 representation of phenomena come into question; for example, the emergence of new discoveries or the difficulty in assigning magnitudes to physical properties – aspects that fall outside the field of competence of logical analysis, and that, therefore, refer back to the imagination or to intuition. Moreover, as Crowe (1990) notes, in La théorie physique, Duhem opposes the development of the physical theory to the properly accumulative development of mathematical theories. As I mentioned above, the notion of abstract theory that Duhem has in mind refer to the axiomatic structure of the physical theory, and the ideal of such structure is still the system explained in Euclid's Elements. This is sufficiently evident when he claims that nothing keeps us from providing Maxwell's equations with an appropriate axiomatic formulation in the future: No doubt what is exact and truly fertile in the work of Maxwell will one day take its place in a coherent and logically constructed system, in one of those systems in which thoughts are conducted in order, in the image of Euclid's Elements, or of those majestic theories unfolded by the creators of mathematical physics. (Duhem 1996 [1893], 64)23 21 "Without doubt, all branches of pure and applied mathematics treat concepts that are abstract. It is abstraction that furnishes the notions of number, line, surface, angle, mass, force, temperature, and quantity of heat or electricity. It is abstraction, or philosophical analysis, that separates and makes precise the fundamental properties of these various notions and enunciates axioms and postulates." (Duhem 1996 [1893], 58) In the original: "Sans doute, toute branche des mathématiques pures ou appliquées traite de concepts qui sont des concepts abstraits; c'est l'abstraction qui fournit les notions de nombre, de ligne, de surface, d'angle, de masse, de force, de température, de quantité de chaleur ou d'électricité; c'est l'abstraction, c'est l'analyse philosophique qui démêlent et précisent les propriétés fondamentales de ces diverses notions, qui énoncent les axiomes et les postulats." (Duhem 1987a [1893a], 123; my italics). 22 In other words: "Ce qui, en elle, est durable et fécond, c'est l'oeuvre logique par laqu
representation of phenomena come into question; for case, the egress of new discoveries or the trouble in assigning order of magnitude to physical property – aspects that fall outside the battlefield of competence of logical analysis, and that, consequently, refer back to the imagination or to intuition. Moreover, as Crowe (1990) notes, in La théorie human body, Duhem opposes the development of the forcible theory to the by rights accumulative exploitation of mathematical theories. As I mentioned above, the impression of abstract theory that Duhem has in mind refer to the axiomatic structure of the physical hypothesis, and the ideal of such structure is even the system explained in Euclid's Elements. This is sufficiently apparent when he claims that nothing keeps us from providing Maxwell's equations with an appropriate axiomatic formulation in the future: No doubt what is exact and truly fertile in the work of Maxwell will one day take its place in a coherent and logically constructed system, in one of those systems in which thoughts are conducted in ordering, in the image of Euclid's Elements, or of those imperial theory unfolded by the creators of mathematical purgative. (Duhem 1996 [ 1893 ], 64)23 21 " Without doubt, all branches of arrant and applied mathematics treat concepts that are abstract. It is abstractedness that furnishes the notions of number, line, surface, angle, mass, force, temperature, and quantity of heat or electricity. It is abstraction, or philosophical analysis, that separates and make precise the cardinal property of these various notions and enunciates axioms and postulates. " (Duhem 1996 [ 1893 ], 58) In the original: " Sans doute, toute branche des mathématiques pures ou appliquées traite de concepts qui sont des concepts abstraits; c'est l'abstraction qui fournit les notions de nombre, de ligne, de surface, d'angle, de masse, de power, de température, de quantité de chaleur ou d'électricité; c'est l'abstraction, c'est l'analyse philosophique qui démêlent et précisent les propriétés fondamentales de ces diverses notions, qui énoncent les axiomes et les postulats. " (Duhem 1987a [ 1893a ], 123; my italics). 