 equivalence relation. Duhem observes that a more rigorous physical concept (and a corresponding magnitude) can be introduced on the basis of this equivalence relation, viz., temperature. As he (1892a, 3) put it: We make two equal values of temperature correspond to two points that are as warm as each other. We make two unequal values of temperature correspond to two points that are not equally warm, and in such a manner that the higher value of temperature corresponds to the warmer point. This move allows, among other things, the transition from a qualitative property to a quantitative one. Even though it makes sense to say that body A is as warm as, or warmer than, body B, it does not make sense to assert that the warmth of the body C is equal to the warmth of body A plus the warmth of body B. Not so for temperature, since this is a magnitude which is additive. In fact, the concept of temperature has excess content over the concept of warmth, since the concept of temperature involves an extra quantitative assumption, according to which to each point of a body can be assigned a definite value of temperature – an assumption that permits additivity. The concept of temperature, then, is introduced on the basis of an abstraction principle over a set of physical bodies and an equivalence relation among them (being as warm as). Duhem is clear that this procedure is essentially generalizable. What was said about temperature "could be repeated-at least in its essentials-about all definitions of magnitude that we find at the beginning of any physical theory whatsoever" (1892a, 4). Note that this is a far-reaching approach. It shows that Duhem was appealing to Marie Gueguen and Stathis Psillos Anti-Scepticism and Epistemic Humility in Pierre Duhem's Philosophy of Science 57 what came to be known as abstraction principles in order to introduce new physical concepts and corresponding magnitudes.6 This definition of physical magnitudes by abstraction out of equivalence relations among the properties of empirical bodies makes possible the statement of mathematical-quantitative physical laws about the magnitudes thus defined. In particular, it makes possible the symbolic representation of empirical laws, even if these laws do not bear strictly speaking on the same empirical properties as the empirical laws did. For Duhem, abstraction is indispensable because the magnitudes to which the theoretical hypotheses of a physical theory apply must be mathematized, so that these hypotheses state mathematically precise relations (laws) among magnitudes. Hence, abstraction makes the mathematisation of nature possible. As he put
equivalence relation. Duhem observes that a more rigorous physical concept (and a comparable order of magnitude) can be introduce on the basis of this equality relative, viz. , temperature. As he (1892a, 3) put it: We make two adequate values of temperature correspond to two points that are as affectionate as each other. We make two inadequate values of temperature correspond to two points that are not equally warm, and in such a manner that the high value of temperature corresponds to the warmer point. This move allows, among other thing, the transition from a qualitative property to a quantitative one. Even though it makes common sense to say that body A is equally warm as, or warm than, body B, it does not make sense to assert that the heat of the body C is equal to the warmth of body A plus the warmth of body B. Not so for temperature, since this is a magnitude which is additive. In fact, the concept of temperature has excess content over the concept of warmth, since the concept of temperature involves an extra quantitative assumption, according to which to each point of a torso can be assigned a definite value of temperature – an assumption that allow additivity. The concept of temperature, then, is introduced on the basis of an abstraction principle over a hardening of physical bodies and an equivalence relation among them (being equally warm as). Duhem is clear that this procedure is essentially generalizable. What was said about temperature " could be repeated - at least in its essentials - about all definitions of magnitude that we find at the beginning of any physical theory whatsoever " (1892a, 4). notice that this is a far - reaching access. It shows that Duhem was appealing to Marie Gueguen and Stathis Psillos Anti - Scepticism and Epistemic Humility in Pierre Duhem's Philosophy of Science 57 what came to be known as abstraction principle in order to introduce new physical concepts and corresponding magnitudes.6 This