Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang

is a prime, not because we think so, or because
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minds are shaped in one way rather than another,
our
because it is, because mathematical reality is
but
that way.
built
Hardy’s prsptiv shapd y his ultural
Is
or is it univrsal? Blow w xplor
ontxt,
aout th origins of mathmatis. Dos it
laims
in th world outsid of human xprin, or
xist
it a produt of th human mind? W will larn
is
rogniz th assumptions that aompany
to
laims, and xplor th impliations of ths
ths
prsptivs towards mathmatis.
diffrnt
many physical systems have mathematical
…
the segmented arrangements in
representations:
pine cones and pineapples (Fibonacci
sunowers,
the curve of nautilus shells, elephant
numbers);
and rams horns (logarithmic spiral); … atoms,
tusks
and galaxies, which all now have powerful
stars
descriptors; even the cosmos as a whole,
mathematical
represented by the equations of general relativity …?
now
does the real world actualise maths at all? …
Why
physicists still explain this by some form of
Most
Platonism, which in its oldest form
philosophical
that the universe is moulded by mathematical
says
ralism assrts that mathmatis
Mathmatial
indpndntly of th human mind, that
xists
is disovrd, and not ratd, y humans.
it
a form of ralism, holds that th
Platonism,
is omposd of astrat and trnal
univrs
ntitis”. This has n among
“mathmatial
most datd topis in th philosophy of
th
If you ar a mathmatial ralist,
mathmatis.
unrasonal fftivnss of mathmatis
th
not sm that unrasonal aftr all,
might
th othr hand, anti-ralist prsptivs
On
that mathmatial ntitis do not xist,
argu
that mathmatis is a languag humans
and
invntd to talk aout quantity, strutur,
hav
and hang. Th philosophr Hugh
spa
famously dsrid mathmatis as
Lhman
“thortial jui xtrator" that is usful for
a
maning out of things, ut has no
squzing
argu that ths anti-ralist prsptivs,
Othrs
as nominalism, might appaling ut
suh
not quit mak sns aus th truths
do
ar rvald to us through mathmatis
whih
fat xistd long for humans startd to
in
thm or had a languag with whih
undrstand
of th omplling anti-ralist argumnts is
On
on th qustion of why humans ar al to
asd
astrat mathmatis in th first pla.
“know”
would w know th diffrn twn
How
ratd y th human mind and
mathmatis
indpndnt of it? Within TOK
mathmatis
nd not solv ths riddls. But anyon
w
alulating and modlling ral-world
masuring,
mathmatially should awar of
phnomna
laims and assumptions aout th natur of
th
why dos any of this mattr?
Ultimatly,
xampls w look at nxt suggst that
Th
prsptivs influn attituds in th
ths
ommunity and, thrfor, th
mathmatis
II. Perspectives
II. Perspectives
I I . P E R S P E C T I V E S
II.1 Was mathematics discovered
or invented?
(Hardy quoted in Tarlach 2014)
aus th univrs is “mathmatial”.
ontnt in itslf.
to dsri thm.
rality thy rst on.
relationships which precede the material world.
(Wertheim 2017)
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