Chemical formula

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https://en.wikipedia.org/wiki/Chemical_formula 

 

${\displaystyle {\text{Al}}_2^{}{({\text{SO}}_4^{})}_3^{}}$

Chemical formula for Aluminium sulfate. The formula of aluminium sulfate hexadecahydrate is Al2(SO4)3 · 16H2O.

${\displaystyle \text{H}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\text{H}}$

Structural formula for butane. Examples of other chemical formulae for butane are the empirical formula C2H5, the molecular formula C4H10 and the condensed (or semi-structural) formula CH3CH2CH2CH3.

In chemistry, a chemical formula is a way of presenting information about the chemical proportions of atoms that constitute a particular chemical compound or molecule, using chemical element symbols, numbers, and sometimes also other symbols, such as parentheses, dashes, brackets, commas and plus (+) and minus (−) signs. These are limited to a single typographic line of symbols, which may include subscripts and superscripts. A chemical formula is not a chemical name, and it contains no words. Although a chemical formula may imply certain simple chemical structures, it is not the same as a full chemical structural formula. Chemical formulae can fully specify the structure of only the simplest of molecules and chemical substances, and are generally more limited in power than chemical names and structural formulae.

The simplest types of chemical formulae are called empirical formulae, which use letters and numbers indicating the numerical proportions of atoms of each type. Molecular formulae indicate the simple numbers of each type of atom in a molecule, with no information on structure. For example, the empirical formula for glucose is CH₂O (twice as many hydrogen atoms as carbon and oxygen), while its molecular formula is C₆H₁₂O₆ (12 hydrogen atoms, six carbon and oxygen atoms).

Sometimes a chemical formula is complicated by being written as a condensed formula (or condensed molecular formula, occasionally called a "semi-structural formula"), which conveys additional information about the particular ways in which the atoms are chemically bonded together, either in covalent bonds, ionic bonds, or various combinations of these types. This is possible if the relevant bonding is easy to show in one dimension. An example is the condensed molecular/chemical formula for ethanol, which is CH₃−CH₂−OH or CH₃CH₂OH. However, even a condensed chemical formula is necessarily limited in its ability to show complex bonding relationships between atoms, especially atoms that have bonds to four or more different substituents.

Since a chemical formula must be expressed as a single line of chemical element symbols, it often cannot be as informative as a true structural formula, which is a graphical representation of the spatial relationship between atoms in chemical compounds (see for example the figure for butane structural and chemical formulae, at right). For reasons of structural complexity, a single condensed chemical formula (or semi-structural formula) may correspond to different molecules, known as isomers. For example, glucose shares its molecular formula C₆H₁₂O₆ with a number of other sugars, including fructose, galactose and mannose. Linear equivalent chemical names exist that can and do specify uniquely any complex structural formula (see chemical nomenclature), but such names must use many terms (words), rather than the simple element symbols, numbers, and simple typographical symbols that define a chemical formula.

Chemical formulae may be used in chemical equations to describe chemical reactions and other chemical transformations, such as the dissolving of ionic compounds into solution. While, as noted, chemical formulae do not have the full power of structural formulae to show chemical relationships between atoms, they are sufficient to keep track of numbers of atoms and numbers of electrical charges in chemical reactions, thus balancing chemical equations so that these equations can be used in chemical problems involving conservation of atoms, and conservation of electric charge.

Overview

A chemical formula identifies each constituent element by its chemical symbol and indicates the proportionate number of atoms of each element. In empirical formulae, these proportions begin with a key element and then assign numbers of atoms of the other elements in the compound, by ratios to the key element. For molecular compounds, these ratio numbers can all be expressed as whole numbers. For example, the empirical formula of ethanol may be written C₂H₆O because the molecules of ethanol all contain two carbon atoms, six hydrogen atoms, and one oxygen atom. Some types of ionic compounds, however, cannot be written with entirely whole-number empirical formulae. An example is boron carbide, whose formula of CB_n is a variable non-whole number ratio with n ranging from over 4 to more than 6.5.

When the chemical compound of the formula consists of simple molecules, chemical formulae often employ ways to suggest the structure of the molecule. These types of formulae are variously known as molecular formulae and condensed formulae. A molecular formula enumerates the number of atoms to reflect those in the molecule, so that the molecular formula for glucose is C₆H₁₂O₆ rather than the glucose empirical formula, which is CH₂O. However, except for very simple substances, molecular chemical formulae lack needed structural information, and are ambiguous.

For simple molecules, a condensed (or semi-structural) formula is a type of chemical formula that may fully imply a correct structural formula. For example, ethanol may be represented by the condensed chemical formula CH₃CH₂OH, and dimethyl ether by the condensed formula CH₃OCH₃. These two molecules have the same empirical and molecular formulae (C₂H₆O), but may be differentiated by the condensed formulae shown, which are sufficient to represent the full structure of these simple organic compounds.

