@Secret Perfect reasoning does not assist any form of immorality. I don't understand why you don't get it. If everyone employed only perfect reasoning, they would not have crazy religions. Only people who are illogical will attempt deliberate murder.

(Except in special circumstances such as killing murderers.)

@Secret You shouldn't make statements without first checking that you are using the correct statement of the theorem, instead of some wrong pop-math version.

The conditions are explicitly stated in that post:

> Take any formal system T with proof verifier V that can reason about programs.

It should be clear which condition propositional logic fails to satisfy.

@user21820 Unless I am missing something obvious, isn't that blue eye islander scenario first having that crazy religion that set up the rules to kill people who knew the eye color, and then that all inhabitants following logic means they will follow the instructions without any questioning?

so in that case, it seems the crazy religion precedes the perfect reasoning used to follow it, not the other way around

Though I agree with you in the general case, if people have perfect reasoning, they will not have a crazy religion in the first place

To make this more precise, I mean:

A: Crazy religion leads to mass killing

B: Logical reasoning does not necessary leads to mass killing

B+A: Logical reasoning plus crazy religion leads to mass killing

@Secret My point is that you cannot use the word "assist", because that English word connotes something beyond what you can justify.

@Secret For the same reason, you cannot make this statement either, because in natural language when you say "A and B leads to C", you are implicitly stating that A and B both play a role in leading to C.

In particular, illogical reasoning plus crazy religion also can lead to mass killing. So it would be incorrect to say (in natural language) that logical reasoning plus crazy religion can lead to mass killing.

In case you need it: TFD definition of "assist".

I think I don't really understand, because the above explanations does not seemed to fully explain my doubts on the 6 possible situations I had, phrased as follow in natural language:

1. Crazy religion always leads to mass killing (you and I probably have no doubt on this one)

2. Logic does not always leads to mass killing

3. Illogic does not always leads to mass killing

4. Logic or crazy religion sometimes leads to mass killing

5. Illogic and crazy religion sometimes leads to mass killing (it cannot be always as illogic can randomly decided to not follow towards the rules of the crazy religion and hence arriving at the conclusion that leads to the mass killing to occur)

6. Logic and crazy religion always leads to mass killing (if the rules of the crazy religion is written in logic, then logic means these rules will be followed without exception, and hence leads to mass killing)

Making this precise will probably need some modal logic, because of words like "always", "sometimes"

You argument is suggesting that 6 is false, which is where I am confused

actually wait...

(1) already claimed that crazy religion always leads to mass killing, so it does not need anything else

But how I can explain the observation of (5), which does get observed in real life when some crazy religious folks failed to initiate bombing because they messed up some of the fuses in the bombs for example?

Trying to simplify further, real life seemed to have weird cases like:

1. A always leads to B

thus adding C somehow make B less likely to happen

Let me think of an example that can remove the modality so it can be phrased in classical logic for easier discussion...:

1. Light reflect off mirror A always reach point p

2. Light reflect off mirror A and mirror B, never reach point p

Thus we end up with a pair of statements, both true:

1. $A \implies p$

2. $(A \land B) \not\implies p$

Therefore, the only way I can think of that can rebutt (5) and hence supporting your conclusion about crazy religions, is that somehow crazy religion has to behave like a false statement, such that placing it with anything automatically give a false statment, thus ensuring the implication "crazy religion and X leads to mass killing" to be true

But what reason we can justify that crazy religion and illogic will not cancel out and hence does not always lead to mass killings?

Anyway, in case this get too convoluted, I now agree with you that "logic plus crazy religion always leads to mass killing" is false because logic can sometimes stop crazy religions

What I am less sure is whether "illogic plus crazy religion always leads to mass killing" is true because illogic can in theory cancel out the effects of the crazy religion because of its rule breaking nature

You are thus correct in saying I cannot use "assist"

@Secret: It seems that your only error is in assuming that logical people can follow crazy religions. That is in fact false, so the only way anyone can follow a crazy religion is by being illogical.

A classical first-order theory whose axioms capture a crazy religion would prove crazy theorems, but that has no implication to anyone's actions in the real world unless they start interpreting those theorems as prescribing what they should do. But to do so would be illogical.

Interesting, so is our interpretation of "illogical" is actually done from some meta system, such that it can show why the crazy religion first order theory is illogical?

In other words, it is illogical for anyone to adopt a crazy religion and to derive what they should do from it.

You can say we are working in a meta-system. We always are, anyway.

I see make sense.

I think I now understood the nature of illogic better now (and might explain why I made all those crazy errors in the past)

Hmm...

many months ago we proved by case by case that propositional calculus is semantically complete

It is also consistent since the truth tables does not give you a contradiction of the form P and not P

It is also sound since every noncontradictory statement is a tautology

So that means, something has to gone wrong with "reason about programs"

I see people always try to solve a system of equations without checking if there is any solution. Why so?