In Romans 11, Paul writes,

What then? Israel failed to obtain what it was seeking. The elect obtained it, but the rest were hardened…

But then only a few sentences later he writes,

As regards the gospel, they are enemies of God for your sake. But as regards election, they are beloved for the sake of their forefathers.

So which is it? Does elect mean chosen to have a soft and believing heart or chosen from among the nations as the covenant people of Abraham and the other patriarchs?

One could make the same comment on Paul’s use of “adoption,” which in Romans 9.6 has a collective reference to Israel, regardless of belief in the Gospel. Just previous, in Romans 8, adopt and adoption are used differently.

So what is the Pauline “definition” of election or adoption?