Condensed chemical formulae may also be used to represent ionic compounds that do not exist as discrete molecules, but nonetheless do contain covalently bound clusters within them. These polyatomic ions are groups of atoms that are covalently bound together and have an overall ionic charge, such as the sulfate [SO₄]^2- ion. Each polyatomic ion in a compound is written individually in order to illustrate the separate groupings. For example, the compound dichlorine hexoxide has an empirical formula ClO₃, and molecular formula Cl₂O₆, but in liquid or solid forms, this compound is more correctly shown by an ionic condensed formula [ClO₂]⁺[ClO₄]⁻, which illustrates that this compound consists of [ClO₂]⁺ ions and [ClO₄]⁻ ions. In such cases, the condensed formula only need be complex enough to show at least one of each ionic species.

Chemical formulae as described here are distinct from the far more complex chemical systematic names that are used in various systems of chemical nomenclature. For example, one systematic name for glucose is (2R,3S,4R,5R)-2,3,4,5,6-pentahydroxyhexanal. This name, interpreted by the rules behind it, fully specifies glucose's structural formula, but the name is not a chemical formula as usually understood, and uses terms and words not used in chemical formulae. Such names, unlike basic formulae, may be able to represent full structural formulae without graphs.

Types

Empirical formula

Main article: Empirical formula

In chemistry, the empirical formula of a chemical is a simple expression of the relative number of each type of atom or ratio of the elements in the compound. Empirical formulae are the standard for ionic compounds, such as CaCl₂, and for macromolecules, such as SiO₂. An empirical formula makes no reference to isomerism, structure, or absolute number of atoms. The term empirical refers to the process of elemental analysis, a technique of analytical chemistry used to determine the relative percent composition of a pure chemical substance by element.

For example, hexane has a molecular formula of C₆H₁₄, and (for one of its isomers, n-hexane) a structural formula CH₃CH₂CH₂CH₂CH₂CH₃, implying that it has a chain structure of 6 carbon atoms, and 14 hydrogen atoms. However, the empirical formula for hexane is C₃H₇. Likewise the empirical formula for hydrogen peroxide, H₂O₂, is simply HO, expressing the 1:1 ratio of component elements. Formaldehyde and acetic acid have the same empirical formula, CH₂O. This is the actual chemical formula for formaldehyde, but acetic acid has double the number of atoms.

Molecular formula

Isobutane structural formula
Molecular formula: C₄H₁₀
Condensed formula: (CH₃)₃CH

 

${\displaystyle \text{H}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\stackrel{\genfrac{}{}{0ex}{}{{\displaystyle \text{H}}}{|}}{\underset{\genfrac{}{}{0ex}{}{|}{{\displaystyle \text{H}}}}{\text{C}}}-\text{H}}$

n-Butane structural formula
Molecular formula: C₄H₁₀
Condensed formula: CH₃CH₂CH₂CH₃

Molecular formulae indicate the simple numbers of each type of atom in a molecule of a molecular substance. They are the same as empirical formulae for molecules that only have one atom of a particular type, but otherwise may have larger numbers. An example of the difference is the empirical formula for glucose, which is CH₂O (ratio 1:2:1), while its molecular formula is C₆H₁₂O₆ (number of atoms 6:12:6). For water, both formulae are H₂O. A molecular formula provides more information about a molecule than its empirical formula, but is more difficult to establish.

A molecular formula shows the number of elements in a molecule, and determines whether it is a binary compound, ternary compound, quaternary compound, or has even more elements.

Structural formula

Main article: Structural formula

In addition to quantitative description of a molecule, a structural formula^[a] captures how the atoms are organized, and shows (or implies) the chemical bonds between the atoms. There are multiple types of structural formulas focused on different aspects of the molecular structure.

The two diagrams show two molecules which are structural isomers of each other, since they both have the same molecular formula C₄H₁₀, but they have different structural formulas as shown.

Condensed formula

Main article: Condensed formula

The connectivity of a molecule often has a strong influence on its physical and chemical properties and behavior. Two molecules composed of the same numbers of the same types of atoms (i.e. a pair of isomers) might have completely different chemical and/or physical properties if the atoms are connected differently or in different positions. In such cases, a structural formula is useful, as it illustrates which atoms are bonded to which other ones. From the connectivity, it is often possible to deduce the approximate shape of the molecule.

A condensed (or semi-structural) formula may represent the types and spatial arrangement of bonds in a simple chemical substance, though it does not necessarily specify isomers or complex structures. For example, ethane consists of two carbon atoms single-bonded to each other, with each carbon atom having three hydrogen atoms bonded to it. Its chemical formula can be rendered as CH₃CH₃. In ethylene there is a double bond between the carbon atoms (and thus each carbon only has two hydrogens), therefore the chemical formula may be written: CH₂CH₂, and the fact that there is a double bond between the carbons is implicit because carbon has a valence of four. However, a more explicit method is to write H₂C=CH₂ or less commonly H₂C::CH₂. The two lines (or two pairs of dots) indicate that a double bond connects the atoms on either side of them.

