Belief in belief: My solution to the final exam.

Harry, being familiar with logic problems would plausibly try to violate the parseltongue
curse using Godel's methods. He does not know that this would not work, and would
not be able to test it in his current situation without being shot. Harry could in
this situation reasonably conclude that knowing the exact mechanics of the parseltongue
curse is critically important, and knowing the prophecy speaks of him ending the world
and that he and Voldemort are literal kindred spirits, it is possible that sharing
secrets with Voldemort might cause the end of the world. It is also possible that
not sharing secrets with Voldemort might end the world.

Since there are too many unknowns for Harry to make a choice one way or the other
the path of least risk is to ask for more information. In order to verify the information
Voldemort needs to explain to him how parseltongue works and allow Harry to test
Voldemorts explanation.

Therefore Harry's first move should be to say:

"Yesss, have power you know not. If not sshared world may end."

(This is plausibly true of partial transfiguration.)

The only reasonable move for Voldemort to make is to demand Harry tell him. At
which point Harry may truthfully reply: "If sshared, chansse world may end. Do
not know which risssk greater and cannot determine without certain information you have."

Now Quirrel has three options here:

1. Allow Harry to continue.

  I believe this is the only rational move Voldemort has, with explanations below.

2. Kill Harry.

  Voldemort can only do this if the projected value of the information to Harry
is worse than the possible X risk increase of killing him. Since Voldemort *knows*
Harry has powers he knows not the former is almost certainly lower than the latter.

3. Attempt to force Harry to give up the info.

  The prior probability of Harry or Voldemort ending the world is the same for
both, that Harry's absolute probability is lower because he is surrounded by 36
death eaters is situational and has no effect on Harry's descision to give
Voldemort the information he wants. Therefore to take this method to its end would
be equivalent to two, which we know Voldemort does not want to do.

Voldemort will make the optimal descision of allowing Harry this, and asking what
information it is he needs to know. At this point Harry can explain that, since
it is critically important to his fulfilling the vow, he needs to be sure that
parseltongue really is a secure method of communication that does not allow lies.

Towards this end, Voldemort must explain to Harry the mechanics of parseltongue
and allow him to test Voldemorts explanation. Voldemort of course has the ability
to say no, but it would be unreasonable to do so given that this really is a thing
the vow would require and it is to Quirrels knowledge impossible to lie in parseltongue
so explaining the mechanics of it to Harry has almost no projected risk versus the X
risk of deciding the power he knows not is not worth knowing and killing him.

Voldemort would explain something similar to what EY explained in a reddit thread
(See footnote zero) that parseltongue has two axioms:

1. You are prevented from saying anything that you believe at the time to be false.

2. You cannot redefine a word in Parseltongue.

Once Voldemort explains the principles to Harry he would be free to test them out
using the Godel method, at which point he would realize that "This statement is false."
, cleverly redefining words and godel numbering are all disallowed as Voldemort says.
Then Harry would consider the axioms. It might occur to Harry that a confundus charm
would allow you to defeat parseltongue, or parseltongue would be able to tell you
if you're confundus'd, creating an information leak. The second axiom says that
words in parseltongue can only have one meaning. This means that since the parseltongue
dictionary necessarily contains a set of words defined by Salazar Slytherin, one
of the greatest wizards to ever live, the definition of every word in parseltongue
is probably its true definition. The dictionary would then be a source of information.

The second axiom says that you can't say "Torch" when you mean "Pen" as that would be a
redefinition and literally interpreted the statement would be a falsehood. But you
can tell a falsehood when you don't believe it is false. However if you say the
sentence "I wrote a letter with the torch." even if you mean what you say in a
certain sense you would be redefining torch and parseltongue would have to correct
you. Harry would realize if parseltongue corrects you then you are saying a sentence
you believe to be false and the first axiom is false, if parseltongue does not
correct you then you are redefining a word and the second axiom is false. The two
axioms contradict each other and therefore the principle of explosion states all
statements in parseltongue are true.

This reasoning is not actually correct. (See footnote 1) Going by the first axiom
of parseltongue however, one does not need actually correct reasoning to defeat it
through this method. They must simply believe that they have found a contradiction
in parseltongue without being motivated by the ability to practice deceit. As Harry's
investigation is taken without this meta-belief that he is being cleverly deceitful
he can say any statement in parseltongue for as long as he does not realize his error.

Harry might spend a few more seconds trying to analyze the implausibility of this
result before realizing on an intuitive level that further investigation can't help
and can only hinder. There are some problems it doesn't make sense to overthink.
If Harry thinks about it too hard this method won't work, precedent exists in
chapter 111 when Harry has the following bit of internal monologue:

"Harry said nothing about expecting his intentions wouldn't change; he'd simply
blurted out the idea fast enough that he hadn't formed any specific intentions yet."

After this Harry can ask for the prophecy as a red herring to throw off Voldemort.
There is a chance that the prophecy could affect Harry's knowledge of how likely
he is to end the world, except that even if it mentions him by name he is still
the same person as Voldemort. We of course know that the prophecy only says 'he'.
In which case Harry will be able to reasonably conclude that Voldemort is more
likely to end the world because Voldemort is mega evil. In this case the vow compels
Harry to consult Herimone as that is his best chance of defeating Voldemort.

Even if this is not a reasonable conclusion, Harry can say that he needs to consult
Herimone and since all statements in parseltongue are true according to your beliefs
that means anything you say in parseltongue you should believe. In this way you can
say any statement and use it to invoke the vow by saying that the vow is invoked.

Since the vow would be invoked Voldemort can reasonably conclude that Harry really
does need to consult Herimone. However since giving information to Voldemort might
cause the end of the world we need to have a *private* consultation with Herimone.
To this end Harry can have Voldemort promise in parseltongue that he will not listen
to the conversation and that Voldemort will use all means available to him magical
otherwise to prevent anybody else including his Death Eaters from listening to the
conversation since they might relay the information to Voldemort. (People listening
through divination might be persuaded to tell Voldemort after he rules Britain.)

All of this can be reasonably obtained because the vow would require Voldemort to do
it for Harry to be able to consult Herimone. As part of this Voldemort would probably
try to confiscate Harry's wand, at which point he can say that he needs the wand to
demonstrate power Voldemort knows not to Herimone, and that even further towards
this end an opaque barrier must be constructed for him to show her behind.

The important question in all this is if the value of the information Harry might
have is still worth more than denying him these things. Since Harry is a first year
wizard who cannot apparate or portkey or phoenix or teleport or otherwise escape
unseen naked without his trousers, and he knows no spells such as Avada Kadavra
that could pierce through a wall except for possibly the power known not, which
Voldemort believes himself immune to and in the worst case only temporarily killed
by, there is still not a terribly large risk in allowing the boy who lived to have
his parseltongue confirmed and vow enforced wishes to consult Herimone.

Once Harry has the private consultation, he should have somewhere around 15 minutes
to come up with a better solution, since this technically fulfills the requirement
to get him to the next chapter we could consider this a complete solution here.
However I do have a suggestion below:

1. Partially transfigure a large volume of explosives under the Death Eaters feet.
Harry still has his wand so any solution that could not be done in 60 seconds
might be accomplished in 15 minutes. This entire class of solution has been discussed
to death so I'll leave the implementation up to the author to choose something reasonable.


[0]: http://www.reddit.com/r/HPMOR/comments/2w526t/chapter_105/conn883?context=3

[1]: Actually this probably isn't true because there is a distinction between
words, their definitions and instances of their use. If you consistently say
things involving a word but all the statements have a truth value of false then
the statements do not effect the acceptable definitions in the set of definitions
for a word.