Faith not Works?

My opinion is like C. S. Lewis's in Mere Christianity : arguing whether faith or works is more important is like arguing which side of a pair of scissors is more important.

But the second reading at Mass today was Galatians 2:16,19-21 (11th Sunday in Ordinary Time, Year C)

"Brothers and Sisters:
We who know that a person is not justified by works of the law
but through faith in Jesus Christ,
even we have believed in Christ Jesus
that we may be justified by faith in Christ
and not by works of the law,
because by works of the law no one will be justified.
For through the law I died to the law,
that I might live for God.
I have been crucified with Christ;
yet I live, no longer I, but Christ lives in me;
insofar as I now live in the flesh,
I live by faith in the Son of God
who has loved me and given himself up for me.
I do not nullify the grace of God;
for if justification comes through the law,
then Christ died for nothing. "

One stereotype is that Catholic Christians think that if they follow "the law" then they will be saved. The other stereotype is that Protestant Christians think that all they have to do in life is think they believe in Jesus and that's all they need to do to go to heaven.

I know the first one isn't true, as evidenced by this passage, and I hope the second one isn't either.

Today's context for this passage was a first reading from Samuel 2 and a Gospel from Luke. In Samuel, King David repented and God forgave him his adultery and murder. In the Gospel, Jesus is eating at the house of Simon the Pharisee, where a sinful woman comes and cleans, kisses and perfumes Jesus's feet. I don't know whether Jesus was mind reading or had really good ears, but he hears Simon's rejection of the woman. Jesus then proposes that the woman, though a sinner, is more welcoming to him than Simon was, and tells a parable: two men were forgiven of their debt, and the one who was forgiven more loves more.

All three passages have the same theme: God's forgiveness.
When King David repents, "The Lord on his part had forgiven (his) sin: (he) shall not die"
Paul says "I live by faith in the Son of God who has loved me and given himself up for me."
Jesus says "Her many sins have been forgiven because she has shown great love. But the one to whom little is forgiven, loves little"

This is nice to say, but what does it mean? What does Paul mean?
The passage's context was Paul writing to the Galatians, a community that had many converts from Judaism. Understandably, they wanted to continue following Jewish/Mosaic Law, and wanted the Gentile converts to follow it as well. This is the "works of the law" that Paul means. Paul wants to make it very clear that salvation is through Jesus rather than through following Jewish practices (especially circumcision).

Maybe defining some words would help:
works of the law: the old Jewish law, circumcision, dietary restrictions, etc...
justification: becoming just, being saved
love: actions that put others before yourself
Christ lives in me/live for God: following Jesus's teachings/imitating Jesus

If Paul is living for God, then he is following what Jesus taught, which, as shown in the Gospels was a new commandment: that they should love one another. To follow this you must die to the old law of "an eye for an eye and a tooth for a tooth." In the end, Paul makes sense when he says that if this old law justified you/if it "saved" you, then there was no need for Jesus to bring the new law, and there was no need for Him to die on the cross for forgiveness of sins. Paul both has faith in forgiveness of sins from Jesus's death and imitates being "crucified with Christ." Is it too much of a stretch to say Paul sees these as the same thing?

Jesus says in the Gospel "her many sins have been forgiven because she has shown great love" and "your faith has saved you; go in peace". To Jesus, showing great love and faith are synonymous. I would say these are the same things as works and faith. If you are forgiven by God, then you are justified; you are saved.

Math! if great love (or works)=forgiven and forgiven=saved then works=saved
and Jesus said faith=saved, so faith=works.