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→Illustrations and analogies: added geometrical illustration of the tetrahedron https://www.mathsisfun.com/geometry/tetrahedron.html - necessary elements for physical existence of a thing - triple aspect of knowledge and of concepts
A good illustration is [[water|H<sub>2</sub>O]], one atom of hydrogen and two atoms of oxygen. It can also take three forms: solid ice, liquid water, and floating clouds, steam, formless fog and invisible vapor, all of which are considered water. However, this [[analogy]] was historically taken too far as applied to God. The denial of the doctrine of the Trinity, as being in essence one Person only, not three divine Persons of One Being, was condemned as [[Monarchianism]] and as [[Modalism]] and as the [[heresy]] of Sabellianism<ref>[https://orthodoxwiki.org/Sabellianism '''Sabellianism''' (orthodoxwiki.org)]</ref>
A good illustration is [[water|H<sub>2</sub>O]], one atom of hydrogen and two atoms of oxygen. It can also take three forms: solid ice, liquid water, and floating clouds, steam, formless fog and invisible vapor, all of which are considered water. However, this [[analogy]] was historically taken too far as applied to God. The denial of the doctrine of the Trinity, as being in essence one Person only, not three divine Persons of One Being, was condemned as [[Monarchianism]] and as [[Modalism]] and as the [[heresy]] of Sabellianism<ref>[https://orthodoxwiki.org/Sabellianism '''Sabellianism''' (orthodoxwiki.org)]</ref>
An excellent [[Mathematics|mathematical]] illustration of the unity of the Trinity is the [[Geometry|geometrical]] form of the [[Triangle|triangular]] three-sided ''tetrahedron'', a [[Pyramid (geometry)|pyramidal]] construct of a single, indivisible point extending into three [[equilateral]] triangular faces simultaneously united to a single triangular base<ref>[https://www.mathsisfun.com/geometry/tetrahedron.html Solid geometry: tetrahedron]</ref>. This is especially evident when an equilateral tetrahedron is made of flawless transparent [[crystal]]. Through any one face of the crystal form each of the other sides is clearly visible. Each of the faces is a distinctly different face (they cannot be the same face) but all of them have exactly the same shape, the same size, and the same substance. What is predicated of any one of them is predicated of each of them. A tetrahedral crystal displayed standing on the flat surface of the jeweler's counter or the shelf of a display case cannot exist without three faces inseparably existing as extending from the single, undivided point of one apex to the same undivided triangular base at its base or foundation on which it stands: a single crystal, not three, with three faces, not one.
Also, for any solid physical object to exist, it must have
:a. position / location <br> b. size / shape <br> and c. matter / mass.
Its color includes the hue of its color, the intensity or purity of its color, and the degree of the brightness of its color (reflected, generated, or absent in darkness without any light). <br> The [[sun]], for example, has size, shape, and luminosity. No one of these facts about the single object of the sun is the same as any one of the other two: size is not luminosity or shape; shape is not size or luminosity; luminosity is not size or shape; yet without these three realities there is no sun.
To be understood, a thing, or even a mental concept, requires knowledge of
:what it is <br> how it works <br> and what it does.
A universal concept involves
:a. its meaning or coherence, its correspondence to [[truth]] <br> b. its purpose or reason for being, its "why" <br> and c. its significance or importance to existent reality, the degree of its impact in or on the universe and the world of mankind.
Another excellent non-physical illustration is the [[mind]], which has three distinct powers of memory, understanding and will, which are not the same thing but are the essential expressions of one mind.<ref>We can remember something we do not understand; we can understand something new which is not something we remember; and we can will to do something which does not need to be understood, which we have never done before.</ref>
Another excellent non-physical illustration is the [[mind]], which has three distinct powers of memory, understanding and will, which are not the same thing but are the essential expressions of one mind.<ref>We can remember something we do not understand; we can understand something new which is not something we remember; and we can will to do something which does not need to be understood, which we have never done before.</ref>
In the same way, God exists as the three distinct but united whole persons of one divine being, utterly unique.<ref>"unique" means the only one, one-of-a-kind. See [http://www.biblehub.com/multi/isaiah/45-21.htm Isaiah 45:21] and [http://www.biblehub.com/multi/isaiah/45-22.htm Isaiah 45:22]</ref> God is the Uncreated Holy ''Good'',<ref>The word "good" was originally the Old English and Middle English word "God".
In the same way, God exists as the three distinct but united whole persons of one divine being, utterly unique.<ref>"unique" means the only one, one-of-a-kind. See [http://www.biblehub.com/multi/isaiah/45-21.htm Isaiah 45:21] and [http://www.biblehub.com/multi/isaiah/45-22.htm Isaiah 45:22]</ref> God is the Uncreated Holy ''Good'',<ref>The word "good" was originally the Old English and Middle English word "God".
*[http://www.bibleanswerstand.org/God.htm The Origin of the English Word for God. Part One. By Craig Bluemal (bibleanswerstand.org)]
*[http://www.bibleanswerstand.org/God.htm The Origin of the English Word for God. Part One. By Craig Bluemal (bibleanswerstand.org)]
*[http://wahiduddin.net/words/name_god.htm Etymology of the Name ''God'' (wahiduddin.net)]</ref> the Perfect, All-powerful, ''Eternal One'', fully Self-expressing and Self-expressed with Loving Self-knowledge, totally ''Complete'', limitlessly expressing the limitless expression of limitless self-giving loving [[Existence|Being]]. "''God is love''" [http://www.biblehub.com/commentaries/1_john/4-8.htm 1 John 4:8b].
*[http://wahiduddin.net/words/name_god.htm Etymology of the Name ''God'' (wahiduddin.net)]</ref> the Perfect, All-powerful, ''Eternal One'', fully Self-expressing and Self-expressed with ''Loving Self-knowledge'', totally ''Complete'', limitlessly expressing the limitless expression of limitless self-giving loving [[Existence|Being]]. "''God is love''" [http://www.biblehub.com/commentaries/1_john/4-8.htm 1 John 4:8b].
==Filioque controversy==
==Filioque controversy==