"Children" and/or "little children" are found 13 times in 1 John. Seven (2:1, 12, 28;3:7, 18; 4:4; 5:21) are the word τεκνίον, which is the diminutive of τέκνον which is used four times (3:1, 2, 10; 5:2). Two are the word παιδίον which is the diminutive of παῖς (which is not used):
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)
While a meaning for the word is child, typically it is one who is mature or undergoing training, which is how it is used in the letter. Also, Jesus is called 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) [also in Acts 3:26, 4:27, and 4:30]
If Peter called Jesus παῖς, then he and John would be the diminutive, παιδίον (cf, John 21:5). True, Jesus also called them by the diminutive, τεκνίον (John 13:33), yet that was before the Resurrection and before John and Peter believed (John 20:8-9).
This leads me to question what is the significance of παιδίον compared to τεκνίον?
- What is the essential distinction between the two? Is one a believer and the other not? Or is one a mature believer and the other new or immature?
- The comparison of the the "diminutive" παιδίον to Jesus (a παῖς) is straightforward, but what does this say about the relationship of the "diminutive" παιδίον to τέκνον?
- Given context, the etymology, and the differences between the other words translated as "little children" or "children" is "children" or "little children" a good translation of παιδία?