A triple bond may be expressed with three lines (HC≡CH) or three pairs of dots (HC:::CH), and if there may be ambiguity, a single line or pair of dots may be used to indicate a single bond.

Molecules with multiple functional groups that are the same may be expressed by enclosing the repeated group in round brackets. For example, isobutane may be written (CH₃)₃CH. This condensed structural formula implies a different connectivity from other molecules that can be formed using the same atoms in the same proportions (isomers). The formula (CH₃)₃CH implies a central carbon atom connected to one hydrogen atom and three methyl groups (CH₃). The same number of atoms of each element (10 hydrogens and 4 carbons, or C₄H₁₀) may be used to make a straight chain molecule, n-butane: CH₃CH₂CH₂CH₃.

Law of composition

In any given chemical compound, the elements always combine in the same proportion with each other. This is the law of constant composition.

The law of constant composition says that, in any particular chemical compound, all samples of that compound will be made up of the same elements in the same proportion or ratio. For example, any water molecule is always made up of two hydrogen atoms and one oxygen atom in a 2:1 ratio. If we look at the relative masses of oxygen and hydrogen in a water molecule, we see that 94% of the mass of a water molecule is accounted for by oxygen and the remaining 6% is the mass of hydrogen. This mass proportion will be the same for any water molecule.^[2]

Chemical names in answer to limitations of chemical formulae

Main article: Chemical nomenclature

The alkene called but-2-ene has two isomers, which the chemical formula CH₃CH=CHCH₃ does not identify. The relative position of the two methyl groups must be indicated by additional notation denoting whether the methyl groups are on the same side of the double bond (cis or Z) or on the opposite sides from each other (trans or E).

As noted above, in order to represent the full structural formulae of many complex organic and inorganic compounds, chemical nomenclature may be needed which goes well beyond the available resources used above in simple condensed formulae. See IUPAC nomenclature of organic chemistry and IUPAC nomenclature of inorganic chemistry 2005 for examples. In addition, linear naming systems such as International Chemical Identifier (InChI) allow a computer to construct a structural formula, and simplified molecular-input line-entry system (SMILES) allows a more human-readable ASCII input. However, all these nomenclature systems go beyond the standards of chemical formulae, and technically are chemical naming systems, not formula systems.

Polymers in condensed formulae

For polymers in condensed chemical formulae, parentheses are placed around the repeating unit. For example, a hydrocarbon molecule that is described as CH₃(CH₂)₅₀CH₃, is a molecule with fifty repeating units. If the number of repeating units is unknown or variable, the letter n may be used to indicate this formula: CH₃(CH₂)_nCH₃.

Ions in condensed formulae

For ions, the charge on a particular atom may be denoted with a right-hand superscript. For example, Na⁺, or Cu²⁺. The total charge on a charged molecule or a polyatomic ion may also be shown in this way, such as for hydronium, H₃O⁺, or sulfate, SO2−4. Note that + and - are used in place of +1 and -1, respectively.

For more complex ions, brackets [ ] are often used to enclose the ionic formula, as in [B₁₂H₁₂]²⁻, which is found in compounds such as caesium dodecaborate, Cs₂[B₁₂H₁₂]. Parentheses ( ) can be nested inside brackets to indicate a repeating unit, as in Hexamminecobalt(III) chloride, [Co(NH₃)₆]³⁺Cl−3. Here, (NH₃)₆ indicates that the ion contains six ammine groups (NH₃) bonded to cobalt, and [ ] encloses the entire formula of the ion with charge +3.

This is strictly optional; a chemical formula is valid with or without ionization information, and Hexamminecobalt(III) chloride may be written as [Co(NH₃)₆]³⁺Cl−3 or [Co(NH₃)₆]Cl₃. Brackets, like parentheses, behave in chemistry as they do in mathematics, grouping terms together – they are not specifically employed only for ionization states. In the latter case here, the parentheses indicate 6 groups all of the same shape, bonded to another group of size 1 (the cobalt atom), and then the entire bundle, as a group, is bonded to 3 chlorine atoms. In the former case, it is clearer that the bond connecting the chlorines is ionic, rather than covalent.

Isotopes

Although isotopes are more relevant to nuclear chemistry or stable isotope chemistry than to conventional chemistry, different isotopes may be indicated with a prefixed superscript in a chemical formula. For example, the phosphate ion containing radioactive phosphorus-32 is [³²PO₄]^3-. Also a study involving stable isotope ratios might include the molecule ¹⁸O¹⁶O.

A left-hand subscript is sometimes used redundantly to indicate the atomic number. For example, ₈O₂ for dioxygen, and ¹⁶
₈O
₂ for the most abundant isotopic species of dioxygen. This is convenient when writing equations for nuclear reactions, in order to show the balance of charge more clearly.

