Can the Three Trapped Individuals Prove They Are Not Irrational?

[Russell Berty]

Definitions for this puzzle:

A rational mind (or person) is one that may make mistakes in reasoning from time to time, but any mistake made will eventually be found and corrected.

An irrational mind (or person) is one that continually makes mistakes in reasoning.

A super-rational mind (or person) is one that never makes mistakes in reasoning.

A Personal Oracle is some agent that is only observable by the person that it belongs to. The personal oracle provides the owner with information. The oracle is simply a black box which is meant to cover any notions of introspection, a priori knowledge, knowledge of the existence (or non-existence) of a god, ineffable truths, and whatever you care to throw in.


The puzzle:

Mr. A is irrational. Miss B is rational. The Amazing Z is super-rational. Each of them has a Personal Oracle. The three of them, A, B, and Z, are trapped together in a locked room. A sign on the wall reads "At least one of you is not irrational."

1) Can any of them prove that he/she is not irrational?

2) Can any of them be absolutely certain that he/she is not irrational?

[Note: Being trapped in the room and the sign on the wall need not have any bearing on this problem.]

 

[epenguin]

The irrational one could do 1 and 2 (though she'd be wrong of course).

 

[Russell Berty]

The irrational one could do 1 and 2 (though she'd be wrong of course).

Yes. And from that important fact, what can be said about the other two?

 

[Moridin]

They are all irrational, since they have a personal oracle?

 

[Russell Berty]

They are all irrational, since they have a personal oracle?

The personal oracle is just a convenience for stating the problem.
The personal oracle need not contain anything at all. In effect, you are free to assume there is no personal oracle. The reason for including the idea of a personal oracle is to allow people to argue using whatever concepts they adhere to.

When a person is trying to persuade someone (including his/herself) they must be able to defend all attacks such as:
"Why do you believe p?"
"How do you know your definitions do not run into contradictions?"
"How can you claim p is true?" etc…

Eventually (in order to prevent an infinite regress) people will resort to the defenses such as:

"It is obvious.”
"It is self-evident."
"I am assuming that..." etc…

These “ultimate” defenses I am allowing for by including the personal oracle. The crucial point is, if you allow p in someone’s oracle, then you must allow p in everyone else’s oracle (relativized to the individual.)

What is relativized? Say, Miss B has “My name is Miss B” in her oracle. Then, we must allow the possibility that Mister A has “My name is Mister A” in his oracle. Here, the statement “My name is Miss B” has been relativized to Mister A’s oracle as “My name is Mister A”.

 

[apeiron]

Is there a problem here in the fact you must smuggle in the further notion of test and measurement?

And that rationality itself is undefined - why presume only one method of modelling, say, cause and effect? I presume you mean rational in the sense that logic gives certain answers. But then logicians like Peirce for example would say hang on a minute there.

Definitions for this puzzle:
A rational mind (or person) is one that may make mistakes in reasoning from time to time, but any mistake made will eventually be found and corrected.

So here is smuggled in the need to make observations which validate the internal modelling.

And even the method of reason being employed could be corrected as a result of learning?

You have a good scientist in other words - and the one most likely to be correct in any conviction of their own soundness of "rationality" in that even this is up for development and refinement.

An irrational mind (or person) is one that continually makes mistakes in reasoning.

So this would be a person who never measures against predictions of their models? Who would also make mistakes if they did measure? Who could not learn to be better as reasoners as they are not responding to feedback - an interaction with the world they are modelling.

You want to know whether such a person could crisply prove/not-prove something. I would instead argue this is a false dichotomy. They could do neither thing in a definite binary (middle excluded) way. So instead their mental state would only be vague as to such an outcome. Even if you forced them to utter one or other statement, in their minds, the supporting thoughts would be a muddy confusion (no matter how much they protest that they are clear thinkers).

Hmm. I know many who would fit this bill then.

A super-rational mind (or person) is one that never makes mistakes in reasoning.

Now we have the impossible person. Because can reason - some system of logic, some model of causality - ever be complete, applicable to all possible tasks?

I have no reason to think that reason is so platonically divorced from our reality. It just seems the most abstract level of world-modelling. A limit that we can approach, perhaps, but not actually a place we can stand.

So maybe your super-rational homunculus would first have to decide they do not even exist as they are not possible. And if they felt they did exist, they would be being irrational.

After all, what is "making mistakes" except generating predictions so as to learn from, or simply even to detect, what was not yet modeled, not yet expected. So making mistakes is not a defect of a rational process - if the actual process is modelling worlds. It is a necessary component.

The answer then would seem to be that the irrational thinker is vague, the super-rational thinker is being irrational, and the rational person will become ever more rational as t => infinity.

The proof of this would have to come itself through a meta-process of prediction and test. Another level of applied rationality.