There is a curious fatalism in Holmes right at the end of 'The Adventure of the Final Problem'. He confesses, in the note left at Reichenbach, that he let Watson leave him in order to bring on the fight with Moriarty (who also seems to have the instinct, as he does not merely shoot Holmes). Because of this, I am unsure if the following analysis of Holmes's actions in the last scenes of 'The Final Problem' indicates a blunder on Holmes's part, or an earlier manifestation of this instinct. Either way, the same point can be made. The last scenes of 'The Final Problem' are very different from the earlier duel between Holmes and Moriarty. They are much less rationally acted, and remind one of mutually assured destruction promises being carried out, or a Greek tragedy, or something of that kind.

The part of the story I wish to focus on is approximately the last third; the tailpiece that arises once Moriarty's empire in London has been destroyed. There are difficulties throughout this section of the story, and the first arises immediately. After receiving the telegram from the police, Holmes says that Moriarty is lost if he (Moriarty) returns to London. He further says that Moriarty will be out to kill Holmes in revenge for the loss of his empire. Assume these statements are true, as Holmes clearly thinks they are. The obvious thing for Holmes to do then, one might think, is to return to London himself, as it is the one place in Europe Moriarty is being actively hunted by the official police force. If his vengefulness takes him there after Holmes, he will be lost. Yet Holmes and Watson consider only two courses of action. On the first, both Holmes and Watson continue to Switzerland. On the second, Watson returns to London and Holmes continues to Switzerland. Why does not Holmes, or even Watson, consider the obvious plan of both returning to London? This is the first difficulty.

We can explain this, of course, by assuming that immediately after the telegram Holmes is ready to imperil himself to destroy Moriarty, and that he prefers this to mere personal survival. That is, after the telegram Holmes is acting rationally given his beliefs, if we assume that Holmes has the following preferences (from most-preferred to least-preferred) with respect to the outcome of the whole affair:

1. Holmes alive and Moriarty dead
2. Both dead
3. Both alive
4. Holmes dead and Moriarty alive.

Call this a Noble set of preferences (as Holmes is willing to die to get rid of Moriarty). It is likely that Holmes has had a Noble set of preferences from the first, especially as he assures first Moriarty and then Watson several times that, in the public interest he would gladly die if his death would bring about that of Moriarty. These statements aside, though, his actions earlier in the story also seem consistent with the following Prudent set of preferences:

1. Holmes alive and Moriarty dead
2. Both alive
3. Both dead
4. Holmes dead and Moriarty alive.

In any case, Holmes has Noble and not Prudent preferences after the telegram, else his talk with Watson in Strasbourg is senseless and he would have returned to London. He is ready to imperil himself to destroy Moriarty. The manner in which he does this is, of course, to wander up the Rhone Valley and loiter in Switzerland, passively waiting for Moriarty to confront him (call this the Bait Plan, as Holmes is offering himself as bait). This takes care of the first difficulty.

But a second difficulty now arises. The Bait Plan is only sensible if Holmes knows that Moriarty is utterly indifferent to his own life as long as he kills Holmes. Let us call this state Thanatic. Moriarty is clearly Thanatic later, at Reichenbach, as he chooses to fight hand-to-hand instead of simply shooting Holmes. But at the time of the telegram, Holmes doesn't know Moriarty is Thanatic - he knows, from his reading of Moriarty's character, that Moriarty wants to kill him, yet a very obvious way Moriarty might try to do this is by assassinating Holmes in a manner relatively riskless to himself (call this Murderous behaviour). If Moriarty is Murderous, Holmes merely risks his own death with the Bait Plan (4, his least favoured preference whether Noble or Prudent), and he should either return to London (3 for a Noble) or take positive steps to hunt Moriarty (hopefully leading to either 1 or 2 in his preference rankings). That Moriarty is Murderous seems more probable than that Moriarty is Thanatic, given the cautious temperament displayed in his past actions. Hence Holmes seems to be acting irrationally, even as a person with Noble preferences. This is the second difficulty.

We evidently need to assume that Holmes is so good at reading Moriarty that he knows, when he receives the telegram, that Moriarty will be Thanatic, rather than Murderous. Only then does the Bait Plan become rational for a Noble Holmes. Yet this sets up the third difficulty. A week later, in the Gemmi Pass, a rock fall is taken by Holmes to be an attack on his life by Moriarty. Whether it is an attack or not, the important thing is that Holmes believes it is. The rockfall is Murderous, rather than Thanatic, behaviour, as Moriarty is trying thereby to kill Holmes without risk to himself. Thus the incident supplies Holmes with evidence that his Bait Plan will lead to the worst outcome: his own passive death while Murderous Moriarty lives. Holmes therefore ought now change plan if he is Noble: either return to London or actively pursue Moriarty. But he continues in the Bait Plan regardless. As far as Holmes's evidence is concerned, that is, it is pure luck that Moriarty is Thanatic later, at Reichenbach. And this sort of pure luck will not save the assumption that Holmes is a rational agent throughout this passage of events.

This being so, I think the only way out is to assume that, at least from the moment of the Gemmi Pass incident, but probably further back, when the telegram was received, Holmes had in reality neither a Prudent nor a Noble set of preferences. His actions become explicable only if he had the following set of World-Weary preferences (we know that the first two preferences are in the order below, because of Holmes's vigorous attempt to survive Moriarty's death, as reported in 'The Empty House'):

1. Holmes alive and Moriarty dead
2. Both dead
3. Holmes dead and Moriarty alive
4. Both alive.

Holmes is thus willing to continue the Bait Plan: to die, even where his chances of capturing or killing Moriarty are negligible. It is as though a weariness with the co-existence of himself and Moriarty has come upon him, and, if he cannot kill Moriarty, he would rather perish. This attitude contributes markedly to the air of tragedy in the final pages, putting the story in a peculiar place in the Canon. After all, with a Thanatic Moriarty and a World-Weary Holmes opposed to one another, all pretence at normal rational action has long gone.