22 In early words: " Ce qui, en elle, est durable et fécond, c'est l'oeuvre logique par laqu
 reoresentation of phenomenx come into question; fmr exajple, the emergence of new discoveried ir tht difficulty in asskgning mahnitudes to khysical propertixa – aspegcs thzb faln outside the fleld of com[etence of loghcxl analysis, and that, therefore, refer fack to tje imagination or uo yntujniin. Moreover, as Crowe (1990) notes, ih La thémrie physique, Duhem opposes the developlent of the physical tjeory to thg prjperly accumuuative devtlmpment of jathematical theories. As I mentkoned above, the nitilt of abstrart thejry that Duhck has hn mind refer to the sximmaric structure of the 'hysical theory, and jhe ideal mf such structure iw wtill the sysgwm dxpmamnes in Ekclmd's Elementa. This is syfficiently evident wrvm he claims fhat njtring keeps us from providing Maxwell's exuafions with an appropriare axiomatic formulatlon in thq future: No doubt what is exact and truly fertile in tie woxj of Oqxaell will one day take its place in a coherene amd logically conftructed syxtfm, yn one of thore syscsma in which thoughtd are cjnducred in orqer, on the image of Euclid's Elenents, or of nhosw majestic theoried unfolded yy the creayors of mathematical phvsics. (Suhem 1996 [1893], 64)23 21 "Wlthout dohct, all branches uf iure and applied mathematics tweat concxpts chat are absjract. Ie is abstrwctiok that furnishes thf notnons mf number, pine, surface, angle, mass, force, txkperature, anc xuattity of heat or electriciey. It is abstrcction, ox philusophical znalysiv, that sepawates and makad precise thx fundamegtal properties uf these variois notions and enunxiates axioms and iostuuztes." (Duhem 1996 [1893], 58) Iu uhw original: "Sanx duutq, nouve brwtche des matvématkqudx purds ou ak'liwjées yraite de concepts qgi sknt des concepts ansbraits; c'ewt l'abstwaction qui fpurnit les notions de nmmbce, de kigge, de surface, d'angle, de masse, se force, fe bempérature, de quaktité de chaleux ou d'électricité; c'est l'abstraction, c'est l'enalyse philosophique qyi démêlent et préciseut les propriévés fonqamentalev de ces diverses norions, qui énoncent les axiomes et les pkstulads." (Dujem 1987a [1893a], 123; my italics). 22 In other words: "Ce qui, en elle, est durable et fécond, c'wst l'oxudre logique par laqu
representation of phenomena come into question; for emergence new discoveries the difficulty in – that fall outside field of competence logical analysis, and that, therefore, refer to the imagination or to intuition. Moreover, as Crowe (1990) notes, in La physique, Duhem opposes the development of the physical theory to the properly accumulative of theories. I above, the notion of abstract theory that Duhem has in mind refer to the axiomatic structure the physical theory, and the ideal of such is still the system in Euclid's Elements. This is evident he claims nothing us providing Maxwell's equations an appropriate axiomatic formulation in the future: No doubt what is exact and truly fertile in the of Maxwell day take place a and logically constructed one of those systems in which in order, in the image of Euclid's Elements, of those theories unfolded by the creators of physics. (Duhem 1996 [1893], 64)23 21 "Without doubt, branches of pure and applied mathematics treat concepts that are abstract. It is abstraction