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Topic: Torkel Franzen argues
Replies: 25   Last Post: May 17, 2013 3:52 PM

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Posts: 2,710
Registered: 12/13/04
Re: Torkel Franzen argues
Posted: May 8, 2013 10:11 AM
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On 08/05/2013 7:28 AM, Frederick Williams wrote:
> Nam Nguyen wrote:
>> On 05/05/2013 8:45 AM, Frederick Williams wrote:

>>> Nam Nguyen wrote:
>>>> On 04/05/2013 10:07 AM, Frederick Williams wrote:

>>>>> Nam Nguyen wrote:
>>>>>> On 26/04/2013 11:09 AM, Nam Nguyen wrote:

>>>>>>> On 2013-04-25, FredJeffries <fredjeffries@gmail.com> wrote:
>>>>>>>> Now PA has been proved consistent in ZF or NBG, but then that
>>>>>>>> brings the consistency of axioms for set theory.

>>>>>> Exactly right. And exactly my point.
>>>>>> Somewhere, somehow, a circularity or an infinite regression
>>>>>> of _mathematical knowledge_ will be reached,

>>>>> How does one reach an infinite regression?

>>>> By claiming that the state of consistency of PA can be
>>>> proved _IN_ a _different formal system_ .

>>> Your notion of infinite is very modest if does not go beyond two.

>> That does _not_ mean there be only two, actually.

>>>>>> and at that point
>>>>>> we still have to confront with the issue of mathematical relativity.

>>>>> It is not the case that either we go round in a circle or we regress
>>>>> forever.

>>>> That's not a refute. Of course.
>>>> (It's just an unsubstantiated claim).

>>> And yet an obviously true one. Suppose the question of the consistency
>>> of PA is raised, a party to the discussion may say 'I accept that PA is
>>> consistent and I feel no need to prove it.' No circle, no regression.

>> The circularity rests with the argument on the _actual and objective_
>> state of consistency of PA, _not_ on the _wishful and subjective_
>> "acceptance" of anything.

> Mathematicians (like the rest of humanity) are forever accepting
> things. It is no big deal.

Verification, proving, is a big deal.

There is no remainder in the mathematics of infinity.


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