the australian philosopher colin leslie dean points out that Mathematics is
systems of epistemological holisim
set theory
arithmetics
geometry
algebra
etc
are systems of epistemological holisim
epistemological holism means
a systems statement coher ie dont contradict with every other statement in
the system A systems statements interlock they share a common logic and
are involved enblock in every proof.A systems statements face the
tribunal of proof as a corporate body of statements. A systems
statements about mathematics face the tribunal of proof not
individually but only as a corporate body.
thus
if a statement contradicts another statement then the system as a
corporate body enblock falls apart into inconsistency
hence skolems paradox reduces set theory thus ZFC to inconsistency
ALSO
a systems statements face the tribunal of proof as a corporate body of
statements. A systems statements about mathematics face the tribunal of
proof not individually but only as a corporate body.
thus systems which are incomplete ie there is one statement that cant be
proven then the system enblock cant prove anything
thus the systems ZFC, PA, Q due to there, incompleteness cant prove
anything
You are trying to tell us things we already know - math is a man-made concept, so of course it’s going to be debatable: like language always is…
Btw, you are abusing the use of language for your own unwarranted gains: which I can predict will end in you losing gains, as the wares you are peddling are faulty goods!
Quit while you are only slighly behind, or you will regret your next few moves…
holism is where there is a proper fit of statements within a system.
This involves 1) the statements coher with each other ie there is logical
consistency This condition is met by mathematical systems thus they are
holistic
2)statements give mutual inferential support to each other. This
condition is met by mathematical systems thus they are holistic
as a corollary
Thus a systems statements face the tribunal of proof as a corporate
body of statements. A systems statements about mathematics face the
tribunal of proof not individually but only as a corporate body
Where systems are incomplete: they are re-thought - well, they were when I was doing math back in the 80s, and things progress not regress so I can’t see this not happening anymore…
These facts are not new to maths: which nearly every single ILP poster has already pointed out to you curriculums are derived from current thought on any given topic, so any inconsistencies are filtered down through the curriculum system… Math is a concept, math works most of the time, where math fails: new mathematical concepts arise to make it work!
Everything around us is conceptual, so everything is up for scrutiny! and what?
godels theorem says there are incomplete system ie ZFC robinson arithmetic etc
so are you saying we should now re-thinks these incomplete systems and make them complete
curriculums are derived from current thought on any given topic, so any inconsistencies are filtered down through the curriculum system… Math is a concept, math works most of the time, where math fails: new mathematical concepts arise to make it work!