Re: Implementable Set Theory and Consistency of ZFC

In article <876fa$472843f6$82a1e228$18666@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Jesse F. Hughes wrote:

I will say it once more. I am typing this slowly, since I don't want
you to miss anything I say. If you have a proof in a theory
consisting of axioms (1)-(4), it is also a proof in the theory
consisting of axioms (1)-(4)+(X).

How do you "know" that? Has the Pope told you, by dogma, that it is so?



HdB, on the other hand, has explicitly claimed that adding an axiom to a
system of axioms can eliminate some statements as theorems. Which is
equally dogmatic, and a good deal less believable.

Which Pope are you appealing to, Han?
.

Relevant Pages

  • Re: Implementable Set Theory and Consistency of ZFC
    ... David C. Ullrich wrote: ... consisting of axioms -+. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... consisting of axioms -+. ... David C. Ullrich ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... consisting of axioms -+. ... a statement is a valid premise for proving that the integral of 1/t ...
    (sci.math)
  • Re: Courage?
    ... He is showing that logical contradiction results from ignoring the question of point dimension. ... Allan is saying that either points have dimension, ... The problem with this is that the axioms don't say anything about how we are ... No one has yet been willing to give me the axiomatic basis for statements that describe a line segment as consisting of an infinite set of points, and how to avoid the inherent contradiction in such statements of points being simultaneously dimensioned and not dimensioned. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... consisting of axioms -+. ... No, you royal ignoramus, it's PROVEN as a basic property of the ... deductive system. ...
    (sci.math)