What does Paul mean by "the Law"?

Some time around or after the Protestant Reformation the Biblical term "Law" had popularly come to mean something along the lines of 'any good work God commands of humans'. This erroneous definition led millions into misunderstand Paul's teaching on Salvation, thinking that Paul was against all works done under any circumstances. But if we really care about the Bible (which I'm starting to think Protestants do not), we cannot go around making up our own definitions of key Biblical terms. The simple truth is, the Bible clearly and consistently defines "the Law" to be the Mosaic Law, and this post will encourage readers to see the plain evidence for themselves.

The Greek term "Law" (Nomos) occurs almost 200 times in the New Testament, so we should be able to get a pretty good idea of its range of meaning, especially in key chapters where Paul is contrasting the Law to the Gospel. Here's my breakdown:

"Not all who are of Israel are Israel!" - A further look at Romans 9

This post builds on a recent post I did, Romans 9 like you've never heard it before. 

Thinking about Romans 9 some more, it seems there's one further detail that ties things together even more: Within the famous Patriarchal trifecta of "Abraham, Isaac, and Jacob," it seems in this passage that Paul only gave examples of the sons of Abraham (9:7-9) and Isaac (9:10-13), but Paul did not seem to mention the sons of Jacob. Or did he? Actually, it seems Paul does mention Jacob, but we probably missed it. 

In the famous (and slightly mysterious) thesis verse of Romans 9:6, Paul says: "But it is not as though the word of God has failed. For not all who are descended from Israel belong to Israel." The standard interpretation of this second sentence is that not all who are biologically Jews belong to "Spiritual Israel". And that makes sense. Calvinists go one step further, and in an erroneous way, and interpret this as basically saying there is a "visible church" and an "invisible church," such that you can be a member of the "visible church" but not actually saved. In this post, I want to consider what I think is a more satisfying interpretation of 9:6.