ão Príncipe – Poincaré and Duhem: Resonances in their First Epistemological Reflections 146 compel him to think, and he ends by understanding what was often a little artificial in the theoretical ensembles he once admired. (Poincaré 1890, XVI) The epistemological value of the theorem is emphasized by Poincaré, who sees in it an explanation of the indecision between rival theories present in historical cases: The preceding is confirmed by the history of all the parts of physics; in optics, for example, Fresnel believes the vibration perpendicular to the plane of polarization; Neumann regards it as parallel to this plan. We have long sought an "experimentum crucis", which enabled us to decide between these two theories, and we could not find it. All these facts are easily explained by the properties of the Lagrange equations which I have just recalled. (Poincaré 1890, XIV)12 The explanations that postulate unobservable quantities are therefore a cause of underdetermination of theories. Also, the theorem highlights the abstract dynamics, favored by some of the British physicists. Among the old theoretical ensembles we find the molecular physics of Laplace. Poincaré establishes a close relationship between the tradition of French mathematical physics and the difficulties in understanding Maxwell's works: The first time that a French reader opens Maxwell's book, a feeling of uneasiness, and often even mistrust, mixes at first with his admiration. (...) Why do the ideas of the English scholar have so much difficulty in acclimatizing among us? It is no doubt that the education received by most enlightened Frenchmen disposes them to taste precision and logic before any other quality. The ancient theories of mathematical physics gave us a complete satisfaction in this respect. All our masters, from Laplace to Cauchy, proceeded in the same manner. Starting from clearly stated hypotheses, they deduced all the consequences with mathematical rigor, and then compared them with experience. (Poincaré 1890, V-VI) Poincaré emphasizes here the style of presentation, the logic and precision favored by the training of French physicists. He also recognizes the persistence of the Laplacian program, which contains an ontology of center-of-force atoms, the conception of an unobservable matter, "which have only purely geometric qualities and whose atoms are nothing but mathematical points subject to the laws of dynamics" (Poincaré, 1890, VI). Simplicity and Coordination of the Rapports Vrais Poincaré seems to favor a physics in which the "differential equations deduced from
ão Príncipe – Poincaré and Duhem: Resonances in their First Epistemological Reflections 146 compel him to think, and he ends by understanding what was frequently a short artificial in the theoretical ensembles he once admired. (Poincaré 1890, XVI) The epistemological value of the theorem is underscore by Poincaré, who sees in it an explanation of the indecision between rival theory present in historical cases: The predate is confirmed by the history of all the parts of purgative; in optics, for example, Fresnel believes the vibration vertical to the plane of polarization; Neumann regards it as parallel to this design. We have long sought an " experimentum crucis ", which enable us to decide between these two theory, and we could not find it. All these facts are easily excuse by the properties of the Lagrange equations which I have just remember. (Poincaré 1890, XIV)12 The explanations that postulate unobservable quantities are therefore a cause of underdetermination of theory. Also, the theorem highlights the abstract dynamics, favored by some of the British physicists. Among the old theoretical ensembles we find the molecular physics of Laplace. Poincaré establishes a close relationship between the tradition of French mathematical physics and the difficulties in understanding Maxwell's oeuvre: The first time that a French proofreader open Maxwell's book, a feeling of malaise, and frequently even mistrust, mixes at foremost with his admiration. (...) Why do the ideas of the English scholar have so much difficulty in acclimatizing among us? It is no doubt that the education received by most enlightened Frenchmen disposes them to sample precision and logic before any early timbre. The ancient theory of mathematical physics gave us a accomplished satisfaction in this respect. All our masters, from Laplace to Cauchy, go in the same manner. Starting from clearly stated hypothesis, they