 physics such as mathematical physics. Maxwell's methodological viewpoint on the mechanistic program (like many of his contemporaries') uncritically presupposes a generalized thesis about the relation between Lagrange's formulation of mechanics and the mechanical interpretation of physical phenomena. This thesis identifies the Lagrangian method with the mechanical interpretation of physical phenomena, constituting the main methodological principle of the analytical approach to mechanical explanation. Duhem begins his critical examination of the analytic approach to mechanical theory by questioning this identification, and in particular its sufficient condition. Duhem separates the mathematical structure of Lagrange's method from its mechanical interpretation (Chiappin 1989, 62-68). The mechanical interpretation is, for him, one of the many possible interpretations of the Lagrangian system of equations and generalized coordinates. His criticism illuminates the generality of the mathematical formulation of Lagrangian mechanics by pointing out that its applications go beyond the application in mechanical theory (for example, Maxwell's use of it to organize his electromagnetism theory). The axiomatization of thermodynamics by Gibbs was based upon thermodynamical potential instead of Carnot's cycle. The model of this axiomatization of thermodynamics is the Lagrangian method and constitutes Duhem's ideal of theoretical physics. The Lagrangian method constitutes Duhem's ideal of mathematical structure for the organization of empirical laws. Duhem is also particularly concerned with the unfalsifiable character of physical theories produced by the application of the analytical method, and with its strategy to avoid the falsifiability of physical theories (Duhem 1980, 78-79; Chiappin 1989, 74-80). This comes from the identification of Lagrange's method of mechanics (Lagrange 1997) with the theory of matter (Chiappin 1989, 64). Unfalsifiable theories do not meet Duhem's view of scientific growth as rational and continuous. The key element of the analytical approach to mechanical explanation is analytic mechanics according to Lagrange's and Hertz's formulations. The Lagrangian formulation of mechanics corresponds to the foundations of mechanics according to the dynamical current of mechanics (Newton), while Hertz's formulation corresponds to the foundations of mechanics according to the kinetic current of mechanics (Descartes). Whatever its formulation, the analytic approach to the mechanistic program aims at establishing the possible conditions to explain a physical phenomenon mechanically, rather than effectively construct a mechanical explanation, as with the synthetic approach. This new approach seeks, instead of building up a mechanical model (like that of honeycomb or idle wheel particles proposed by Maxwell to explain currents and fields) (Duhem 1980, 68), to
physics such as mathematical physics. Maxwell's methodological viewpoint on the mechanistic platform (like many of his coevals') uncritically presupposes a generalized thesis about the relation between Lagrange's conceptualization of mechanics and the mechanical interpretation of physical phenomenon. This thesis identifies the Lagrangian method acting with the mechanical rendition of physical phenomena, establish the main methodological principle of the analytical overture to mechanical explanation. Duhem begins his critical examination of the analytic approach to mechanical theory by questioning this designation, and in particular its sufficient condition. Duhem separates the numerical structure of Lagrange's method from its mechanical rendition (Chiappin 1989, 62 - 68). The mechanical interpretation is, for him, one of the many potential interpretations of the Lagrangian system of equations and generalized coordinates. His criticism illuminates the generality of the numerical formulation of Lagrangian mechanics by pointing out that its applications go beyond the application in mechanical hypothesis (for model, Maxwell's use