Trapped atoms

Traditional formula: MC₆₀
The "@" notation: M@C₆₀

 

Main article: Endohedral fullerene

The @ symbol (at sign) indicates an atom or molecule trapped inside a cage but not chemically bound to it. For example, a buckminsterfullerene (C₆₀) with an atom (M) would simply be represented as MC₆₀ regardless of whether M was inside the fullerene without chemical bonding or outside, bound to one of the carbon atoms. Using the @ symbol, this would be denoted M@C₆₀ if M was inside the carbon network. A non-fullerene example is [As@Ni₁₂As₂₀]³⁻, an ion in which one arsenic (As) atom is trapped in a cage formed by the other 32 atoms.

This notation was proposed in 1991 with the discovery of fullerene cages (endohedral fullerenes), which can trap atoms such as La to form, for example, La@C₆₀ or La@C₈₂. The choice of the symbol has been explained by the authors as being concise, readily printed and transmitted electronically (the at sign is included in ASCII, which most modern character encoding schemes are based on), and the visual aspects suggesting the structure of an endohedral fullerene.

Non-stoichiometric chemical formulae

Main article: Non-stoichiometric compound

Chemical formulae most often use integers for each element. However, there is a class of compounds, called non-stoichiometric compounds, that cannot be represented by small integers. Such a formula might be written using decimal fractions, as in Fe_0.95O, or it might include a variable part represented by a letter, as in Fe_1-xO, where x is normally much less than 1.

General forms for organic compounds

A chemical formula used for a series of compounds that differ from each other by a constant unit is called a general formula. It generates a homologous series of chemical formulae. For example, alcohols may be represented by the formula C_nH_{2n + 1}OH (n ≥ 1), giving the homologs methanol, ethanol, propanol for 1 ≤ n ≤ 3.

Hill system

The Hill system (or Hill notation) is a system of writing empirical chemical formulae, molecular chemical formulae and components of a condensed formula such that the number of carbon atoms in a molecule is indicated first, the number of hydrogen atoms next, and then the number of all other chemical elements subsequently, in alphabetical order of the chemical symbols. When the formula contains no carbon, all the elements, including hydrogen, are listed alphabetically.

By sorting formulae according to the number of atoms of each element present in the formula according to these rules, with differences in earlier elements or numbers being treated as more significant than differences in any later element or number—like sorting text strings into lexicographical order—it is possible to collate chemical formulae into what is known as Hill system order.

The Hill system was first published by Edwin A. Hill of the United States Patent and Trademark Office in 1900. It is the most commonly used system in chemical databases and printed indexes to sort lists of compounds.

A list of formulae in Hill system order is arranged alphabetically, as above, with single-letter elements coming before two-letter symbols when the symbols begin with the same letter (so "B" comes before "Be", which comes before "Br").

The following example formulae are written using the Hill system, and listed in Hill order:

• BrI
• BrClH₂Si
• CCl₄
• CH₃I
• C₂H₅Br
• H₂O₄S

Demiurge

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Demiurge 

In the Platonic, Neopythagorean, Middle Platonic, and Neoplatonic schools of philosophy, the demiurge (/ˈdɛmi.ɜːrdʒ/) is an artisan-like figure responsible for fashioning and maintaining the physical universe. The Gnostics adopted the term demiurge. Although a fashioner, the demiurge is not necessarily the same as the Creator figure in the monotheistic sense, because the demiurge itself and the material from which the demiurge fashions the universe are both considered consequences of something else. Depending on the system, they may be considered either uncreated and eternal or the product of some other entity.

The word demiurge is an English word derived from demiurgus, a Latinised form of the Greek δημιουργός or dēmiurgós. It was originally a common noun meaning "craftsman" or "artisan", but gradually came to mean "producer", and eventually "creator". The philosophical usage and the proper noun derive from Plato's Timaeus, written c. 360 BC, where the demiurge is presented as the creator of the universe. The demiurge is also described as a creator in the Platonic (c. 310–90 BC) and Middle Platonic (c. 90 BC–AD 300) philosophical traditions. In the various branches of the Neoplatonic school (third century onwards), the demiurge is the fashioner of the real, perceptible world after the model of the Ideas, but (in most Neoplatonic systems) is still not itself "the One". In the arch-dualist ideology of the various Gnostic systems, the material universe is evil, while the non-material world is good. According to some strains of Gnosticism, the demiurge is malevolent, as it is linked to the material world. In others, including the teaching of Valentinus, the demiurge is simply ignorant or misguided.

Platonism and Neoplatonism

Plato and the Timaeus

Plato, as the speaker Timaeus, refers to the Demiurge frequently in the Socratic dialogue Timaeus (28a ff.), c. 360 BC. The main character refers to the Demiurge as the entity who "fashioned and shaped" the material world. Timaeus describes the Demiurge as unreservedly benevolent, and so it desires a world as good as possible. Plato's work Timaeus is a philosophical reconciliation of Hesiod's cosmology in his Theogony, syncretically reconciling Hesiod to Homer.