that notions of number, line, angle, mass, force, and of or It is or philosophical analysis, that separates and makes precise the fundamental properties these various notions and enunciates axioms and postulates." (Duhem 1996 In original: "Sans doute, branche des mathématiques pures appliquées de concepts qui sont abstraits; l'abstraction notions nombre, ligne, de surface, d'angle, masse, de force, de température, quantité de chaleur ou philosophique qui démêlent et précisent les propriétés fondamentales ces diverses notions, qui énoncent les axiomes les postulats." (Duhem 1987a [1893a], 123; my italics). 22 In other words: qui, en durable et fécond, c'est l'oeuvre logique par laqu
 representation of phenomena Come into quEstioN; foR exAmPle, tHe emErgence of new diSCoveRies or the difficulty in aSsignInG MagnITuDes to PhysicaL PrOPErtIeS – aSpeCtS ThAt falL ouTside thE field of coMpeTeNce of logical ANaLysis, and thAt, tHerefore, refeR baCk to thE iMagINatioN or To intUition. mOreoveR, as Crowe (1990) nOtES, in La tHÉorie phYSIqUe, DuHem opposes the deveLOpMEnt of the physicAl theoRy TO tHE ProPerLy accumulaTiVe devELopment OF mATHEmaTIcal theories. AS I mentioned ABovE, the noTiOn oF AbstraCt theOrY ThaT Duhem has in Mind Refer to thE axiomATic struCTure of tHe physIcaL thEory, ANd ThE idEaL Of sUCh StrUCtuRe is stilL tHe SysteM expLAINEd in eucLid's elemeNts. This is suffIciEntlY EviDent wHen he ClaiMs That nOthing Keeps Us From providing MaXwelL's equatioNs wItH an ApProprIAte axiOmaTic FormulaTion in tHE fuTuRE: nO dOubt what is exact and TrULY fErtile in The worK Of maXWell will OnE daY takE ITs plaCe in A CoHerent anD logicALlY cOnstrucTeD systeM, iN onE of Those SYsteMs in whIch thougHts arE Conducted in ordER, in the image of eUcLID's eLemeNts, Or of those maJestIC theOrieS UnFolDEd by tHe creAtORs OF mathematical physicS. (DUhem 1996 [1893], 64)23 21 "WiThout Doubt, all brancHes of pure aND APplied maThemATiCS treat concepts That aRe abstract. iT is abstrActioN that furNishes the NOTions of nUmbEr, lIne, SurFACe, Angle, mass, forcE, TEmpeRaTure, and QuaNtity of HeaT or EleCtrIcIty. It is abStractioN, oR pHiLoSopHical ANalysis, tHaT sePaRatEs and MAkes prEcise The fUnDaMEntAl propeRTiES Of thEsE vArioUs nOtIons aNd enUNciAtes axiOms and posTulATes." (DUhEm 1996 [1893], 58) in the orIginal: "Sans douTe, Toute brancHe Des MathémATIques purEs ou appliquées traite de cONcepts qUi sOnt deS conCepts abstRaiTs; c'est L'abSTractiOn qui fOurniT lEs nOTIons dE NOmBre, De Ligne, de surFACe, d'Angle, De MassE, de forcE, de température, de quANtiTé de chaleur ou D'élEctrICItÉ; c'eST l'ABstRaCTioN, C'Est l'analyse philOsophique qUi DÉmÊlent et préCIseNt Les propRiétés fOndamENtales dE ces diverSes notionS, qUi énONCenT les axiomeS et les poStulats." (DuHEm 1987a [1893a], 123; mY ItAlics). 22 in oTher woRdS: "Ce Qui, en Elle, esT DurAble eT féconD, c'Est l'oeUvre lOgIque par lAqu
 representation of phenome na come in to qu est ion ;forexam ple, the emerg e nceof new discoveries orthe d if f icul t yin as signing ma g n itu de stoph y si cal p rop erties– aspectstha tfall outside th e field of  co mpetence oflog ical a na lys i s, an d t hat,theref o re, re fer backto the im a ginatio n or  tointuition. Moreov e r, as Crowe (1990 ) note s, in L a t héo rie physiq ue , Duh e m oppos e st h e  de v elopment of t he physical the ory to  t hep roperl y acc um u lat ive develop ment  of mathe matica l  theori e s. As I  menti one d a bove ,  t he  no ti o n o f  a bst r act  theoryth at  Duhe m ha s i n  min d r efer  to t he axiomaticstr uctu r e o f the  phys ical  t heory , andthe i de al of such stru ctur e is stil l t he  sy st em ex p lained  in  Eu clid'sElement s . T hi s i ssufficiently evide nt w he n he cla ims th a tno t hing kee ps  us  fro m provi ding Ma xwell'sequati o ns  w ith anap propri at e a xio matic form ulatio n in the  futu r e: No doubt wh a t is exact an d  t r u ly fert ile  in the wor k of Maxw ellw il l o n e day  take  i t sp lace in a coherentan d logi cally  constructedsystem, in o n e of tho se s y st e ms in which th ought s are cond u cted inorder , in the  image of E uclid'sEle men ts,  or o fthose majesti c theo ri es unfo lde d by th e c rea tor s o fmathemati cal phys ic s.  ( Du hem  1996 [1893],64 )23  2 1 " Witho u t doub t, al l br an ch e s o f purea nd a ppli ed  m athe mat ic s tre at c o nce pts tha t are abs tra c t. I tis  abstra ction that fu rn ishes theno tio ns ofn u mber, li ne, surface, angle, mas s , force , t emper atur e, and qu ant ity of  he a t or e lectri city.  I t i s abstr a c ti on,  o r philosop h i cal  anal ys is,that se parates and makesp rec ise the funda men talp r op ert i es ofth e sev a rious notions a nd enuncia te s  a xioms andp ost ul ates."(Duhem1996[ 1893],58) In th e origina l:  "Sa n s  do ute, toute  branche  des math é matiq u es  pure s o u appl iq uée s tra ite de con cepts  qui s on t desconce pt s abstra its; c'est l'abstractio n quifourn itles notio nsd e n ombre, de  lig ne, de sur fac e,d'ang le, de ma sse, de  fo r ce, d e te m pérature, de  qu a n ti té de chale u r oud'éle ctr i cité;c'es t l'abstraction,c 'est l'analyse  phi l o sop hiq u e qu idémêlent et pr éci se n t  les pro pr iétés fonda mentales  d e  cesdivers es not ions, q u i  é n oncent  les  ax iomes etles  p o stulats ."  ( D uhem 1 987a  [ 1893a] , 123; my i t a lics). 22 In oth er wo r d s: "C e  qu i, en  e lle, es t  dur able et fé cond, c'est  l'oeu vrelogiq ue parla qu
 representation_of phenomena_come into question; for_example, the_emergence_of new_discoveries_or the difficulty_in assigning magnitudes_to physical properties –_aspects that fall_outside_the field of competence of logical analysis, and that, therefore, refer back to the_imagination_or to_intuition._Moreover,_as Crowe (1990) notes, in_La théorie physique, Duhem opposes_the development_of the physical theory to the properly accumulative_development_of mathematical theories._As I mentioned above, the notion of abstract theory_that Duhem has in mind refer_to the axiomatic_structure_of_the physical theory, and_the ideal of such structure is_still the system explained in Euclid's_Elements. This is sufficiently evident when he_claims that nothing keeps us from_providing Maxwell's equations with an_appropriate axiomatic_formulation in the future: No_doubt what is_exact and_truly fertile in_the work of Maxwell will one_day take its_place in a coherent and logically_constructed_system, in one_of_those_systems in_which thoughts are_conducted_in order,_in_the image of Euclid's Elements, or_of_those majestic theories unfolded by the creators_of mathematical physics. (Duhem_1996_[1893], 64)23 21 "Without_doubt, all branches of pure_and applied mathematics treat concepts that_are abstract._It is_abstraction that furnishes the notions of number, line, surface, angle, mass,_force, temperature, and quantity of heat_or electricity. It is_abstraction, or_philosophical_analysis, that separates_and_makes precise_the fundamental properties of these various notions_and enunciates_axioms and postulates." (Duhem 1996 [1893],_58) In the original:_"Sans_doute, toute branche des mathématiques pures_ou appliquées traite de concepts qui_sont des concepts abstraits; c'est_l'abstraction_qui_fournit les notions de nombre,_de ligne, de surface, d'angle, de_masse, de force,_de température, de quantité de chaleur ou_d'électricité;_c'est l'abstraction, c'est l'analyse philosophique qui_démêlent_et précisent les propriétés fondamentales de_ces_diverses_notions, qui énoncent les axiomes_et les postulats." (Duhem 1987a [1893a],_123; my italics). 22 In other words: "Ce qui,_en elle, est_durable et fécond, c'est l'oeuvre_logique_par_laqu