If the Bible didn't say "God is love", would we have figured it out?

I've recently traded some comments with a thoughtful skeptic. Christians take it as a given that God is love because one of Jesus' apostles left a letter saying that God is love. We take his word for that. But do we have anything besides his word for it?

So here are some lines of reasoning that support the idea that God is love. These aren't intended as full proper axiomatic proofs; they all have their premises that aren't in-scope here. But for those who accept the premises, these support the idea that love is what most defines God:

The Nature of Morality

1. For Christians, the nature of morality is to be like God. Many commandments in the Bible are backed with this reasoning: do a certain thing because God does it. 
2. According to Jesus, the greatest commandments are the commandments to love God and neighbor. 
3. It would follow that the greatest way to be like God is to love. 
4. So the action that most defines God is love.

The Nature of Virtue

Some people see this as the same as #1 morality; others don't, depending on their school of thought on morality and virtue. So to cover all the bases:

1. Virtue is to be like God; 
2. The greatest virtue is love; 
3. It would follow that the greatest way to be like God is to be loving. 
4. So again the virtue that most defines God is love.

The Origin of Creation

This one takes as given that God doesn't hate himself; it is also informed by the book of Genesis regardless of how analogically you take it.

1. As any creator or artist, or as any parent, God created based on his own thoughts and will and imagination, and his own being. Everything that was created was based on his own being, and was good. 
2. Everyone has goodwill and compassion towards what they have made that they recognize as good, because of the intrinsic nature of the relationship between the good in them and the good in what they have made. 
3. God's love is therefore intrinsic in his relationship with everything he has made. 

 If anyone has another line of reasoning to add to the collection, I'd be glad to learn of it.