Thinking about this on the drive home.
One of the problems we are encountering is that we are using vague language to mean multiple things. One example is "I want", as in "I want to attack the orc." As has been mentioned, technically this just a statement not even of intent but just of desire. No action has yet been declared. Even though, at the table, we might understand this to mean a declaration of action.
The more important phrase, though, is "You can't". Both parts of this statement are vague. "You" can mean the player, or the character. And "can't" can mean both "are unable to succeed" and "do not have permission".
To take some examples from this thread:
"I recite the first 10 digits of Pi."
"You can't."
This one is an edge case, because the DM might be saying, "I adjudicated that action declaration and your character didn't say the correct digits". Or the DM might be saying, "I'm not giving you, the player, permission to do this."
"I say out loud 'three one four one five nine two six five three five'"
"You can't"
Here it's clearly a matter of permission. There's nothing that would obviously prevent the character from speaking those numbers out loud, so the real meaning is that you, the player, don't have permission to declare that action." (Reminder: this is a valid ruling, if your table rule is "no OOC knowledge". I'm just pointing out the meaning of the words, not rendering judgment.). (EDIT: oops, tacked the following onto the wrong paragraph). This is not adjudication of the outcome of the action; it's adjudication of the player's statement. The DM is rewinding the tape and saying, "The action never happened because that's an invalid move."
"Even though I failed my saving throw against
hold person, I'll attack the orc"
"You can't"
Here it's a valid action declaration, but it fails. The character is in control of their thoughts, and wills their muscles into action, and nothing happens. So the "you" is the character, and the "can't" means "tried and failed".
This is not adjudication of the outcome of the action; it's adjudication of the player's statement. The DM is rewinding the tape and saying, "The action never happened because that's an invalid move."
The logical error Max is making is to use "you can't" in these different ways, but treating them as identical. Or, at least, suggesting that if one version of "you can't" is ok, they all are.
EDIT: And maybe the precision error
we are making is to say "DMs adjudicate actions" when really we mean "DMs adjudicate the
outcome of the action". (I'm guessing
@iserith has been very precise about this; I may have been sloppier. I'm not really going to read through the thread checking.)