```Date: Apr 7, 2013 12:54 PM
Author: namducnguyen
Subject: Re: Matheology § 224

On 06/04/2013 4:34 PM, fom wrote:> On 4/6/2013 4:56 PM, Nam Nguyen wrote:>> On 06/04/2013 2:34 PM, fom wrote:>>> 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.>>>> You seem to misinterpret the principle, which is actually>> a logical one.>>>> Assuming that the formula A is neither a tautology or contradiction,>> it's impossible to conclude A or to conclude ~A from (A \/ ~A).>> Therefore it's _relative_ to your choice to choose which of A, or ~A>> be your axiom. Ditto for the dichotomy (A \/ B): it's relative to>> which of A and B you'd choose. This is in the realm of syntactical proof>> via rules of inference.>> I have not misinterpreted your principle.You have; and I will explain why.>> You are free to construct axioms and the theories> that constitute their deductive closure.>> If, however, you wish to apply that freedom to an> established theory, other responsibilities arise.>> First of all, it will be a different theory.  To> claim that it is a corrected theory is to make a> philosophical argument that the difference between> the original theory and the corrected theory reflects> some typical expectation or standard practice of> mathematicians -- outside of foundations -- that> has not been represented in the original theory.First according to the principle, "corrected theory","original theory", "typical expectation", "standard practice",or the like, are all relativistic terms. Hence you've misinterpretedthe principle.>> Second, if one is not claiming that it is a> corrected theory, then one must be clear that> it is not the standard theory.  If it is not> the standard theory, then the relation to the> standard theory becomes an issue.  The relativity> principle you espouse must be shown to be> applicable.  It can only be applicable if it> does not interfere with the possibility of a> proof within the standard theory.  This> criterion of applicability translates into> a restriction of relativity to those statements> which have been shown to be independent.Again, "the standard theory" is a term of relativity, bymy Principle (3).>> Statements are shown to be independent by> formulating a model in which the statement> is true and formulating a model in which> the statement is false.You get confused between 2 different kinds of relativity:one about formal system provability (which is what Godel talkedabout), the other about language structure verification (that I'vebeen  talking). The two are _not_ the same.>> There is nothing in these remarks that does> not respect, first and foremost, the possibility> of a syntactic proof of an unproven statement> within the standard, established axioms.Not sure I understand what you'd like to convey here, but"standard" is a relativistic term, by Principle (3).-- ----------------------------------------------------There is no remainder in the mathematics of infinity.                                       NYOGEN SENZAKI----------------------------------------------------
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