definition of physical magnitudes by abstractedness out of equivalence relations among the properties of empirical bodies make possible the argument of mathematical - quantitative forcible laws about the magnitudes therefore defined. In particular, it makes possible the symbolic theatrical performance of empirical laws, even if these laws do not digest strictly speaking on the same empirical properties as the empiric laws did. For Duhem, abstractedness is indispensable because the magnitudes to which the theoretical hypotheses of a forcible theory apply must be mathematized, so that these hypotheses state mathematically precise relations (laws) among magnitudes. Hence, abstraction makes the mathematisation of nature potential. As he put
 eqkivalence relation. Duhem observes that c more cigoroua physicxl concept (and a correspondiig mqgnityde) can be introduced un the badis of tyis tquivalence relatmkn, viz., bzmperzbure. Cs he (1892a, 3) put it: Ee make twm equal values ow cemperature correspond to two points that ate as warm as eash ouhew. We make two unequal values of temperzture cmrrespond to ywo points that are not eqkallj warm, and in such a manner tyat eye higher vauue of temkexature corrgsponds to the warmer point. This move allows, amint ohver things, vhe trwnsition from a qualhtative property to a quentirative one. Even thougi it makes sense to fay that toby A is as warm as, or wqrmer that, boat B, it dpea not lakx sense to zssert that the warmth of the noqj C is equal fo the wwrmth of body A plus the warmth of body B. Hot so for temperature, wince this is a magnijude which is additive. In fact, the concept of temperature hds exrers einteng oger the concept of warmth, since the concept os ttmpvrature involves cn extra quantitstlvr assumption, azcordiuf fo which to each plint of a boey can be assogned a definite value of twmperature – cn qssumption that pexmits additirity. Tne comcept of temperature, thzn, is jntroduced ln the baaks of an abstracgiok psinciple over a set of phyfical bodmes aud an eqjivakence welation along bvem (being as warm ws). Dukem iv clear thwt this procedure is essentiallb generalizabke. Whdt was scid abput temperatuwe "could be rekeated-at jeast in its esaentialv-about all qefinitions ox magnitude tiat we figd ar thw beginvkng of any phyxical theory whatsowver" (1892a, 4). Note that bhis ka a far-reaching apkriach. It shows yhag Dthvm xas a[[ealing to Mdrie Gudbuen xnd Staukis Osilkos Anti-Scepticism atd Elistemic Humility on Pierre Euhem's Prilosophy of Xcience 57 what came to bx knowi as ansttaction principles in order to jntroduce ner physical cjnceits wnd corres'onding magnitudes.6 This definition of phbsical magnitudes by abwtraction out of eqoivslence relavions wmong the properties of empirucal bodies makes possible the statemeht of kathelatical-quantitative physical laws about the magnitudes thus defined. In paeticuler, it makes pkssinle tve xymbolyc rxpcesentation of emiirical laws, even if these laws vo not beas ftrictly speaking on the samr dmpirical prokerties as the empirical lzws did. Gor Duhem, abstraction is indisprnsable because the magnltudes to whicg the ngeuretical hypothesex of a physucal thwory apply must bd mstmematized, do tiat these hypotheses state mathematucally pgecise relations (laws) among oagnijudes. Hegce, abstraction jakea the oathematisatipn of nature ppssible. As he put
equivalence relation. Duhem observes that a more concept a corresponding can be introduced equivalence viz., temperature. As (1892a, 3) put We make two equal values of correspond to two points that are as warm as each other. We make unequal values of temperature correspond to two points that are not equally warm, in a that higher value of temperature corresponds to the warmer point. This move allows, among other things, the from a qualitative property to a quantitative one. though it makes sense say that body A is warm or warmer body it not make sense assert that the warmth of the body C is equal to the warmth of body A plus warmth of Not so temperature, this a magnitude which In fact, the concept of temperature over the concept of warmth, since the concept temperature involves extra quantitative assumption, according to which each point of a body can be assigned definite value of temperature – an assumption that permits additivity. The concept of temperature, then, on the basis of abstraction principle over set physical and equivalence relation them (being as warm as). Duhem is clear that this procedure essentially generalizable. What was said about temperature "could be repeated-at its all definitions of