Pippen

Thx, nagase, also for the link.

Hm...let's switch gears: 1. ~p 2. ~p -> p 3. p | mp 4. ~p |premise 5. p & ~p, so 1. or 2. must be false. I think we agree on that proof, do we? So it'...

@Sophisticat: I understand "nothing can come from nothing" as: it is false that something can follow from nothing. I see causality as a special case o...

@nagase: What about this? Is this a correct, but rough, sketch of the 2nd theorem? Second Incompleteness Theorem Because of the First Incompleteness T...

So would you say my modified rough sketch of the 2nd theorem is correct? Or is it still too far off?

Ok, I added your remark about "multiplication" for the First Theorem and heavily modified the Second Theorem, let me know what you think about it, nag...

Here is what I originally wanted to proof: If I have my perception p1 of the world then I cannot have a second perception p2 of the world that is diff...

Here's another look at the previous argument: 1. premise: Pippen has a left hand (LH). 2. premise: Pippen has a right hand (RH). 3. premise: It is not...

You wrote that the 2nd Incompleteness Theorem finds a proof inside S to show that the statement "S is consistent" (ConS) is equivalent to G and so it ...

Here's another question that kind of belong to this topic: Is equality ("=") and biconditionality ("<->") the same and you could interchange both symb...

Nobody?

@nagase: Ah, I see. So when I have a premise P1 and a premise P2 I can always introduce P1 <-> P2, just as I could introduce P1 & P2, in the calculus ...

Ok, let me give a more complete example: 1. premise: Pippen has a left hand (LH). 2. premise: Pippen has a right hand (RH). 3. premise: It is not the ...

x*x = -1 has no solution in IR. IC doesn't change that. It doesn't solve the problem (solution for x*x=-1 in IR), it just solves a different problem (...

I agree with you, and told you so in a german forum already. :) The problem is that with this kind of logic the language becomes not closed anymore an...

@Nagase: What you do in 3. is using the AND-introduction. My question is if I could instead introduce an implication "A -> ~A". I doubt that. I doubt ...

I think layer logic is pretty much a meta-linguistic-system where you just don't allow sentences (language) to mix up with their truth values (meta-la...

@srap: Yes, we talking about natural deduction, take this example: 1. premise: 1 2. premise: 2 3. premise: 3 4. 1 <-> 1 5. 1 <-> 2 6. 1 <-> 3 Would th...

How would you explain the Second Therorem based on my version with S, G(G is unprovable in S) and my explanation of the Frist Theorem? Maybe that is t...

But this can't be true since it leads to contradictions. Just an example: 1. premise: 1 2. premise: 2 3. premise: 3 ... 5. 1 <-> 1 6. 1 <-> 2 . 7. 1 <...