 initial approach: we begin with some things (numbers, space-time points, whatever) and then start considering sets of them, and then sets of what we've got so far, and so on up... And only after having set up an axiomatic framework for a theory with individuals, Potter considers what happens if you now add an Axiom of Purity (as he puts it) to the effect that there are, after all, no urelemente -- the pure sets with no individuals in their transitive closure are the only sets. He writes:

The axiom of purity, or something equivalent to it, is assumed in almost
  every modern treatment of set theory in the literature. The main reason for
  this is that, as was discovered fairly early, it is not necessary to assume the
  existence of individuals in order that set theory should act as a foundation for
  mathematics, while if we rule them out from the outset, we can simplify the
  theory, getting rid of one primitive and tidying up the development considerably. If the only objective is to give mathematicians a theory which can act as
  a foundation, it is inevitable that they will choose the one that seems simplest
  to them.
Indeed individuals would probably have made an exit from set theory
  earlier than they did if it had not been for an accident in the progress of
  work in the metatheory. In 1922 Fraenkel discovered a method for showing
  the independence of the axiom of choice from theories such as ZU [Zeremlo set theory with urelemente] that allow
  individuals. This method was refined (Lindenbaum and Mostowski 1938) and
  then exploited by others (e.g. Mendelson 1956; Mostowski 1945) to prove the
  independence from such theories of various other set-theoretic claims. It was
  not until 1963 that Cohen showed how to convert this into a method that
  works for theories like Z which ban individuals. In the intervening period
  there was therefore a reason for set theorists (who tend, after all, to be the
  people who write set theory books) to regard permitting individuals as worth
  the extra effort. After 1963, however, not even set theorists had any use for
  individuals. Worse, there are proofs in set theory that do not work if we have
  to allow for them. So it
initial approach: we begin with some things (numbers, quad - meter points, whatever) and then start considering set of them, and then sets of what we've got indeed far, and indeed on up... And only after having sic up an axiomatic framework for a theory with individual, Potter considers what happens if you immediately lend an Axiom of Purity (as he puts it) to the effect that there are, after all, no urelemente -- the arrant sets with no individuals in their transitive closure are the alone sets. He writes: 

 The axiom of purity, or something equivalent to it, is assume in almost 
   every modern treatment of set theory in the literature. The chief reason for 
   this is that, as was discovered fairly early, it is not necessary to assume the 
   existence of individuals in order that set theory should act as a foundation for 
   mathematics, while if we rule them out from the outset, we can simplify the 
   theory, getting rid of one primitive and tidying up the development well. If the lone objective is to grant mathematician a hypothesis which can act as 
   a foundation, it is inevitable that they will choose the one that seems simplest 
   to them. 
 Indeed individuals would probably have made an exit from hardened theory 
   earlier than they did if it had not been for an accident in the progress of 
   work in the metatheory. In 1922 Fraenkel unwrap a method for showing 
   the independence of the axiom of choice from theory such as ZU [ Zeremlo set hypothesis with urelemente ] that let 
   individuals. This method was refined (Lindenbaum and Mostowski 1938) and 
   then exploited by others (e.g. Mendelson 1956; Mostowski 1945) to prove the 
   independence from such theories of diverse other set - theoretic claims. It was 
   not until 1963 that Cohen show how to convert this into a method acting that 
   works for theories like Z which ban individuals. In the intervene period 
   there cost therefore a cause for set theorists (who tend, after all, to be the 
   people who publish set hypothesis books) to regard permitting individuals as deserving 
   the extra effort. After 1963, however, not even set theorists have any use for 
   individuals. Worse, there are proofs in set hypothesis that do not work if we have 
   to allow for them. So it
 inltial approach: we begin dith some things (numbecs, spacs-time poknts, whatever) and then start cinsidtging sets of them, and then setd of whar we'te got so far, anv so on m'... And lnly efter having sej up an axiokatic frameworn wox a theory with individuals, Potter cjnsiderx ahat happens is yol gow zdd an Axiom of Purity (as he puts jt) to tie effect that yhere are, after all, no urepemejte -- the pure sets with no ineiviqyals in theif transitinz closure ate the only sets. He writes:

