Shroedingers Death saves.
Fact is, the PC is about to die and that was a result of HP loss.
In turn that means that at least some part of the HP loss must have been a physical, potentially mortal, wound.
I don't see how this differs in any fundamental way from stabilisation rolls in 4e, or even from 1st ed AD&D, where (with minor medical attention) a wound that otherwise would have been fatal can be recovered from in a week or so. D&D has never had mechanics for implementing your notion of a mortal wound (if it did, the Regeneration spell might have actually seen play).
You don't die from a lack of will.
In the world of D&D you can - consider Lancelot in the 1981 version of Excalibur, for example, or Aragorn in Peter Jackson's version of The Two Towers, or Kull diving into the taboo lake and fighting all sorts of beasts underwater and not drowning only because of the strength of his will (I think the story is Delcarde's Cat).
I think both these matters are best viewed as a genre thing. If you don't like the genre, then 4e is not for you - but I'm personally baffled as to how any earlier edition of D&D (except perhaps Moldvay basic or low-level OD&D, which combine a certain grittiness with no death's door rules) was.
Linking together "hit point damage" and "physical injury" as an automatic assumption is something that I can understand. It's fairly obvious and consistent with D&D throughout the editions.
However, linking together "regaining hit points" and "injuries disappearing" is an assumption that D&D players in this thread are making - it is not something that is in the rules. It doesn't matter if this assumption is referred to over and over again - it is not in the RAW, nor the RAI.
Therefore - when a Warlord uses Inspiring Word, all they are doing is the mechanical "regaining hit points" effect, not the "making injuries disappear" effect that is being added on. And as such, when a Warlord uses Inspiring Word they are helping a character continue with the fight, not fixing physical injuries.
As such, Schrodinger's Wounding disappears in a puff of logic.
Agreed. I've been saying the same thing (as have LostSoul, Hypersmurf and others) for many months in many threads.
Leaving a worse problem in its wake........The characters are at full power the next day, and never need worry about wounds that now exist (narratively) and do not exist (mechanically).
In a sandbox game, if you completely disjoin hit points from physical injury, as you suggest, and everyone is always in perfect (game mechanics) health the next day, the problem is worse, not better.
I think I already posted that the healing surge/short rest/dying mechanics (roughly, the bundle of mechanics that are said to yield "Schroedinger's Wounding") are quite distinct from the extended rest mechanics, which are what you seem to be complaining about above.
One solution to the extended rest problem, if you can't embrace the underying genre assumption (that also serves a useful game mechanical function for at least some values of "useful"), is (as others have said) to slow down the rate of recovery. Ari Marmell's APG has rules for this based on the disease track. One surge per day might also do the job, making natural healing actually slower than it is in 3E, I think.
Another is my oft-repeated suggestion of simply narrating the passage of time. I know you think that this is at odds with sandbox play, but I don't really see why, provided the players are doing the narrating. (I think there are other features of 4e that don't fit especially well with sandbox - such as the quest rules and the emphasis on highly metagamed encounter design.)
If it grates for the sandbox players, they can choose stop and rest - it's their sandbox!
If it grates for the sandbox DM, he can narrate less-severe injuries next time.
I've been saying this for a billion pages on the "Dissapointed in 4e" thread. But for some reason I don't really get it's not a solution.
If there are mechanical advantages to pressing on*, and none for resting, players will be grated by the idea of giving up a mechanical advantage for the sole purpose of avoiding grating.
But in a sandbox game, as opposed to in a railroad or at the culmination of a dramatic episode, I'm hard-pressed to see what those advantages might be.
(1) In a sandbox, there is always more to do than can ever be done. The world is larger than the characters. Players can only be offered meaningful choices between X and Y if, in some sense, choosing X excludes Y. In a sandbox, the most precious commodity is time.
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Smart play includes pressing on, because the most precious commodity in the sandbox is time.
It's obvious that this claim about ingame time is crucial to the argument. But like Hypersmurf I don't see it. Are the players really worried that their PCs will die of old age before reaching a level high enough to use magic that renders old age irrelevant if they narrate some down time? Certainly, in a sandbox, the world will still be there to be explored in the future.
Sure. But.....
(1) The world continues to move while you recover.
(2) In the best sandboxes, there are other player groups, and those groups may also be moving on the same goal. Heck, there might even be NPCs that the players are aware of, moving on the same goal.
(3) A well-run sandbox contains a tension between the desire to move and the desire to wait until you are at your best. This makes the decision to rest or go meaningful.
(4) Remember all of those threads about the 15-minute adventuring day, and the reasons why players might not want to just rest whenever they get low on resources? They still apply.
My feeling about (1), (2) and (4) is that these really signal the existence of ongoing episodes, in which case the teeth-gritting solution can be used until the episode comes to an end. Where (1) is not about an episode, but just a generic worry that time is passing, then in a sandbox game surely the answer is that the sandbox is temporal as well as spatial.
Number (3) above is a bit different. But in my long experience GMing more-or-less sandbox Rolemaster, penalties from injury are one of the least satisfactory ways of generating the tension you refer to, as opposed to (for example) trading of striking now versus negotiating an alliance first. The second choice is dramatic and meaningful. The first simply makes the players resent their lack of a decent healer.
I don't like "You're causing this problem by ignoring the rules" when I am not at all convinced that your interpretation is the rules, or what the designers intended.
Given the games that have obviously influenced the desing of 4e, including it's conflict resolution mechanics, not to mention some of what Chris Sims posted on a pre-release hit point thread, I think the better-warranted view is that some version of a flexible-narration approach to hit points and damage is exactly what was intended.