Theory of Knowledge - Course Companion for Students Marija Uzunova Dang Arvin Singh Uzunov Dang
argue that, while there’s a biological grounding,I’dand cultural traits are necessary for thelanguageanimals hav a quantitativ sns, forManying al to distinguish whih undlxamplwith newborns and infants show that, ifStudiesshow them eight dots repeatedly and thenyouit to 16 dots, areas in the right parietalchangeof the brain respond to a change incortexhas ld som rsarhrs to thoriz thatThisnumrial sns is innat.asuh as Rafal Núñz, argu that thOthrs,of a iologially ndowd numrargumntis asd on skthy sin: inauratsnsof iologial volution, ovr-undrstandingon WEIRD population sampls (asmphasisin Chaptr 8) and ovrintrprtationdisussdrsults from traind animals. W must alsoofth diffrn twn quantial andnotognition: quantial rlats to hownumrialappls thr ar in a askt, or how manymanyon a oard, whras numrial ognitiondotswith symols suh as 3, 4 and 5.dalsbecause a behaviour seems to derive from anJustcapacity, that doesn’t mean the behaviourinnateitself innate. ... No non-human animal has yetisfound able to distinguish 152 items from 153.beencan’t do that, no matter how hard you trainChimpsyet many children can tell you even by thethem,of ve that the two numbers dier in the sameageas do the equally abstract numbers 2 and 3:wayrsarhrs do not apt that numrialOthris a ulturally drivd aility.ognitionthat th rain is “prdisposd to aquirargusnumr systm” that ultur an furthraand rfin. But without this iologialshaphumans would nvr hav a numrapaity,Chaptr 8 w nountr th ida ofInan argumnt that naturnaturultur,ultur ar so tightly onntd inandrlationships that w ar ttr offologialsparating thm. If w apt Núñz’snotfor th momnt, that quantialargumntannot volv into numrialognitionwithout th influn of ultur, whatognitiondo w hav? Núñz suggsts thatvidnulturs around th world hav no wordsmanysymols for numrs largr than fiv or six.orwords quivalnt to “many” ar usd.Instad,the language of the Munduruku people of theInfor example, adesu indicates ‘several’Amazon,ade implies ‘really lots’. These cultureswhereaswith what to us looks like imprecision: it reallylivematter if, when the oranges are divideddoesn’tone person gets 152 and the other 153. Andup,if we aren’t so number-xated, it reallyfrankly,matter. So why bother having words todoesn’tdiffrns twn larg numrsSmallmattr for many thnologial andlarlyappliations. Howvr, on argumntsintifithat humans’ innat quantial sns isisth diffrn twn on andlogarithmi:is muh gratr than twn fiv and six,twofor most ativitis in th human ra, thisandsuffiint.wasII. PerspectivesII. Perspectivesestablishment of number itself’.(Ball 2017)aility (Nidr quotd in Ball 2017).of food is iggr, and it appars innat to humans.numerosity. This response is very similar in adults.(Ansari quoted in Ball 2017)distinguish them?(Ball 2017)Arithmetic scale1 2 3 4 56 7 8 9 10 13 16namely, by 1 … .Logarithmic scale(Núñez quoted in Ball 2017)6 7 8 9 12 161 2 3 4 5Arithmti and logarithmi salsFigure 11.3Nuroiologist Andras Nidr, for xampl,333
II. Perspectivesognitiv nurosintist StanislasThhas suggstd that whil WstrnDhanand hildrn gnrally us an vnlyadultsnumr lin, th Mundurukuspada logarithmi sal. Th rsarhrsusthat hildrn who larn to spaspulatarithmtially must first ovromnumrslogarithmi intuitions. Howvr,innatis an insapal irony in Wstrnthrattmpting to prisly quantifysintistsimpris mapping of quantitis y athgroup of Indignous Popl doingsmallTh rsarhrs hav notd that thpuzzls.in thir rsults is too grat to allowvariailityaout outoms from th rpliationThinkingto what xtnt would you gnralizrisis,aout humans having a logarithmilaimssns?quantialeasy to read this as a ‘primitive’ way of reasoning,It’santhropology has long dispelled such patronisingbut… . You develop words and concepts forprejudicetruly matters to your society. From a practicalwhatone could argue that it’s actually theperspective,homogeneous