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

I. Scope
mathmatis arris an aura of
Notaly,
aus mathmatial proofs ar 100%
authority
and a supposd usfulnss that justifis
rtain
privilgd status in many duation systms.
its
ar th limits of mathmatis? It is
Whr
assumd that thr ar non—that
somtims
is a univrsal form of knowldg and fatur
it
intllignt lif. S th opning xampl in
of
4 aout how mathmatis was hosn as
Chaptr
ommon ground on whih to ommuniat
th
pla to look for th limits of mathmatis
On
in what it an dsri, xplain or prdit. As
is
xampl of physis nvy in Chaptr 8 shows,
th
may hav n takn too far in th
mathmatis
for rigour in th soial sins. In 1931
qust
mathmatiian Kurt Gödl pulishd two
th
thorms that logially provd that
inompltnss
formal systm of mathmatis will ontain
any
that annot provn from within that
truths
Through mathmatis, Gödl gav us
systm.
limitations of mathmatis and snt powrful
th
through th disiplin. Othrs hav
shokwavs
that mathmatis sts th nhmark for what
said
think of as truth, and is th oldst “sintifi
w
in Wstrn thinking”, with “prhaps th
tool
sintifi authority”, as long as w do
gratst
aout Gödl’s thorms! (Chiodo,
notthink
Bursill-Hall2018).
Whr would you outlin th sop of
1.
Considr what happns
mathmatis?
its sop—think of phnomna
outsid
would say ar yond mathmatis.
you
What vidn is thr to suggst that
2.
ar som things that w will
thr
al to dsri or xplain
nvr
mathmatially?
Is mathmatial dsription mor
3.
ar mathmatial xplanations
aurat,
tru and ar mathmatial
mor
mor rtain than thos of
prditions
this statmnt writtn y Galilo
Considr
(1564–1642).
Galili
philosophrs hav agrd with, uilt on
Many
srutinizd his words. “Th Unrasonal
or
of Mathmatis in th Natural
Efftivnss
an ssay writtn y thortial
Sins”,
and mathmatiian Eugn Wignr,
physiist
Galilo’s vision of mathmatis.
hos
wrot that it is a “miral” that
Wignr
onpts lad to “amazingly
mathmatial
dsriptions” of physial phnomna
aurat
1960). H idntifid th following thr
(Wignr
Mathmatis xplains th strutur of th
•
univrs.
Thr is an apparnt dp strutur to th
•
univrs.
Human ings ar apal of this
•
mathmatis.
it rally as miraulous as Wignr suggsts—
Is
thr no rational xplanation? H was
ould
th ompany of Alrt Einstin (1922), who
in
wondrd, “how an it that mathmatis,
also
aftr all a produt of human thought whih
ing
indpndnt of xprin, is so admiraly
is
11
I.1 Becoming conversant in the
language of the universe
[The universe] cannot be read until we have learnt
the language and become familiar with the characters
in which it is written. It is written in mathematical
language, and the letters are triangles, circles and other
geometrical gures, without which means it is humanly
impossible to comprehend a single word.
with any xtratrrstrial intlligns.
(Galileo 1632)
miraulous oinidns.
For discussion
The enormous usefulness of mathematics in the
The nature and limits of mathematics
natural sciences is something bordering on the
mysterious, and there is no rational explanation for
it. It is dicult to avoid the impression that a miracle
confronts us here.
(Wigner 1960)
othr AOKs?
appropriat to th ojts of rality?”.
322