Two senses of the word Son, 1. adoptive; 2. essential; attempts of Ariansto find a third meaning between these; e.g. that our Lord only was created immediately by God (Asterius's view), or that our Lord alone partakes the Father. The second and true sense; God begets as He makes, really; though His creation and generation are not like man's; His generation independent of time; generation implies an internal, and therefore an eternal, act in God; explanation of Proverbs 8:22
9 But though we were to allow some prerogative to the Protoplast as having been deemed worthy of the hand of God, still it must be one of honour not of nature. For he came of the earth, as other men; and the hand which then fashioned Adam, is also both now and ever fashioning and giving entire consistence to those who come after him. And God Himself declares this to Jeremiah, as I said before; 'Before I formed you in the womb, I knew you;' and so He says of all, 'All those things has My hand made;' and again by Isaiah, 'Thus says the Lord, your redeemer, and He that formed you from the womb, I am the Lord that makes all things; that stretches forth the heavens alone; that spreads abroad the earth by Myself. ' And David, knowing this, says in the Psalm, 'Your hands have made me and fashioned me;' and he who says in Isaiah, 'Thus says the Lord who formed me from the womb to be His servant,' signifies the same. Therefore, in respect of nature, he differs nothing from us though he precede us in time, so long as we all consist and are created by the same hand. If then these be your thoughts, O Arians, about the Son of God too, that thus He subsists and came to be, then in your judgment He will differ nothing on the score of nature from others, so long as He too was not, and came to be, and the name was by grace united to Him in His creation for His virtue's sake. For He Himself is one of those, from what you say, of whom the Spirit says in the Psalms, 'He spoke the word, and they were made; He commanded, and they were created. ' If so, who was it by whom God gave command for the Son's creation? For a Word there must be by whom God gave command, and in whom the works are created; but you have no other to show than the Word you deny, unless indeed you should devise again some new notion.
“Yes,” they will say, “we have another;” (which indeed I formerly heard Eusebius and his fellows use), “on this score do we consider that the Son of God has a prerogative over others, and is called Only-begotten, because He alone partakes the Father, and all other things partake the Son.” Thus they weary themselves in changing and in varying their phrases like colours; however, this shall not save them from an exposure, as men that are of the earth, speaking vainly, and wallowing in their own conceits as in mire.
10. For if He were called God's Son, and we the Son's sons, their fiction were plausible; but if we too are said to be sons of that God, of whom He is Son, then we too partake the Father, who says, 'I have begotten and exalted children.' For if we did not partake Him, He had not said, 'I have begotten;' but if He Himself begot us, no other than He is our Father. And, as before, it matters not, whether the Son has something more and was made first, but we something less, and were made afterwards, as long as we all partake, and are called sons, of the same Father. For the more or less does not indicate a different nature; but attaches to each according to the practice of virtue; and one is placed over ten cities, another over five; and some sit on twelve thrones judging the twelve tribes of Israel; and others hear the words, 'Come, you blessed of My Father,' and, 'Well done, good and faithful servant. ' With such ideas, however, no wonder they imagine that of such a Son God was not always Father, and such a Son was not always in being, but was generated from nothing as a creature, and was not before His generation; for such an one is other than the True Son of God.
But to persist in such teaching does not consist with piety, for it is rather the tone of thought of Sadducees and the Samosatene; it remains then to say that the Son of God is so called according to the other sense, in which Isaac was son of Abraham; for what is naturally begotten from any one and does not accrue to him from without, that in the nature of things is a son, and that is what the name implies. Is then the Son's generation one of human affection? (for this perhaps, as their predecessors, they too will be ready to object in their ignorance;)— in no wise; for God is not as man, nor men as God. Men were created of matter, and that passible; but God is immaterial and incorporeal. And if so be the same terms are used of God and man in divine Scripture, yet the clear-sighted, as Paul enjoins, will study it, and thereby discriminate, and dispose of what is written according to the nature of each subject, and avoid any confusion of sense, so as neither to conceive of the things of God in a human way, nor to ascribe the things of man to God. For this were to mix wine with water, and to place upon the altar strange fire with that which is divine.
11. For God creates, and to create is also ascribed to men; and God has being, and men are said to be, having received from God this gift also. Yet does God create as men do? Or is His being as man's being? Perish the thought; we understand the terms in one sense of God, and in another of men. For God creates, in that He calls what is not into being, needing nothing thereunto; but men work some existing material, first praying, and so gaining the wit to make, from that God who has framed all things by His proper Word. And again men, being incapable of self-existence, are enclosed in place, and consist in the Word of God; but God is self-existent, enclosing all things, and enclosed by none; within all according to His own goodness and power, yet without all in His proper nature. As then men create not as God creates, as their being is not such as God's being, so men's generation is in one way, and the Son is from the Father in another. For the offspring of men are portions of their fathers, since the very nature of bodies is not uncompounded, but in a state of flux, and composed of parts; and men lose their substance in begetting, and again they gain substance from the accession of food. And on this account men in their time become fathers of many children; but God, being without parts, is Father of the Son without partition or passion; for there is neither effluence of the Immaterial, nor influx from without, as among men; and being uncompounded in nature, He is Father of One Only Son. This is why He is Only-begotten, and alone in the Father's bosom, and alone is acknowledged by the Father to be from Him, saying, 'This is My beloved Son, in whom I am well pleased.' And He too is the Father's Word, from which may be understood the impassible and impartitive nature of the Father, in that not even a human word is begotten with passion or partition, much less the Word of God. Wherefore also He sits, as Word, at the Father's right hand; for where the Father is, there also is His Word; but we, as His works, stand in judgment before Him; and, while He is adored, because He is Son of the adorable Father, we adore, confessing Him Lord and God, because we are creatures and other than He.
Source: De Decretis (New Advent)