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

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namducnguyen

Posts: 2,699
Registered: 12/13/04
Re: Matheology S 224
Posted: Apr 20, 2013 11:27 AM
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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 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_ .



--
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There is no remainder in the mathematics of infinity.

NYOGEN SENZAKI
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