as a Lewis acid (as an acceptor of the electron pair from the transition metal); termed a "Z-type" ligand in Green's covalent bond classification method. The caveat originates from the simplifying use of electronegativity instead of the MO-based electron allegiance to decide the ionic sign. One early example is the O2S\sRhCl(CO)(PPh3)2 complex with sulfur dioxide (SO2) as the reversibly-bonded acceptor ligand (released upon heating). The Rh−S bond is therefore extrapolated ionic against Allen electronegativities of rhodium and sulfur, yielding oxidation state +1 for rhodium:

 * 8oxstate.svg

Algorithm of summing bond orders
This algorithm works on Lewis structures and bond graphs of extended (non-molecular) solids: "Oxidation state is obtained by summing the heteronuclear-bond orders at the atom as positive if that atom is the electropositive partner in a particular bond and as negative if not, and the atom’s formal charge (if any) is added to that sum. The same caveat as above applies."

Applied to a Lewis structure
An example of a Lewis structure with no formal charge,
 * 9oxstate.svg

illustrates that, in this algorithm, homonuclear bonds are simply ignored (the bond orders are in blue).

Carbon monoxide exemplifies a Lewis structure with formal charges:

 * 10oxstate.svg

To obtain the oxidation states, the formal charges are summed with the bond-order value taken positively at the carbon and negatively at the oxygen.

Applied to molecular ions, this algorithm considers the actual location of the formal (ionic) charge, as drawn in the Lewis structure. As an example, summing bond orders in the ammonium cation yields −4 at the nitrogen of formal charge +1, with the two numbers adding to the oxidation state of −3:

 * 11oxstate.svg

The sum of oxidation states in the ion equals its charge (as it equals zero for a neutral molecule).

Also in anions, the formal (ionic) charges have to be considered when nonzero. For sulfate this is exemplified with the skeletal or Lewis structures (top), compared with the bond-order formula of all oxygens equivalent and fulfilling the octet and 8 − N rules (bottom):

 * 13oxstate.svg

Applied to bond graph
A bond graph in solid-state chemistry is a chemical formula of an extended structure, in which direct bonding connectivities are shown. An example is the AuORb3 perovskite, the unit cell of which is drawn on the left and the bond graph (with added numerical values) on the right:

 * 14oxstate.svg

We see that the oxygen atom bonds to the six nearest rubidium cations, each of which has 4 bonds to the auride anion. The bond graph summarizes these connectivities. The bond orders (also called bond valences) sum up to oxidation states according to the attached sign of the bond's ionic approximation (there are no formal charges in bond graphs).

Determination of oxidation states from a bond graph can be illustrated on ilmenite, FeTiO3. We may ask whether the mineral contains Fe(2+) and Ti(4+), or Fe(3+) and Ti(3+). Its crystal structure has each metal atom bonded to six oxygens and each of the equivalent oxygens to two irons and two titaniums, as in the bond graph below. Experimental data show that three metal-oxygen bonds in the octahedron are short and three are long (the metals are off-center). The bond orders (valences), obtained from the bond lengths by the bond valence method, sum up to 2.01 at Fe and 3.99 at Ti; which can be rounded off to oxidation states +2 and +4, respectively:

 * 15oxstate.svg

Balancing redox
Oxidation states can be useful for balancing chemical equations for oxidation-reduction (or redox) reactions, because the changes in the oxidized atoms have to be balanced by the changes in the reduced atoms. For example, in the reaction of acetaldehyde with Tollens' reagent to form acetic acid (shown below), the carbonyl carbon atom changes its oxidation state from +1 to +3 (loses two electrons). This oxidation is balanced by reducing two Ag+ cations to Ag^{0} (gaining two electrons in total).

 * Redox eqn 1.svg

An inorganic example is the Bettendorf reaction using tin dichloride (SnCl2) to prove the presence of arsenite ions in a concentrated HCl extract. When arsenic(III) is present, a brown coloration appears forming a dark precipitate of arsenic, according to the following simplified reaction:

Here three tin atoms are oxidized from oxidation state +2 to +4, yielding six electrons that reduce two arsenic atoms from oxidation state +3 to 0. The simple one-line balancing goes as follows: the two redox couples are written down as they react;

One tin is oxidized from oxidation state +2 to +4, a two-electron step, hence 2 is written in front of the two arsenic partners. One arsenic is reduced from +3 to 0, a three-electron step, hence 3 goes in front of the two tin partners. An alternative three-line procedure is to write separately the half-reactions for oxidation and reduction, each balanced with electrons, and then to sum them up such that the electrons cross out. In general, these redox balances (the one-line balance or each half-reaction) need to be checked for the ionic and electron charge sums on both sides of the equation being indeed equal. If they are not equal, suitable ions are added to balance the charges and the non-redox elemental balance.

Nominal oxidation states
A nominal oxidation state is a general term with two different definitions:
 * Electrochemical oxidation state represents a molecule or ion in the Latimer diagram or Frost diagram for its redox-active element. An example is the Latimer diagram for sulfur at pH 0 where the electrochemical oxidation state +2 for sulfur puts thiosulfate between S and H2SO3:

 * 16oxstate.svg

 * Systematic oxidation state is chosen from close alternatives as a pedagogical description. An example is the oxidation state of phosphorus in H3PO3 (structurally diprotic HPO(OH)2) taken nominally as +3, while Allen electronegativities of phosphorus and hydrogen suggest +5 by a narrow margin that makes the two alternatives almost equivalent:
 * 17oxstate.svg
 * Both alternative oxidation numbers for phosphorus make chemical sense, depending on which chemical property or reaction is emphasized. By contrast, a calculated alternative, such as the average (+4) does not.

Ambiguous oxidation states
Lewis formulae are rule-based approximations of chemical reality, as are Allen electronegativities. Still, oxidation states may seem ambiguous when their determination is not straightforward. If only an experiment can determine the oxidation state, the rule-based determination is ambiguous (insufficient). There are also truly dichotomous values that are decided arbitrarily.

Oxidation-state determination from resonance formulas
Seemingly ambiguous oxidation states are derived from a set of resonance formulas of equal weights for a molecule having heteronuclear bonds where the atom connectivity does not correspond to the number of two-electron bonds dictated by the 8 − N rule. An example is S2N2 where four resonance formulas featuring one S=N double bond have oxidation states +2 and +4 for the two sulfur atoms, which average to +3 because the two sulfur atoms are equivalent in this square-shaped molecule.

A physical measurement is needed to determine oxidation state

 * when a non-innocent ligand is present, of hidden or unexpected redox properties that could otherwise be assigned to the central atom. An example is the nickel dithiolate complex,.
 * when the redox ambiguity of a central atom and ligand yields dichotomous oxidation states of close stability, thermally induced tautomerism may result, as exemplified by manganese catecholate, Mn(C6H4O2)3. Assignment of such oxidation states requires spectroscopic, magnetic or structural data.
 * when the bond order has to be ascertained along with an isolated tandem of a heteronuclear and a homonuclear bond. An example is thiosulfate having two possible oxidation states (bond orders are in blue and formal charges in green):

 * 21oxstate.svg

 * The S–S distance measurement in thiosulfate is needed to reveal that this bond order is very close to 1, as in the formula on the left.

Ambiguous/arbitrary oxidation states

 * when the electronegativity difference between two bonded atoms is very small (as in H3PO3). Two almost equivalent pairs of oxidation states, arbitrarily chosen, are obtained for these atoms.
 * when an electronegative p-block atom forms solely homonuclear bonds, the number of which differs from the number of two-electron bonds suggested by rules. Examples are homonuclear finite chains like azide (the central nitrogen connects two atoms with four two-electron bonds while only three two-electron bonds are required by the 8 − N rule ) or triiodide (the central iodine connects two atoms with two two-electron bonds while only one two-electron bond fulfills the 8 − N rule). A sensible approach is to distribute the ionic charge over the two outer atoms. Such a placement of charges in a polysulfide (where all inner sulfurs form two bonds, fulfilling the 8 − N rule) follows already from its Lewis structure.
 * when the isolated tandem of a heteronuclear and a homonuclear bond leads to a bonding compromise in between two Lewis structures of limiting bond orders. An example is N2O:

 * 18oxstate.svg

 * The typical oxidation state of nitrogen in N2O is +1, which also obtains for both nitrogens by a molecular orbital approach. The formal charges on the right comply with electronegativities, which implies an added ionic bonding contribution. Indeed, the estimated N−N and N−O bond orders are 2.76 and 1.9, respectively, approaching the formula of integer bond orders that would include the ionic contribution explicitly as a bond (in green):

 * 19oxstate.svg

 * Conversely, formal charges against electronegativities in a Lewis structure decrease the bond order of the corresponding bond. An example is carbon monoxide with a bond-order estimate of 2.6.

Fractional oxidation states
Fractional oxidation states are often used to represent the average oxidation state of several atoms of the same element in a structure. For example, the formula of magnetite is, implying an average oxidation state for iron of +$8⁄3$. However, this average value may not be representative if the atoms are not equivalent. In a crystal below 120 K, two-thirds of the cations are  and one-third are, and the formula may be more clearly represented as FeO·.

