[FOM] Tangential to Slater and Numbers

[Arnon Avron]

> Arnon Avron  wrote:
> >   On the other hand I find as extremely odd Slater's argument
> >that identifying the natural numbers with the finite von Neumann ordinals is
> >a grammatical mistake. ...
> 
> >I bet that most people, if pressed about this point,
> >    will say at the end that a number n is always the cardinality of the
> >    set of numbers less than n (including 0):
> >
> >    n=Card({k| k<n})
> 
> 
> So {{}, {{}}} = Card ({k| k<2})?

Yes, since by the law of identity

    {{}, {{}}} = {{}, {{}}} 

More seriously: If one accepts that

    {{}, {{}}} = {k| k<2} (i.e. accepts von-Neumann definition of 0 and 1)

Then it would be very strange if s/he refuses to accept

  {{}, {{}}} = Card ({k| k<2} (i.e.: von-Neumann definition of 2)

Now start with accepting 0={}.


Arnon Avron