deduced all the consequences with numerical rigor, and then compared them with experience. (Poincaré 1890, V - VI) Poincaré emphasizes here the style of display, the logic and precision favored by the education of French physicists. He also recognizes the persistence of the Laplacian program, which incorporate an ontology of center - of - violence atoms, the conception of an unobservable matter, " which have only strictly geometric qualities and whose atoms are nothing but numerical points subject to the laws of moral force " (Poincaré, 1890, VI). Simplicity and Coordination of the Rapports Vrais Poincaré seems to favor a physics in which the " differential equations deduced from
ão Pgíncipe – Poincaré and Duheo: Resonances in their Hirst Elistemolugical Reflections 146 compel hmm ti thibk, and he ends by undefstanding what waw ofuen a little artihjcial ik the bheorztmcal ensembles me once admhred. (Poincaré 1890, FVK) Che epistemological value of the thejrem is elphasized by Pjincswé, whk sees in it an explanation of the indecivion between tival theories present in jistlrical cases: The pgeceding is consurmed by the history of all the patts of physics; in optics, for exaople, Yresnel belueces jhe vibratioi perpvndicular to bne plate of pplarization; Nemmann retards it as parallel vo this plan. We have long souchc an "experimentum cruxiw", whiwh etablde ur tk vecjde behwexn these twk theories, qnd we could not fimd py. All these racts wrq easily explained by the properties of ths Lagrange equations whuch I have just recalped. (Poincwré 1890, XIV)12 The explanations that postulate unobservatle qnavtiuicf qrf therefore a cause of underdetermination of egeprpes. Also, the theovem highlights the ahsytact dynamics, wavoreb bg some of the Britlsh phyficisrs. Among uhe okd theoretical ensembles we find the mojwcular physics of Paplace. Poiucaré extabloshes a close relationskip befween the tgadition kw French mathemagicsl physics and the difficultyes in unverstcnding Mxxwekl's wowks: The figst tlke that a French rfader o[ens Maxwepl's book, a feeling of uneasiness, and often evgn kisnrust, mixzs at nirst with his wdmiration. (...) Whi do the ndeas uf the Engmish sciolar have sj much difficgpty in acclikatizing amobg uw? It is vo doubt that yhe educanijn rwceived by most enkigffened Frenchmen diwposes them to yasge [rvcixijt and logic tefofe xmy otfer quality. Ghe sncient theories of kathsmatical physics gsvc us a conplete swtisfaction im this respect. All our kasvers, ftom Laplace to Cauchy, proceeded ih the samf mwnner. Startigg fvom slearly stcted hypotheses, they deduced all the conwequences with majhematical rigor, and jhek compared tiem wieh experiance. (Poincaré 1890, V-VI) Pouncaré emphasizes mere the style of pressntatimn, thf logic and precision favored by the training of French physicists. He alsi recojnyzes the pedsisyence oy tke Laplwciai 'rogram, which connains an ontology of center-of-forre atoms, tve conception of an unobservabke matter, "which have only purely geometdic qualoties and whose atoms are nothimg but mathematical poinbs subjecr to fhe laws oh dynamics" (Poincaré, 1890, FI). Sim'licitt and Ciordlnation of the Ralplrts Vraid Pomnccré seems to favor a physics in whuch thw "fifferential equetions deduccd from
ão Príncipe – Poincaré and Duhem: Resonances First Reflections 146 him to think, what often a little in the theoretical he once admired. (Poincaré 1890, XVI) epistemological value of the theorem is emphasized by Poincaré, who sees in it explanation of the indecision between rival theories present in historical cases: The preceding confirmed the of the parts of physics; in optics, for example, Fresnel believes the vibration perpendicular to the plane polarization; Neumann regards it as parallel to this We have long sought "experimentum crucis", which enabled us decide these two and could find it. All facts are easily explained by the properties of the Lagrange equations which I have just recalled. (Poincaré XIV)12 The postulate unobservable are a of underdetermination of the theorem highlights the abstract dynamics, of the British physicists. Among the old theoretical we find molecular physics of Laplace. Poincaré establishes close relationship between the tradition of French mathematical and the difficulties in understanding Maxwell's works: The first time that a French reader opens a feeling of uneasiness, often even mistrust, at with admiration. Why do ideas of the English scholar have so much difficulty in acclimatizing us? It is no doubt that the education received by Frenchmen them to taste and logic before any quality. ancient theories of mathematical us complete respect. our from Laplace to Cauchy, in the same manner. Starting clearly stated hypotheses, they mathematical rigor, and then compared them with experience. 1890, V-VI) Poincaré emphasizes here the style presentation, the logic and precision favored by the training of French physicists. also recognizes of the Laplacian program, which contains an ontology center-of-force atoms, the conception an unobservable matter, "which have only purely geometric qualities whose are nothing mathematical points subject the laws of (Poincaré, 1890, VI). Coordination of Rapports Poincaré a physics in which the "differential deduced
ão Príncipe – Poincaré and DuheM: ResonanceS in thEir firSt episTemoLogical ReflectIOns 146 cOmpel him to think, and he enDs by uNdERstaNDiNg whaT was oftEN a LITtlE aRtIfiCiAL iN the tHeoRetical Ensembles hE onCe Admired. (PoincARé 1890, xVI) The episTemOlogical valuE of The theOrEm iS EmphaSizEd by POincarÉ, Who seeS in it an exPlANation OF the indECIsIon bEtween rival theoriES pREsent in historiCal casEs: tHe PREceDinG is confirmEd By the HIstory oF AlL THE paRTs of physics; in Optics, for exAMplE, FresnEl BelIEves thE vibrAtIOn pErpendiculaR to tHe plane of PolariZAtion; NeUMann regArds it As pAraLlel TO tHiS plAn. wE haVE lOng SOugHt an "expeRiMeNtum cRuciS", WHICh enAblEd us To decIde between theSe tWo thEOriEs, and We couLd noT fInd it. all theSe facTs Are easily explaiNed bY the propeRtiEs Of tHe lagraNGe equaTioNs wHich I haVe just rECalLeD. (pOInCaré 1890, XIV)12 The explanatIoNS ThAt postulAte unoBSeRvABle quantItIes Are tHEReforE a caUSe Of underdEtermiNAtIoN of theoRiEs. Also, ThE thEorEm higHLighTs the aBstract dYnamiCS, favored by some OF the British phYSiCIStS. amonG thE old theoretIcal ENsemBles WE fInd THe molEculaR pHYsICs of Laplace. Poincaré EsTablisHes a cLose relationsHip between THE TraditioN of FREnCH mathematical pHysicS and the difFIculties In undErstandiNg Maxwell'S WOrks: The fIrsT tiMe tHat A fReNch reader openS mAxweLl'S book, a fEelIng of unEasIneSs, aNd oFtEn even misTrust, mixEs At FiRsT wiTh his ADmiratioN. (...) WHy dO tHe iDeas oF The EngLish sCholAr HaVE so Much difFIcULTy in AcClImatIziNg Among Us? It IS no Doubt thAt the educAtiON recEiVeD by most Enlightened FrEnChmen dispoSeS thEm to taSTE precisiOn and logic before any otheR Quality. the AncieNt thEories of mAthEmaticAl pHYsics gAve us a ComplEtE saTISfactION iN thIs Respect. All OUR maSters, FrOm LaPlace to cauchy, proceeded in tHE saMe manner. StartIng From CLEaRly STaTEd hYpOTheSES, they deduced all The consequEnCEs With mathemATicAl Rigor, anD then coMpareD Them witH experienCe. (PoincarÉ 1890, V-vI) PoINCarÉ emphasizeS here the Style of prESentaTIoN, the lOgiC and prEcIsiOn favOred by THe tRainiNg of FrEnCh physIcistS. HE also recOgnizes the persistence of The LapLaciaN prOgram, whicH coNTaiNs an ontolOgy oF center-of-fOrcE atOms, thE coNCeptiOn of AN uNobSErvabLe maTTer, "which hAVe OnlY PUrEly geometriC QUAliTies aNd wHOse atoMs arE nothing but mathemATical points subJect TO The LawS Of dyNaMics" (Poincaré, 1890, VI). simPlICIty and CoOrDination of tHe RapporTs vRais POincarÉ seems To favor A PHySIcs in wHich The "DifferentIal EqUAtions dEdUcED from
ão Príncipe – Poincaré and  Duhem: Re sonan ces  in  t heir  Fir st Epistemolog i calReflections 146 compel  himto thin k ,and h e endsb yu n der st an din gw ha t was  of ten a l ittle arti fic ia l in the the o re tical ense mbl es he once a dmi red. ( Po inc a ré 18 90,  XVI)  The e p istemo logical v al u e of t h e theor e m  i s em phasized by Poinc a ré ,  who sees in i t an e xp l an a t ion  of  the indec is ion b e tween r i va l t heo r ies present i n historica l  ca ses: T he  pr e ceding  is c on f irm ed by the h isto ry of all  the p a rts ofp hysics;  in op tic s,fore xa mp le,  F r esn e lbel i eve s the vi br at ion p erpe n d i c ular  to  the  plan e of polariza tio n; N e uma nn re gards  itas  para llel t o thi splan. We have l ongsought an  "e xp eri me ntumc rucis" , w hic h enabl ed us t o  de ci d e be tween these two th eo r i es , and we  could no tf ind it.Al l t hese f actsaree as ily expl ainedb yth e prope rt ies of  t heLag range equa tionswhich Ihavej ust recalled.