Speculative details of mathematization?

From Lukasgirtanner
Jump to: navigation, search

Alternative titles

  • eschatological philosophy of mathematics?
  • eschatology and (philosophy of) mathematics? (how) inconceivable?
  • The unproven eschatology of mathematics
  • (see also http://en.wikipedia.org/wiki/Eschatology )

Content

  • just because I might have roughly understood numbers or numeral systems, I haven't understood mathematics, isn't it? or didn't I have even understood numbers and numeral systems because it is not possible to understand mathematics from bottom-up but only from top-down which means the most fundamental axioms? so only when one develops and fully understands mathematics from the most fundamental axioms top-down, you can be sure that one has understood relatively remote concepts like numbers (apart from the fact that one might still challenge or question a particular axiomatic system)?
  • to which extent is a preference for a number or numeral system incomparable to a mathematical topic as a whole and/or even to an axiomatic system?
  • did I simply mix up learning or preferring a particular topic (because of time, energy and intelligence learning constraints in the real world) with learning within a particular axiomatic system?
  • so, are there three distinctive areas: numeral systems, topics and axiomatic systems, each with more profound implications, the numeral systems having the least profound implications?
  • ideological viewpoint: just increasingly "deeply" understanding mathematics? / or becoming and ultimately "being" mathematics? (probably a new topic for a new page) or something in between? or all at the same time?
  • wouldn't it be recommendable to strictly separate general eschatology and the philosophy of mathematics (in the stricter sense)? (I tried that subsequently by indicating if the point is mathematical or ideological)
  • ideological viewpoint: what exactly would an "ultimate" mathematical "insight" mean? and by whom / which entity?
  • are there really "levels"? isn't the notion of "levels" too visual?
  • what about "formal" and "abstract"? what is "formal" and "abstract"? how to define it mathematically? is it or will it be possible?
  • extrapolating from the infinite number of numeral systems into really pure mathematics? a good idea? isn't such a cognitive jump a little bit a too large leap?
  • problems: would that be philosophy of mathematics?
  • ideological viewpoint: what about individualism and collectivism?
  • mathematical viewpoint: where rigor or exact or indeed foreseeable predictions stop and only (primarily? mainly?) intuition and guess begins
  • m/i topic: who is entitled at which "stage" to voice speculative details of mathematization?
  • ideological topic: "stage" - what is a "stage"? or "state"? is there still time?
  • ideological/mathematical topic: mixing up "philosophy" (eschatology) and philosophy of mathematics? how restricted should the philosophy of mathematics be? where does the philosophy of mathematics end and "general philosophy" begin? and how strictly should such a separation - if it exists - be declared and respected?
  • why does the page's title have a question mark?
  • ideological topic: trying to ideologically conjecture or "achieve" (in a negative sense maybe also "enforce") oneness on an ultimate level by hook or by crook? is it a good idea actually, but might mathematics be the wrong idea and if yes what might the ("rational"?) explanation be?
  • simplicity yes, but no mathematical simplification (and oversimplification doesn't exist, does it? there is not distinction between simplification and oversimplification?) - the simplicity is only (or mainly? primarily?) on the highest or better most fundamental/axiomatic level in the deepest insight
  • don't mix up processes of learning mathematics and what mathematics is or implies. mathematics does need learners, it is self sufficient, isn't it? learning all mathematics seems like an almost impossible endeavor, doesn't it?
  • mathematical topic: might simplicity in complexity imply oneness?
  • mathematical topic: mathematical depth: "deep/profound" links between various areas of mathematics and oneness
  • mathematical topic: what about the (most fundamental) axioms of mathematics? might they ultimately imply oneness? and how many axioms are at the moment to a certain degree part of a consensus? are there different axiomatic systems? is "how many" important in terms of the number of axioms or axiomatic systems? a new mathematics with one most fundamental axiom? but one remains one, isn't it? and wouldn't it be impossible anyway to imply all mathematics just from a unique/single and most fundamental axiom, would it?
  • ideological topic: mathematics and desire: isn't it problematic if desire for oneness is mixed up with mathematics? or if desire and mathematics is mixed up generally?
  • mathematical viewpoint: isn't it impossible and futile to conjecture (conjecture in the ideological sense, not mathematical) any statement with unmathematical intuition about the ultimate and last stages of mathematics? and shouldn't one finally and ultimately accept that (at least for now?)?
  • what about UTSARAHL? UTSARAHL and this page here?

How this page here was developed/created

  • This was originally the section that I copied from the page (originally "the hexadecimal numeral system" until 2010-07-11) numeral systems diversity on the late evening of Tuesday, 2010-06-15 (0x7da-0x6-0x0f): "But/And wouldn't in the ultimately mathematized stage the (infinite) number of numeral systems have become obsolete anyway in a similar way like the different (and possibly infinite? or finite?) topics of mathematics might have become obsolete too since on an ultimately formal and abstract level of mathematization, the separating nature of the distinctions (but not the distinctions themselves on the lower level) might be comprised by an ultimate all-encompassing mathematized insight (but then, wouldn't there be an ultimate, universal finite insight in perfect mathematization? a finite theory?)?" It was relatively late in the evening and I was probably increasingly tired. After I had written this section here, the wiki seemed to slow down somehow significantly. On that evening, I also misspelled the word "copyright" and I had a difficult afternoon in terms of salt intake. So maybe, wasn't this section written a little bit too quickly and carelessly? And when writing about mathematics, shouldn't more care be observed?

See also

See also mathematization