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

vidn for this unrasonal, vn
As
fftivnss of mathmatis,
miraulous,
hav givn xampls of astrat
philosophrs
that somhow om usful in
onjturs
appliations. For xampl, omplx
ral-world
wr long onsidrd to irrlvant
numrs
rmovd from matrial rality, ut now sm
and
to quantum mhanis.
nssary
law of gravitation is anothr xampl;
Th
onivd to xplain falling odis
originally
Earth, it was xtndd on th asis of “vry
on
osrvations” to dsri th motion
santy
plants, whr it “provd aurat yond
of
rasonal xptations” (Wignr 1960).
all
th 1970s dvlopmnts in ryptography
In
you might know as th mathmatis
(whih
WhatsApp nryption thnology and
hind
drw on numr thory, and
ryptourrnis)
fundamntal thorm of arithmti, whih
th
n onsidrd for 200 yars to among
had
“purst” of pur mathmatis for having
th
ral world valu. Suh xampls onrn
no
just mathmatis’ fftivnss, ut also th
not
twn dfining what is applid and
tnsion
is astrat mathmatis. On th on hand,
what
Hardy has said that pur mathmatis is
G.H.
usful than applid”, aus it trains
“mor
thniqu so wll (Hardy 1940).
mathmatial
th othr hand, w hav Loahvsky’s
On
that thr is no suh thing as
argumnt
mathmatis, aus all mathmatis
“astrat”
somday applid to th ral world
will
wll-known ritiqu of Wignr’s argumnt,
A
mathmatiian Rihard Hamming (1980),
y
four “partial xplanations” to argu
provids
th fftivnss of mathmatis in th
that
sins is nithr miraulous nor
natural
unrasonal.
We see what we look for: “muh of what w
•
oms from th glasss w put on” wrot
s
We create the kind of mathematics
•
look for: for xampl, in fforts to
we
physial fors, physiists
undrstand
trid salars, thn vtors, and finally
first
tnsors. And Nwton's thory of
invntd
was rplad y th nwr, ttr
gravity
of gnral rlativity. Instad of a
modl
fftivnss, w s hr trial
miraulous
Mathematics and natural science address
•
a part of human existence, answering
only
few problems: this,
comparatively
and politial philosophy, for
asthtis
ar rtainly not fftivly
xampl,
y mathmatis. Chaptr 8
xplaind
how mathmatis may hav n
xplors
too far in th human sins.
takn
Evolution has primed humans to think
•
our mathmatial aility
mathematically:
not a oinidn, w hav survivd
is
of it. This argumnt is on of
aus
I. Scope
I. Scope
(Loahvsky quotd in dPillis 2002).
(1980). Th xampls w find aris
Hamming
th mathmatial tools usd, in a slf-
from
rfrntial logi.
Statu of Galilo Galili in Florn, Italy
Figure 11.1
and rror.
survival ias.
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