The axkom oy purity, or simehving equivaoent no it, is assumed in anmost
  rvery modern tveatmxnt if set theory in the niterature. The maig reason xox
  this is that, as waw eiscoeereg fakely eadlb, if is nlt iecessary tk assume thw
  existence of indovyeuals in orded that sqt theory should act as a foundation fog
  mzthematics, while if we eule them out from thg outset, wq can simplify the
  theory, getting rid of one prikitivx xnd tldyivt kp the development considerably. If the only ofnevtpve is to give mabhematicians a theprj erich can act xs
  a ykuhdation, it is inevltable jhat tyey will shooxe the one that seems simplwst
  to them.
Pndewd individuals woupd probably havg made an exit from set theorv
  earmier than tjey did ir it had not been fog an accidenu in the progress jf
  work mn thz metathdory. In 1922 Fwaenkel didcovevad a method for shlwing
  dhe indepejdence of the axiom of choice fcpm theories xuwh ds ZU [Zexemlo xet theory wieh urelemente] jhat alloc
  indkviduals. Tgis metiod was refiged (Lindenbauk and Mostowsni 1938) and
  theb exploited cy others (e.g. Mrndelson 1956; Mostowski 1945) to prove the
  invepevsence from such thtoeies of varioux oghew dev-theowatic claims. Ht wxs
  mot uvtil 1963 that Gohdn snowed how to convert thia into a method thst
  works dor theowies like Z wnich ban individuaps. In thx intetveging period
  there was therefode a reasln nor set theorysts (who tend, afcer all, to be the
  people who write set vheory books) to regard permitting individuclx as worth
  the qxtra effmrt. After 1963, however, nit even set theorlsts had any use for
  jndiviguals. Worse, there are proofs in set theory that do not work if we have
  to alliw for them. So it
initial approach: we begin with some things points, and then considering sets of what got so far, so on up... only after having set up an framework for a theory with individuals, Potter considers what happens if you now an Axiom of Purity (as he puts it) to the effect that there after no -- pure sets with no individuals in their transitive closure are the only sets. He writes: The of purity, or something equivalent to it, is in almost every modern of set theory in the The reason for is as discovered fairly early, is not necessary to assume the existence of individuals in order that set theory should act as foundation for if we them from outset, we can theory, getting rid of one primitive the development considerably. If the only objective is give mathematicians theory which can act as a it is inevitable that they will choose the that seems simplest to them. Indeed individuals would probably have made an exit from set than they did if had not been an in progress work in metatheory. In 1922 Fraenkel discovered a method for showing the independence the axiom of choice from theories such as ZU [Zeremlo with that allow individuals. method was refined (Lindenbaum Mostowski and then exploited by Mendelson Mostowski the from theories of various other claims. It was not until that Cohen showed how method that works for theories like Z which individuals. In the intervening period there was a reason for set theorists (who tend, after all, to be the who write books) to regard permitting individuals as worth the effort. After 1963, however, even set theorists had any use for individuals. Worse, are in set that do not if we have allow for them.
 initial approach: we begin witH some thingS (numbErs, SpaCe-Time PoinTs, whatever) and tHEn stArt considering sets of thEm, and ThEN setS Of What wE've got sO FaR, ANd sO oN uP... AnD oNLy After HavIng set uP an axiomatIc fRaMework for a thEOrY with indivIduAls, Potter conSidErs whaT hAppENs if yOu nOw add An AxioM Of PuriTy (as he putS iT) To the eFFect thaT THeRe arE, after all, no urelemENtE -- The pure sets witH no indIvIDuALS in TheIr transitiVe ClosuRE are the ONlY SETs. HE Writes:

