The review brings up issues which I—with the carriage horses pointed toward eternity—feel there can be no stopping for. But Conrad H. Roth, in his posting (Varieties of Unreligious Experience appears to have ceased activity five years ago), gives a summation of the conflict's crux, at least as Momigliano saw it:
White's basic point had been—and still is, apparently—that historiography is a branch of rhetoric, and that the way one writes history is governed by the same sorts of rhetorical tropes as are found in oratory and fictional literature. Style becomes more important than truth: what could be more postmodern? Momigliano, the old-guard Warburg philologian, objected: what sense can we make of history if we forget that it centres on facts and problems?
Amélie Kuhrt, in the discussion after Murray's paper, described Momigliano's response to White as a moral distaste: the aim of historiography should be an ethical engagement with the problems of the past in relation to those of the present, not mere games with words and ideas, as White, the formalist, wanted to give us.
As you might surmise from my previous blog post titled "The All-Redeeming Virtue of the Liberal Mind", I should prefer to adhere to a historian "determined to understand and respect evidence from whatever part it came" instead of one for whom history is "mere games with words and ideas". Certainly it was important to Finley to get the facts right; and I doubt he would approve a history that was also not "an ethical engagement".