Middle Platonism

In Numenius's Neo-Pythagorean and Middle Platonist cosmogony, the Demiurge is second God as the nous or thought of intelligibles and sensibles.

Neoplatonism

Plotinus and the later Platonists worked to clarify the Demiurge. To Plotinus, the second emanation represents an uncreated second cause (see Pythagoras' Dyad). Plotinus sought to reconcile Aristotle's energeia with Plato's Demiurge, which, as Demiurge and mind (nous), is a critical component in the ontological construct of human consciousness used to explain and clarify substance theory within Platonic realism (also called idealism). In order to reconcile Aristotelian with Platonian philosophy, Plotinus metaphorically identified the demiurge (or nous) within the pantheon of the Greek Gods as Zeus.

Henology

The first and highest aspect of God is described by Plato as the One (Τὸ Ἕν, 'To Hen'), the source, or the Monad. This is the God above the Demiurge, and manifests through the actions of the Demiurge. The Monad emanated the demiurge or Nous (consciousness) from its "indeterminate" vitality due to the monad being so abundant that it overflowed back onto itself, causing self-reflection. This self-reflection of the indeterminate vitality was referred to by Plotinus as the "Demiurge" or creator. The second principle is organization in its reflection of the nonsentient force or dynamis, also called the one or the Monad. The dyad is energeia emanated by the one that is then the work, process or activity called nous, Demiurge, mind, consciousness that organizes the indeterminate vitality into the experience called the material world, universe, cosmos. Plotinus also elucidates the equation of matter with nothing or non-being in The Enneads which more correctly is to express the concept of idealism or that there is not anything or anywhere outside of the "mind" or nous (c.f. pantheism).

Plotinus' form of Platonic idealism is to treat the Demiurge, nous as the contemplative faculty (ergon) within man which orders the force (dynamis) into conscious reality. In this, he claimed to reveal Plato's true meaning: a doctrine he learned from Platonic tradition that did not appear outside the academy or in Plato's text. This tradition of creator God as nous (the manifestation of consciousness), can be validated in the works of pre-Plotinus philosophers such as Numenius, as well as a connection between Hebrew and Platonic cosmology (see also Philo).

The Demiurge of Neoplatonism is the Nous (mind of God), and is one of the three ordering principles:

• Arche (Gr. 'beginning') – the source of all things,
• Logos (Gr. 'reason/cause') – the underlying order that is hidden beneath appearances,
• Harmonia (Gr. 'harmony') – numerical ratios in mathematics.

Before Numenius of Apamea and Plotinus' Enneads, no Platonic works ontologically clarified the Demiurge from the allegory in Plato's Timaeus. The idea of Demiurge was, however, addressed before Plotinus in the works of Christian writer Justin Martyr who built his understanding of the Demiurge on the works of Numenius.

Iamblichus

See also: Panentheism

Later, the Neoplatonist Iamblichus changed the role of the "One", effectively altering the role of the Demiurge as second cause or dyad, which was one of the reasons that Iamblichus and his teacher Porphyry came into conflict.

The figure of the Demiurge emerges in the theoretic of Iamblichus, which conjoins the transcendent, incommunicable “One,” or Source. Here, at the summit of this system, the Source and Demiurge (material realm) coexist via the process of henosis. Iamblichus describes the One as a monad whose first principle or emanation is intellect (nous), while among "the many" that follow it there is a second, super-existent "One" that is the producer of intellect or soul (psyche).

The "One" is further separated into spheres of intelligence; the first and superior sphere is objects of thought, while the latter sphere is the domain of thought. Thus, a triad is formed of the intelligible nous, the intellective nous, and the psyche in order to reconcile further the various Hellenistic philosophical schools of Aristotle's actus and potentia (actuality and potentiality) of the unmoved mover and Plato's Demiurge.

Then within this intellectual triad Iamblichus assigns the third rank to the Demiurge, identifying it with the perfect or Divine nous with the intellectual triad being promoted to a hebdomad (pure intellect).

In the theoretic of Plotinus, nous produces nature through intellectual mediation, thus the intellectualizing gods are followed by a triad of psychic gods.

Gnosticism

Gnosticism presents a distinction between the highest, unknowable God or Supreme Being and the demiurgic "creator" of the material. Several systems of Gnostic thought present the Demiurge as antagonistic to the will of the Supreme Being: his act of creation occurs in an unconscious semblance of the divine model, and thus is fundamentally flawed, or else is formed with the malevolent intention of entrapping aspects of the divine in materiality. Thus, in such systems, the Demiurge acts as a solution to (or, at least possibly, the problem or cause that gives rise to) the problem of evil.

Mythos

One Gnostic mythos describes the declination of aspects of the divine into human form. Sophia (Greek: Σοφία, lit. 'wisdom'), the Demiurge's mother and partial aspect of the divine Pleroma or "Fullness," desired to create something apart from the divine totality, without the receipt of divine assent. In this act of separate creation, she gave birth to the monstrous Demiurge and, being ashamed of her deed, wrapped him in a cloud and created a throne for him within it. The Demiurge, isolated, did not behold his mother, nor anyone else, and concluded that only he existed, ignorant of the superior levels of reality.