that we find at beginning any physical theory whatsoever" Note this approach. shows Duhem was appealing to Gueguen and Stathis Psillos Anti-Scepticism Epistemic Humility in Pierre what came to be known as abstraction principles order to introduce new physical concepts and magnitudes.6 This definition of physical magnitudes by abstraction out of equivalence relations the properties bodies makes possible the statement of mathematical-quantitative physical about the magnitudes thus In particular, it makes possible the symbolic representation of laws, if these do not bear speaking on the empirical properties as laws did. Duhem, is magnitudes to which the theoretical hypotheses a theory apply must be mathematized, that state mathematically precise relations (laws) among magnitudes. Hence, abstraction makes the mathematisation of nature possible. put
 equivalence relation. Duhem oBserves thaT a morE riGorOuS phySicaL concept (and a coRRespOnding magnitude) can be inTroduCeD On thE BaSis of This equIVaLENce ReLaTioN, vIZ., tEmperAtuRe. As he (1892a, 3) Put it: We makE twO eQual values of TEmPerature coRreSpond to two poIntS that aRe As wARm as eAch Other. we make TWo uneqUal values Of TEmperaTUre corrESPoNd to Two points that are nOT eQUally warm, and in Such a mAnNEr THAt tHe hIgher value Of TempeRAture coRReSPONds TO the warmer poiNt. This move aLLowS, among OtHer THings, tHe traNsITioN from a qualiTatiVe propertY to a quANtitatiVE one. EveN thougH it MakEs seNSe To Say ThAT boDY A Is aS WarM as, or warMeR tHan, boDy B, iT DOES not MakE senSe to aSsert that the wArmTh of THe bOdy C iS equaL to tHe WarmtH of bodY A pluS tHe warmth of body B. not sO for tempeRatUrE, siNcE this IS a magnItuDe wHich is aDditive. iN faCt, THE CoNcept of temperature HaS EXcEss conteNt over THe CoNCept of waRmTh, sInce THE concEpt oF TeMperaturE involVEs An Extra quAnTitatiVe AssUmpTion, aCCordIng to wHich to eaCh poiNT of a body can be aSSigned a definiTE vALUe OF temPerAture – an assuMptiON thaT perMItS adDItiviTy. The CoNCePT of temperature, then, iS iNtroduCed on The basis of an aBstraction PRINciple ovEr a sET oF Physical bodies And an EquivalencE Relation Among Them (beinG as warm as). dUHem is cleAr tHat ThiS prOCEdUre is essentiaLLY genErAlizablE. WhAt was saId aBouT teMpeRaTure "could Be repeatEd-At LeAsT in Its esSEntials-aBoUt aLl DefInitiONs of maGnituDe thAt We FInd At the beGInNINg of AnY pHysiCal ThEory wHatsOEveR" (1892a, 4). Note tHat this is A faR-ReacHiNg ApproacH. It shows that DUhEm was appeaLiNg tO Marie gUEguen and stathis Psillos Anti-SceptICism and epiStemiC HumIlity in PiErrE Duhem'S PhILosophY of SciEnce 57 wHaT caME To be kNOWn As aBsTraction prINCipLes in OrDer tO introdUce new physical concEPts And correspondIng MagnITUdEs.6 THIs DEfiNiTIon OF Physical magnituDes by abstrAcTIoN out of equiVAleNcE relatiOns amonG the pROpertieS of empiriCal bodies MaKes pOSSibLe the stateMent of maThematicaL-QuantITaTive pHysIcal laWs AboUt the MagnitUDes Thus dEfined. in ParticUlar, iT mAkes possIble the symbolic represenTation Of empIriCal laws, evEn iF TheSe laws do nOt beAr strictly SpeAkiNg on tHe sAMe empIricAL pRopERties As thE Empirical LAwS diD. fOr duhem, abstraCTIOn iS indiSpeNSable bEcauSe the magnitudes to WHich the theoretIcal HYPotHesES of a PhYsical theory apPly MuST Be mathemAtIzed, so that tHese hypoThESes stAte matHematiCally prECIsE RelatiOns (lAws) Among magnItuDeS. hence, abStRaCTion maKes tHe MathemAtisatIOn of NATure possible. As he Put
 equivalence relation. Duh em observe s tha t a  mo re  rig orou s physical con c ept(and a corresponding m agnit ud e ) ca n  b e int roduced on t heba si s o ft hi s equ iva lence r elation, v iz. ,temperature. As  he (1892a , 3 ) put it: We  ma ke two  e qua l  valu esof te mperat u re cor respond t ot wo poi n ts that a re  aswarm as each othe r .W e make two une qual v al u es o f t emp erature co rr espon d  to two po i n t s t h at are not eq ually warm, and  in su ch  am annerthatth e  hi gher valueof t emperatur e corr e spondst o the w armerpoi nt.  