was therefore a very welcome distraction from all of this.

Our problem is this: Hegel rates figures below concepts but he needn’t always do so. In his mind, figures are just a bunch of numbers and lines annoyingly uncommitted to either Thought or Being. He also dislikes figures because they aren’t language, or are a lesser language. Hegel has his reasons for these positions. But those reasons may not be good enough, judging by the way he seems to equivocate about figures. Sometimes figures are so perfect as to figurate the very significance of his philosophy (and that’s no small feat!). And sometimes they are pretenders to proper conceptuality, conceptual thinking by other means. Hegel is all over the place on this question, as we’ll soon see. But if one applies even a modicum of mathematical wit to the figures Hegel does offer us—and most of them are circles, with triangles as a close runner-up—then we discover some rather interesting spaces in which dialectics might wander.

I want to divide my talk into four themes:

Over the portal of the new world,

Indeed, in his Foreword to instead of allegory he said

Barnard’s photograph, taken in those same days, says that Atlanta is taken, that Sherman is victorious, and that the war needs to be fought to its conclusion. The proof is in the photographic glass, in the stone and rail and wood, and in the man at the center of the ash. Neither black nor white (it is impossible to tell his race), he solemnly acknowledges the massive destruction of the southern war machine and makes the case implicitly for more of the same violence as the only way to bring peace. In Photographic Views of Sherman’s Campaign, true enough, there will be many scenes of obliteration still to come after the Destruction of Hood’s Ordnance Train. Relentlessly, the rebellion will be flattened to the ground. When it is not flattened, picturesque windows will be left in its broken walls only so that the viewer can examine how little of the defeated place still exists. On September 12, Sherman wrote to the mayor of Atlanta, who had implored him to stop bombarding the city: “You might as well appeal against the thunder storm as against these terrible hardships of war.”

There is no self-understanding without God-understanding.

Tolkien’s decision not to invent an eternal destiny for the elves or orcs or dwarves helps him avoid creating a new theology. Men do have a destiny beyond the grave (and there is no reason to suspect that this is not a similar destiny to that which Christians believe comes after death). Tolkien does not put the elves on a par with God. Here, surely, are the angelic hosts, the cherubim and seraphim, who make up the heavenly order and whose history sometimes meets our own. Lothlorien is their domain: and here "no blemish or sickness or deformity could be seen…On the land of Lorien there was no stain."

In his letters he is less emphatic, admitting that,
The best way of knowing the inwardness of our neighbor is to know ourselves.

Without humility there can be no illuminating self-knowledge.

A non-Christian reading of often points to the rather violent and occasionally gory nature of the story, with the numerous battle scenes. The vivid and gratuitously bloodthirsty orc-slaying by Legolas and Gimli might offend a pacifist but as part of a just war against the invasion and devastation of Middle Earth by the evil forces of Sauron they provoke us to ask legitimate questions about the licit use of force; and, indeed, the nature of warfare. These are highly relevant questions in the days of precision attacks by cruise missiles, aerial bombardment of cities, and the use of weapons of mass destruction.

It is in men as in soils, where sometimes there is a vein of gold which the owner knows not of.

Too bad we didn't learn it sooner.

For Aristotle, the phainomenon of fallacies is elusive, but so is the language we use to speak of them. They are “really” fallacies, paralogismoi, statements that lie outside of reason or of rational discourse (para-, outside, beyond + logizomai, to think, to calculate, to consider; the word is from logos, the Greek word that means anything from word to reason to order). That is, not only can we recognize sophistical refutations only by what they are not; we also cannot use the term itself to describe them, since they occupy a position outside of discourse. Sophistical refutations are actually not refutations at all (ouk elenchon legomen). Strictly speaking, a treatise on sophistical refutation is a logical impossibility, the first deception in a treatise full of them.

We could have gone to the movies instead.

Taking the inner journey will lead you into some very shadowy places.

In any event, Tolkien was, among other things, celebrating the deep kindred of male fellowship. Cardinal Basil Hume once said, "we need to reclaim the idea of friendship—friendship for its own sake." does that. The breaking of the fellowship perhaps also recalls the saddening consequences of the fracturing of friendship and community. St. Thomas More mourned the consequences of the Reformation, not because he was opposed to renewal and reform (quite the reverse) but because it broke "the unity of life". Tolkien’s writing celebrates this unity and reflects on the weakened condition of Middle Earth when the old alliances and unity are broken.