The claim
Paul never speaks of a true Israel or a spiritual Israel. The chapter's claim is that simple and that absolute: the phrases are not in the corpus, and the idea they name is post-Pauline.
Origen shows how the inference was made. "The apostle says somewhere, Behold Israel according to the flesh, as if there were an Israel according to the spirit." The "as if" is the whole move, and it does not follow. Israel according to the flesh, at 1 Corinthians 10:18, means simply Israel, the people whose temple is in Jerusalem, and κατὰ σάρκα carries no disparagement; the Messiah himself comes from Israel κατὰ σάρκα. There is no spiritual seed of David and no spiritual messiah in Paul either.
The proof-texts
Novenson takes the supposed evidence in turn.
Romans 2:28 to 29, the "true Jew", rests on a mistranslation that has persisted because of the assumption it serves. The adjectives "true" and "real" are not in the Greek at any point in the manuscript tradition; translators supply them. Read with "Jew" as subject rather than predicate, as Arneson proposes, the passage asks not who is a Jew but who receives praise from God, and answers: the Jew in secret rather than the Jew on display. The ostentatious circumcision in view is proselyte circumcision, which is by definition in the flesh and for show.
Philippians 3:3, "we are the circumcision", is Paul reclaiming the title from proselyte-circumcised gentiles on behalf of eighth-day-circumcised Jewish apostles like himself. That is the opposite of a transfer. The RSV's "true" is again supplied.
Romans 9:6, "not all those from Israel are Israel", does the reverse of what the verus Israel reading requires. It winnows Israel rather than expanding it; Paul reasons to fewer, not to more, and certainly not to others. Nothing in the verse concerns outsiders finding a way in.
Romans 11:26 turns on the verb. σῴζω means to survive, to be preserved through the day of the Lord, and "all Israel will be preserved" is close to the Mishnah's "all Israel have a share in the age to come". The citation attached to it names Jacob, who is the father of the twelve tribes, which Novenson takes as decisive. The referent is the whole Jewish people, as against the small part currently persuaded by Paul's message. Gentiles-in-Christ will survive the judgment too; they are simply not Israel.
The objections
Wright would defend the substance of his reading of the double existence of Israel in Romans 11 by pointing at what Romans 9 does. Once "not the children of the flesh but the children of the promise are counted as seed", promise rather than descent defines the seed, and the term has been prised open in principle; Galatians then walks through the opening, since those who belong to the Messiah are Abraham's seed and heirs according to promise. Novenson says Paul never completes the redefinition. Wright would say the argument performs it, and that Justin merely wrote down what the logic had already done.
Novenson's answer is a distinction and a parable. Abraham's seed is not Israel. 1 Maccabees reports that the Spartans too were found in writing to be of the clan of Abraham; it does not follow that Spartans are Jews, because Spartans are not descended from Isaac and Jacob. Paul's gentiles are in the same position: seed and sons of Abraham, not sons of Isaac or Jacob. Abraham is the father of us all; Jacob, which is to say Israel, is not. Gentiles-in-Christ are annexed to God's people without becoming God's people Israel. The cost of the alternative is that it leaves Paul with no vocabulary at all for his own co-ethnics, which he needs constantly.
Sanders enters twice and fares differently each time. His long-held view that Galatians 6:16 is the one place Paul uses "Israel" of something other than the Jewish people is retired: read as two parallel clauses, peace on those who walk by this rule and mercy also on God's people Israel, the exception dissolves, and Eastman's observation that mercy is Paul's word for God's posture towards Israel in Romans 9 to 11 supports it. His "third race" proposal fares worse, and the book calls the idea ingenious but not finally convincing. On the main claim he would agree that the lexicon is with Novenson and that the extension of "Israel" to the church is post-Pauline, while noting that the lexicon cannot dispose of the pressure Wright feels in the argument.
Paul's own account
The letters keep the word where the chapter says they keep it. When Paul writes about Israel he writes about his kinsmen: the people of the adoption and the glory, his brothers according to the flesh, for whose sake he could wish himself accursed. The grief in Romans 9 is unintelligible if Israel has meanwhile become a term for the assemblies he is writing to.
The letters also contain the pressure. Paul does make gentiles sons of Abraham, and does so on the ground that the promise to Abraham was that in him all the nations would be blessed. He treats the nations as having been inside that promise from the beginning. What he does not do, anywhere, is take the next step and call them Israel; and when he wants a word for the relation, he reaches for Deuteronomy: rejoice, O gentiles, with his people.
Why he stopped at that line the letters do not say. The chapter's contribution is to establish that he stopped.
The remaining disagreement
Both sides agree about what Paul wrote and disagree about what his argument implies.
Novenson holds that an argument's implications are not its contents, and that the historian's job ends at what the text says. Wright holds that a redefinition performed is a redefinition made, and that the later tradition drew a conclusion already present in the premises. Sanders holds that Paul did not tidy this and declines to tidy it for him.
The disagreement is therefore methodological rather than exegetical, which is why it has lasted.
The same chapter as a dialogue sets these positions in the participants' own voices, which is how this was first written.