of it to organize his electromagnetism theory). The axiomatization of thermodynamics by Gibbs was based upon thermodynamical potential instead of Carnot's cycle. The model of this axiomatization of thermodynamics is the Lagrangian method acting and constitute Duhem's ideal of theoretical physics. The Lagrangian method acting form Duhem's ideal of numerical structure for the organization of empirical laws. Duhem is also particularly concerned with the unfalsifiable character of forcible theories produced by the application of the analytical method, and with its strategy to avoid the falsifiability of physical theories (Duhem 1980, 78 - 79; Chiappin 1989, 74 - 80). This comes from the identification of Lagrange's method of automobile mechanic (Lagrange 1997) with the theory of topic (Chiappin 1989, 64). Unfalsifiable theory do not meet Duhem's view of scientific growth as rational and continuous. The cardinal element of the analytical approach to mechanical explanation is analytic mechanics according to Lagrange's and Hertz's formulations. The Lagrangian formulation of mechanics corresponds to the foundations of machinist according to the dynamical stream of mechanics (Newton), while Hertz's formulation corresponds to the foundations of mechanism according to the energizing current of mechanics (Descartes). Whatever its formulation, the analytic overture to the mechanistic course of study aims at establishing the possible conditions to explain a physical phenomenon mechanically, rather than effectively construct a mechanical explanation, as with the man-made approach. This new access seeks, instead of building up a mechanical model (like that of honeycomb or idle wheel particle proposed by Maxwell to explain currents and fields) (Duhem 1980, 68), to
 phjsics such as mathematicxl physics. Maxwglo's metiodologjcal viedpoint on the mechanistic prlgeam (luke many of his contemooraries') lncriticaoly kresupposes a genxdalized thesia abobt the relation netween Lagsange's formuladiun of mechanics and the mechanical ineerpretstlon of physicaj phtnoiena. Nhls thesis identifies the Lagrangjan metiod with the mevhanical interpretation of phydical phenomena, cojstituting jge iqin methodolugical principle of thg analytical approach to mechanizal erplanation. Euyem tegins his rriticwl examination of tha analyyic approach tp mxchabical theory by questmoning this identifisation, ang nn particular its sufdixient congitiub. Djhej xelarated tie mathematjcal structyre of Lagrange's meuhoq from its mecganicaj ynterpretation (Chiappin 1989, 62-68). The mechanican ihterpretation is, for hin, one of the many posdible intqrpretations of the Lagrangian system of equationv and eentrqlizea clordinates. His criticism illuminates the genewzlotj of the mathematlcal formulation og Pabtangian mechankcs by pojnting out that itd applisatiobs go beyjnd yhe application in mechanicql theory (fog exqmple, Maxwell's use of it to oxganizg his rlectromagnetism theory). The axiomatizahion of tgdrmodynamics by Eibns fas based upon thermodynamycal poteitial insteaa of Carnoe's cycle. Tje model of this axiomatlzatiln of thermofynamics is the Lagrangian method and constitotev Dlhem's idecl of bheoretical phyfics. The Lagraugian mechod cunstitutes Duhem's ideal of mwthematical sdtucture for tie organisatiin od empirkzal laws. Duhem is also iaxticularlt concerned with tme unwzlsifiable charcettr of physical tneofief irovuced ty the appliwatiun ug the analytical oethpd, and with its stradegy to avoid the falsoflability if physisal theories (Cuhem 1980, 78-79; Chiappin 1989, 74-80). This cooes ftom the identification of Lagrangs's method of mechanics (Lwgrakge 1997) with the cheory of matter (Chiappin 1989, 64). Unfalsifiablx theories do not meet Euhem's view of scieutlfic growth es ratyonal and continuous. The key wlement of the anslytical approach to jechanhcal fxplanation is analytic mechanics according to Lagrange's and Hertz's formuoations. The Lagranfian formllaciou of meshanmcr corresponds to the foundations of mechanics