Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


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

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 ]
fom

Posts: 1,968
Registered: 12/4/12
Re: Matheology S 224
Posted: Apr 20, 2013 10:59 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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 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.



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

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.