[FOM] RE: FOM Continuum Hypothesis

[Neil Tennant]

On Sun, 18 May 2003, Miguel A. Lerma wrote:

>  > Insall:
>  > [...] For example, if we could show
>  > that CH implies that some particular subatomic particle cannot exist, but we
>  > perform experiments and these show that such a particle does exist, then we
>  > would have physical ``proof'' that CH is false. 
> 
> I do not think that any physical experience can decide anything 
> in pure mathematics.  After Einstein we know that the universe 
> is not Euclidean, but that does not imply that the postulates 
> of Euclidean geometry are "wrong" in any absolute sense, it just 
> shows that Euclidean geometry is not an appropriate model for 
> our physical universe.  If a physical theory made false predictions
> based on the assumption of the existence of large cardinals, that
> would not mean that there are no large cardinals, just that there
> are no large cardinals in our physical universe. If CH implied 
> that certain particle cannot exists but we find it anyway, then 
> that would not necessarily mean that CH is false, just that it
> does not hold in our universe (say because certain bijections
> used to state equal cardinality among sets turn out not to have
> a physical meaning). 

Against this, one could say: whatever truth-value CH has in V, it has it
necessarily. If CH is true, it is necessary; it CH is false, it is
impossible.

Since CH is only about necessary existent (pure sets), the number and
disposition of contingent existents (physical particles etc.) is
absolutely irrelevant to the truth-value of CH.

Neil Tennant