group of industrialisedsomewhatthat look odd, with their pedantic distinctioncultures1,000,002 and 1,000,003.betweenmathmatiian Morris Klin has writtnThthat “ompard with thondsndinglyof thir immdiat sussors,aomplishmntsGrks, th mathmatis of th EgyptiansthBaylonians is th srawling of hildrn justandto writ as opposd to grat litratur”larningattituds xprssd in this quot havThstrongly ritiizd and nouragd thnffort in mathmatis. Klin’sdolonizationhos th sam myths nountrdommntfurthr ompliat mattrs, thr isTothat th two systms—quantial andvidnprossd diffrntly in thnumrial—arand thrfor appar to unorrlatd.rain,hallngs th ida that th quantialThisvolvd into a numrial systm.systmdos this mattr for knowldg? ThHowinflun mathmatis duation,impliationsxampl. Rsarhrs at th Johns Hopkinsforshowd a orrlation twnUnivrsityaility to disriminat twn14-yar-olds’numrial quantitis (suh as th numrxatdots in an imag) and thir tst sors inofall th way ak to kindrgartnmathmatiset al 2008). Th orrlation has n(Halrdato dvlop duational tools to assss andusdmathmatial aility, for xampl inimprovthat ask hildrn to quikly assss howtstslanguag th origin of our numrialCouldand of mathmatis? Did w ginsns,in itself may be a necessary condition forLanguagebut it is not sucient for it … . All knownnumber,cultures have language, but by no means allhumanexact quantication in the form of number.havehistory and th human andlswhr—insins—that non-Wstrn ulturs andnaturalis a urious and hallngingMathmatisin th widr movmnt for duationalasand dolonizing duation. Enrgizdquityhav arisn in at last two aras. Ondatshow th history of mathmatis is told andisTh sond takls th prsistnt liftaught.mathmatis is nutral from th point ofthatlass and gndr. This has n th sit ofra,dat and ontrovrsy, suh as thsignifiantmovmnt in lat 2017.#IStandWithRohll11for strong onlusions.many dots ar on a pag.ounting whn w ould nam numrs?(Núñez quoted in Ball 2017)(Ball 2017)II.4 Diversity and many mathematicsintlltual traditions lag hind.(Klin 1985).334
- Page 289 and 290: I. Scopehas the status of women art
- Page 291 and 292: I. ScopeTruth and knowledge in art:
- Page 293 and 294: I. Scopeterms: ElizabethSearchDesir
- Page 295 and 296: II. Perspectivesby Vermeer were rar
- Page 297 and 298: II. Perspectiveswas one thing van M
- Page 299 and 300: II. Perspectivesare found in the br
- Page 301 and 302: II. Perspectivesterms: CNN Business
- Page 303 and 304: II. Perspectivesof the time, to dra
- Page 305 and 306: II. Perspectivesthe last few hundre
- Page 307 and 308: II. Perspectivesafter that date, bu
- Page 309 and 310: II. Perspectiveshave been examples
- Page 311 and 312: II. PerspectivesIII. Methods and to
- Page 313 and 314: III. Methods and tools1. Is having
- Page 315 and 316: III. Methods and toolsThe rst thing
- Page 317 and 318: III. Methods and toolscan be deeply
- Page 319 and 320: IV. Ethicsmay notice that many know
- Page 321 and 322: IV. Ethicsartist’s intent to conf
- Page 323 and 324: IV. Ethicsor moral boundaries of th
- Page 325 and 326: IV. Ethicsfact that people far away
- Page 327 and 328: IV. Ethicsterms: NorthrupSearchtrue
- Page 329 and 330: I. Scopemathmatis arris an aura ofN
- Page 331 and 332: I. Scopeof th arly xampls of this
- Page 333 and 334: II. Perspectivesof mathmatial knowl
- Page 335 and 336: II. Perspectivesonpts an appar so s
- Page 337 and 338: II. Perspectivesdid th st minds of
- Page 339: II. Perspectiveswrits that long for
- Page 343 and 344: II. Perspectivesprptuat inquality o
- Page 345 and 346: III. Methods and toolsonsidr two on
- Page 347 and 348: III. Methods and toolsproofs wr rit
- Page 349 and 350: III. Methods and tools10 features a
- Page 351 and 352: III. Methods and toolsmathmatis is
- Page 353 and 354: III. Methods and toolswritrs of The
- Page 355 and 356: IV. Ethicsthat “I hav nvr don any
- Page 357 and 358: IV. Ethicsold adag, widly itd and o