The Demiurge, having received a portion of power from his mother, sets about a work of creation in unconscious imitation of the superior Pleromatic realm: He frames the seven heavens, as well as all material and animal things, according to forms furnished by his mother; working, however, blindly and ignorant even of the existence of the mother who is the source of all his energy. He is blind to all that is spiritual, but he is king over the other two provinces. The word dēmiurgos properly describes his relation to the material; he is the father of that which is animal like himself.

Thus Sophia's power becomes enclosed within the material forms of humanity, themselves entrapped within the material universe: the goal of Gnostic movements was typically the awakening of this spark, which permitted a return by the subject to the superior, non-material realities which were its primal source.

Angels

Psalm 82 begins, "God stands in the assembly of El [LXX: assembly of gods], in the midst of the gods he renders judgment", indicating a plurality of gods, although it does not indicate that these gods were co-actors in creation. Philo had inferred from the expression "Let us make man" of the Book of Genesis that God had used other beings as assistants in the creation of man, and he explains in this way why man is capable of vice as well as virtue, ascribing the origin of the latter to God, of the former to his helpers in the work of creation.

The earliest Gnostic sects ascribe the work of creation to angels, some of them using the same passage in Genesis. So Irenaeus tells of the system of Simon Magus, of the system of Menander, of the system of Saturninus, in which the number of these angels is reckoned as seven, and of the system of Carpocrates. In the report of the system of Basilides, we are told that our world was made by the angels who occupy the lowest heaven; but special mention is made of their chief, who is said to have been the God of the Jews, to have led that people out of the land of Egypt, and to have given them their law. The prophecies are ascribed not to the chief but to the other world-making angels.

The Latin translation, confirmed by Hippolytus of Rome, makes Irenaeus state that according to Cerinthus (who shows Ebionite influence), creation was made by a power quite separate from the Supreme God and ignorant of him. Theodoret, who here copies Irenaeus, turns this into the plural number "powers", and so Epiphanius of Salamis represents Cerinthus as agreeing with Carpocrates in the doctrine that the world was made by angels.

Yaldabaoth

Main article: Yaldabaoth

 

A lion-faced, serpentine deity found on a Gnostic gem in Bernard de Montfaucon's L'antiquité expliquée et représentée en figures may be a depiction of the Demiurge.

In the Archontic, Sethian, and Ophite systems, which have many affinities with the doctrine of Valentinus, the making of the world is ascribed to a company of seven archons, whose names are given, but still more prominent is their chief, "Yaldabaoth" (also known as "Yaltabaoth" or "Ialdabaoth").

In the Apocryphon of John c. AD 120–180, the demiurge arrogantly declares that he has made the world by himself:

Now the archon ["ruler"] who is weak has three names. The first name is Yaltabaoth ["child of chaos"], the second is Saklas ["fool"], and the third is Samael ["blind god"]. And he is impious in his arrogance which is in him. For he said, 'I am God and there is no other God beside me,' for he is ignorant of his strength, the place from which he had come.

He is Demiurge and maker of man, but as a ray of light from above enters the body of man and gives him a soul, Yaldabaoth is filled with envy; he tries to limit man's knowledge by forbidding him the fruit of knowledge in paradise. At the consummation of all things, all light will return to the Pleroma. But Yaldabaoth, the Demiurge, with the material world, will be cast into the lower depths.

Yaldabaoth is frequently called "the Lion-faced", leontoeides, and is said to have the body of a serpent. The demiurge is also described as having a fiery nature, applying the words of Moses to him: "the Lord our God is a burning and consuming fire". Hippolytus claims that Simon used a similar description.

In Pistis Sophia, Yaldabaoth has already sunk from his high estate and resides in Chaos, where, with his forty-nine demons, he tortures wicked souls in boiling rivers of pitch, and with other punishments (pp. 257, 382). He is an archon with the face of a lion, half flame, and half darkness.

In the Nag Hammadi text On the Origin of the World, the three sons of Yaldabaoth are listed as Yao, Eloai, and Astaphaios.

Under the name of Nebro (rebel), Yaldabaoth is called an angel in the apocryphal Gospel of Judas. He is first mentioned in "The Cosmos, Chaos, and the Underworld" as one of the twelve angels to come "into being [to] rule over chaos and the [underworld]". He comes from heaven, and it is said his "face flashed with fire and [his] appearance was defiled with blood". Nebro creates six angels in addition to the angel Saklas to be his assistants. These six, in turn, create another twelve angels "with each one receiving a portion in the heavens".

Names

Drawing of the lion-headed figure found at the Mithraeum of C. Valerius Heracles and sons, dedicated 190 CE at Ostia Antica, Italy (CIMRM 312).

