On 3/18/2013 6:43 AM, WM wrote: > On 18 Mrz., 07:26, fom <fomJ...@nyms.net> wrote: >> >> You turn to an outdated strategy directed to >> a situation that no longer exists rather >> than do the hard work of grounding your >> claims. You do this to say that just >> because you do not believe a particular >> axiom, > > Wrong. I prove that the axiom is nonsense liek the axiom that a > triangle with four edges exists.
You have *proven* nothing.
> > Of course I presume that in mathematics facts can be proven.
Mathematics is a system of facts systematized through deductions.
Its statements have facticity relative to that methodology.
> A simple > statement of faith in the Cartesian product cannot be overcome. So be > satisfied, nobody will ever cause you to change your belief, if it is > only fimr enough.
Where my faith lies with reality, there are normative moral laws which I fail to fulfill with each day.
> You may even include the belief that you are doing > mathematics or logic. >
No. I do not confuse these things.
Unlike you, when I ran across something that I considered problematic, I wrote axioms.
I wrote the necessary proofs to address the relationship of those axioms to standard mathematics.
When it became clear that I was unlikely to ever return to an academic career, I visited sci.logic and sci.math with hope of finding someone with whom to discuss that material.
Instead, I had been flamed by a talented, philosophically-trained individual whose interest lies with proof generation.
He was write about one thing: having been ignorant of the role of philosophy in the shaping of modern mathematics, I had been trying to address certain issues without having researched them.
My skills are deteriorated because I am not immersed in a work environment where I have the option to *apply* symbolic logic and abstract mathematics daily.
As for *doing* mathematics, I cannot be held accountable for others who are unwilling to engage with *questions* that might help them to see what I had tried to accomplish. As for my own engagement, I do what is called for by the paradigm. And, I do it responsibly.
Once again, you make an ill-fitting comparison.
> > >> Yet, there is an >> established criterion for demonstrating >> that the axiom you do not believe >> is, in fact, in error. > > If the inhabitants of a mad house establish a criterion I am not > obliged to accept it. >
Nor did my remarks say that.
>> You say that >> you do not need to respect this >> criterion. Nor, do you elucidate >> an alternate criterion that others >> might consider. > > Hahaha. Every axiom, beginning with Euclid, established or formalized > a triviality.
There is nothing trivial about what makes Euclid's axioms different from Hilbert's.
I would hold that were one to say Hilbert's axioms are *better* than Euclid's that there is a problem.
But, the two taken together give insight to both mathematics and the ideas of men.
> AC formalizes a counterfactuality.
At best, AC formalizes a counter-WMbelief.
Counterfactuals statements take a form of conditional in which the antecedent is expressly intended to propose a counterfactual situation.
Mathematics does not treat conditional statements of that form, except in the sense of different axiom systems or different models for the same axiom system. It certainly does not *formalize* any counterfactual.
Since you are so much a student of what is real and what is not, you should take your statement to sci.physics and discuss David Lewis' counterpart theory with the supporters of the many-worlds interpretation of quantum mechanics.
Then, at least, your statement invoking counterfactuals would have appropriate context.
> To choose a number means to name it.
Science is based on principles.
One may choose *in principle*
One may name *in principle*
Although related, they are not the same.
And I see that you continue to insist that
'A is B'
where B has the same grammatical form as A is an adequate form of explaining yourself.