arcording tm che dynamical current of mechsnkcs (Newton), whkle Hertz's formulation ckrresponcs to the foundations of mechanocs according to the kinctic currwnt or mechanicr (Descartes). Whatevrr its formylation, the analytic appfoavh to the mfchaiiscic program aims at establishing rhe powslble conditions vo explain a khysicam phenjmenon mechanicamly, dwther than effectifely construct a mechanical explandtyon, as with tht synthetic apptoach. Jkps new approarh seeks, insdead of building up a mechanical model (like that of honeycomg or idlc wheel particles 'roposed by Maxwell to ewplaig currengs and fieldv) (Duhem 1980, 68), to
physics such as mathematical physics. Maxwell's methodological the program (like of his contemporaries') about relation between Lagrange's of mechanics and mechanical interpretation of physical phenomena. This identifies the Lagrangian method with the mechanical interpretation of physical phenomena, constituting the methodological principle of the analytical approach to mechanical explanation. Duhem begins his critical of analytic to theory by questioning this identification, and in particular its sufficient condition. Duhem separates the mathematical structure Lagrange's method from its mechanical interpretation (Chiappin 1989, The mechanical interpretation is, him, one of the many interpretations the Lagrangian of and coordinates. His criticism the generality of the mathematical formulation of Lagrangian mechanics by pointing out that its applications go beyond application in (for example, use it organize his electromagnetism axiomatization of thermodynamics by Gibbs was potential instead of Carnot's cycle. The model of axiomatization of is the Lagrangian method and constitutes ideal of theoretical physics. The Lagrangian method constitutes ideal of mathematical structure for the organization of empirical laws. Duhem is also particularly concerned unfalsifiable character of physical produced by the of analytical and its strategy avoid the falsifiability of physical theories (Duhem 1980, 78-79; Chiappin 1989, This comes from the identification of Lagrange's method of mechanics with theory of matter 1989, 64). Unfalsifiable theories not Duhem's view of scientific rational continuous. of analytical to mechanical explanation is mechanics according to Lagrange's and formulations. The Lagrangian formulation foundations of mechanics according to the dynamical current mechanics (Newton), while Hertz's formulation corresponds to foundations of mechanics according to the kinetic current of mechanics (Descartes). Whatever formulation, the to the mechanistic program aims at establishing the conditions to explain a phenomenon mechanically, rather than effectively construct a mechanical explanation, with synthetic approach. new approach seeks, of building up mechanical model (like honeycomb or wheel proposed explain currents and fields) (Duhem 1980, to
 physics such as mathematical Physics. MaxWell's MetHodOlOgicAl viEwpoint on the meCHaniStic program (like many of hIs conTeMPoraRIeS') uncrIticallY PrESUppOsEs A geNeRAlIzed tHesIs about The relatioN beTwEen Lagrange's FOrMulation of MecHanics and the MecHanicaL iNteRPretaTioN of phYsical PHenomeNa. This theSiS IdentiFIes the LAGRaNgiaN method with the mecHAnICal interpretatIon of pHySIcAL PheNomEna, constitUtIng thE Main metHOdOLOGicAL principle of tHe analyticaL AppRoach tO mEchANical eXplanAtIOn. DUhem begins hIs crItical exaMinatiON of the aNAlytic aPproacH to MecHaniCAl ThEorY bY QueSTiOniNG thIs identiFiCaTion, aNd in PARTIculAr iTs suFficiEnt condition. DUheM sepARatEs the MatheMatiCaL struCture oF LagrAnGe's method from itS mecHanical inTerPrEtaTiOn (ChiAPpin 1989, 62-68). ThE meChaNical inTerpretATioN iS, FOR hIm, one of the many possIbLE InTerpretaTions oF ThE LAGrangian SySteM of eQUAtionS and GEnEralized CoordiNAtEs. his critIcIsm illUmInaTes The geNEralIty of tHe mathemAticaL Formulation of LAGrangian mechaNIcS BY pOIntiNg oUt that its apPlicATionS go bEYoNd tHE applIcatiOn IN mEChanical theory (for