Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang
on or mor of th statmntsConsidrdrawn from past prsrid titlslow,th TOK ssay. Basd on what wfordisussd so far or on your prvioushavwhat an you laim, argu orknowldg,as an xampl from th prsptiv ofoffrin mathmatis is vry ommonlyEthiswith th thial impliations of applidonrndin nvironmntal sin, onomimathmatisindustry and thnology. In hr ookpoliy,of Math Destruction, mathmatiian CathyWeaponsillustrats th dangrs of our rlian onO’Nilpowrd y mathmatis. Thsappliationssh xplains, wr programmdappliations,“fallil human ings”. Built with goodyth modls hav unavoidaly inhritdintntions,prjudis and iass of thir human ratorsthas suh, thy prptuat th injustis in ourand,Th programms ar so omplx that, savsoity.a fw xprts, thir outputs ar not qustiond.forth sam tim, algorithms in “ig data” andAtrisk managmnt hav n idntifidfinanialpotntial sours of privay violations andasinstaility.onomith powr and valu of mathmatialGivnto ths domains, an argumnt anknowldgmad that spial thial rsponsiilitis fallmathmatiians.onshould that rsponsiility rst withOrsintists, thnologists, onomiststhnginrs rsponsil for applyingandknowldg to thir rsptivmathmatialWhr is th lin of rsponsiilitydomains?mathmatis and its appliation? Fortwnlt’s onsidr David Li, rditd withxampl,innovations that powrd th ollatralizdtholigations that playd a starring rol indtfinanial risis of 2007–08. His work onthknowldg thr is always a trad-off twn“Inand simpliity.” (IBO May 2016)aurayth group to vrify it, knowldg is“Withoutpossil.” (IBO Novmr 2015)nototh nals us to produ“Thnologyand limits th knowldg that isknowldgopula was usd to alulat finanialGaussiany invstmnt anks in th run-up to thriskrisis. Th writr Flix Salmon dsrid2007as a “rip for disastr” and “th formulaitkilld Wall Strt” (Salmon 2009).Yt, vnthatadmirrs wr singing his praiss in 2005,whnfor th risis, Li himslf was autioningwllth limitations of his modl, saying “Thaoutdangrous part is whn popl livmostoming out of it” (Li quotd invrything2005). H would latr xplain thatWhithousformula “gains its popularity owing to itshisut that thr was “littl thortialsimpliity”to it (Li quotd in Missnr 2008).justifiation”2007–08 finanial risis was ausd y manyThinluding govrnmnt suprvisoryprolmsfraud, moral hazard and prdatoryfailurs,pratis. It prsntd an nylopdiausinssthial ollapss. To fous th lam on Liof as ridiulous as it isignorant.wouldissu of attriuting thial rsponsiilityThmathmatiians for appliations of thirtois dply ompliatd. It may also havworksom mathmatiians to rtrat intoinspirdsupposd safty of pur mathmatis, inthlif that suh work is not rlvant tothommon, vulgar or violnt intrsts ofthhumankind.Hardy rjoid that pur mathmatisG.H.so far rmovd from human ativitis thatwaswould stay “gntl and lan” (1940). Hitto tak prid in this aspt of his work,appardIV. EthicsIII. Methods and toolsIV. EthicsPractising skills: Exploring perspectivesmathmatis in rspons?produd.” (IBO Novmr 2013)I V. E T H I C S347
IV. Ethicsthat “I hav nvr don anythingassrtingNo disovry of min has mad, or is‘usful’.to mak, dirtly or indirtly, for goodliklyill, th last diffrn to th amnity of thor(1940). Though Hardy was ultimatlyworld”aout th lak of utility of purlywrongrsarh, as w saw in stion I,mathmatialould not hav known that at th tim. Evnhsom mathmatiians ontinu to argutoday,pur mathmatial rsarh is rmovdthatqustions of this aus it is nutralfromandharmlss.the extent that an applied mathematician getsTowith a real-world activity, like geology orinvolvedhe has to deal with the ethical issuesengineering,that eld, not because he’s a mathematician, butof[W]hat about pure mathematics? Mathematicians…merely prove theorems. Is there any ethicalwhocomparable to what you nd in othercomponentof science…?eldspure mathematics, when restricted just to researchInnot considering the rest of our professional life,andethical component is very small … . I can’t thinktheany other eld of which you could say that. That’sofpeople say pure mathematicians live in an ivorywhyOne answer to this could be, “…There’s notower.whatever we like”. … But when I think about thisdol nd it rather scary. Because it means thatattitude,we become totally immersed in research on pureifwe can enter a mental state which ismathematics,asid th prolms of dmaratingLavingand pur mathmatis, Run Hrsh’sapplidsntns rval a mathmatial onrnlosingaout mathmatial knowldg itslf, utnotth rursiv impat on mathmatis, thataoutprhaps uniqu to th disiplin: its potntialisto, and dtahmnt from humanity. Airrlvanargumnt along th sam lins was madrntPaul Ernst. “Thr is signifiant ollatralyausd y larning mathmatis … thdamagof pur mathmatis itslf lads to stylsnaturthinking that an damaging whn applidofmathmatis to soial and human issus”yond2018).