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

with Wignr’s unrasonal fftivnss
opnd
and xampls of pur mathmatial
thsis,
that had no appliation for dads,
thorms
nturis, inluding omplx numrs (now
or
in quantum mhanis) and numr
applid
(ntral to ryptography). Hardy’s sap
thory
pur mathmatis in th 1940s was drivn
into
his prption of th lak of usfulnss of
y
thory or quantum mhanis. What
numr
sm thially nutral today may wll
an
prolmati tomorrow. How thn
thially
w think of fators that afft th this of
should
Should w sk to untangl intnt
knowldg?
impliation and fft?
from
and Bursill-Hall add that many
Chiodo
ar taught to liv that
mathmatiians
is thially nutral, that any thial
mathmatis
lay with th usr of th tools that thy rat.
issus
many usrs of ths tools will also dny soial
Yt
laiming thy ar using only what
rsponsiility,
givn to thm, or that somody ls would
was
us what xists towards thir own
invitaly
Bhind many a pur mathmatiian, thr
nds.
funding for th rsarh—from a univrsity, a
is
a think-tank or a orporation. It is
govrnmnt,
that all of ths organizations ar funding
unlikly
pursuit for th sak of knowldg, lgan or
th
Do mathmatiians hav a rsponsiility
auty.
omprhnd, influn or hallng
to
thsagndas?
th widly hld Platonist viw of mathmatis,
In
ss mathmatis as oupying an astrat
whih
transndntal rality, thial impliations
or
do not aris. Howvr, Chiodo and
simply
knowledge and truth
Ethics,
Intnt is a fundamntal onrn within
1.
Do good intntions, or th lak of
(a)
intntions, asolv produrs
ad
mathmatial knowldg from
of
for th appliation of
rsponsiility
What ritria might w us whn
(b)
intntions, and who
onsidring
Th statistiian and hdg fund managr
2.
Tal (quotd in a Royal
Nassim
Soity rport 2001) said:
Statistial
got vry xitd aout
“[p]opl
Gaussian opula aus of its
th
lgan, ut th thing
mathmatial
workd … anything that rlis on
nvr
is harlatanism”. To what
orrlation
an w us statistial orrlations
xtnt
infr truths aout rality?
to
3. Mor gnrally:
In mathmatis is thr a trad-off
(a)
auray and simpliity?
twn
How is th rlationship twn
(b)
and simpliity in
auray
similar to or diffrnt
mathmatis
th othr AOKs?
from
IV. Ethics
IV. Ethics
Bursill-Hall argu that:
no matter how Platonist they may be, it does not
obviate their social and ethical responsibilities.
Mathematics may well ‘exist’ in the sense of being
a dierent kind or type of reality, but it is done
(discovered, developed, studied, understood, used)
by humans in our very material, social world and
therefore exists for us in some sort of social matrix or
social context.
(Chiodo, Bursill-Hall 2018)
Sophisticated mathematics is already ubiquitous
in 21st century technology. Even the most ardent
purists in number theory or algebra can no longer
For discussion
claim to ‘just do the mathematics’ and ‘leave the
implications to ethicists’ as recent revelations
about global mass surveillance have underscored
the immediate social and political impact of their
work. It is now evident that one can wield practically
this.
all branches of mathematics in ways that have
profound social consequences, both for good and
occasionally for ill, and that ethical questions can be
raised everywhere in pure and applied mathematics.
It seems that professional social responsibility
and engagement in mathematics-specic ethical
that knowldg?
issues is unavoidable for mathematicians; we would
suggest that those who deny this may be abdicating
responsibility and power to others in the most
would did thos ritria?
dangerous way.
(Chiodo, Bursill-Hall 2018)
349