The most probable derivation of the name "Yaldabaoth" was that given by Johann Karl Ludwig Gieseler. Gieseler believed the name was derived from the Aramaic yaldā bahuth, ילדאבהות, meaning "Son of Chaos". However, Gilles Quispel notes:

Gershom Scholem, the third genius in this field, more specifically the genius of precision, has taught us that some of us were wrong when they believed that Jaldabaoth means "son of chaos", because the Aramaic word bahutha in the sense of chaos only existed in the imagination of the author of a well-known dictionary. This is a pity because this name would suit the demiurge risen from chaos to a nicety. And perhaps the author of the Untitled Document did not know Aramaic and also supposed as we did once, that baoth had something to do with tohuwabohu, one of the few Hebrew words that everybody knows. ... It would seem then that the Orphic view of the demiurge was integrated into Jewish Gnosticism even before the redaction of the myth contained in the original Apocryphon of John. ... Phanes is represented with the mask of a lion's head on his breast, while from his sides the heads of a ram and a buck are budding forth: his body is encircled by a snake. This type was accepted by the Mithras mysteries, to indicate Aion, the new year, and Mithras, whose numerical value is 365. Sometimes he is also identified with Jao Adonai, the creator of the Hebrews. His hieratic attitude indicates Egyptian origin. The same is true of the monstrous figure with the head of a lion, which symbolises Time, Chronos, in Mithraism; Alexandrian origin of this type is probable.

"Samael" literally means "Blind God" or "God of the Blind" in Hebrew (סמאל‎). This being is considered not only blind, or ignorant of its own origins, but may, in addition, be evil; its name is also found in Judaism as the Angel of Death and in Christian demonology. This link to Judeo-Christian tradition leads to a further comparison with Satan. Another alternative title for the demiurge is "Saklas", Aramaic for "fool". In the Apocryphon of John, Yaldabaoth is also known as both Sakla and Samael.

The angelic name "Ariel" (Hebrew: 'the lion of God') has also been used to refer to the Demiurge and is called his "perfect" name; in some Gnostic lore, Ariel has been called an ancient or original name for Ialdabaoth. The name has also been inscribed on amulets as "Ariel Ialdabaoth", and the figure of the archon inscribed with "Aariel".

Marcion

According to Marcion, the title God was given to the Demiurge, who was to be sharply distinguished from the higher Good God. The former was díkaios, severely just, the latter agathós, or loving-kind; the former was the "god of this world", the God of the Old Testament, the latter the true God of the New Testament. Christ, in reality, is the Son of the Good God. The true believer in Christ entered into God's kingdom, the unbeliever remained forever the slave of the Demiurge.

Valentinus

It is in the system of Valentinus that the name Dēmiurgos is used, which occurs nowhere in Irenaeus except in connection with the Valentinian system; we may reasonably conclude that it was Valentinus who adopted from Platonism the use of this word. When it is employed by other Gnostics either it is not used in a technical sense, or its use has been borrowed from Valentinus. But it is only the name that can be said to be specially Valentinian; the personage intended by it corresponds more or less closely with the Yaldabaoth of the Ophites, the great Archon of Basilides, the Elohim of Justinus, etc.

The Valentinian theory elaborates that from Achamoth (he kátō sophía or lower wisdom) three kinds of substance take their origin, the spiritual (pneumatikoí), the animal (psychikoí) and the material (hylikoí). The Demiurge belongs to the second kind, as he was the offspring of a union of Achamoth with matter. And as Achamoth herself was only the daughter of Sophía the last of the thirty Aeons, the Demiurge was distant by many emanations from the Propatôr, or Supreme God.

In creating this world out of Chaos the Demiurge was unconsciously influenced for good; and the universe, to the surprise even of its Maker, became almost perfect. The Demiurge regretted even its slight imperfection, and as he thought himself the Supreme God, he attempted to remedy this by sending a Messiah. To this Messiah, however, was actually united with Jesus the Saviour, Who redeemed men. These are either hylikoí or pneumatikoí.

The first, or material men, will return to the grossness of matter and finally be consumed by fire; the second, or animal men, together with the Demiurge, will enter a middle state, neither Pleroma nor hyle; the purely spiritual men will be completely freed from the influence of the Demiurge and together with the Saviour and Achamoth, his spouse, will enter the Pleroma divested of body (hyle) and soul (psyché). In this most common form of Gnosticism the Demiurge had an inferior though not intrinsically evil function in the universe as the head of the animal, or psychic world.

The devil

Opinions on the devil, and his relationship to the Demiurge, varied. The Ophites held that he and his demons constantly oppose and thwart the human race, as it was on their account the devil was cast down into this world. According to one variant of the Valentinian system, the Demiurge is also the maker, out of the appropriate substance, of an order of spiritual beings, the devil, the prince of this world, and his angels. But the devil, as being a spirit of wickedness, is able to recognise the higher spiritual world, of which his maker the Demiurge, who is only animal, has no real knowledge. The devil resides in this lower world, of which he is the prince, the Demiurge in the heavens; his mother Sophia in the middle region, above the heavens and below the Pleroma.

