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

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Posts: 2,777
Registered: 12/13/04
Re: Torkel Franzen argues
Posted: May 5, 2013 2:26 AM
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On 05/05/2013 12:20 AM, fom wrote:
> On 5/5/2013 12:52 AM, Nam Nguyen wrote:
>> On 04/05/2013 6:04 PM, 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 <> 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 have
>>> come to the exact opposite conclusion.

>>> The only sense I can
>>> make of foundations is that it is more like a jigsaw puzzle
>>> that must address circularity and regress directly and with
>>> the objective of making it harmless.

>> I couldn't agree less; and that is exactly what I've proposed
>> for the past years.

> Well, I will not dispute your opinions.
> I simply know what I have done and how it fits
> in with established literature. I also know how
> it is non-standard and, thereby, easily subject to
> criticism.

Yes. Non-standard and non-canonical is a lightning rod
to criticism. But more often than not non-standard
has its past and criticism would be gone.

There is no remainder in the mathematics of infinity.


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