The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Matheology S 224
Replies: 16   Last Post: Apr 21, 2013 6:53 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]

Posts: 2,777
Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 20, 2013 11:27 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 <> 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 non-empty 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 non-empty
>>>>> 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 non-empty you
>>>> have to say that something is in x, not that x is in something.

>>> but the claim was that x *is in* a non-empty set --
>>> in this case S', which is non-empty, 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 (definition-in-use)
>> 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 second-order 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.


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.