The Valentinian Heracleon interpreted the devil as the principle of evil, that of hyle (matter). As he writes in his commentary on John 4:21,

The mountain represents the Devil, or his world, since the Devil was one part of the whole of matter, but the world is the total mountain of evil, a deserted dwelling place of beasts, to which all who lived before the law and all Gentiles render worship. But Jerusalem represents the creation or the Creator whom the Jews worship. ... You then who are spiritual should worship neither the creation nor the Craftsman, but the Father of Truth.

This vilification of the creator was held to be inimical to Christianity by the early fathers of the church. In refuting the beliefs of the gnostics, Irenaeus stated that "Plato is proved to be more religious than these men, for he allowed that the same God was both just and good, having power over all things, and himself executing judgment."

Cathars

Catharism apparently inherited their idea of Satan as the creator of the evil world from Gnosticism. Quispel writes,

There is a direct link between ancient Gnosticism and Catharism. The Cathars held that the creator of the world, Satanael, had usurped the name of God, but that he had subsequently been unmasked and told that he was not really God.

Neoplatonism and Gnosticism

Main article: Neoplatonism and Gnosticism

Gnosticism attributed falsehood or evil to the concept of the Demiurge or creator, though in some Gnostic traditions the creator is from a fallen, ignorant, or lesser—rather than evil—perspective, such as that of Valentinius.

Plotinus

The Neoplatonic philosopher Plotinus addressed within his works Gnosticism's conception of the Demiurge, which he saw as un-Hellenic and blasphemous to the Demiurge or creator of Plato. Plotinus, along with his teacher Ammonius Saccas, was the founder of Neoplatonism. In the ninth tractate of the second of his Enneads, Plotinus criticizes his opponents for their appropriation of ideas from Plato:

From Plato come their punishments, their rivers of the underworld and the changing from body to body; as for the plurality they assert in the Intellectual Realm—the Authentic Existent, the Intellectual-Principle, the Second Creator and the Soul—all this is taken over from the Timaeus.

— Ennead 2.9.vi; emphasis added from A. H. Armstrong's introduction to Ennead 2.9

Of note here is the remark concerning the second hypostasis or Creator and third hypostasis or World Soul. Plotinus criticizes his opponents for "all the novelties through which they seek to establish a philosophy of their own" which, he declares, "have been picked up outside of the truth"; they attempt to conceal rather than admit their indebtedness to ancient philosophy, which they have corrupted by their extraneous and misguided embellishments. Thus their understanding of the Demiurge is similarly flawed in comparison to Plato’s original intentions.

Whereas Plato's Demiurge is good wishing good on his creation, Gnosticism contends that the Demiurge is not only the originator of evil but is evil as well. Hence the title of Plotinus' refutation: "Against Those That Affirm the Creator of the Kosmos and the Kosmos Itself to be Evil" (generally quoted as "Against the Gnostics"). Plotinus argues of the disconnect or great barrier that is created between the nous or mind's noumenon (see Heraclitus) and the material world (phenomenon) by believing the material world is evil.

The majority of scholars tend to understand Plotinus' opponents as being a Gnostic sect—certainly (specifically Sethian), several such groups were present in Alexandria and elsewhere about the Mediterranean during Plotinus' lifetime. Plotinus specifically points to the Gnostic doctrine of Sophia and her emission of the Demiurge.

Though the former understanding certainly enjoys the greatest popularity, the identification of Plotinus' opponents as Gnostic is not without some contention. Christos Evangeliou has contended that Plotinus' opponents might be better described as simply "Christian Gnostics", arguing that several of Plotinus' criticisms are as applicable to orthodox Christian doctrine as well. Also, considering the evidence from the time, Evangeliou thought the definition of the term "Gnostics" was unclear. Of note here is that while Plotinus' student Porphyry names Christianity specifically in Porphyry's own works, and Plotinus is to have been a known associate of the Christian Origen, none of Plotinus' works mention Christ or Christianity—whereas Plotinus specifically addresses his target in the Enneads as the Gnostics.

A. H. Armstrong identified the so-called "Gnostics" that Plotinus was attacking as Jewish and Pagan, in his introduction to the tract in his translation of the Enneads. Armstrong alluding to Gnosticism being a Hellenic philosophical heresy of sorts, which later engaged Christianity and Neoplatonism.

John D. Turner, professor of religious studies at the University of Nebraska, and famed translator and editor of the Nag Hammadi library, stated that the text Plotinus and his students read was Sethian Gnosticism, which predates Christianity. It appears that Plotinus attempted to clarify how the philosophers of the academy had not arrived at the same conclusions (such as dystheism or misotheism for the creator God as an answer to the problem of evil) as the targets of his criticism.

Emil Cioran also wrote his Le mauvais démiurge ("The Evil Demiurge"), published in 1969, influenced by Gnosticism and Schopenhauerian interpretation of Platonic ontology, as well as that of Plotinus.