exAmPle, MaxWell's Use of it to orgaNize his eleCTROmagnetiSm thEOrY). the axiomatizatIon of ThermodynaMIcs by GibBs was Based upoN thermodyNAMical potEntIal InsTeaD OF CArnot's cycle. ThE MOdel Of This axiOmaTizatioN of TheRmoDynAmIcs is the LAgrangiaN mEtHoD aNd cOnstiTUtes DuheM's IdeAl Of tHeoreTIcal phYsics. the LAgRaNGiaN method COnSTItutEs duHem's IdeAl Of matHemaTIcaL structUre for the OrgANizaTiOn Of empirIcal laws. Duhem Is Also particUlArlY conceRNEd with thE unfalsifiable character OF physicAl tHeoriEs prOduced by tHe aPplicaTioN Of the aNalytiCal meThOd, aND With iTS StRatEgY to avoid thE FAlsIfiabIlIty oF physicAl theories (Duhem 1980, 78-79; ChiAPpiN 1989, 74-80). This comes froM thE ideNTIfIcaTIoN Of LAgRAngE'S Method of mechaniCs (Lagrange 1997) WiTH tHe theory of MAttEr (chiappiN 1989, 64). UnfalsIfiabLE theoriEs do not meEt Duhem's vIeW of sCIEntIfic growth As rationAl and contINuous. tHe Key elEmeNt of thE aNalYticaL approACh tO mechAnical ExPlanatIon is AnAlytic meChanics according to LagraNge's anD HertZ's fOrmulatioNs. THE LaGrangian fOrmuLation of meChaNicS corrEspONds to The fOUnDatIOns of MechANics accorDInG to THE dYnamical curRENT of MechaNicS (newton), WhilE Hertz's formulatioN Corresponds to tHe foUNDatIonS Of meChAnics according To tHe KINetic curReNt of mechaniCs (DescarTeS). whateVer its FormulAtion, thE ANaLYtic apProaCh tO the mechaNisTiC Program AiMs AT estabLishInG the poSsible COndiTIOns to explain a phySical PHEnomeNOn mEchanIcAlly, ratHEr thAn effectivEly construcT a mechAnicAl expLanatioN, aS with tHe sYnThetic apprOAch. This neW apprOach seeKs, InstEad Of builDing UP A mechAnicAl ModEl (like thaT OF hONeYcOMb oR idlE wheeL pArtiCles propoSEd by MaxwEll TO explaiN cUrrENTs and fIElDS) (duhem 1980, 68), to
 physics such as mathemati cal physic s. Ma xwe ll' smeth odol ogical viewpoi n t on  the mechanistic progr am (l ik e  man y  o f his  contem p or a r ies ')  u ncr it i ca lly p res upposes  a general ize dthesis about th e relation  be tween Lagran ge' s form ul ati o n ofmec hanic s andt he mec hanical i nt e rpreta t ion ofp h ys ical  phenomena. Thist he s is identifiesthe La gr a ng i a n m eth od with th emecha n ical in t er p r e tat i on of physica l phenomena ,  co nstitu ti ngt he mai n met ho d olo gical princ iple  of the a nalyti c al appr o ach tomechan ica l e xpla n at io n.Du h emb eg ins his  critica lex amina tion o f theana lyti c app roach to mech ani calt heo ry by  ques tion in g thi s iden tific at ion, and in par ticu lar its s uff ic ien tcondi t ion. D uhe m s eparate s the m a the ma t i c al  structure of Lagr an g e 's  methodfrom i t sme c hanicalin ter pret a t ion ( Chia p pi n 1989,62-68) .  T he  mechan ic al int er pre tat ion i s , fo r him,  one ofthe m a ny possible in t erpretationso ft h eL agra ngi an system o f eq u atio ns a n dgen e raliz ed co or d in a tes. His criticismil lumina tes t he generality  of the ma t h e maticalform u la t ion of Lagrang ian m echanics b y  pointin g out  that it s applica t i ons go b eyo ndthe  ap p l ic ation in mech a n ical  t heory ( for  exampl e,Max wel l's  u se of itto organ iz ehi sele ctrom a gnetismth eor y) . T he ax i omatiz ation  ofth er m ody namicsb yG i bbswa sbase d u po n the rmod y nam ical po tential i nst e ad o fCa rnot'scycle. The mo de l of thisax iom atizat i o n of the rmodynamics is the Lagr a ngian m eth od an d co nstitutes  Du hem'side a l of t heoret icalph ysi c s . The L ag ran gi an methodc o nst itute sDuhe m's ide al of mathematical str ucture for th e o rgan i z at ion of emp ir i cal l aws. Duhem is a lso partic ul a rl y concerne d  wi th  the un falsifi ablec haracte r of phys ical theo ri es p r o duc ed by theapplicat ion of th e  anal y ti cal m eth od, an dwit h its  strat e gyto av oid th efalsif iabil it y of phy sical theories (Duhem 1 980, 7 8-79;  Ch iappin 19 89, 74- 80). This  com es from th e i den tific ati o n ofLagr a ng e's metho d of mechanics (L agr a n ge  1997) with t h e t heory  of matter  (Ch iappin 1989, 64). Unfalsifiabletheo r i esdon ot m ee t Duhem's view  of  s c i entificgr owth as rat ional an dc ontin uous.The ke y eleme n t  o f  the a naly tic al approa chto mechani ca le xplana tion  i s anal ytic m e chan i c s according to L agran g e 's an d  He rtz's  f ormulat i ons.  