[FOM] Re: natural language and the F of M

[Harvey Friedman]

Reply to Slater.

>
>On Bunt's formal work, his 'Ensemble Theory', as I said, *includes* 
>Set Theory as just a special case, so his treatment of mass terms is 
>*additional to* his treatment of count terms, which means that, from 
>his point of view, there is *more to* mathematics than what can be 
>included in Set Theory.

I would like to see you indicate enough of the theory to justify that 
claim: That there is "more to" mathematics than what can be included 
in Set Theory.

For example, class theory goes beyond set theory in certain senses. 
But the claim that class theory shows that there is "more to" 
mathematics than what can be included in Set Theory is unconvincing. 
I would be surprised if the situation with regard to mass terms is 
any different.
>
>So Friedman might find Bunt's book of considerable interest (I am 
>surprised he has not already read Lavine's).

I didn't say that I haven't read Lavine's. I have, and I even own it. 
Sometimes I write for the benefit of the FOM list, and not just 
myself.

>My own contribution has been to point out that, by replacing 'being 
>a member of a proper class' with 'being part of a mereological 
>totality' one can do justice to mass terms while producing a 
>combined theory with some resemblance to the von Neumann-style 
>axiomatisation of traditional Set Theory.  It also gives an 
>immediate and natural way out of Russell's Paradox, and the like.

The claim that it gives a new way out of Russell's Paradox above and 
beyond what normal class theory does is surprising.