|
|
Stan wrote:
> Why did not you say so earlier? Now all is much clearer. ;-)
> This is [almost] the essence of meta-mathematics and many people
> dedicated some mental effort to it (with no definitive answer).
Because it was not my intention to get this gorup involved in the
discussion of linked article.
I just was looking for help in clarification how terms like "element"
and "set" are defined in the Set Theory.
Stan wrote:
> My own opinion is that yes, math does start from a bare minimum
> of "observations".
Thank you for agreeing with my position. If you don't mind, can you
exapnd on this a little bit, and answer, if it is possible to build ANY
advanced math without having such foundation as concepts built from
"bare minium of observations"?
>Such as that some objects can be split, that
> multiple objects can be associated into a single one, that objects
> can be referred-to and the references (labels) can be replicated
> without limit. From these few points, math can extract the bare
> essence and take off and on its own wings.
>
> So, I think that math certainly received an initial empirical
> stimulus, but there is no need to push it as far as to say that
> it can accomodate all reality or, vice versa, that all math
> concepts need to have an analogy in reality.
I think that advancing math may provide some solution that indeed don't
have an obvious analogy in reality. Good example was "i", but it
finally have found one in describing reactive component in alternating
current.
|
|