Likewise, propane,, has been described as having a carbon oxidation state of −$8⁄3$. Again, this is an average value since the structure of the molecule is, with the first and third carbon atoms each having an oxidation state of −3 and the central one −2.

An example with true fractional oxidation states for equivalent atoms is potassium superoxide,. The diatomic superoxide ion has an overall charge of −1, so each of its two equivalent oxygen atoms is assigned an oxidation state of −$1⁄2$. This ion can be described as a resonance hybrid of two Lewis structures, where each oxygen has an oxidation state of 0 in one structure and −1 in the other.

For the cyclopentadienyl anion, the oxidation state of C is −1 + −$1⁄5$ = −$6⁄5$. The −1 occurs because each carbon is bonded to one hydrogen atom (a less electronegative element), and the −$1⁄5$ because the total ionic charge of −1 is divided among five equivalent carbons. Again this can be described as a resonance hybrid of five equivalent structures, each having four carbons with oxidation state −1 and one with −2.

 * {| class="wikitable"

! Oxidation state !! Example species
 * + Examples of fractional oxidation states for carbon
 * −$6⁄5$ || Cyclopentadienyl anion
 * −$6⁄7$ || tropylium
 * +$3⁄2$ || Squarate ion
 * }
 * +$III 2$ || Squarate ion
 * }
 * }

Finally, fractional oxidation numbers are not used in the chemical nomenclature. For example the red lead Lead(II,IV) oxide is represented as lead(II,IV) oxide, showing the oxidation states of the two nonequivalent lead atoms.

Elements with multiple oxidation states
Most elements have more than one possible oxidation state. For example, carbon has nine possible integer oxidation states from −4 to +4:
 * {| class="wikitable"

! Oxidation state !! Example compound
 * + Integer oxidation states of carbon
 * −4 || methane
 * −3 || ethane
 * −2 || ethylene, chloromethane
 * −1 || acetylene, benzene, ethylene glycol
 * 0 || formaldehyde, dichloromethane
 * +1 || glyoxal, 1,1,2,2-Tetrachloroethane
 * +2 || formic acid, chloroform
 * +3 || oxalic acid, hexachloroethane
 * +4 || carbon tetrachloride, carbon dioxide
 * }
 * +1 || glyoxal, 1,1,2,2-Tetrachloroethane
 * +2 || formic acid, chloroform
 * +3 || oxalic acid, hexachloroethane
 * +4 || carbon tetrachloride, carbon dioxide
 * }
 * +3 || oxalic acid, hexachloroethane
 * +4 || carbon tetrachloride, carbon dioxide
 * }
 * }

Oxidation state in metals
Many compounds with luster and electrical conductivity maintain a simple stoichiometric formula, such as the golden TiO, blue-black RuO2 or coppery ReO3, all of obvious oxidation state. Ultimately, assigning the free metallic electrons to one of the bonded atoms is not comprehensive and can yield unusual oxidation states. Examples are the LiPb and ordered alloys, the composition and structure of which are largely determined by atomic size and packing factors. Should oxidation state be needed for redox balancing, it is best set to 0 for all atoms of such an alloy.

List of oxidation states of the elements
This is a list of known oxidation states of the chemical elements, excluding nonintegral values. The most common states appear in bold. The table is based on that of Greenwood and Earnshaw, with additions noted. Every element exists in oxidation state 0 when it is the pure non-ionized element in any phase, whether monatomic or polyatomic allotrope. The column for oxidation state 0 only shows elements known to exist in oxidation state 0 in compounds.

Early forms (octet rule)
A figure with a similar format was used by Irving Langmuir in 1919 in one of the early papers about the octet rule. The periodicity of the oxidation states was one of the pieces of evidence that led Langmuir to adopt the rule.

 * Langmuir valence.png

Use in nomenclature
The oxidation state in compound naming for transition metals and lanthanides and actinides is placed either as a right superscript to the element symbol in a chemical formula, such as FeIII or in parentheses after the name of the element in chemical names, such as iron(III). For example, is named iron(III) sulfate and its formula can be shown as Fe⇭⇭⇭. This is because a sulfate ion has a charge of −2, so each iron atom takes a charge of +3.

Early days
Oxidation itself was first studied by Antoine Lavoisier, who defined it as the result of reactions with oxygen (hence the name). The term has since been generalized to imply a formal loss of electrons. Oxidation states, called oxidation grades by Friedrich Wöhler in 1835, were one of the intellectual stepping stones that Dmitri Mendeleev used to derive the periodic table. William B. Jensen gives an overview of the history up to 1938.

Use in nomenclature
When it was realized that some metals form two different binary compounds with the same nonmetal, the two compounds were often distinguished by using the ending -ic for the higher metal oxidation state and the ending -ous for the lower. For example, FeCl3 is ferric chloride and FeCl2 is ferrous chloride. This system is not very satisfactory (although sometimes still used) because different metals have different oxidation states which have to be learned: ferric and ferrous are +3 and +2 respectively, but cupric and cuprous are +2 and +1, and stannic and stannous are +4 and +2. Also, there was no allowance for metals with more than two oxidation states, such as vanadium with oxidation states +2, +3, +4, and +5.

This system has been largely replaced by one suggested by Alfred Stock in 1919 and adopted by IUPAC in 1940. Thus, FeCl2 was written as iron(II) chloride rather than ferrous chloride. The Roman numeral II at the central atom came to be called the "Stock number" (now an obsolete term), and its value was obtained as a charge at the central atom after removing its ligands along with the electron pairs they shared with it.

Development towards the current concept
The term "oxidation state" in English chemical literature was popularized by Wendell Mitchell Latimer in his 1938 book about electrochemical potentials. He used it for the value (synonymous with the German term Wertigkeit) previously termed "valence", "polar valence" or "polar number" in English, or "oxidation stage" or indeed the "state of oxidation". Since 1938, the term "oxidation state" has been connected with electrochemical potentials and electrons exchanged in redox couples participating in redox reactions. By 1948, IUPAC used the 1940 nomenclature rules with the term "oxidation state", instead of the original valency. In 1948 Linus Pauling proposed that oxidation number could be determined by extrapolating bonds to being completely ionic in the direction of electronegativity. A full acceptance of this suggestion was complicated by the fact that the Pauling electronegativities as such depend on the oxidation state and that they may lead to unusual values of oxidation states for some transition metals. In 1990 IUPAC resorted to a postulatory (rule-based) method to determine the oxidation state. This was complemented by the synonymous term oxidation number as a descendant of the Stock number introduced in 1940 into the nomenclature. However, the terminology using "ligands" gave the impression that oxidation number might be something specific to coordination complexes. This situation and the lack of a real single definition generated numerous debates about the meaning of oxidation state, suggestions about methods to obtain it and definitions of it. To resolve the issue, an IUPAC project (2008-040-1-200) was started in 2008 on the "Comprehensive Definition of Oxidation State", and was concluded by two reports and by the revised entries "Oxidation State" and "Oxidation Number" in the IUPAC Gold Book. The outcomes were a single definition of oxidation state and two algorithms to calculate it in molecular and extended-solid compounds, guided by Allen electronegativities that are independent of oxidation state.

title: Oxidation state


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Talk:Oxidation state

Image correction
I have added a correction to redox equation 1 which was pointed out by DIRAC66 in 2017 but which I missed until nowMcardlep (talk) 08:28, 24 May 2019 (UTC)
 * thanks! I don't see which old discussion it is, but I assume the relevant change is O.S. on the carboxyl carbon in the product? If so, I can tweak the SVG. DMacks (talk) 12:01, 24 May 2019 (UTC)
 * Yes, thanks for fixing this image. I also cannot find what you say is my previous comment, but I note now that the real problem with the previous version is that the supposed acetic acid was missing an oxygen, so we were showing the oxidation of acetaldehyde to ... acetaldehyde!??? Of course this incorrect equation was unbalanced in number of oxygens as well as charge. I am glad you have the required software to fix the diagram. Dirac66 (talk) 15:21, 24 May 2019 (UTC)
 * ✅. I didn't draw out the O–H bond because that detail is not really relevant to the point being made here (and it's a harder edit for me to make:) DMacks (talk) 12:02, 28 May 2019 (UTC)

 * @Mcardlep 2409:4042:2313:9133:0:0:2038:40AC (talk) 07:47, 23 March 2022 (UTC)

Copernicium
I see that in the article copernicium 0 charge is counted as an observed oxidation state, bold because it is a main one. This is not included in whatever the file that looks like File:Langmuir valence.png|700px with all the oxidation states is. Is this accurate, and if it is, how should it be added? --Ammonium121 (talk) 18:40, 22 April 2021 (UTC)
 * That file stops at uranium, doesn't it? Double sharp (talk) 03:05, 26 April 2021 (UTC)

IUPAC definition
"Several criteria were considered for the ionic approximation:

 * 1) Extrapolation of the bond’s polarity; 1. from the electronegativity difference,

2. from the dipole moment, and

3. from quantum‐chemical calculations of charges.