- Page 359 and 360: IV. Ethicswll-puliisd figur of 1 in
- Page 361 and 362: IV. EthicsMathematics. Th artil prs
- Page 363 and 364: I. THE EXHIBITIONquestions are ques
- Page 365 and 366: I. THE EXHIBITION11. Can new knowle
- Page 367 and 368: I. THE EXHIBITIONa new subject can
- Page 369 and 370: I. THE EXHIBITIONthat objects do no
- Page 371 and 372: I. THE EXHIBITIONyou describe them,
- Page 373 and 374: I. THE EXHIBITIONdoubt, and a tweet
- Page 375 and 376: II. THE ESSAYother way you demonstr
- Page 377 and 378: II. THE ESSAYwhat extent do the con
- Page 379 and 380: II. THE ESSAYAnother weak approach
- Page 381 and 382: II. THE ESSAYto present the conclus
- Page 383 and 384: as unspoken and unspeakable truthsa
- Page 385 and 386: otherwise by measuring differentlyk
- Page 387 and 388: J. 2017. “The Triage of Truth: Do
- Page 389 and 390: H. 2017. “Cambridge Analytica, Tr
II. Perspectives
ognitiv nurosintist Stanislas
Th
has suggstd that whil Wstrn
Dhan
and hildrn gnrally us an vnly
adults
numr lin, th Munduruku
spad
a logarithmi sal. Th rsarhrs
us
that hildrn who larn to spa
spulat
arithmtially must first ovrom
numrs
logarithmi intuitions. Howvr,
innat
is an insapal irony in Wstrn
thr
attmpting to prisly quantify
sintists
impris mapping of quantitis y a
th
group of Indignous Popl doing
small
Th rsarhrs hav notd that th
puzzls.
in thir rsults is too grat to allow
variaility
aout outoms from th rpliation
Thinking
to what xtnt would you gnraliz
risis,
aout humans having a logarithmi
laims
sns?
quantial
easy to read this as a ‘primitive’ way of reasoning,
It’s
anthropology has long dispelled such patronising
but
… . You develop words and concepts for
prejudice
truly matters to your society. From a practical
what
one could argue that it’s actually the
perspective,
homogeneous group of industrialised
somewhat
that look odd, with their pedantic distinction
cultures
1,000,002 and 1,000,003.
between
mathmatiian Morris Klin has writtn
Th
that “ompard with th
ondsndingly
of thir immdiat sussors,
aomplishmnts
Grks, th mathmatis of th Egyptians
th
Baylonians is th srawling of hildrn just
and
to writ as opposd to grat litratur”
larning
attituds xprssd in this quot hav
Th
strongly ritiizd and nouragd th
n
ffort in mathmatis. Klin’s
dolonization
hos th sam myths nountrd
ommnt
furthr ompliat mattrs, thr is
To
that th two systms—quantial and
vidn
prossd diffrntly in th
numrial—ar
and thrfor appar to unorrlatd.
rain,
hallngs th ida that th quantial
This
volvd into a numrial systm.
systm
dos this mattr for knowldg? Th
How
influn mathmatis duation,
impliations
xampl. Rsarhrs at th Johns Hopkins
for
showd a orrlation twn
Univrsity
aility to disriminat twn
14-yar-olds’
numrial quantitis (suh as th numr
xat
dots in an imag) and thir tst sors in
of
all th way ak to kindrgartn
mathmatis
et al 2008). Th orrlation has n
(Halrda
to dvlop duational tools to assss and
usd
mathmatial aility, for xampl in
improv
that ask hildrn to quikly assss how
tsts
languag th origin of our numrial
Could
and of mathmatis? Did w gin
sns,
in itself may be a necessary condition for
Language
but it is not sucient for it … . All known
number,
cultures have language, but by no means all
human
exact quantication in the form of number.
have
history and th human and
lswhr—in
sins—that non-Wstrn ulturs and
natural
is a urious and hallnging
Mathmatis
in th widr movmnt for duational
as
and dolonizing duation. Enrgizd
quity
hav arisn in at last two aras. On
dats
how th history of mathmatis is told and
is
Th sond takls th prsistnt lif
taught.
mathmatis is nutral from th point of
that
lass and gndr. This has n th sit of
ra,
dat and ontrovrsy, suh as th
signifiant
movmnt in lat 2017.
#IStandWithRohll
11
for strong onlusions.
many dots ar on a pag.
ounting whn w ould nam numrs?
(Núñez quoted in Ball 2017)
(Ball 2017)
II.4 Diversity and many mathematics
intlltual traditions lag hind.
(Klin 1985).
334