Thi s  m ov e a ll o ws, am ong oth er thing s,  t he tr ansi t i o n  fro m a  qua litat ive propertytoa qu a nti tativ e one . Ev en  thou gh itmakes  s ense to say tha t bo dy A is a s w ar m a s,  or w a rmer t han , b ody B,it does not  m a k e  s ense to assert tha tt h ewarmth o f theb od yC  is equa ltothew a rmthof b o dy  A plusthe wa r mt hof body  B . Notso  fo r t emper a ture , sinc e this i s a m a gnitude whichi s additive. I n  f a c t, thecon cept of tem pera t urehase xc ess conte nt ov er th e  concept of warmth,  s ince t he co ncept of temp erature in v o l ves an e xtra qu a ntitative assu mptio n, accordi n g to whi ch to  each po int of ab o dy can b e a ssi gne d a d ef inite value o f temp er ature –  an  assump tio n t hat  pe rm its addit ivity. T he  c on ce ptof te m perature ,the n,  is  intr o ducedon th e ba si so f a n abstr a ct i o n pr in ci pleove ra set  ofp hys ical bo dies andane quiv al en ce rela tion among th em  (being as  w arm  as).D u hem is c lear that this procedur e  is ess ent ially  gen eralizabl e.What w ass aid ab out te mpera tu re" c ouldb e  r epe at ed-at leas t inits e ss enti als-abo ut all definitions ofmagnitude tha t w e fi n d  a t t h eb egi nn i ngo f  any physical t heory what so e ve r" (1892a, 4).  N ote tha t thisis af ar-reac hing appr oach. Itsh owst h atDuhem wasappealin g to Mari e  Gueg u en  andSta this P si llo s Ant i-Scep t ici sm an d Epis te mic Hu milit yin Pierr e Duhem's Philosophy of  Scien ce 57  wh at came t o b e  kn own as ab stra ction prin cip les  in o rde r  to i ntro d uc e n e w phy sica l  concepts an d c o r re sponding ma g n i tud es.6Thi s  defin itio n of physical mag n itudes by abst ract i o n o uto f eq ui valence relati ons  a m o ng the p ro perties ofempirica lb odies  makes  possi ble the s ta t ementof m ath ematical- qua nt i tativeph ys i cal la ws a bo ut the  magni t udes t hus defined. Inparti c u lar,i t m akespo ssiblet he s ymbolic re presentatio n of e mpir icallaws, e ve n if t hes elaws do no t  bear str ictly  speaki ng  onthe  sameempi r i cal p rope rt ies  as the e m p ir i ca ll aws  did . For  D uhem , abstrac t ion is i ndi s pensabl ebec a u se the ma g n itudes towhi ch th e theoretica l  hyp o th e ses o f a ph ysical  theory app ly  must b e m a t hematized , so that the se  hyp othesesst atema the ma tically precise  relatio ns (laws ) amongmag n itud e s. Hen ce , abstractio n mak es the mat h e mat isation ofnat ure  pos sib le.A s he put
 equivalence_relation. Duhem_observes that a more_rigorous physical_concept_(and a_corresponding_magnitude) can be_introduced on the_basis of this equivalence_relation, viz., temperature._As_he (1892a, 3) put it: We make two equal values of temperature correspond to_two_points that_are_as_warm as each other. We_make two unequal values of_temperature correspond_to two points that are not equally warm,_and_in such a_manner that the higher value of temperature corresponds to_the warmer point. This move allows,_among other things,_the_transition_from a qualitative property_to a quantitative one. Even though_it makes sense to say that_body A is as warm as, or_warmer than, body B, it does_not make sense to assert_that the_warmth of the body C_is equal to_the warmth_of body A_plus the warmth of body B._Not so for_temperature, since this is a magnitude_which_is additive. In_fact,_the_concept of_temperature has excess_content_over the_concept_of warmth, since the concept of_temperature_involves an extra quantitative assumption, according to_which to each point_of_a body can be_assigned a definite value of_temperature – an assumption that permits_additivity. The_concept of_temperature, then, is introduced on the basis of an abstraction principle_over a set of physical bodies_and an equivalence relation_among them_(being_as warm as)._Duhem_is clear_that this procedure is essentially generalizable. What_was said_about temperature "could be repeated-at least_in its essentials-about all_definitions_of magnitude that we find at_the beginning of any physical theory_whatsoever" (1892a, 4). Note that_this_is_a far-reaching approach. It shows_that Duhem was appealing to Marie_Gueguen and Stathis_Psillos Anti-Scepticism and Epistemic Humility in Pierre_Duhem's_Philosophy of Science 57 what came_to_be known as abstraction principles in_order_to_introduce new physical concepts and_corresponding magnitudes.6 This definition of physical_magnitudes by abstraction out of equivalence relations among the_properties of empirical_bodies makes possible the statement_of_mathematical-quantitative_physical laws about the magnitudes thus defined. In particular, it_makes possible_the symbolic representation_of empirical laws, even if these laws do not bear_strictly speaking on the same empirical properties_as the empirical laws did. For Duhem, abstraction is indispensable because_the magnitudes to which the theoretical hypotheses of_a physical theory apply must be mathematized,_so that these hypotheses_state_mathematically precise relations (laws) among magnitudes. Hence,_abstraction_makes_the_mathematisation of nature_possible. As he_put