Point b may be deceptive: in CO the negative end of the dipole is C; in pyrrole the dipole vector points from N to a direction in the middle of the ring. Patrizio 93.147.230.142 (talk) 16:28, 8 January 2023 (UTC)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Oxidation state


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Gravitational constant

The gravitational constant is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's theory of general relativity. It is also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant, denoted by the capital letter $G$.

In Newton's law, it is the proportionality constant connecting the gravitational force between two bodies with the product of their masses and the inverse square of their distance. In the Einstein field equations, it quantifies the relation between the geometry of spacetime and the energy–momentum tensor (also referred to as the stress–energy tensor).

The measured value of the constant is known with some certainty to four significant digits. In SI units, its value is approximately

The modern notation of Newton's law involving $G$ was introduced in the 1890s by C. V. Boys. The first implicit measurement with an accuracy within about 1% is attributed to Henry Cavendish in a 1798 experiment.

Definition
According to Newton's law of universal gravitation, the magnitude of the attractive force ($G$) between two bodies each with a spherically symmetric density distribution is directly proportional to the product of their masses, $G$ and $F$, and inversely proportional to the square of the distance, $m_{1}$, directed along the line connecting their centres of mass: $$F=G\frac{m_1m_2}{r^2}.$$ The constant of proportionality, $m_{2}$, in this non-relativistic formulation is the gravitational constant. Colloquially, the gravitational constant is also called "Big G", distinct from "small g" ($r$), which is the local gravitational field of Earth (equivalent to the free-fall acceleration). Where $$M_\oplus$$ is the mass of the Earth and $$r_\oplus$$ is the radius of the Earth, the two quantities are related by: $$g = G\frac{M_\oplus}{r_\oplus^2}.$$

The gravitational constant appears in the Einstein field equations of general relativity, $$G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu} \,,$$ where $G$ is the Einstein tensor (not the gravitational constant despite the use of $g$), $g$ is the cosmological constant, $G$ is the metric tensor, $2$ is the stress–energy tensor, and $Gμν$ is the Einstein gravitational constant, a constant originally introduced by Einstein that is directly related to the Newtonian constant of gravitation: $$\kappa = \frac{8\pi G}{c^4} \approx 2.076647(46) \times 10^{-43} \mathrm{\,N^{-1}}.$$

Value and uncertainty
The gravitational constant is a physical constant that is difficult to measure with high accuracy. This is because the gravitational force is an extremely weak force as compared to other fundamental forces at the laboratory scale.

In SI units, the CODATA-recommended value of the gravitational constant is:
 * $$G$$ =

The relative standard uncertainty is.

Natural units
Due to its use as a defining constant in some systems of natural units, particularly geometrized unit systems such as Planck units and Stoney units, the value of the gravitational constant will generally have a numeric value of 1 or a value close to it when expressed in terms of those units. Due to the significant uncertainty in the measured value of G in terms of other known fundamental constants, a similar level of uncertainty will show up in the value of many quantities when expressed in such a unit system.

Orbital mechanics
In astrophysics, it is convenient to measure distances in parsecs (pc), velocities in kilometres per second (km/s) and masses in solar units $Λ$. In these units, the gravitational constant is: $$ G \approx 4.3009 \times 10^{-3} \ {\mathrm{pc{\cdot}(km/s)^2} \, M_\odot}^{-1} .$$ For situations where tides are important, the relevant length scales are solar radii rather than parsecs. In these units, the gravitational constant is: $$ G \approx 1.90809\times 10^{5} \mathrm{\ (km/s)^2 } \, R_\odot M_\odot^{-1} .$$ In orbital mechanics, the period $κ$ of an object in circular orbit around a spherical object obeys $$ GM=\frac{3\pi V}{P^2} ,$$ where $κ = 8πG⁄c^{2} ≈ 1.866 m⋅kg^{−1}$ is the volume inside the radius of the orbit. It follows that
 * $$ P^2=\frac{3\pi}{G}\frac{V}{M}\approx 10.896 \, \mathrm{ h^2 {\cdot} g {\cdot} cm^{-3} \,}\frac{V}{M}.$$

This way of expressing $M⊙$ shows the relationship between the average density of a planet and the period of a satellite orbiting just above its surface.

For elliptical orbits, applying Kepler's 3rd law, expressed in units characteristic of Earth's orbit:
 * $$ G = 4 \pi^2 \mathrm{\ AU^3 {\cdot} yr^{-2}} \ M^{-1} \approx 39.478 \mathrm{\ AU^3 {\cdot} yr^{-2}} \ M_\odot^{-1} ,$$

where distance is measured in terms of the semi-major axis of Earth's orbit (the astronomical unit, AU), time in years, and mass in the total mass of the orbiting system ($P$).

The above equation is exact only within the approximation of the Earth's orbit around the Sun as a two-body problem in Newtonian mechanics, the measured quantities contain corrections from the perturbations from other bodies in the solar system and from general relativity.

From 1964 until 2012, however, it was used as the definition of the astronomical unit and thus held by definition: $$ 1\ \mathrm{AU} = \left( \frac{GM}{4 \pi^2} \mathrm{yr}^2 \right)^{\frac{1}{3}} \approx 1.495979 \times 10^{11}\ \mathrm{m}.$$ Since 2012, the AU is defined as $−2$ exactly, and the equation can no longer be taken as holding precisely.

The quantity $V$—the product of the gravitational constant and the mass of a given astronomical body such as the Sun or Earth—is known as the standard gravitational parameter (also denoted $G$). The standard gravitational parameter $M = + +$ appears as above in Newton's law of universal gravitation, as well as in formulas for the deflection of light caused by gravitational lensing, in Kepler's laws of planetary motion, and in the formula for escape velocity.

This quantity gives a convenient simplification of various gravity-related formulas. The product $$ is known much more accurately than either factor is.

Calculations in celestial mechanics can also be carried out using the units of solar masses, mean solar days and astronomical units rather than standard SI units. For this purpose, the Gaussian gravitational constant was historically in widespread use, $$, expressing the mean angular velocity of the Sun–Earth system. The use of this constant, and the implied definition of the astronomical unit discussed above, has been deprecated by the IAU since 2012.

Early history
The existence of the constant is implied in Newton's law of universal gravitation as published in the 1680s (although its notation as $GM$ dates to the 1890s), but is not calculated in his Philosophiæ Naturalis Principia Mathematica where it postulates the inverse-square law of gravitation. In the Principia, Newton considered the possibility of measuring gravity's strength by measuring the deflection of a pendulum in the vicinity of a large hill, but thought that the effect would be too small to be measurable. Nevertheless, he had the opportunity to estimate the order of magnitude of the constant when he surmised that "the mean density of the earth might be five or six times as great as the density of water", which is equivalent to a gravitational constant of the order:

A measurement was attempted in 1738 by Pierre Bouguer and Charles Marie de La Condamine in their "Peruvian expedition". Bouguer downplayed the significance of their results in 1740, suggesting that the experiment had at least proved that the Earth could not be a hollow shell, as some thinkers of the day, including Edmond Halley, had suggested.

The Schiehallion experiment, proposed in 1772 and completed in 1776, was the first successful measurement of the mean density of the Earth, and thus indirectly of the gravitational constant. The result reported by Charles Hutton (1778) suggested a density of $6.674$ ($2$ times the density of water), about 20% below the modern value. This immediately led to estimates on the densities and masses of the Sun, Moon and planets, sent by Hutton to Jérôme Lalande for inclusion in his planetary tables. As discussed above, establishing the average density of Earth is equivalent to measuring the gravitational constant, given Earth's mean radius and the mean gravitational acceleration at Earth's surface, by setting

$$G = g\frac{R_\oplus^2}{M_\oplus} = \frac{3g}{4\pi R_\oplus\rho_\oplus}.$$ Based on this, Hutton's 1778 result is equivalent to $μ$.

The first direct measurement of gravitational attraction between two bodies in the laboratory was performed in 1798, seventy-one years after Newton's death, by Henry Cavendish. He determined a value for $GM$ implicitly, using a torsion balance invented by the geologist Rev. John Michell (1753). He used a horizontal torsion beam with lead balls whose inertia (in relation to the torsion constant) he could tell by timing the beam's oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused. In spite of the experimental design being due to Michell, the experiment is now known as the Cavendish experiment for its first successful execution by Cavendish.

Cavendish's stated aim was the "weighing of Earth", that is, determining the average density of Earth and the Earth's mass. His result, $GM$, corresponds to value of $μ = GM$. It is surprisingly accurate, about 1% above the modern value (comparable to the claimed relative standard uncertainty of 0.6%).

19th century
The accuracy of the measured value of $G$ has increased only modestly since the original Cavendish experiment. $G$ is quite difficult to measure because gravity is much weaker than other fundamental forces, and an experimental apparatus cannot be separated from the gravitational influence of other bodies.

