
Re: Matheology S 224
Posted:
Apr 20, 2013 11:24 AM


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. 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).
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

