What are the personal properties of the three persons in the Godhead?
It is proper to the Father to beget the Son,1 and to the Son to be begotten of the Father,2 and to the Holy Ghost to proceed from the Father and the Son from all eternity.3
Scripture proofs
The Westminster Assembly's proof texts (KJV). The bracketed numbers in the answer above mark the clause each set of references supports; expand a row to read the verses.
1 Heb. 1:5–6, 8
Heb. 1:5 For unto which of the angels said he at any time, Thou art my Son, this day have I begotten thee? And again, I will be to him a Father, and he shall be to me a Son?
Heb. 1:6 And again, when he bringeth in the firstbegotten into the world, he saith, And let all the angels of God worship him.
Heb. 1:8 But unto the Son he saith, Thy throne, O God, is for ever and ever: a sceptre of righteousness is the sceptre of thy kingdom.
2 John 1:14, 18
John 1:14 And the Word was made flesh, and dwelt among us, (and we beheld his glory, the glory as of the only begotten of the Father,) full of grace and truth.
John 1:18 No man hath seen God at any time; the only begotten Son, which is in the bosom of the Father, he hath declared him.
3 John 15:26; Gal. 4:6
But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father, he shall testify of me:
And because ye are sons, God hath sent forth the Spirit of his Son into your hearts, crying, Abba, Father.
This doctrine across the Standards
Where the Confession and the Westminster Shorter Catechism treat the same matter, so the question can be studied alongside its parallel statements.
In the Westminster Confession
II.3 In the unity of the Godhead there be three persons, of one substance, power, and eternity: God the …
In the unity of the Godhead there be three persons, of one substance, power, and eternity: God the Father, God the Son, and God the Holy Ghost. The Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Ghost eternally proceeding from the Father and the Son.
→ II.3 · Of God, and of the Holy TrinityVIII.2 The Son of God, the second person in the Trinity, being very and eternal God, of one substance, …
The Son of God, the second person in the Trinity, being very and eternal God, of one substance, and equal with the Father, did, when the fulness of time was come, take upon him man's nature, with all the essential properties and common infirmities thereof, yet without sin: being conceived by the power of the Holy Ghost in the womb of the Virgin Mary, of her substance. So that two whole, perfect, and distinct natures, the Godhead and the manhood, were inseparably joined together in one person, without conversion, composition, or confusion. Which person is very God and very man, yet one Christ, the only mediator between God and man.
→ VIII.2 · Of Christ the MediatorIn the Westminster Shorter Catechism
Q.5 Are there more Gods than one?
There is but one only, the living and true God.
→ Open Q.5Q.6 How many persons are there in the Godhead?
There are three persons in the Godhead; the Father, the Son, and the Holy Ghost; and these three are one God, the same in substance, equal in power and glory.
→ Open Q.6