Measurements with pendulums were made by Francesco Carlini (1821, $−2$), Edward Sabine (1827, $4.301$), Carlo Ignazio Giulio (1841, $⊙$) and George Biddell Airy (1854, $−1$).

Cavendish's experiment was first repeated by Ferdinand Reich (1838, 1842, 1853), who found a value of $2$, which is actually worse than Cavendish's result, differing from the modern value by 1.5%. Cornu and Baille (1873), found $5.448 g.cm-3$.

Cavendish's experiment proved to result in more reliable measurements than pendulum experiments of the "Schiehallion" (deflection) type or "Peruvian" (period as a function of altitude) type. Pendulum experiments still continued to be performed, by Robert von Sterneck (1883, results between 5.0 and $G$) and Thomas Corwin Mendenhall (1880, $gμν$).

Cavendish's result was first improved upon by John Henry Poynting (1891), who published a value of $Tμν$, differing from the modern value by 0.2%, but compatible with the modern value within the cited relative standard uncertainty of 0.55%. In addition to Poynting, measurements were made by C. V. Boys (1895) and Carl Braun (1897), with compatible results suggesting $k = 0.017 radians per day$ = $N$. The modern notation involving the constant $G$ was introduced by Boys in 1894 and becomes standard by the end of the 1890s, with values usually cited in the cgs system. Richarz and Krigar-Menzel (1898) attempted a repetition of the Cavendish experiment using 100,000 kg of lead for the attracting mass. The precision of their result of $N$ was, however, of the same order of magnitude as the other results at the time.

Arthur Stanley Mackenzie in The Laws of Gravitation (1899) reviews the work done in the 19th century. Poynting is the author of the article "Gravitation" in the Encyclopædia Britannica Eleventh Edition (1911). Here, he cites a value of $G$ = $M$ with an relative uncertainty of 0.2%.

Modern value
Paul R. Heyl (1930) published the value of $M$ (relative uncertainty 0.1%), improved to $1.496 m$ (relative uncertainty 0.045% = 450 ppm) in 1942.

However, Heyl used the statistical spread as his standard deviation, and he admitted himself that measurements using the same material yielded very similar results while measurements using different materials yielded vastly different results. He spent the next 12 years after his 1930-paper to do more precise measurements, hoping that the composition-dependent effect would go away, but it did not, as he noted in his final paper from the year 1942.

Published values of $1.327 m3⋅s−2$ derived from high-precision measurements since the 1950s have remained compatible with Heyl (1930), but within the relative uncertainty of about 0.1% (or 1000 ppm) have varied rather broadly, and it is not entirely clear if the uncertainty has been reduced at all since the 1942 measurement. Some measurements published in the 1980s to 2000s were, in fact, mutually exclusive. Establishing a standard value for $6$ with a relative standard uncertainty better than 0.1% has therefore remained rather speculative.

By 1969, the value recommended by the National Institute of Standards and Technology (NIST) was cited with a relative standard uncertainty of 0.046% (460 ppm), lowered to 0.012% (120 ppm) by 1986. But the continued publication of conflicting measurements led NIST to considerably increase the standard uncertainty in the 1998 recommended value, by a factor of 12, to a standard uncertainty of 0.15%, larger than the one given by Heyl (1930).

The uncertainty was again lowered in 2002 and 2006, but once again raised, by a more conservative 20%, in 2010, matching the relative standard uncertainty of 120 ppm published in 1986. For the 2014 update, CODATA reduced the uncertainty to 46 ppm, less than half the 2010 value, and one order of magnitude below the 1969 recommendation.

The following table shows the NIST recommended values published since 1969: In the January 2007 issue of Science, Fixler et al. described a measurement of the gravitational constant by a new technique, atom interferometry, reporting a value of $G ≈ 8 m^{3}⋅kg^{−1}⋅s^{−2}$ = $3.986 m3⋅s−2$, 0.28% (2800 ppm) higher than the 2006 CODATA value. An improved cold atom measurement by Rosi et al. was published in 2014 of $G$ = $2$. Although much closer to the accepted value (suggesting that the Fixler et al. measurement was erroneous), this result was 325 ppm below the recommended 2014 CODATA value, with non-overlapping standard uncertainty intervals.

As of 2018, efforts to re-evaluate the conflicting results of measurements are underway, coordinated by NIST, notably a repetition of the experiments reported by Quinn et al. (2013).

In August 2018, a Chinese research group announced new measurements based on torsion balances, $6.7 m^{3}⋅kg^{−1}⋅s^{−2}$ and $4.5 g/cm3$ based on two different methods. These are claimed as the most accurate measurements ever made, with a standard uncertainties cited as low as 12 ppm. The difference of 2.7σ between the two results suggests there could be sources of error unaccounted for.

Constancy
Analysis of observations of 580 type Ia supernovae shows that the gravitational constant has varied by less than one part in ten billion per year over the last nine billion years.

title: Gravitational constant


text:
Imre Lakatos

Imre Lakatos (, ; Lakatos Imre ; 9 November 1922 – 2 February 1974) was a Hungarian philosopher of mathematics and science, known for his thesis of the fallibility of mathematics and its "methodology of proofs and refutations" in its pre-axiomatic stages of development, and also for introducing the concept of the "research programme" in his methodology of scientific research programmes.

Life
Lakatos was born Imre (Avrum) Lipsitz to a Jewish family in Debrecen, Hungary, in 1922. He received a degree in mathematics, physics, and philosophy from the University of Debrecen in 1944. In March 1944 the Germans invaded Hungary, and Lakatos along with Éva Révész, his then-girlfriend and subsequent wife, formed soon after that event a Marxist resistance group. In May of that year, the group was joined by Éva Izsák, a 19-year-old Jewish antifascist activist. Lakatos, considering that there was a risk that she would be captured and forced to betray them, decided that her duty to the group was to commit suicide. Subsequently, a member of the group took her to Debrecen and gave her cyanide.

During the occupation, Lakatos avoided Nazi persecution of Jews by changing his surname to Molnár. His mother and grandmother were murdered in Auschwitz. He changed his surname once again to Lakatos (Locksmith) in honor of Géza Lakatos.

After the war, from 1947, he worked as a senior official in the Hungarian ministry of education. He also continued his education with a PhD at Debrecen University awarded in 1948 and also attended György Lukács's weekly Wednesday afternoon private seminars. He also studied at the Moscow State University under the supervision of Sofya Yanovskaya in 1949. When he returned, however, he found himself on the losing side of internal arguments within the Hungarian communist party and was imprisoned on charges of revisionism from 1950 to 1953. More of Lakatos' activities in Hungary after World War II have recently become known. In fact, Lakatos was a hardline Stalinist and, despite his young age, had an important role between 1945 and 1950 (his own arrest and jailing) in building up the Communist rule, especially in cultural life and the academia, in Hungary.

After his release, Lakatos returned to academic life, doing mathematical research and translating George Pólya's How to Solve It into Hungarian. Still nominally a communist, his political views had shifted markedly, and he was involved with at least one dissident student group in the lead-up to the 1956 Hungarian Revolution.

After the Soviet Union invaded Hungary in November 1956, Lakatos fled to Vienna and later reached England. He lived there for the rest of his life however he never achieved a British citizenship. He received a PhD in philosophy in 1961 from the University of Cambridge; his doctoral thesis was entitled Essays in the Logic of Mathematical Discovery, and his doctoral advisor was R. B. Braithwaite. The book Proofs and Refutations: The Logic of Mathematical Discovery, published after his death, is based on this work.

In 1960, he was appointed to a position in the London School of Economics (LSE), where he wrote on the philosophy of mathematics and the philosophy of science. The LSE philosophy of science department at that time included Karl Popper, Joseph Agassi and J. O. Wisdom. It was Agassi who first introduced Lakatos to Popper under the rubric of his applying a fallibilist methodology of conjectures and refutations to mathematics in his Cambridge PhD thesis.

With co-editor Alan Musgrave, he edited the often cited Criticism and the Growth of Knowledge, the Proceedings of the International Colloquium in the Philosophy of Science, London, 1965. Published in 1970, the 1965 Colloquium included well-known speakers delivering papers in response to Thomas Kuhn's The Structure of Scientific Revolutions.

In January 1971, he became editor of the British Journal for the Philosophy of Science, which J. O. Wisdom had built up before departing in 1965, and he continued as editor until his death in 1974, after which it was then edited jointly for many years by his LSE colleagues John W. N. Watkins and John Worrall, Lakatos's ex-research assistant.

Lakatos and his colleague Spiro Latsis organized an international conference in Greece in 1975, and went ahead despite his death. It was devoted entirely to historical case studies in Lakatos's methodology of research programmes in physical sciences and economics. These case studies in such as Einstein's relativity programme, Fresnel's wave theory of light and neoclassical economics, were published by Cambridge University Press in two separate volumes in 1976, one devoted to physical sciences and Lakatos's general programme for rewriting the history of science, with a concluding critique by his great friend Paul Feyerabend, and the other devoted to economics.

