[FOM] Foreman's preface to HST

[Roger Bishop Jones]

On Saturday 01 May 2010 06:02, Monroe Eskew wrote:
> On Thu, Apr 29, 2010 at 10:16 PM, Roger Bishop Jones 
<rbj at rbjones.com> wrote:
> > And how does that differ from doing second order set
> > theory?

>  If you say the main advantage of second order set theory
>  is its semantic definiteness and thus "settling" some
>  questions, then I'm saying you can still view those as
>  "settled" in the same sense by simply saying they are
>  settled by what a "standard model" says of them.  (Or if
>  you are bold enough, or realist enough, just whether
>  they are true.)  And then you proceed with first order
>  set theory and all of its great methods and results.

My only reason for mentioning second order logic in this 
context was (I am repeating myself here, tying to be more 
explicit), that the phrase "standard model of ZFC" does not 
have a definite accepted meaning which corresponds to "model 
of second order ZFC" and the latter phrase is therefore  
less likely to be misunderstood.

I would be delighted if there were a general recognition 
that the idea of a "standard model" of ZFC is important and 
that unsolved questions such as CH should be interpreted in 
that context rather than supposed to be lacking a truth 
value, (or worse, supposed to have a truth value without any 
semantic clarification).

Roger Jones