On 3/16/2013 1:00 PM, WM wrote: > On 16 Mrz., 18:17, fom <fomJ...@nyms.net> wrote: > >> >>> 2) Do you agree that choosing a number from a set with more than 1 >>> element means writing or speaking or at least thinking the name of the >>> number? >> >> No. The use of logic and axioms is justifiable as >> representations that formalize mathematical practice. > > The practice must not become unpracticable by logic.
There is nothing unpracticeable about it. You simply misunderstand the requirements of using singular terms and the difficulties presented by the logic that preceded the late nineteenth century.
Frege's paper introducing a new deductive calculus is extremely sophisticated.
> >> They are normative ideals against which mathematical >> practice is measured. > > Logic and formalization *describe* practice, they cannot change it. >
No. The represent practice. That is different.
What makes it different are metamathematical results such as the completeness and soundness theorems.
A description of practice is the educational abuse of Euclidean geometry in the secondary education of young adults in the United States. It has become a proxy for teaching logic at the expense of teaching mathematics.
>> Your question applies to the faithfulness of those >> representations. What is "nameable in principle" may >> not be materially nameable. > > Here is the question whether something can be chosen, not whether it > can be "in priciple" chosen. >>
And, once again you show your ignorance of science. Your failure to grasp its sense with regard to mathematics as a demonstrative science is one thing. But, a comment such as that indicates a contempt for empirical science as well.
>>> 5) Zermelo's AC requires that uncountably many names can be written, >>> said or thought. >> >> No. Zermelo's AC requires that one name can be written >> with certainty. >> >> "the cartesian product of non-empty sets is non-empty" >
As you seemed to have ignored today's science lesson, the remainder is snipped.