
Re: Matheology S 224
Posted:
Apr 20, 2013 11:27 AM


On 20/04/2013 9:24 AM, 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. 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).
And mainly _borrowing them for notation purposes_ .
  There is no remainder in the mathematics of infinity.
NYOGEN SENZAKI 

