I'd like to build on Dottard's answer. The key for me is the adverbial and linking nature of the word. I'd probably call οὕτως a conjunctive adverb.1
In all cases, I don't think 'so' works very well. It's too weak a translation choice. 'Thus' or 'thusly' or 'as in this manner' are relatively close to the Greek meaning.
However, I think part of the key to answering the OP is to understand the word right next to οὕτως, γάρ. What does it do? And then, perhaps even more importantly, what do they mean together? Words massage and shape each other's meaning as they flow across a text. That is one reason we say, "words have meaning in context." It's not that there is not a core meaning signaled by the word-symbol. It's the in context shaping. That's also why lexicons list different glosses. The glosses are the result of contextual molding. So, we need to think of οὕτως γάρ as working together.
First, what does γάρ mean? Recent research suggests γάρ signals to the reader that the author is about to answer a perceived question or objection. (see "Reclaiming γάῥ") Thus the common gloss of 'for' though this common gloss doesn't go far enough. 'For' suggests a reason, or sometimes purpose, for what has just been said. And that's good as far as it goes. However, it's more accurate understanding of the original to seek a reason for why the author thinks that the reader would be puzzled by something or would be raising an objection.
So, combining the two ideas, I suggest something like, "that fits since" as a translation of οὕτως γάρ.
There are 9 occurrences of οὕτως γάρ in the NT. Something to note is that the text immediately preceding οὕτως γάρ suggests an expectation of surprise which needs resolved. That aligns with the meaning of γάρ. γάρ suggests an implied question, and the οὕτως suggests a 'as in this manner' connection. And so, the "that fits since" brings together the two concepts offered when οὕτως and γάρ are taken together as a semantic unit.
So, I think the significance of οὕτως is better answered by grasping the significance of οὕτως γάρ.
The phrase 'οὕτως γάρ' signals that an explanation will immediately follow.
Here are the 9 occurrences of οὕτως γάρ in the New Testament. These are from the NASB20 modified with my insertion of the phrase 'that fits since'. [Note: Links send the reader to the larger context.]
- Matthew 2:5 They said to him, "In Bethlehem of Judea; that fits since this is what has been written by the prophet:
A king being born in Bethlehem was a bit surprising since Bethlehem was not a town of importance.
- Matthew 3:15 But Jesus, answering, said to him, "Allow it at this time; that fits since it is fitting for us to fulfill all righteousness." Then he allowed Him.
Being baptized was viewed as a cleansing and repenting symbol. For Jesus to enter into such a symbolic action surprised John. And so, it needed an explanation.
- Matthew 5:12 Rejoice and be glad, for your reward in heaven is great; that fits since they persecuted the prophets who were before you.
It's surprising that we are to rejoice at such wrongful treatment.
- John 3:16 "That fits since God so loved the world, that He gave His only Son, so that everyone who believes in Him will not perish, but have eternal life.
The lifting up of a snake2 on a pole as an answer to Nicodemus' question was surprising. Not to mention the surprising statement that the Son of Man was somehow similar.
- Acts 13:8 But Elymas the magician (that fits since (that translates his name [original: so his name is translated]) was opposing them, seeking to turn the proconsul away from the faith.
The fact that the translation of the name Elymas was magician is a somewhat surprising (at least, intriguing) fact.
- Acts 13:47 That fits since the Lord has commanded us, 'I have appointed You as a light to the Gentiles, That You may bring salvation to the end of the earth.'"
The Apostles had just announced they were turning to preach to the Gentiles. That's a surprising turn of events. The explanation comes right from the prophetic word.
- Acts 20:13 But we went ahead to the ship and set sail for Assos, intending from there to take Paul on board; that fits since that was what he had arranged, intending himself to go by land.
The surprise here is that Paul doesn't go with them on the ship.
- 1 Peter 3:5 That fits since in this way the holy women of former times, who hoped in God, also used to adorn themselves, being subject to their own husbands,
Perhaps this is surprising since it pits physical beauty over against spiritual beauty saying the spiritual beauty is actually more attractive.
- 2 Peter 1:11 that fits since the entrance into the eternal kingdom of our Lord and Savior Jesus Christ will be abundantly supplied to you.
Perhaps the surprise is that "adding virtue to faith, knowledge to virtue, etc" would prevent stumbling. And so, the entrance into the eternal kingdom would be significantly successful.
How does this help answer the question of, "What does this tell us about God's love?"
In verses 13-15 Jesus says that the Son of Man has dominion and yet he must be "lifted up" just like the snake of Numbers 21. This is a puzzling statement and needs explanation. And so, the phrase, "that fits since..." introduces the explanation expressed by 3:16-21. This explanation defines the manner in which God loves.
Numbers story |
Explanation |
Snake lifted up |
Son of Man lifted up |
Snake doesn't judge |
Christ on the cross does not judge (ie. condemn) |
The person who looks is healed |
The person who believes is saved |
The Snake (aka Apophris) is darkness |
Sin is darkness |
The one true God conquers darkness |
Jesus has come into the world as light |
Publicly look at the snake |
Publicly believe in Christ |
Person is miraculously healed |
Person is miraculously saved |
The right side of the table shows how God loves.
1Lexicons suggest things like, "to such an extent, so, so much, so very, so excessively" (LSJ). This will confuse people. The intensity suggested by these glosses does not come from the word itself, but is supplied by the context. And so, in certain contexts, such wording might be right. But, the suggestions should not be construed as the meaning of the word.
2 A possible reference to the Egyptian god of all that was wrong in the world, Apophis. This allusion to Egyptian mythology would add to the surprise. And I don't make this suggestion lightly. The Egyptian god Ra (god of order and good) ascended and descended the sky every day only to battle Apophis, the snake, every night. And then there's also a direct connection to the battle between light and dark in both the text and the mythology.