He remained at LSE until his sudden death in 1974 of a heart attack at the age of 51. The Lakatos Award was set up by the school in his memory. His last lectures along with some correspondance were published in Against Method. His last lectures along with parts of his correspondence with Paul Feyerabend have been published in For and Against Method.

Philosophy of mathematics
Lakatos' philosophy of mathematics was inspired by both Hegel's and Marx's dialectic, by Karl Popper's theory of knowledge, and by the work of mathematician George Pólya.

The 1976 book Proofs and Refutations is based on the first three chapters of his 1961 four-chapter doctoral thesis Essays in the Logic of Mathematical Discovery. But its first chapter is Lakatos' own revision of its chapter 1 that was first published as Proofs and Refutations in four parts in 1963–64 in the British Journal for the Philosophy of Science. It is largely taken up by a fictional dialogue set in a mathematics class. The students are attempting to prove the formula for the Euler characteristic in algebraic topology, which is a theorem about the properties of polyhedra, namely that for all polyhedra the number of their vertices V minus the number of their edges E plus the number of their faces F is 2 (V − E + F = 2). The dialogue is meant to represent the actual series of attempted proofs that mathematicians historically offered for the conjecture, only to be repeatedly refuted by counterexamples. Often the students paraphrase famous mathematicians such as Cauchy, as noted in Lakatos's extensive footnotes.

Lakatos termed the polyhedral counterexamples to Euler's formula monsters and distinguished three ways of handling these objects: Firstly, monster-barring, by which means the theorem in question could not be applied to such objects. Secondly, monster-adjustment, whereby by making a re-appraisal of the monster it could be made to obey the proposed theorem. Thirdly, exception handling, a further distinct process. These distinct strategies have been taken up in qualitative physics, where the terminology of monsters has been applied to apparent counterexamples, and the techniques of monster-barring and monster-adjustment recognized as approaches to the refinement of the analysis of a physical issue.

What Lakatos tried to establish was that no theorem of informal mathematics is final or perfect. This means that we should not think that a theorem is ultimately true, only that no counterexample has yet been found. Once a counterexample is found, we adjust the theorem, possibly extending the domain of its validity. This is a continuous way our knowledge accumulates, through the logic and process of proofs and refutations. (If axioms are given for a branch of mathematics, however, Lakatos claimed that proofs from those axioms were tautological, i.e. logically true.)

Lakatos proposed an account of mathematical knowledge based on the idea of heuristics. In Proofs and Refutations the concept of "heuristic" was not well developed, although Lakatos gave several basic rules for finding proofs and counterexamples to conjectures. He thought that mathematical "thought experiments" are a valid way to discover mathematical conjectures and proofs, and sometimes called his philosophy "quasi-empiricism".

However, he also conceived of the mathematical community as carrying on a kind of dialectic to decide which mathematical proofs are valid and which are not. Therefore, he fundamentally disagreed with the "formalist" conception of proof prevailed in Frege's and Russell's logicism, which defines proof simply in terms of formal validity.

On its first publication as an article in the British Journal for the Philosophy of Science in 1963–64, Proofs and Refutations became highly influential on new work in the philosophy of mathematics, although few agreed with Lakatos' strong disapproval of formal proof. Before his death he had been planning to return to the philosophy of mathematics and apply his theory of research programmes to it. Lakatos, Worrall and Zahar use Poincaré (1893) to answer one of the major problems perceived by critics, namely that the pattern of mathematical research depicted in Proofs and Refutations does not faithfully represent most of the actual activity of contemporary mathematicians.

Cauchy and uniform convergence
In a 1966 text Cauchy and the continuum, Lakatos re-examines the history of the calculus, with special regard to Augustin-Louis Cauchy and the concept of uniform convergence, in the light of non-standard analysis. Lakatos is concerned that historians of mathematics should not judge the evolution of mathematics in terms of currently fashionable theories. As an illustration, he examines Cauchy's proof that the sum of a series of continuous functions is itself continuous. Lakatos is critical of those who would see Cauchy's proof, with its failure to make explicit a suitable convergence hypothesis, merely as an inadequate approach to Weierstrassian analysis. Lakatos sees in such an approach a failure to realize that Cauchy's concept of the continuum differed from currently dominant views.

Research programmes
Lakatos's second major contribution to the philosophy of science was his model of the "research programme", which he formulated in an attempt to resolve the perceived conflict between Popper's falsificationism and the revolutionary structure of science described by Kuhn. Popper's standard of falsificationism was widely taken to imply that a theory should be abandoned as soon as any evidence appears to challenge it, while Kuhn's descriptions of scientific activity were taken to imply that science is most fruitful during periods in which popular, or "normal", theories are supported despite known anomalies. Lakatos' model of the research programme aims to combine Popper's adherence to empirical validity with Kuhn's appreciation for conventional consistency.

A Lakatosian research programme is based on a hard core of theoretical assumptions that cannot be abandoned or altered without abandoning the programme altogether. More modest and specific theories that are formulated in order to explain evidence that threatens the "hard core" are termed auxiliary hypotheses. Auxiliary hypotheses are considered expendable by the adherents of the research programme—they may be altered or abandoned as empirical discoveries require in order to "protect" the "hard core". Whereas Popper was generally read as hostile toward such ad hoc theoretical amendments, Lakatos argued that they can be progressive, i.e. productive, when they enhance the programme's explanatory and/or predictive power, and that they are at least permissible until some better system of theories is devised and the research programme is replaced entirely. The difference between a progressive and a degenerative research programme lies, for Lakatos, in whether the recent changes to its auxiliary hypotheses have achieved this greater explanatory/predictive power or whether they have been made simply out of the necessity of offering some response in the face of new and troublesome evidence. A degenerative research programme indicates that a new and more progressive system of theories should be sought to replace the currently prevailing one, but until such a system of theories can be conceived of and agreed upon, abandonment of the current one would only further weaken our explanatory power and was therefore unacceptable for Lakatos. Lakatos's primary example of a research programme that had been successful in its time and then progressively replaced is that founded by Isaac Newton, with his three laws of motion forming the "hard core".

The Lakatosian research programme deliberately provides a framework within which research can be conducted on the basis of "first principles" (the "hard core"), which are shared by those involved in the research programme and accepted for the purpose of that research without further proof or debate. In this regard, it is similar to Kuhn's notion of a paradigm. Lakatos sought to replace Kuhn's paradigm, guided by an irrational "psychology of discovery", with a research programme no less coherent or consistent, yet guided by Popper's objectively valid logic of discovery.

Lakatos was following Pierre Duhem's idea that one can always protect a cherished theory (or part of one) from hostile evidence by redirecting the criticism toward other theories or parts thereof. (See Confirmation holism and Duhem–Quine thesis). This aspect of falsification had been acknowledged by Popper.

Popper's theory, falsificationism, proposed that scientists put forward theories and that nature "shouts NO" in the form of an inconsistent observation. According to Popper, it is irrational for scientists to maintain their theories in the face of nature's rejection, as Kuhn had described them doing. For Lakatos, however, "It is not that we propose a theory and Nature may shout NO; rather, we propose a maze of theories, and nature may shout INCONSISTENT". The continued adherence to a programme's "hard core", augmented with adaptable auxiliary hypotheses, reflects Lakatos's less strict standard of falsificationism.

Lakatos saw himself as merely extending Popper's ideas, which changed over time and were interpreted by many in conflicting ways. In his 1968 article "Criticism and the Methodology of Scientific Research Programmes", Lakatos contrasted Popper0, the "naive falsificationist" who demanded unconditional rejection of any theory in the face of any anomaly (an interpretation Lakatos saw as erroneous but that he nevertheless referred to often); Popper1, the more nuanced and conservatively interpreted philosopher; and Popper2, the "sophisticated methodological falsificationist" that Lakatos claims is the logical extension of the correctly interpreted ideas of Popper1 (and who is therefore essentially Lakatos himself). It is, therefore, very difficult to determine which ideas and arguments concerning the research programme should be credited to whom.

While Lakatos dubbed his theory "sophisticated methodological falsificationism", it is not "methodological" in the strict sense of asserting universal methodological rules by which all scientific research must abide. Rather, it is methodological only in that theories are only abandoned according to a methodical progression from worse theories to better theories—a stipulation overlooked by what Lakatos terms "dogmatic falsificationism". Methodological assertions in the strict sense, pertaining to which methods are valid and which are invalid, are, themselves, contained within the research programmes that choose to adhere to them, and should be judged according to whether the research programmes that adhere to them prove progressive or degenerative. Lakatos divided these "methodological rules" within a research programme into its "negative heuristics", i.e., what research methods and approaches to avoid, and its "positive heuristics", i.e., what research methods and approaches to prefer. While the "negative heuristic" protects the hard core, the "positive heuristic" directs the modification of the hard core and auxiliary hypotheses in a general direction.

Lakatos claimed that not all changes of the auxiliary hypotheses of a research programme (which he calls "problem shifts") are equally productive or acceptable. He took the view that these "problem shifts" should be evaluated not just by their ability to defend the "hard core" by explaining apparent anomalies, but also by their ability to produce new facts, in the form of predictions or additional explanations. Adjustments that accomplish nothing more than the maintenance of the "hard core" mark the research programme as degenerative.

