Board Thread:General Discussion/@comment-32182236-20200214154305

Part 1:https://undertale.fandom.com/wiki/Thread:170064

Part 2:https://undertale.fandom.com/wiki/Thread:170066 (Post 5 of this thread contains the second half of Part 2)

Part 3:https://undertale.fandom.com/wiki/Thread:170278

Last time, we dealt with many of the fallacies dealt with in logic. But we haven't gone over all of them. You may have noticed that I skipped some.

That's because the ones I skipped all rely on something called the burden of proof.

The burden of proof is a concept so easily misunderstood. It's hard to tell who has the burden of proof, especially as both sides tend to claim the other has it.

Usually, the burden of proof falls upon the one making the initial claim. This is why argument from ignorance is a fallacy.

But there's a simple way to make it easy and intuitive to find out who has it. However, this "simple" way requires us to expand our horizons. Of course, expanding our horizons will also give us other benefits as well, which I'll go over in this part as well.

So, where do we need to expand? Well, we should probably drop an assumption that we've all been following for all too long.

It's easy to believe that every proposition always is, and always was, either true or false. But that just simply isn't the case.

Some things are yet to be determined, and it's possible to create a proposition of such an event. Like stating that the quantum spin of an observed particle will be observed to be spin +1.

This is what we know as quantum superposition, though it's really a special case of a more general undefined truth. The events of a game's sequel are not determined until the story of said sequel has been finalized. Sometimes, a proposition is neither true nor false, because it has not yet been given a definite value. And we need to add that idea into our logical system.

Meet the third value in logic:One that is neither true, nor false.

A value that we should have been taught long, long ago..

The indeterminate value, stating that such value hasn't been determined yet.

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So, what exactly is the indeterminate value? Believe it or not, it's the default value of a proposition, before it becomes definitely true or false.

For example, the proposition that Final Fantasy XIX will have exactly 6 character in the player's party. That hasn't been determined yet, as the game hasn't even started development. So, the truth value is indeterminate.

So, it's both true and false?

No, it's still impossible for a statement to be both true and false.

Wait, so it's neither?

Not exactly.

It's what we call a superposition. And this superposition "collapses" into one of the two when said one is now the only possibility. We don't really know much about what a superposition actually is, ontologically speaking, but we do know they exist, and how they function.

So, what are the effects of adding this new value to our system of logic?

Well, you see, it allows us to derive the idea of the burden of proof completely from scratch.

As we all know, making an affirmative claim is the same thing as stating that the proposition is true.

Alice:Sans is a human, because you didn't prove it wrong!

Bob:I don't need to prove it wrong, you have to prove it right!

..Who has the burden of proof?

Well, if neither side presents any evidence, then the proposition "Sans is a human" can be said to be indeterminate:In superposition, at least in terms of the argument in question. (It's possible that it really was either true and false, and we're just trying to find out which one it is, ala the Bohmian interpretation, but in terms of our knowledge, it's in superposition.)

But Alice said that the proposition is TRUE, not indeterminate. Therefore, she has the burden of proof, since indeterminate is not the same thing as true.

This is pretty much way there's actually THREE ways a rational debate over a theory can end-The theory being proven, the theory being proven WRONG, and it being possible, but not necessarily true. (In the latter case, we're better off trying to find other theories, and then comparing them to each other:More on that in Part 5.)

In essence, when you make an absolute claim, you're the one with the burden of proof. So if you present your theory as if you solved the game, you're the one that must prove it so, because indeterminate is not the same thing as true.

Likewise, one could make an agnostic claim, claiming that it is indeed indeterminate after all, in which case, we are the ones that must collapse it into a definite value (assuming it hasn't already been done so, in which case they messed up by making a false claim.)

..And one more thing. Because the indeterminate value is like a superposition, it's possible for it to lean more towards a definite value. An electron could conceivably exist anywhere around the atom, and in fact, is in superposition under the entire wave function, but it's more likely to be in places where the peaks and troughs of the probability wave lie. (The likelihood being proportional to the square of the wave.)

We'll explore more about what we can do with this value later on, but right now, we're going to be taking another look at the burden of proof, and explain some of the fallacies we missed, with our newfound knowledge. 