Twice John uses the word παιδία:
I am writing to you, fathers, because you know him who is from the beginning. I am writing to you, young men, because you have overcome the evil one. I write to you, children (παιδία), because you know the Father. (2:13 ESV)
Children (παιδία), it is the last hour, and as you have heard that antichrist is coming, so now many antichrists have come. Therefore we know that it is the last hour. (2:18 ESV)
Rendering the word as "children" in verse 13 is understandable given it placement after fathers and young men. (Although the παιδία "know the Father" a claim not made of any others). In the second use "children" is out of context since what follows is the issue underlying the necessity to write and the unique phrase "anointed by the Holy One:"
They went out from us, but they were not of us; for if they had been of us, they would have continued with us. But they went out, that it might become plain that they all are not of us. But you have been anointed by the Holy One, and you all have knowledge. (2:19-20 ESV)
While a meaning for the word is child (yet not the same sense as τεκνία used elsewhere in the letter), the type of child is one who is more mature, which is consistent with both uses in the letter. Etymologically the word is the diminutive of παῖς [G3813 - παιδίον] which can mean child, or servant, specifically a king's attendant or minister [G3816 - παῖς].
Significantly, Jesus is known as a παῖς:
The God of Abraham, the God of Isaac, and the God of Jacob, the God of our fathers, glorified his servant (παῖδα) Jesus, whom you delivered over and denied in the presence of Pilate, when he had decided to release him. (Acts 3:13 ESV) [also in Acts 3:26, 4:27, and 4:30]
If Jesus is παῖς, a true disciple could be called by the diminutive, παιδίον.
In addition, John's use of τέκνα throughout 1,2, and 3 John and its diminutive form, τεκνία, in 1 John seems purposeful. As Judith Lieu states in New Testament Theology:1
In the second part of 1 John a key theme is that believers are born of God (3:9; 4:7; 5:1,4,18) or are children of God (3:1f.,10; 5:2). Here the author uses a different word for 'children' of God (tekna) from when he address his readers as 'children' (teknia, paidia: 2:1; 12,28; 3:7,18; 4:4; 5:21 2:14,18) 17
17: The same distinction is followed in the Gospel: 'children of God' or 'children of Abraham' (1:12; 11:52; 8:39) uses tekna, but Jesus addresses his disciples as teknia or paidia (13:33; 21:5). In contrast 2 and 3 John only use tekna - of members of the community (2 John 1,4,13; 3 John 4).
Given context, the etymology, and the differences between teknia and tekna used in the letter, is "children" or "little children" the best translation of παιδία?
- Judith Lieu, New Testament Theology, The Theology of the Johnannine Epistles, Cambridge University Press, 1991, p. 33