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

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fom

Posts: 1,969
Registered: 12/4/12
Re: Torkel Franzen argues
Posted: May 5, 2013 11:03 AM
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On 5/5/2013 9:47 AM, Frederick Williams wrote:
> fom wrote:
>>
>> On 5/4/2013 11:07 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?
>>>

>>>> 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.

>>
>> Out of curiosity, how do you come to that conclusion?

>
> I was thinking of the question of PA's consistency. If someone just
> accepts it, then he neither goes in a circle nor does he regress
> forever.
>


That is probably "standard mathematics". In a thread discussing
belief and proof I pointed out that there can be second-order
consequences that cannot be proven in a sound deductive system.
That may be an analog to the notion of true justified belief since
it is related to consequence but cannot be adequately proven.

I suppose I can place your statement into that kind of context
unproblematically.

What I would like to think is that there is an implicit circularity
if one takes belief out of the picture.

Thanks.









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