The Historical Reliability of the New Testament

[Randy Carson]

It doesn’t matter whether you’re asserting the existence or non-existence of Plato’s Forms, claiming the truth or falsity of a particular view of epistemology, or asserting that moral judgments are just expressions of emotion or something else. The principle remains the same: The burden is on you to argue for your own claims. Philosophy may use a different method than science, but its assignation of the burden of proof is the same.

This is where you fail.  Asserting the existence of Plato's forms is a claim and has the burden of proof.  Not being convinced of the existence of those forms is not a claim and has no burden of proof.  

Read the part I highlighted in red, Jenny. Someone asserting that Plato's Forms do not exist has the burden of proof.

Similarly asserting the existence of god or the resurrection are claims.  Being unconvinced of those claims is not. The reason for this is obvious.  It is not possible to prove a negative, therefore the person asserting the positive claim has the burden of proof.  

Actually, it can be argued that you can prove a negative (four-sided triangles, for example), but that's not the point. The point is that atheists make a positive claim that God does not exist.

It works this way in a court of law.  No one is required to prove they didn't commit a crime, the burden is on the state to show that they did commit a crime. However, the burden shifts when we move from positive to negative claims.  If I sue you for money owed, the burden is on me to show there is a debt.  However, should I prove there is one, and you claim you've paid it, the burden is on you to prove payment.  Like the existence of the debt, payment is a positive claim.

Agreed.

Your suggestion that a person asserting that Plato's forms exist and someone asserting they don't both have the burden of proof is silly.  You have given both sides the burden of proof thus rendering the burden of proof meaningless.

Yes, I have. And it is up to others to evaluate both arguments. It's no different from the science example which you were okay with:

If you want to propose that Particle X exists, the burden of proof falls to you.
If you want to propose that Particle X does not exist, the burden again falls to you.

If you want to propose that God exists, the burden of proof falls to you.
If you want to propose that God does not exist, the burden of proof again falls to you.

You cannot use science to prove or disprove God. This is why these proofs fall into the domain of philosophy.