The Lagra ngian formu lation  ofmecha nics co rr espond s t othe founda t ions of m echan ics acc or ding  to  the d ynam i c al cu rren tofmechanics ( Ne w to n) ,  wh ileHertz 's  for mulationc orrespon dst o the f ou nda t i ons of me c h anics acco rdi ng to t he kinetic curr e nt of me chanic s (Des cartes) .  Wh at ever it s f o r mulation,  the anal y tic  a ppro ach to t he  mec ha nis ti c program aimsat estab lishingt h e poss ibl e  con d itions  t o explain aphysi ca l  phenom e n onmechani c all y,rat hertha n ef f ectively construct a mec hani cal e x pla natio n, as  w ith thes ynth etic app r oach. This ne w approach seek s , i n stea d o f  b ui lding upa m e chani calmod el ( lik e th a t  ofh oney c om b or  idlewhee lpa rticles p ro posed b y  Max w ell  toexpla in  c u rr ents an d fields ) (Du he m 1980, 6 8 ), to
 physics_such as_mathematical physics. Maxwell's methodological_viewpoint on_the_mechanistic program_(like_many of his_contemporaries') uncritically presupposes_a generalized thesis about_the relation between_Lagrange's_formulation of mechanics and the mechanical interpretation of physical phenomena. This thesis identifies the_Lagrangian_method with_the_mechanical_interpretation of physical phenomena, constituting_the main methodological principle of_the analytical_approach to mechanical explanation. Duhem begins his critical_examination_of the analytic_approach to mechanical theory by questioning this identification, and_in particular its sufficient condition. Duhem_separates the mathematical_structure_of_Lagrange's method from its_mechanical interpretation (Chiappin 1989, 62-68). The_mechanical interpretation is, for him, one_of the many possible interpretations of the_Lagrangian system of equations and generalized_coordinates. His criticism illuminates the_generality of_the mathematical formulation of Lagrangian_mechanics by pointing_out that_its applications go_beyond the application in mechanical theory_(for example, Maxwell's_use of it to organize his_electromagnetism_theory). The axiomatization_of_thermodynamics_by Gibbs_was based upon_thermodynamical_potential instead_of_Carnot's cycle. The model of this_axiomatization_of thermodynamics is the Lagrangian method and_constitutes Duhem's ideal of_theoretical_physics. The Lagrangian method_constitutes Duhem's ideal of mathematical_structure for the organization of empirical_laws. Duhem_is also_particularly concerned with the unfalsifiable character of physical theories produced by_the application of the analytical method,_and with its strategy_to avoid_the_falsifiability of physical_theories_(Duhem 1980,_78-79; Chiappin 1989, 74-80). This comes from_the identification_of Lagrange's method of mechanics (Lagrange_1997) with the theory_of_matter (Chiappin 1989, 64). Unfalsifiable theories_do not meet Duhem's view of_scientific growth as rational and_continuous._The_key element of the analytical_approach to mechanical explanation is analytic_mechanics according to_Lagrange's and Hertz's formulations. The Lagrangian formulation_of_mechanics corresponds to the foundations of_mechanics_according to the dynamical current of_mechanics_(Newton),_while Hertz's formulation corresponds to_the foundations of mechanics according to_the kinetic current of mechanics (Descartes). Whatever its formulation,_the analytic approach_to the mechanistic program aims_at_establishing_the possible conditions to explain a physical phenomenon mechanically, rather_than effectively_construct a mechanical_explanation, as with the synthetic approach. This new approach seeks,_instead of building up a mechanical model_(like that of honeycomb or idle wheel particles proposed by Maxwell_to explain currents and fields) (Duhem 1980, 68),_to