Daniel Fleming of NYU (in an lecture on iTunes titled “Ancient Israel”) defines “Israel” a few different ways:
Religious: “The name of the people who worship the god named YHWH in much of Bible writing.” This is a definition of Israel based on the Bible. Israel is the “people of the god YHWH”.
Political-Historical: “The name of the people who act as a group between at least the year 1200-720 BCE.” He marks 1200 as the beginning because that is where out external, Egyptian evidence is dated and he marks 720 as the end because of the Assyrian invasion. He notes that Israel is not Judah, Judah is not Israel, but that these names become convoluted later.
For readers of this blog this may be a helpful distinction. I have noticed that at time there is some debate over how to define “Israel”, especially as it relates to Jewishness. Usually, I am using the term from a Political-Historical perspective, which acknowledges that Second Temple Jews often discuss “Israel”–whether it be the Qumran sect, the Gospels, the Book of Acts, or the writings of Paul–even if this label is problematic. Other are discussing Israel “theologically”, i.e., true Israel is this or that. Paul argues that true Israel is the Israel who acknowledges Jesus as the Christ. Qumran (at least documents like 1QS) presents true Israel at those who submit to becoming part of the “Unity”. I understand that there are passionate views of what defines Israel theologically, some that date back to antiquity, but I am not trying to make a statement about this definition of Israel, usually.