Re: Peano's Axioms are Inconsistent

RussellE wrote:
Then you are right. I can't prove PA is inconsistent if
I am required to assume it is consistent. All I can do
is ask embarrassing questions, point out more "paradoxes",
and generally be a pain in the neck.

You are way over your head here, I think. You seem to have this distorted reality bubble surrounding you that makes your view of the world work and refuses to admit any possibility that clashes with said world view.

How can a statement be neither true or false?
Doesn't "undecidable" mean PA is inconsistent
whichever way you decide?

I'm not saying that the statement is neither true nor false. All I'm saying is that you have failed to produce a formal proof of the verity or falsehood of what you claim is proof.

I can't stop you if you want to believe PA is consistent.

Yes you can: you can prove to me that it is inconsistent. It is totally possible--people have demonstrated proofs of inconsistency before. Your inability to admit the possibility merely shows either pigheadedness or just plain ignorance. In either case, it does not prove your point.

--
Beware of bugs in the above code; I have only proved it correct, not tried it. -- Donald E. Knuth
.

Relevant Pages

  • Re: Who believes/believed that set theory is/was inconsistent?
    ... |>inconsistent is a different story. ... |My first reading of this was that saying someone believes ... in ~X as necessarily following from doubting X. Native ... remark. ...
    (sci.logic)
  • Re: Who believes/believed that set theory is/was inconsistent?
    ... >|>inconsistent is a different story. ... >|My first reading of this was that saying someone believes ... >in ~X as necessarily following from doubting X. Native ... >remark. ...
    (sci.logic)
  • Re: Born To Run: What Humans Really Evolved To Do
    ... hominid was Homo erectus. ... It's the sort of habitat ... You have no dispute with anything I'm saying and--more ... Admit it - you didn't read what I posted. ...
    (sci.anthropology.paleo)
  • Re: OT: Racial superiority / Intelligent design was Re: OT:Thanksgiving
    ... the bible is inconsistent and, ... as the word of god, is evidence for his inconsistency too. ... I won't admit that, I would be dishonest if I did, and I'll tell you why. ...
    (comp.lang.cobol)
  • Re: Registering Event Handlers in C# vs. VB .NET
    ... Only a complete jerk would continue to persist on insisting that they know better than the author of the original words what the intent of those words are. ... doesn't take a dictionary or an English major to see that you are now saying ... but it does take someone who simply cannot admit that they have misread something that was plain enough to everyone else. ... Instead, you continued to insist that you understood, leaving you here without any way to acknowledge the truth in what I'm saying without admitting a mistake on your own part. ...
    (microsoft.public.dotnet.languages.csharp)