Lakatos' model provides for the possibility of a research programme that is not only continued in the presence of troublesome anomalies but that remains progressive despite them. For Lakatos, it is essentially necessary to continue on with a theory that we basically know cannot be completely true, and it is even possible to make scientific progress in doing so, as long as we remain receptive to a better research programme that may eventually be conceived of. In this sense, it is, for Lakatos, an acknowledged misnomer to refer to "falsification" or "refutation", when it is not the truth or falsity of a theory that is solely determining whether we consider it "falsified", but also the availability of a less false theory. A theory cannot be rightfully "falsified", according to Lakatos, until it is superseded by a better (i.e. more progressive) research programme. This is what he says is happening in the historical periods Kuhn describes as revolutions and what makes them rational as opposed to mere leaps of faith or periods of deranged social psychology, as Kuhn argued.

Pseudoscience
According to the demarcation criterion of pseudoscience proposed by Lakatos, a theory is pseudoscientific if it fails to make any novel predictions of previously unknown phenomena or its predictions were mostly falsified, in contrast with scientific theories, which predict novel fact(s). Progressive scientific theories are those that have their novel facts confirmed, and degenerate scientific theories, which can degenerate so much that they become pseudo-science, are those whose predictions of novel facts are refuted. As he put it:
 * "A given fact is explained scientifically only if a new fact is predicted with it... The idea of growth and the concept of empirical character are soldered into one." See pages 34–35 of The Methodology of Scientific Research Programmes, 1978.

Lakatos's own key examples of pseudoscience were Ptolemaic astronomy, Immanuel Velikovsky's planetary cosmogony, Freudian psychoanalysis, 20th-century Soviet Marxism, Lysenko's biology, Niels Bohr's quantum mechanics post-1924, astrology, psychiatry, and neoclassical economics.

Darwin's theory
In his 1973 Scientific Method Lecture 1 at the London School of Economics, he also claimed that "nobody to date has yet found a demarcation criterion according to which Darwin can be described as scientific".

Almost 20 years after Lakatos's 1973 challenge to the scientificity of Darwin, in her 1991 The Ant and the Peacock, LSE lecturer and ex-colleague of Lakatos, Helena Cronin, attempted to establish that Darwinian theory was empirically scientific in respect of at least being supported by evidence of likeness in the diversity of life forms in the world, explained by descent with modification. She wrote that our usual idea of corroboration as requiring the successful prediction of novel facts... Darwinian theory was not strong on temporally novel predictions. ... however familiar the evidence and whatever role it played in the construction of the theory, it still confirms the theory.

Rational reconstructions of the history of science
In his 1970 article "History of Science and Its Rational Reconstructions" Lakatos proposed a dialectical historiographical meta-method for evaluating different theories of scientific method, namely by means of their comparative success in explaining the actual history of science and scientific revolutions on the one hand, whilst on the other providing a historiographical framework for rationally reconstructing the history of science as anything more than merely inconsequential rambling. The article started with his now renowned dictum "Philosophy of science without history of science is empty; history of science without philosophy of science is blind".

However, neither Lakatos himself nor his collaborators ever completed the first part of this dictum by showing that in any scientific revolution the great majority of the relevant scientific community converted just when Lakatos's criterion – one programme successfully predicting some novel facts whilst its competitor degenerated – was satisfied. Indeed, for the historical case studies in his 1968 article "Criticism and the Methodology of Scientific Research Programmes" he had openly admitted as much, commenting: "In this paper it is not my purpose to go on seriously to the second stage of comparing rational reconstructions with actual history for any lack of historicity."

Feyerabend
Paul Feyerabend argued that Lakatos's methodology was not a methodology at all, but merely "words that sound like the elements of a methodology". He argued that Lakatos's methodology was no different in practice from epistemological anarchism, Feyerabend's own position. He wrote in Science in a Free Society (after Lakatos's death) that: Lakatos realized and admitted that the existing standards of rationality, standards of logic included, were too restrictive and would have hindered science had they been applied with determination. He therefore permitted the scientist to violate them (he admits that science is not "rational" in the sense of these standards). However, he demanded that research programmes show certain features in the long run — they must be progressive... I have argued that this demand no longer restricts scientific practice. Any development agrees with it. Lakatos and Feyerabend planned to produce a joint work in which Lakatos would develop a rationalist description of science, and Feyerabend would attack it. The correspondence between Lakatos and Feyerabend, where the two discussed the project, has since been reproduced, with commentary, by Matteo Motterlini.

Archives

 * Imre Lakatos's papers are held at the London School of Economics. His personal is also held at the School.

title: Imre Lakatos


text:
Talk:List of German monarchs

Pretenders of Germany
I want to readd the pretenders section. Under the German Empire's Constitution, the King of Prussia was German Emperor; therefore, the pretenders to the Prussian throne are also pretenders to the German throne. Just check the articles House of Hohenzollern, Line of succession to the German throne, List of rulers of Prussia. Emperor001 (talk) 02:21, 16 January 2009 (UTC)

Liudolfing or Ottonian?
Since Liudolfing is piped to Ottonian, which redirects to Ottonian dynasty, is there any particular reason why we can't just say "Ottonian". Certainly I think of those kings as "Ottonian". Scolaire (talk) 19:20, 22 May 2009 (UTC)

Ferdinand II
Could somebody cite a source for Ferdinand being elected during Matthias's lifetime and becoming king of the Romans? I've never heard of such a thing, and I've read a decent amount about the period. My understanding was that he was only elected after Matthias's death. john k (talk) 01:09, 6 July 2009 (UTC)

Alright, looks like this was just vandalism by an anon that nobody caught. Sigh. john k (talk) 01:18, 6 July 2009 (UTC)

Confusion about names/titles
The sections from the German_Emperor downwards have separate columns for rulers name and title, yet the titles are actually confusingly split between name and title. Example: Frederick William IV has also the title "King of Prussia" in his name and only "President of the German Union" in his title column; presumably the "King of Prussia" should be moved to the title column as well. Also, to clear the confusion, the intro should discuss the usage of the title of German Emperor from 1871 onwards. --Piotr Konieczny aka Prokonsul Piotrus 01:17, 31 August 2009 (UTC)
 * I think the idea of the "title" column is that we're talking about the title they held that gave them authority over Germany, not all titles they held. "King of Prussia" identifies who he was, but has nothing, technically speaking, to do with ruling over Germany.  The idea is that there were various different organizations formed between 1806 and 1871 that were confederations or federations that had authority over the whole of Germany.  The heads of those organizations had titles, which is what the title column is for.  The text should perhaps explain this, though. john k (talk) 02:24, 31 August 2009 (UTC)

Also regarding the titles: they are provided in English and Modern High German, both languages unknown to the rulers (at least in the early days). It would be nice to have them in OHG/MHG as appropriate if someone has the ability and time, unfortunately I have neither. 138.162.128.53 (talk) 17:24, 22 February 2010 (UTC)
 * No, it would not be appropriate and totaly useless to put them here in a language no reader understands. Certainly not in this list, maybe (if it really must be) in the articles about the various offices. Str1977 (talk) 18:27, 23 July 2010 (UTC)

Lead
The article is called List_of_German_monarchs not List_of_monarchs of Germany. All we have in here is: Eastern Frankish Kingdom German Kingdom, Holy Roman Empire German confederations, 1806-1871 Confederation of the Rhine, 1806-1813 German Confederation, 1815-1866 North German Confederation, 1867-1871 German Empire (1871–1918) Where is Germany? Mootros (talk) 16:04, 14 April 2011 (UTC)
 * Where is Germany? Between France and Poland, as always.

