On 4/6/2013 11:48 AM, Nam Nguyen wrote: > On 05/04/2013 12:20 AM, fom wrote: >> On 4/5/2013 12:57 AM, Nam Nguyen wrote: >>> On 04/04/2013 10:55 PM, fom wrote: >>>> >>>> Who knows what is and what is not -- even >>>> in the simple realm of mathematics -- claims >>>> a certain knowledge that is revealed rather >>>> than discerned. >>> >>> So, since Godel, is the knowledge of the natural numbers >>> a revealed or discerned one? >>> >>> Revealed by whom? Discerned from what? >>> >> >> I thought you claimed to be a relativist. ??? > > I am, by at least the 3rd Principle "Principle of Symmetry (of > Non-Logicality)" mentioned in: > > http://groups.google.com/group/sci.math/msg/20bb0e7c183ae502?hl=en >
What appears to be a problem with your principle is that one does not know what is and what is not provable to begin with.
To establish the "relativity" of which you speak, one must demonstrate a model for a given statement and and a model for that given statement's negation.
>> >> The history of mathematical logic is entwined >> with a philosophical perspective that is collapsing >> from its own analyses. Goedel argued for >> idealism and platonism. That is not the logicism, >> logical positivism, or predicativism that tried >> to ground mathematics on the basis of realism >> and otherwise characterized the era in which he >> worked. > > So why do people react negatively with the _logical notion_ that the > concept of the natural numbers Godel used is a relativistic concept? > >