(ErnstRohll Gutiérrz’s argumnt, from II.4,Rallw nd to “rhumaniz” mathmatisthatdivrsity and inlusion. It is nottowardsto Ernst’s fars that “thialdissimilarin th tahing of mathmatisnutrality”support a “dhumanizing outlook” thatmaystudnts to sparat thir intlltualtrainsmotional livs. This onrn is shardandmathmatis duators who work towardsyquity, as w disussd in stion II.duationalspifi rommndation is thatErnst’sand this ar inludd in thphilosophy3 explores the sources of bias in machineChapterand articial intelligence, and the implicationslearningthis for the predictive power and application of thatofA recurring tension is whether we canknowledge.biases inherent to the algorithim versusseparatein the data sets used to train the articialbiaseshav sn that th prolm with thWnutrality of pur mathmatis is thatsupposdlin twn pur and applid mathmatis isthand ontinuously shifting. This haptrimpris11IV.1 Is pure mathematics ethicallyneutral?tahing of mathmatis at all lvls.Making connectionsbecause he’s involved in that application.The myth of impartialityintelligence.for mathematicians to have a code of ethics,needwhat we do matters so little that we canbecauserather inhuman, rather totally cut o from humanity.(Hersh 1990)348
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IV. Ethics
that “I hav nvr don anything
assrting
No disovry of min has mad, or is
‘usful’.
to mak, dirtly or indirtly, for good
likly
ill, th last diffrn to th amnity of th
or
(1940). Though Hardy was ultimatly
world”
aout th lak of utility of purly
wrong
rsarh, as w saw in stion I,
mathmatial
ould not hav known that at th tim. Evn
h
som mathmatiians ontinu to argu
today,
pur mathmatial rsarh is rmovd
that
qustions of this aus it is nutral
from
andharmlss.
the extent that an applied mathematician gets
To
with a real-world activity, like geology or
involved
he has to deal with the ethical issues
engineering,
that eld, not because he’s a mathematician, but
of
[W]hat about pure mathematics? Mathematicians
…
merely prove theorems. Is there any ethical
who
comparable to what you nd in other
component
of science…?
elds
pure mathematics, when restricted just to research
In
not considering the rest of our professional life,
and
ethical component is very small … . I can’t think
the
any other eld of which you could say that. That’s
of
people say pure mathematicians live in an ivory
why
One answer to this could be, “…There’s no
tower.
whatever we like”. … But when I think about this
do
l nd it rather scary. Because it means that
attitude,
we become totally immersed in research on pure
if
we can enter a mental state which is
mathematics,
asid th prolms of dmarating
Laving
and pur mathmatis, Run Hrsh’s
applid
sntns rval a mathmatial onrn
losing
aout mathmatial knowldg itslf, ut
not
th rursiv impat on mathmatis, that
aout
prhaps uniqu to th disiplin: its potntial
is
to, and dtahmnt from humanity. A
irrlvan
argumnt along th sam lins was mad
rnt
Paul Ernst. “Thr is signifiant ollatral
y
ausd y larning mathmatis … th
damag
of pur mathmatis itslf lads to styls
natur
thinking that an damaging whn applid
of
mathmatis to soial and human issus”
yond
2018).
(Ernst
Rohll Gutiérrz’s argumnt, from II.4,
Rall
w nd to “rhumaniz” mathmatis
that
divrsity and inlusion. It is not
towards
to Ernst’s fars that “thial
dissimilar
in th tahing of mathmatis
nutrality”
support a “dhumanizing outlook” that
may
studnts to sparat thir intlltual
trains
motional livs. This onrn is shard
and
mathmatis duators who work towards
y
quity, as w disussd in stion II.
duational
spifi rommndation is that
Ernst’s
and this ar inludd in th
philosophy
3 explores the sources of bias in machine
Chapter
and articial intelligence, and the implications
learning
this for the predictive power and application of that
of
A recurring tension is whether we can
knowledge.
biases inherent to the algorithim versus
separate
in the data sets used to train the articial
biases
hav sn that th prolm with th
W
nutrality of pur mathmatis is that
supposd
lin twn pur and applid mathmatis is
th
and ontinuously shifting. This haptr
impris
11
IV.1 Is pure mathematics ethically
neutral?
tahing of mathmatis at all lvls.
Making connections
because he’s involved in that application.
The myth of impartiality
intelligence.
for mathematicians to have a code of ethics,
need
what we do matters so little that we can
because
rather inhuman, rather totally cut o from humanity.
(Hersh 1990)
348