 * But it is quite true that this should be the list of monarchs of Germany; Frederick the Great and Ludwig the Mad were German monarchs. Septentrionalis PMAnderson 16:15, 14 April 2011 (UTC)
 * I'm afraid this is a rather ahistorical perspective. The sources I've added, especially with regards to kings prior to Henry IV (Heinrich IV) clearly show this. Mootros (talk) 17:58, 14 April 2011 (UTC)
 * What sources? These edits have none. Septentrionalis PMAnderson 18:44, 14 April 2011 (UTC)
 * No. 18:54, 14 April 2011 (UTC)

 * -> ^ a b c d Medieval Europeans: studies in ethnic identity and national perspectives in medieval Europe By Alfred P. Smyth, Palgrave Macmillan (1998), p. 64
 * This is an anthology; I presume you actually mean Chapter 3: The Making of England and Germany 850–1050; which uses kingdom of Germany and Germany throughout. Since this applies only to the rise of the Saxon dynasty, and says that their Germany may have been as well organized as Anglo-Saxon England, the strongest state in Europe, this fails verification. Septentrionalis PMAnderson 01:29, 15 April 2011 (UTC)

Emperor-elect
I think that the "Emperor-elect" identifications in the list should be preceded with "de jure" because in our modern understanding an "-elect" is someone without power. СЛУЖБА (talk) 07:00, 30 December 2011 (UTC)

It might be what it means now, for example in the period between where an American President is elected and when he is inaugurated, but it isn't what it meant then. It was just the title the Holy Roman Emperor used before his coronation (which, btw, does NOT make a monarch a monarch. an uncrowned monarch is still a monarch.). (Holy) Roman Emperor Elect' and 'President-Elect' are not the same thing.JWULTRABLIZZARD (talk) 07:31, 13 May 2013 (UTC)
 * An uncrowned monarch is not always a monarch. The notion that coronation does not make one a monarch is a British tradition. In Hungary, coronation very much did make monarch a monarch. In medieval times, uncrowned popes such as Pope-elect Stephen were not considered legitimate popes - Stephen still isn't. Coronation was also indispensable in Poland. Surtsicna (talk) 10:23, 13 May 2013 (UTC)

But that is the exception to the rule, and if anything is more connected to monarchies where the crown has some national/semi-divine status, which was certainly the case with the Crowns of Charlemagne and St. Stephen: to give but a few examples: no monarch of the Netherlands has ever been crowned (though the Kingdom does have a crown, it has never been worn), no King of Norway has been crowned since Haakon VII, nor any of Sweden since Oscar II. None of the Kings of the modern Kingdom of Italy were crowned, neither have any of the Grand-Dukes/Duchesses of Luxembourg, nor any of the Kings of Greece, Yugoslavia, modern Bulgaria, Albania, post-1871 German Emperors, any of the Emperors of Austria or any of the Kings/Queens of Portugal after the sixteenth century, nor any of the Kings or Queens of a unified Spain, nor the vast majority of Islamic monarchies, modern and past. Each was no less a monarch in the eyes of the law and indeed the eyes of the international community for lack of a coronation, so your assertion that this is somehow a 'British' tradition is simply not true: furthermore, in most monarchies, both pre-modern and modern, a monarch was proclaimed immediately after the death or abdication of their predecessor, the coronation simply acting as a spectacular event of undoubted religious significance, but of very little legal significance. Whilst, of course, there are exceptions as you rightly point out, this was exceptional and in most cases the adage 'the King is dead, long live the King' was quite literally true. Likewise, the monarchs of France (until 1830), Russia, Serbia, Britain (and its predecessor states), Romania, Prussia, (and Norway and Sweden til the early 20th century),whilst they did have coronations, the coronation was of absolutely no legal significance as to whether they were King or not.

Note also that until the time of Edward I, the English King was not titled 'King' (being merely titled 'dominus anglorum' or 'Lord of the English' before his coronation. So where this supposed 'British' tradition is supposed to come from, I have no idea.

I will however draw a curious, albeit isolated modern-day parallel however: the Kings of the Belgians, whilst none of them have ever been crowned (the only Crown of Belgium only exists in heraldry on paper: a real physical crown does not and has never existed), nonetheless the throne is considered vacant until the monarch takes the oath as King at their inauguration, at which point they legally become monarch

My point is there is often an assumption amongst readers (usually American, but by no means always) that, like a President of a Republic becomes President not upon election, but upon inauguration, that the same applies in a monarchy, and moreover that Emperor-Elect=the same meaning as 'President-Elect' when, in most cases (though there are exceptions) this is untrue. The title of 'Emperor-Elect' was simply used (with papal approval) from 1508, so the person elected by the imperial college of electors did not have to bother with the costly and often dangerous business of the imperial coronation, and still legitimately call themselves 'Emperor'. It also meant the Pope did not have to worry too much about imperial interference in matters relating to Italy.JWULTRABLIZZARD (talk) 11:14, 13 May 2013 (UTC)

Otto II. `the red´????
Never heard anyone calling him the red - even his wiki-page lacks that title. (a historian)--92.226.16.184 (talk) 00:26, 2 December 2012 (UTC)
 * Check his wiki-page again. For a primary source, try the Gesta principum Polonorum. —Srnec (talk) 22:37, 2 December 2012 (UTC)

Merge with German monarchy 1918
This article appears to cover the same ground as German monarchy 1918. I suggest that the two articles be merged.

IMO this should be done to form a retitled/another page titled: "German monarchy" which should then tie back to both German Empire and Holy Roman Empire

--LookingGlass (talk) 19:17, 15 December 2012 (UTC)

Hitler
As the term Reich was used to denote Nazi Germany, and that the Holy Roman Emperorship was elective, I figure that Hitler should be included as he was the de facto "monarch" of Germany.Ericl (talk) 15:09, 14 August 2013 (UTC)

The term Reich as "Realm" was used by both the Weimar Republic and Nazi Germany in their official name: German Reich. This did not mean that their leaders were monarchs. Dimadick (talk) 15:59, 14 August 2013 (UTC)

Disputed elections of 1247 and 1257
It is not the job of Wikipedia's editors to pronounce on the legality of an election held in 1257. The election of Richard on 13 January was not regular, and involved only three electors. Maybe it gained the support of Bohemia later. Alfonso's election on 1 April had the support of four electors, including Bohemia.

William of Holland secured election post facto by all the electors save Bavaria in 1252. He was basically the undisputed king of Germany, recognised almost everywhere, after Conrad's death in 1254. It is only the circumstances of his initial election in 1247 that get him marked off in the history books as merely an anti-king. Srnec (talk) 23:36, 24 June 2015 (UTC)

 * You make some important points, both of which suggest that the "Interregnum" should be removed and changed to a hybrid of what I attempted to change it to and what you suggest. First, I think we can both agree that Henry Raspe does not belong in the "Interregnum period since he was indisputably an anti-king to Frederick II, during whose reign his entire pretension occurred. His name belongs with the other Hohenstaufen anti-kings such as Philip of Swabia and Otto IV. Second, if William of Holland secured the throne by a majority of electors in 1252, then he should not be noted purely as an anti-king, as he currently is. He should be afforded the title of king, with a reference to his pretension prior to 1252, as with most of the other articles of anti-kings who became kings. Similarly, Richard's election in 1257 was not illegal or illegitimate and the majority of European kingdoms, including notably France, eventually accepted it except for those few that supported Alfonso of Castile. Alfonso's election was irregular in that another man had already been proclaimed king by many of the electors. Richard also held some, albeit very little, power in Germany while Alfonso held none and never even went there. Richard received the crown, Alfonso did not.

 * The larger issue, I think, is that there is no article on the "Interregnum" which suggests to me that it is primarily a wikipedia construct – no other historical source I can find references this period as such. True, none of the kings of this period had much power in Germany, but there was almost continuously a nominated king in Germany. In fact, only Alfonso of Castile's antagonism toward Richard of Cornwall really represents a conflict at all. The bigger issue in this period is that there was no authoritative ruler in Germany so everybody was simply doing as they wished.

 * I suggest the section get replaced with this:

Continued from Hohenstaufen

Holland

Plantagenet

 * This cleans up the period significantly, makes all the table fields consistent with the rest of the list, and matches things closer to their historical context. Two minor corrections I made are that I removed the reference of Richard being brother-in-law to Frederick – this relationship does not appear to have played into his election. I also added the full date of death for Alfonso to match the consistency of other similar dates on the list.

 * Please let me know your opinion of this revised scheme. – Darius von Whaleyland,  Great Khan   of the Barbarian Horde  05:49, 25 June 2015 (UTC)

 * The "Great Interregnum" is defined by Britannica as the period of 1250–73 in the history of Germany.
 * I don't really think that separate headings for Holland and Plantagenet make much sense. In fact, the dynastic headings make no sense at all between the deaths of Conrad IV (1254) and Sigismund (1437). Even for the earlier period we are forced to have one-king sections (Supplinburger) or to lump them together (Welf with Hohenstaufen). And this ignores the anti-kings of Henry IV's reign. I'd suggest just one table and put the house names of the true dynasties (Carolingian, Ottonian, Salian, Hohenstaufen, maybe Luxembourg, Habsburg and Habsburg-Lorraine) in bold so that a reader can follow them while scanning the list. Use bold for the names of those crowned emperor (as currently). Ditch the italics. Note irregular elections (i.e. anti-kings) and limited real authority in the notes. The problem is that pretty much each case of kingly rivalry is sui generis. Srnec (talk) 23:20, 25 June 2015 (UTC)

 * That is a generally good point and I had not seen the heading in Britannica, I've only been looking at more specific sources which may be why the period isn't especially called out. I agree that one table may be better. Could it be color-coordinated as some other genealogical tables are? Each dynasty gets its own color and single-reign dynasties are white. I hesitantly agree that Italics should be removed, but only because of the vagueness of some imperial elections. I definitely think that people designated as anti-kings by most authorities should be cited as such in the comments box, though. I also agree that if the current dynastic organization is maintained, then Conrad IV should be pulled out of the Hohenstaufen section and placed squarely in the Interregnum, while Henry Raspe gets moved into the Hohenstaufen since he never pretended during the interregnum period. But I think combining the entire list is a better option due to the elective, non-dynastic nature of the Holy Roman Empire. – Darius von Whaleyland,  Great Khan   of the Barbarian Horde  23:33, 25 June 2015 (UTC)

