
Re: Matheology S 224
Posted:
Apr 20, 2013 4:40 PM


Nam Nguyen wrote: > > On 20/04/2013 8:59 AM, fom wrote: > > On 4/20/2013 5:25 AM, Alan Smaill wrote: > >> Frederick Williams <freddywilliams@btinternet.com> writes: > >> > >>> Nam Nguyen wrote: > >>>> > >>>> On 19/04/2013 5:55 AM, Frederick Williams wrote: > >>>>> Nam Nguyen wrote: > >>>>>> > >>>>>> On 18/04/2013 7:19 AM, Frederick Williams wrote: > >>> > >>>> > >>>>> > >>>>>>> Also, as I remarked elsewhere, "x e S' /\ Ay[ y e S' > y e S]" > >>>>>>> doesn't > >>>>>>> express "x is in a nonempty subset of S". > >>>>>> > >>>>>> Why? > >>>>> > >>>>> It says that x is in S' and S' is a subset of S. > >>>> > >>>> How does that contradict that it would express "x is in a nonempty > >>>> subset of S", in this context where we'd borrow the expressibility > >>>> of L(ZF) as much as we could, as I had alluded before? > >>> > >>> You really are plumbing the depths. To express that x is nonempty you > >>> have to say that something is in x, not that x is in something. > >> > >> but the claim was that x *is in* a nonempty set  > >> in this case S', which is nonempty, since x is an element of S', > >> and S' is a subset of S. > >> > >> (Much though it would be good for Nam to realise that > >> some background set theory axioms would be kind of useful here) > >> > > > > Yes. I thought about posting some links indicating > > that primitive symbols are undefined outside of a > > system of axioms (definitioninuse) > > > > The other aspect, though, is that Nam appears to be using an > > implicit existence assumption. So, > > > > AxASES'(xeS' /\ Ay(yeS' > yeS)) > > > > clarifies the statement and exhibits its secondorder nature. > > This is fine since he claims that his work is not in the > > object language. > > Right.
If fom's formula is to express "x is in a nonempty subset of S" then it needs to have both x and S free, so delete the first two quantifiers.
> Fwiw, I had claimed I'd "borrow", say, 'e' and others like '=' > as much as I could to express meta level objects (unformalized sets, > individuals, and what not).
 When a true genius appears in the world, you may know him by this sign, that the dunces are all in confederacy against him. Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting

