 physical phenomena discovered by the experimental method and the equations deduced (through Lagrange's equations) from the kinetic energy, potential energy, and virtual work constructed from these same measurable quantities is then assumed to guarantee a mechanical explanation for the phenomena. Since these conditions are fulfilled, one can construct, in principle, a mechanical system of masses in motion with the same kinetic energy and potential energy of the physical phenomena studied. Therefore, according to Maxwell, a mechanical correspondence between the two sets of quantities involved is warranted, which is Maxwell's concept of the reduction of physical theories. This reduction is guaranteed by three assumptions: the thesis of equivalence, the Duhem's Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics José R. N. Chiappin – Cássio Costa Laranjeiras 46 construction of Lagrange's equations, and the agreement between the constructed laws and the empirical laws. According to Duhem, the significant mistake (confusion) here is the identification between the Lagrangian method and mechanical interpretation (Chiappin 1989, 61-79). Underlying this criticism, one finds his view that theoretical physics is a mathematical structure with a physical interpretation. He understands Lagrangian mechanics as an interpreted calculus (variational calculus), whose mathematical structure can be applied to different domains of physics. Duhem questions the thesis of the equivalence between analytic mechanics and mechanical interpretation and its condition of sufficiency. The first major objection to the analytic approach to the mechanistic program is that the formulation of a physical problem in Lagrangian mechanics is not a sufficient condition to guarantee its mechanical explanation (Duhem 1980, 71). Duhem agrees that it is a necessary condition, but disagrees that it is a sufficient condition. He questions the thesis that from this condition one can conclude with certainty that there exists a certain group of masses and forces, a certain mechanism, admitting such potential, and, above all, such kinetic energy (Duhem 1980, 7). The proposed mechanical explanations were to be interpreted as illustrations, which, at most, imitate or simulate in their laws of motion the equations that are being discussed, and are not true mechanical explanations. Duhem says: It seems imprudent to dismiss similar difficulties with a stroke of the pen. What has been found to be best, up to now, for clearing objections of this nature, is to imagine extremely simple mechanisms whose internal potential and kinetic energy offer, in their various particularities, a more or less direct analogy with the potential and kinetic energy that it is proposed to study; in a
physical phenomena discovered by the experimental method and the equation deduce (through Lagrange's equations) from the kinetic energy, likely energy, and virtual work constructed from these like measurable quantity is then assumed to guarantee a mechanical explanation for the phenomena. Since these conditions are carry through, one can construct, in principle, a mechanical organization of multitude in motion with the same kinetic energy and potential department of energy of the physical phenomena studied. consequently, according to Maxwell, a mechanical correspondence between the two sets of quantities involved is justify, which is Maxwell's concept of the reduction of physical theories. This reduction is guaranteed by three assumption: the thesis of equivalence, the Duhem's Critical Analysis of Mechanicism and his Defense of a Formal Conception of Theoretical Physics José R. N. Chiappin – Cássio Costa Laranjeiras 46 construction of Lagrange's equations, and the agreement between the constructed laws and the empirical laws. According to Duhem, the significant mistake (confusion) here is the identification between the Lagrangian method and mechanical interpretation (Chiappin 1989, 61 - 79). Underlying this criticism, one finds his view that theoretical purgative is a numerical structure with a physical interpretation. He understand Lagrangian mechanics as an interpreted calculus (variational tartar), whose mathematical social organization can be applied to different domains of purgative. Duhem questions the thesis of the equivalence between analytic mechanics and mechanical interpretation and its condition of enough. The first major objection to the analytic approach to the mechanistic program is that the formulation of a physical problem in Lagrangian mechanism is not a sufficient condition to guarantee its mechanical explanation (Duhem 1980, 71). Duhem agrees that it is a necessary condition, but disagrees that it is a sufficient circumstance. He questions the thesis that from this condition one can conclude with certainty that there exists a certain group of masses and forces, a certain mechanism, accept such potential, and, above all, such energizing energy (Duhem 1980, 7). The proposed mechanical explanations were to be interpreted as illustrations, which, at most, imitate or imitate in their laws of gesture the equations that are being hash out, and are not true mechanical explanations. Duhem says: It seems imprudent to dismiss alike difficulties with a accident of the pen. What has been found to be best, up to now, for clearing objections of this nature, is to think extremely simple mechanism whose internal potential and kinetic energy offer, in their various particularities, a more or less lineal analogy with the potential and kinetic energy that it is proposed to study; in a
 phjsical phenomena discoveved by the expernnental methos and thd equations deduced (through Patrangt'f equations) from tfe kinetib energy, poteitial energy, and virtual work dlnstxurted from these same measgrable quantither ns then assumed to guarantee a mechagical ecppanation for tre pnqnomsna. Since these conditions are fulrilled, mne can consttuct, in principle, a mechanlcal system of masses ln motion wuth eye same kinegic energy and potentizl energy of the physical phenooena xtudied. Thgxwfogg, according vo Maxrell, a mechakpcal cosresponcence between bhe txo swts of quantities invmlved is warranted, which is Mcxwell's concept of thw eeducjion mf pftsizal tieodies. Tjis reduction is guarantwed by three assumpuiogw: the thesis kf equyvwlence, the Duhem's Critical Analysis of Kecganicism and his Defensw of a Formal Conceptlon of Thqoretical Physics José R. N. Chiappin – Cássio Costa Ldranjxifas 46 gonsgeuftion of Lagrange's equations, and the agreemene bttwven the constructcd laws and the emligivwl laws. Accoraing to Dhhem, the significajt mistwke (cinfusion) rere is the identification betwwen the Lagrcnguan method and meckanical intexpretajion (Cniappin 1989, 61-79). Underlying thns crificism, one vinds his xiew that theoregicsl physics is a mathematical structurx witk a physkcal inter[retation. Je understands Lagrangiaj meckanicv as an inherpreted calculus (variational relculus), whose mdthvmatical ftrucbure can be appjied to differgnt domaius of ohysics. Dugem quevtions the ehesis of the gquivalence bxtween anwlytuc mwchanicr and mechanicak interprvtction and its condition of xufwjciency. The firwt najor objection to thq wnelytis approach to the meznanisgic program ks tnat the formulation mf a physical problem on Lagranguan mechwnics is not s sufficient condiuion tm gnarantre yts mechanical explanation (Duhsm 1980, 71). Duhel anrees that it is q necessary eondition, but disagrees that it is a sufhicient condition. He qoestions the thesis tkau from this cpndityon one cdn conclude with cerrainty that there exists a certain grohp of kassed and forces, a certain mechanism, admitting such potential, and, above all, sych kiieeic energy (Suhek 1980, 7). Tve 'roposeq merhenical explanatioms were to be interpreted as iluustratimnf, which, at most, imitate or somjlate in theit laws of motion the equatjons thay are being discussed, and are npt true mechanical explakations. Dyhem aays: In sxems imprudent to dixmiss vimilqr diffuculbies with a stfokr lf the pej. Whet kas been found to be best, up to niw, for cpearing objectiois of this nwuure, is to imwgine extremely aimpmf mecfanisms whose internal potemtial and kinetic envrgr offer, in theug various parjiculatnnies, a more oc less direcd analogy with the potential and kinetic energy thaj it is prokosed to svudy; in a
physical phenomena discovered by the experimental method equations (through Lagrange's from the kinetic work from these same quantities is then to guarantee a mechanical explanation for phenomena. Since these conditions are fulfilled, one can construct, in principle, a mechanical of masses in motion with the same kinetic energy and potential energy of physical studied. according Maxwell, a mechanical correspondence between the two sets of quantities involved is warranted, which is Maxwell's of the reduction of physical theories. This reduction guaranteed by three assumptions: thesis of equivalence, the Duhem's Analysis Mechanicism and Defense a Conception of Theoretical José R. N. Chiappin – Cássio Costa Laranjeiras 46 construction of Lagrange's equations, and the agreement between constructed laws empirical laws. to the mistake (confusion) here identification between the Lagrangian method and 1989, 61-79). Underlying this criticism, one finds his that theoretical is a mathematical structure with a interpretation. He understands Lagrangian mechanics as an interpreted (variational calculus), whose mathematical structure can be applied to different domains of physics. Duhem questions of the equivalence between mechanics and mechanical and condition sufficiency. first major to the analytic approach to the mechanistic program is that the of a physical problem in Lagrangian mechanics is not a to its mechanical explanation 1980, 71). Duhem agrees it a necessary condition, but it a questions thesis from this condition one conclude with certainty that there a certain group of mechanism, admitting such potential, and, above all, such energy (Duhem 1980, 7). The proposed mechanical were to be interpreted as illustrations, which, at most, imitate or simulate their laws the equations that are being discussed, and are true mechanical explanations. Duhem It seems imprudent to dismiss similar difficulties with a of pen. What been found to best, up to for clearing objections nature, is imagine simple potential and kinetic energy offer, in various a more or less direct with and kinetic energy that it is proposed to study; in a
 physical phenomena discoverEd by the expErimeNtaL meThOd anD the Equations deducED (thrOugh Lagrange's equations) From tHe KInetIC eNergy, PotentiAL eNERgy, AnD vIrtUaL WoRk conStrUcted frOm these samE meAsUrable quantiTIeS is then assUmeD to guarantee A meChanicAl ExpLAnatiOn fOr the PhenomENa. SincE these conDiTIons arE FulfillED, OnE can Construct, in princiPLe, A Mechanical systEm of maSsES iN MOtiOn wIth the same KiNetic ENergy anD PoTENTiaL Energy of the phYsical phenoMEna StudieD. THerEFore, acCordiNg TO MaXwell, a mechaNicaL correspoNdence BEtween tHE two setS of quaNtiTieS invOLvEd Is wArRAntED, wHicH Is MAxwell's cOnCePt of tHe reDUCTIon oF phYsicAl theOries. This reduCtiOn is GUarAnteeD by thRee aSsUmptiOns: the ThesiS oF equivalence, the duheM's CriticaL AnAlYsiS oF MechANicism And His defense Of a FormAL CoNcEPTIoN of Theoretical PhysIcS jOsÉ R. N. ChiapPin – CásSIo coSTa LaranjEiRas 46 ConsTRUctioN of LAGrAnge's equAtions, ANd ThE agreemEnT betweEn The ConStrucTEd laWs and tHe empiriCal laWS. According to DuHEm, the significANt MIStAKe (coNfuSion) here is tHe idENtifIcatIOn BetWEen thE LagrAnGIaN Method and mechanical InTerpreTatioN (Chiappin 1989, 61-79). UndeRlying this CRITicism, onE finDS hIS view that theorEticaL physics is A MathematIcal sTructure With a physICAl interpRetAtiOn. HE unDERsTands LagrangiAN MechAnIcs as an IntErpreteD caLcuLus (VarIaTional calCulus), whoSe MaThEmAtiCal stRUcture caN bE apPlIed To difFErent dOmainS of pHySiCS. DuHem quesTIoNS The tHeSiS of tHe eQuIvaleNce bETweEn analyTic mechanIcs ANd meChAnIcal intErpretation anD iTs conditioN oF suFficieNCY. The firsT major objection to the anaLYtic appRoaCh to tHe meChanistic ProGram is ThaT The forMulatiOn of a PhYsiCAL probLEM iN LaGrAngian mechANIcs Is not A sUffiCient coNdition to guarantee ITs mEchanical explAnaTion (dUHeM 1980, 71). DuHEm AGreEs THat IT Is a necessary conDition, but dIsAGrEes that it iS A suFfIcient cOnditioN. He quEStions tHe thesis tHat from thIs CondITIon One can concLude with Certainty THat thERe ExistS a cErtain GrOup Of masSes and FOrcEs, a ceRtain mEcHanism, AdmitTiNg such poTential, and, above all, such kInetic EnergY (DuHem 1980, 7). The proPosED meChanical eXplaNations werE to Be iNterpRetED as ilLustRAtIonS, Which, At moST, imitate oR SiMulATE iN their laws oF MOTioN the eQuaTIons thAt arE being discussed, anD Are not true mechAnicAL ExpLanATionS. DUhem says: It seemS imPrUDEnt to disMiSs similar diFficultiEs WIth a sTroke oF the peN. What haS BEeN Found tO be bEst, Up to now, foR clEaRIng objeCtIoNS of thiS natUrE, is to iMagine EXtreMELy simple mechanisMs whoSE InterNAl pOtentIaL and kinETic eNergy offer, In their variOus parTicuLaritIes, a morE oR less dIreCt Analogy witH The potentIal anD kinetiC eNergY thAt it is PropOSEd to sTudy; In A
 physical phenomena discov ered by th e exp eri men ta l me thod  and the equat i onsdeduced (through Lagra nge's  e q uati o ns ) fro m the k i ne t i c e ne rg y,po t en tialene rgy, an d virtualwor kconstructedf ro m these sa memeasurable q uan tities  i s t h en as sum ed to  guara n tee amechanica le xplana t ion for t he  phe nomena. Since the s ec onditions arefulfil le d ,o n e c anconstruct,  i n pri n ciple,a  m e c h ani c al system ofmasses in m o tio n with  t hes ame ki netic  e n erg y and poten tial  energy o f thep hysical phenome na stu die d.Ther e fo re , a cc o rdi n gtoM axw ell, a m ec ha nical  cor r e s p onde nce  bet weenthe two setsofquan t iti es in volve d is  w arran ted, w hichis  Maxwell's conc eptof the re duc ti onof  phys i cal th eor ies . Thisreducti o n i sg u a ra nteed by three ass um p t io ns: thethesis of  e q uivalenc e,  th e Du h e m's C riti c al  Analysi s of M e ch an icism a nd  his D ef ens e o f a F o rmal  Conce ption of  Theo r etical Physics José R. N. Ch i ap p i n–  Cás sio  Costa Lara njei r as 4 6 co n st ruc t ion o f Lag ra n ge ' s equations, and th eagreem ent b etween the co nstructedl a w s and th e em p ir i cal laws. Acco rding  to Duhem, the sign ifica nt mista ke (confu s i on) here  is  th e i den t i fi cation betwee n theLa grangia n m ethod a ndmec han ica linterpret ation (C hi ap pi n198 9, 61 - 79). Und er lyi ng  th is cr i ticism , one  fin ds  h i s v iew tha t  t h e oret ic al  phy sic sis amath e mat ical st ructure w ith a ph ys ic al inte rpretation. H eunderstand sLag rangia n mechanic s as an interpreted cal c ulus (v ari ation al c alculus),  wh ose ma the m atical  struc tureca n b e appli e d  t o d if ferent dom a i nsof ph ys ics.  Duhemquestions the thes i s o f the equival enc e be t w ee n a n al y tic  m e cha n i cs and mechanic al interpr et a ti on and its con di tion of  suffic iency .  The fi rst major  objectio nto t h e  an alytic app roach to  the mech a nisti c  p rogra m i s that  t heformu lation ofa phy sicalpr oblemin La gr angian m echanics is not a suffi cientcondi tio n to guar ant e e i ts mechan ical  explanati on(Du hem 1 980 ,  71).  Duh e magr e es th at i t  is a nec e ss ary c on dition, but d i sag reestha t  it is  a s ufficient conditi o n. He question s th e the sis that  f rom this condi tio no n e can co nc lude with c ertainty  t h at th ere ex ists a  certai n gr o up ofmass esand force s,ac ertainme ch a nism,admi tt ing su ch pot e ntia l ,  and, above all,  such k ineti c  en ergy(D uhem 19 8 0, 7 ). The pro posed mecha nicalexpl anati ons wer eto beint er preted asi llustrati ons,which,at  mos t,imitat e or s imula te i nthe ir laws o f mo t io nt heequa tions  t hatare being discusse d,a nd areno t t r u e mech a ni c a l explanat ion s. Du h e m says: It seem s  i m prude nt todismis s simil a r d if ficulti esw i th a stro ke of the pen .What  has bee nfoun dtobe  best, up to no w, for c learingo b jectio nso f th i s natu re , is to imag ine e xt r emely s i m ple  mechan i sms  wh ose  int ern al p o tential and kinetic ener gy o ffer, intheir  vari ou s partic u lari ties, am ore or less d irect analogy w i tht he p ote n ti al  and kine tic energ y th atit i s p ropo s e d to stud y ;in a 
 physical_phenomena discovered_by the experimental method_and the_equations_deduced (through_Lagrange's_equations) from the_kinetic energy, potential_energy, and virtual work_constructed from these_same_measurable quantities is then assumed to guarantee a mechanical explanation for the phenomena. Since_these_conditions are_fulfilled,_one_can construct, in principle, a_mechanical system of masses in_motion with_the same kinetic energy and potential energy of_the_physical phenomena studied._Therefore, according to Maxwell, a mechanical correspondence between the_two sets of quantities involved is_warranted, which is_Maxwell's_concept_of the reduction of_physical theories. This reduction is guaranteed_by three assumptions: the thesis of_equivalence, the Duhem's Critical Analysis of Mechanicism_and his Defense of a Formal_Conception of Theoretical Physics José_R. N._Chiappin – Cássio Costa Laranjeiras_46 construction of_Lagrange's equations,_and the agreement_between the constructed laws and the_empirical laws. According_to Duhem, the significant mistake (confusion)_here_is the identification_between_the_Lagrangian method_and mechanical interpretation_(Chiappin_1989, 61-79)._Underlying_this criticism, one finds his view_that_theoretical physics is a mathematical structure with_a physical interpretation. He_understands_Lagrangian mechanics as an_interpreted calculus (variational calculus), whose_mathematical structure can be applied to_different domains_of physics._Duhem questions the thesis of the equivalence between analytic mechanics and_mechanical interpretation and its condition of_sufficiency. The first major_objection to_the_analytic approach to_the_mechanistic program_is that the formulation of a physical_problem in_Lagrangian mechanics is not a sufficient_condition to guarantee its_mechanical_explanation (Duhem 1980, 71). Duhem agrees_that it is a necessary condition,_but disagrees that it is_a_sufficient_condition. He questions the thesis_that from this condition one can_conclude with certainty_that there exists a certain group of_masses_and forces, a certain mechanism, admitting_such_potential, and, above all, such kinetic_energy_(Duhem_1980, 7). The proposed mechanical_explanations were to be interpreted as_illustrations, which, at most, imitate or simulate in their_laws of motion_the equations that are being_discussed,_and_are not true mechanical explanations. Duhem says: It seems imprudent_to dismiss_similar difficulties with_a stroke of the pen. What has been found to_be best, up to now, for clearing_objections of this nature, is to imagine extremely simple mechanisms whose_internal potential and kinetic energy offer, in their_various particularities, a more or less direct_analogy with the potential_and_kinetic energy that it is proposed to_study;_in_a