( Poincaré 1890 ,  X I V )1 2  The  ex planationsthat post ulat e  u nob s ervab le qu an t it i es are therefore aca use of  unde rdeterminatio n of theor i e s . Also,thet he o rem highlights  theabstract d y namics,favor ed by so me of the B ritish p hys ici sts . A m o ng  the old theo r e tica lensembl eswe find  th e m ole cul ar  physicsof Lapla ce .Po in car é est a blishesaclo se  re latio n ship b etwee n th etr a dit ion ofF re n c h ma th em atic alph ysics  and the  diffic ulties in  un d erst an di ng Maxw ell's works:Th e first ti me  th at a F r e nch read er opens Maxwell's book ,  a feel ing  of u neas iness, an d o ften e ven mistru st, mi xes a tfir s t  with h is  ad mi ration. (. . . ) W hy do  t he i deas of  the English schol a r h ave so much d iff icul t y  i n a c cl i mat iz i nga m ong us? It is n o doubt th at th e educatio n  re ce ived by  most e nligh t ened Fr enchmen d isposes t he m to t ast e precisio n and lo gic befor e  anyo th er qu ali ty. Th eanc ienttheori e s o f mat hemati ca l phys ics g av e us a c omplete satisfaction in  thisrespe ct.  All ourmas t ers , from La plac e to Cauch y,pro ceede d i n  thesame ma nne r . Sta rtin g  from cle a rl y s t a te d hypothese s , the y ded uce d  all t he c onsequences withm athematical ri gor, a ndthe n  com pa red them withexp er i e nce. (Po in caré 1890,V-VI) Po in c aré e mphasi zes he re thes t yl e  of pr esen tat ion, thelog ic and pre ci si o n favo redby  the t rainin g  ofF r ench physicists.  He a l s o rec o gni zes t he  persis t ence  of the La placian pro gram,whic h con tains a nontolo gyof  center-of - force ato ms, t he conc ep tion  of  an un obse r v ablematt er , " which hav e on l ypu r ely  geo metri cqual ities and whose at oms are not hi ngb u t math e ma t i cal points  su bject t o the laws of d y na m ics"(Poinc aré, 1 890, VI ) . S im plicity  an d Coordinat ion of th e  Ra pp orts  Vrais P oi ncar ésee ms  to favor a phy sics inwhich th e "diffe ren t iale quatio ns  deduced fro m
ão Príncipe_– Poincaré_and Duhem: Resonances in_their First_Epistemological_Reflections 146_compel_him to think,_and he ends_by understanding what was_often a little_artificial_in the theoretical ensembles he once admired. (Poincaré 1890, XVI) The epistemological value of_the_theorem is_emphasized_by_Poincaré, who sees in it_an explanation of the indecision_between rival_theories present in historical cases: The preceding is_confirmed_by the history_of all the parts of physics; in optics, for_example, Fresnel believes the vibration perpendicular_to the plane_of_polarization;_Neumann regards it as_parallel to this plan. We have_long sought an "experimentum crucis", which_enabled us to decide between these two_theories, and we could not find_it. All these facts are_easily explained_by the properties of the_Lagrange equations which_I have_just recalled. (Poincaré_1890, XIV)12 The explanations that postulate_unobservable quantities are_therefore a cause of underdetermination of_theories._Also, the theorem_highlights_the_abstract dynamics,_favored by some_of_the British_physicists._Among the old theoretical ensembles we_find_the molecular physics of Laplace. Poincaré establishes_a close relationship between_the_tradition of French mathematical_physics and the difficulties in_understanding Maxwell's works: The first time_that a_French reader_opens Maxwell's book, a feeling of uneasiness, and often even mistrust,_mixes at first with his admiration._(...) Why do the_ideas of_the_English scholar have_so_much difficulty_in acclimatizing among us? It is no_doubt that_the education received by most enlightened_Frenchmen disposes them to_taste_precision and logic before any other_quality. The ancient theories of mathematical_physics gave us a complete_satisfaction_in_this respect. All our masters,_from Laplace to Cauchy, proceeded in_the same manner._Starting from clearly stated hypotheses, they deduced_all_the consequences with mathematical rigor, and_then_compared them with experience. (Poincaré 1890,_V-VI)_Poincaré_emphasizes here the style of_presentation, the logic and precision favored_by the training of French physicists. He also recognizes_the persistence of_the Laplacian program, which contains_an_ontology_of center-of-force atoms, the conception of an unobservable matter, "which_have only_purely geometric qualities_and whose atoms are nothing but mathematical points subject to_the laws of dynamics" (Poincaré, 1890, VI)._Simplicity and Coordination of the Rapports Vrais Poincaré seems to favor_a physics in which the "differential equations deduced_from