Anachronistic titles
Can we please stop applying German nationalism to the middle ages by referring to various historic titles like "King of the Romans" (rex romanorum) "King of East Francia" (rex francorum orientalium) as "King of Germany"? The only thing that could even be considered remotely appropriate for this translation are contemporary terms like "rex teutonicorum", "rex alemannie", etc. Most of which had a polemic intent in their usage, see Heimerich IV & the Investiture Controversy Goodpoints (talk) 00:54, 15 December 2015 (UTC)
 * Well, that's basically accepted historiography. Gerard von Hebel (talk) 02:34, 15 December 2015 (UTC)
 * I'd agree with you in theory but since this is primarily an informative site, exclusively using the title "King of the Romans", especially after 1556, could be confusing to many people. "King of East Francia", however, is more important and is used with the Carolingians, but not their German successors because those successors never used the title. Regarding your statement about German nationalism, though, simply stated, it isn't. Medieval chroniclers in France were using the title "king of the Germans" to refer to non-Holy Roman Emperors in the thirteenth and fourteenth century, long before any notion of nationalism existed in Germany or really anywhere in Europe. It's not anachronistic; it is precisely what their European counterparts thought of them. That's why Richard of Germany is called that and not Richard of Rome. Even Richard's son used that title within and outside of England. "Germany" is not anachronistic, it is historical. – Whaleyland ( Talk •  Contributions ) 07:47, 15 December 2015 (UTC)
 * Should not an 'informative site' provide correct historical information even if it does not necessarily conform with modern understandings of political geography? Lack of familiarity on the part of the average reader is not an excuse to not use the person's historically attested title or a direct translation of such, that is what hyperlinking is for. There already exists an article, though a pretty poor one, on the title of King of the Romans. Can you provide an example of these French chroniclers? I've never come across anything like "rex germanorum" or "rex germani"/"rex germaniae" in any primary source. If you're referring to Richard, 1st Earl of Cornwall; he is referred to as "King of Germany" only by modern English historians, not by any contemporary sources. The Chronica Majora of Matthew of Paris refers to Richard upon his coronation in Aachen as "regem [rex] Alemanniae sive [or] Romanorum". (Luard, ed., Vol. 5, pg. 640 — Royal MS 14 C VII f.200r) The Chronicon ex Chronicis records him as "Ricardus, Alemmaniae rex" and refers to his son as "Eadmundus de Alemmania" (Thorpe, ed., Vol. 2, pg. 207-209)
 * Also in the c. 1300 Middle English poem "Richard Coeur de Lion", the titular Richard has an encounter with the otherwise unnamed "kyng of Almayn(e)" (lines 271-300, etc.). Derivatives of "Germania" were mostly used in a historical context (i.e. Julius Caesar's Germani), not to be confused with the Frankish derived use referring to close relatives ("cousin-german" / "cosyn germayn"), until the 15th century. Even then I've only seen it used to refer to a general region & its people, and not as any sort of title or polity. See: quotation search results for "germayn" and "german" in the Uni. of Michigan Middle English Dictionary. A rather humorous example being the given excerpt from Capgrave's "The Life of St. Norbert" (1440) where he's reading the 12th c. manuscript "Vita S. Norbertus" and  says (in the full text): 'This mannys name Norbert thoo þei called Of Teutonye nacioun, the story seith rith soo. Whech word made me of stody al apalled; For whethir it is a cyte weel iwalled, Or ellis a cuntre, auctouris touch him nowt. But aftirward whann I was bettir beþowt ¶ I supposed þan þis cuntre stant in Germayne, Because þis man of whech we haue now told Was sumtyme dwellinge in the þe cyte of Colayne". ('This man's name is Norbert, though they called him 'of Teutonye nation', the story sayeth right so. This word made me so weary of study; For whether it ['Teutonye'] is a well-walled city, or else a country, the author didn't bother [explaining]. But afterward, when I was better bethought ¶ I supposed than this country stands in 'Germayne', Because this man of which we have now told was sometime dwelling in the city of Cologne.') This being evidence that "Germania" derivations might have just eclipsed "Teutonia" and "Alemannia" in English very recently to Capgrave's life as he should have otherwise been familiar with the terms. Goodpoints (talk) 23:21, 7 January 2016 (UTC)

 * "King of Germany" is a perfect translation of "rex Alemanniae" into modern English. We aren't writing in Middle English. In fact, we can't write at all about the Middle Ages without translating. You can find rex germaniae (applied to Louis the German) in the image at right. Srnec (talk) 01:12, 8 January 2016 (UTC)
 * A perfect translation how? It is neither literal nor does it clarify. It only causes confusion by conflating various medieval polities, titles, and appellations with the post-19th c. states known in English as "Germany". A literal translation would be "rex Alemanniae" = "King of Alemannia". But that's not my main point, references like "rex alemanniae" are not the official title ("rex romanorum"), historical persons should be referred to by their official titles (or a direct translation of) in an encyclopedia. Should the article for Leonid Brezhnev refer to him as "The Premier" rather than "General Secretary of the Central Committee of the Communist Party of the Soviet Union"? Should Obama's refer to him as "The American President" rather than "President of the United States of America"?
 * In the image you give, from the Chronicon Universale, Louis is the top male figure on the right section labelled "Lothuwicus", the scroll he holds reads (upsidedown) "rex Germania". It's an example I did not remember, but it's not relevant to the broader discussion. The appellation "Ludovicus Germanicus" refers to the Roman "Germania" as Frankish culture was heavily influenced by the Gallo-Roman culture and Louis' kingdom (still referred to officially as "regnum francorum orientalium") was largely within the Roman defined Magna Germania. Caligula's full name was "Gaius Julius Caesar Augustus Germanicus", would you refer to him as "Caligula the German"? Note that in the image, none of Louis' descendants bear that same appellation, but are labelled "rex alemannia", "rex bawaria", "rex oster francia", etc. Goodpoints (talk) 03:27, 8 January 2016 (UTC)
 * Do you think that the French term roi d'Allemagne is correct, but that the corresponding English term, which must have the same connotations, is not?
 * The "official" title of a medieval monarch is whatever title his chancery was using, which could change at any time. We do not, nor should we, distinguish between rex Anglorum and rex Angliae when translating. Nor should we demand the anachronistic "Angles" or "Anglia" where "English" and "England" would be appropriate. High medieval Alemannia is just modern English Germany and French Allemagne. Official titles and direct translations are sometimes appropriate, but at other times they don't, as you say, clarify. Mariano Rajoy is called Prime Minister of Spain, not President of the Government. It's Byzantine Empire, not Romania.
 * Of course, the various titles a ruler used can be explained in his article. Srnec (talk) 04:32, 8 January 2016 (UTC)
 * I strongly agree, but German nationalism is rooted into the German language. Older German writers have typically always translated Deutsch/Teutonic/Germani/etc. to "German" in the sense of Germany. Though misconceptional, this is hard to actually make clear without resorting to original research. That's mostly why a lot of this lingers around on the wiki. Bataaf van Oranje (Prinsgezinde) (talk) 10:26, 23 May 2016 (UTC)

Napoleon
Napoleon shouldn't be in this. He might have been the protector of the Confederation of the Rhine, but he wasn't it's head. The conferderation had a Prince-Primat. Gerard von Hebel (talk) 20:08, 1 January 2016 (UTC)

Some corrections German Confederation / North German Confederation
Hello, I made some correction with regard to the German Confederation and the North German Conferederation. The G.C. did not have a president or any head of state etc. The Austrian delegate presided the Bundestag. Therefore, Austria was unofficially called the Präsidialmacht. The supreme organ of the G.C. was the Bundestag, so one might name the delegate a kind of chairman. In the monarchal world of the time, it is okay to use here the Emperor instead.

The North German Confederation did not have a head of state expressis verbis, but the Prussian King was given the title and function of bearer of the Bundespräsidium. The N.G.C. and the title ended with the new constitution of January 1st, 1871. Ziko (talk) 12:24, 8 August 2016 (UTC)

 * Hello, I think that the Erfurt Union should be removed as it had no formal relationship to the German Confederation. Ziko (talk) 16:54, 11 August 2020 (UTC)

 * It is not true that the North German Confederation (which actually was a Federation) had no head of state as the Norddeutscher Bund (NDB) was identical in its constitution to the German Reich. The later was merely an expanded version of the NDB, with three and a half states and a Reichsland added and the head of state renamed. Two chief institutions, the Bundesrat and the Reichstag actually retained their names - so the NDB had a REICHStag and the German Reich had a BUNDESrat. Str1977 (talk) 09:49, 22 August 2020 (UTC)

A Commons file used on this page has been nominated for deletion
The following Wikimedia Commons file used on this page has been nominated for deletion: Participate in the deletion discussion at the. —Community Tech bot (talk) 16:07, 16 January 2019 (UTC)
 * OttoIVgb.jpg

title: Talk:List of German monarchs