Re: Implementable Set Theory and Consistency of ZFC

In article <b3c4e$47304704$82a1e228$6480@xxxxxxxxxxxxxxxx>,
Han de Bruijn <Han.deBruijn@xxxxxxxxxxxxxx> wrote:

Virgil wrote:

In which case (negation of axiom of infinity unprovable) how does HdB
come to be so certain that the axiom of infinity must be false in IST?

Can you imagine a machine where it is implemented in?

I am not a mechanic. My 'models' of mathematical objects, however much
they may have been suggested by the physical world, have no need of any
non-mental mechanisms to justify their existence.

That those with less flexible imaginations are more limited is not my
problem.
.

Relevant Pages

  • Re: Cantor Confusion
    ... for the tenth time: Without the axiom of infinity it is ... For the eleventh time: Infinity is NOWHERE. ... To assume that one can imagine what one has imagined is scarcely ... "Foundations of Set Theory", North Holland, Amsterdam. ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... come to be so certain that the axiom of infinity must be false in IST? ... Can you imagine a machine where it is implemented in? ... Will you only believe it when I present it as a TeX'ed pdf link? ...
    (sci.math)
  • Re: Implementable Set Theory and Consistency of ZFC
    ... come to be so certain that the axiom of infinity must be false in IST? ... Can you imagine a machine where it is implemented in? ... Han de Bruijn ...
    (sci.math)
  • Re: Oldest Bible On-line
    ... implies mass, and mass at the speed of light is outside ... It may be that it is just plain wrong to imagine ... number system at which negative infinity = postive infinity ... points seem closer at high velocity speeds. ...
    (soc.religion.quaker)
  • Re: Oldest Bible On-line
    ... Another indicator I would imagine that they may ... identity with the second derivative of the wave function ... In math we can create all sorts of useful abstractions we ... number system at which negative infinity = postive infinity ...
    (soc.religion.quaker)
Quantcast