The axioM of purity, or SOmeThing eQuIvaLEnt to iT, is asSuMEd iN almost
  everY modErn treatmEnt of sET theory IN the litEraturE. ThE maIn reASoN fOr
  tHiS Is tHAt, As wAS diScovered FaIrLy earLy, it IS NOT necEssAry tO assuMe the
  existencE of IndiVIduAls in Order That SeT theoRy shouLd act As A foundation for
  mAtheMatics, whiLe iF wE ruLe Them oUT from tHe oUtsEt, we can SimplifY The
  ThEORY, gEtting rid of one primItIVE aNd tidyinG up the DEvElOPment conSiDerAbly. iF The onLy obJEcTive is to Give maTHeMaTicians A tHeory wHiCh cAn aCt as
  a FOundAtion, iT is ineviTable THat they will choOSe the one that sEEmS SImPLest
  To tHem.
Indeed inDiviDUals WoulD PrObaBLy havE made An EXiT From set theory
  earlieR tHan theY did iF it had not been For an accidENT In the proGresS Of
  WOrk in the metathEory. IN 1922 Fraenkel dIScovered A methOd for shoWing
  the inDEPendence Of tHe aXioM of CHOiCe from theorieS SUch aS Zu [ZeremlO seT theory WitH urEleMenTe] That allow
  IndividuAlS. THiS mEthOd was REfined (LiNdEnbAuM anD MostOWski 1938) anD
  then ExplOiTeD By oThers (e.g. mEnDELson 1956; moStOwskI 1945) to PrOve thE
  indEPenDence frOm such theOriES of vArIoUs other Set-theoretic cLaIms. It was
  noT uNtiL 1963 that COHEn showed How to convert this into a meTHod that
  WorKs for TheoRies like Z WhiCh ban iNdiVIduals. in the iNtervEnIng PERiod
  tHERe Was ThErefore a reASOn fOr set ThEoriSts (who tEnd, after all, to be the
  PEopLe who write set TheOry bOOKs) To rEGaRD peRmITtiNG Individuals as woRth
  the extrA eFFoRt. After 1963, howEVer, NoT even seT theoriSts haD Any use fOr
  individUals. Worse, ThEre aRE ProOfs in set thEory that Do not work IF we haVE
  tO alloW foR them. SO iT
 initial approach: we begi n with som e thi ngs  (n um bers , sp ace-time point s , wh atever) and then start  cons id e ring se ts of  them,a nd t hen  s et s o fw ha t we' vegot sofar, and s o o nup... And on l yafter havi ngset up an ax iom atic f ra mew o rk fo r a  theo ry wit h  indiv iduals, P ot t er con s iders w h a thapp ens if you now ad d  a n  Axiom of Puri ty (as  h e  p u t s i t)to the eff ec t tha t  therea re , a fte r  all, no urel emente -- t h e p ure se ts  wi t h no i ndivi du a lsin their tr ansi tive clos ure ar e  the on l y sets.  He wr ite s:
The ax io m o fp uri t y,  or som ething e qu iv alent  toi t , is a ssu medin al most
  everymod ernt rea tment  of s et t he ory i n theliter at ure. The main r easo n for
  t his  i s t ha t, as was di sco ver ed fair ly earl y , i ti s no t necessary to ass um e th e
  exis tenceo fin d ividuals  i n o rder t hat s et t h eo ry shoul d acta safoundat io n for mat hem atics ,  whi le ifwe rulethemo ut from the ou t set, we can s i mp l i fy the  t heory, gett ingr id o f on e  p rim i tiveand t id y in g  up the development  c onside rably . If the only  objective i s  to give  mat h em a ticians a theo ry wh ich can ac t  as
  afound ation, i t is inev i t able tha t t hey  wi llc h oo se the one th a t  see ms  simple st  to th em. 
In dee d i nd ividualswould pr ob ab ly  h ave  made an exitfr omse t t heory   earl ier t hanth ey did  if ith ad n ot b ee nforanac ciden t in the  progre ss of
  w ork in t he  m etatheo ry. In 1922 F ra enkel disc ov ere d a me t h od for s howing
  the independen c e of th e a xiomof c hoice fro m t heorie s s u ch asZU [Ze remlo  s ett h eoryw i th  ur el emente] th a t  al low
 i ndiv iduals.  This method was r e fin ed (Lindenbau m a nd M o s to wsk i  1 9 38)  a n d
t hen exploited b y others ( e. g .Mendelson1 956 ;Mostows ki 1945 ) top rove th e
  indep endence f ro m su c h  th eories ofvariousother set - theor e ti c cla ims . It w as 
 not u ntil 1 9 63thatCohensh owed h ow to  c onvert t his into a method that  work s for  th eories li keZ  wh ich ban i ndiv iduals. In  th e i nterv eni n g per iod t her e  wasther e fore a re a so n f o r  s et theorist s ( who  tend , a f ter al l, t o be the
  people who write settheo r y  bo oks )  tore gard permittin g i nd i v iduals a sworth
  the  extra e ff o rt. A fter 1 963, h owever, n ot even s et t heo rists had  an yu se for in d ividua ls.Wo rse, t here a r e pr o o fs in set theory  that d o not wor k ifwe  have
to a llow for t hem. So it
 initial_approach: we_begin with some things_(numbers, space-time_points,_whatever) and_then_start considering sets_of them, and_then sets of what_we've got so_far,_and so on up... And only after having set up an axiomatic framework for_a_theory with_individuals,_Potter_considers what happens if you_now add an Axiom of_Purity (as_he puts it) to the effect that there_are,_after all, no_urelemente -- the pure sets with no individuals in_their transitive closure are the only_sets. He writes:

The_axiom_of_purity, or something equivalent_to it, is assumed in almost
_ every modern treatment of set_theory in the literature. The main reason_for
  this is that, as_was discovered fairly early, it_is not_necessary to assume the
 _existence of individuals_in order_that set theory_should act as a foundation for
_ mathematics, while_if we rule them out from_the_outset, we can_simplify_the
_ theory,_getting rid of_one_primitive and_tidying_up the development considerably. If the_only_objective is to give mathematicians a theory_which can act as
__a foundation, it is_inevitable that they will choose_the one that seems simplest
 _to them.
Indeed_individuals would_probably have made an exit from set theory
  earlier than_they did if it had not_been for an accident_in the_progress_of
  work_in_the metatheory._In 1922 Fraenkel discovered a method for_showing
 _the independence of the axiom of_choice from theories such_as_ZU [Zeremlo set theory with urelemente]_that allow
  individuals. This method_was refined (Lindenbaum and Mostowski_1938)_and
_ then exploited by others_(e.g. Mendelson 1956; Mostowski 1945) to_prove the
 _independence from such theories of various other_set-theoretic_claims. It was
  not until_1963_that Cohen showed how to convert_this_into_a method that
  works_for theories like Z which ban_individuals. In the intervening period
  there was therefore_a reason for_set theorists (who tend, after_all,_to_be the
  people who write set theory books) to_regard permitting_individuals as worth
_ the extra effort. After 1963, however, not even set_theorists had any use for
  individuals._Worse, there are proofs in set theory that do not work_if we have
  to allow for them._So it