fom
Posts:
1,968
Registered:
12/4/12


Re: Matheology S 224
Posted:
Apr 21, 2013 1:20 PM


On 4/21/2013 11:03 AM, Frederick Williams wrote: > fom wrote: >> >> On 4/20/2013 3:40 PM, Frederick Williams wrote: >>> 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. >>> >> >> Do you have a particular x and S in mind? > > I probably misunderstood. If Nam saying that, for every x and every set > S, x is in a nonempty subset of S, then your formula expresses that. > But clearly it is false.
The mistake is mine
ES'(xeS' /\ Ay(yeS' > yeS))

