 it in (1893b, 58), 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. But abstraction, when used within a physical theory, also implies that, as Duhem (1906, 128-131) explains, a physical magnitude need only possess the relevant mathematical properties (to be expressed by a number and to be additive) and to obey the relevant mathematical laws (commutativity and associativity). Hence, different symbols could be chosen for a given physical property, as long as the mathematical features of interest of the latter are captured by the symbol. Apart from this requirement, the definition of the physical magnitude is arbitrary, like a sign is arbitrarily chosen to represent the thing it signifies. Hypotheses and Beyond The second step in theory construction consists in relating these symbols to each other through hypotheses. Here again, there is absolutely no constraint whatsoever on the choice of hypotheses provided that, taken as a whole, they represent the totality of the experimental laws. From his early work Some Reflections on the Subject of Physical Theories, published in 1892, to The Aim and the Structure of Physical Theory, Duhem kept defining the 'ideal' method for choosing the hypotheses as "accepting no hypotheses except the symbolic translation, in mathematical language, of some of the experimental laws from the group (...) [the physicist] wished to represent" (1892a, 6, see also 1906, 190-191). Concerning the recourse to hypotheses, Duhem made clear that their formulation should be as little restricted from above by metaphysics as possible, the only logical constraint on their adoption being the principle of non-contradiction. Enter the third step. From these hypotheses, the theoretical physicist proceeds via mathematical deduction to derive the (mathematical) consequences of the chosen hypotheses. This mathematical development of the theory is committed only to the rules of logic: the physical world is put in brackets at this stage of the process. Finally, however (and this is the fourth step), the consequences of the mathematical deduction will be translated back into claims about observational and testable predictions, allowing the physicist to submit his theory to the verdict of experimentation. As famously put by Duhem, the agreement with the experiment is the only criterion of truth for a theory. If the consequences of the deduction tally with the
it in (1893b, 58), It is abstraction that furnishes the notions of number, course, open, angle, mass, force, temperature and quantity of heat or electricity. It is abstractedness, or philosophical analysis, that separates and have precise the fundamental property of these various notions and articulate axioms and postulates. But abstractedness, when used within a physical theory, also implies that, as Duhem (1906, 128 - 131) explains, a physical order of magnitude need only possess the relevant mathematical property (to be expressed by a number and to be linear) and to obey the relevant mathematical jurisprudence (commutativity and associativity). Hence, unlike symbols could be chosen for a given physical place, as long as the mathematical features of interest of the latter are captured by the symbol. Apart from this requirement, the definition of the physical magnitude is arbitrary, like a sign is arbitrarily chosen to represent the thing it signifies. Hypotheses and Beyond The second step in hypothesis structure consists in relating these symbols to each early through guess. Here again, there is absolutely no constraint whatsoever on the choice of hypotheses provided that, taken as a whole, they represent the entirety of the experimental laws. From his early work Some Reflections on the Subject of Physical Theories, published in 1892, to The Aim and the Structure of Physical Theory, Duhem kept defining the' ideal' method acting for choosing the hypotheses as " accepting no hypotheses except the symbolic translation, in mathematical speech, of some of the experimental laws from the group (...) [ the physicist ] wished to represent " (1892a, 6, see also 1906, 190 - 191). refer the recourse to hypotheses, Duhem made clear that their conceptualization should be as fiddling restricted from above by metaphysics as possible, the alone logical restraint on their adoption being the principle of non - contradiction. Enter the third step. From these hypotheses, the theoretical physicist return via mathematical deduction to derive the (mathematical) consequence of the chosen hypotheses. This numerical development of the theory is committed only to the rules of logic: the physical world is put in brackets at this stage of the process. Finally, however (and this is the fourth measure), the consequences of the mathematical tax write-off will be translated back into claims about observational and testable predictions, allowing the physicist to submit his hypothesis to the verdict of experimentation. As famously put by Duhem, the agreement with the experiment is the only criterion of truth for a theory. If the consequences of the discount run with the
 it in (1893b, 58), It is abstraction that furnishes the novions or number, line, surface, angle, mass, forre, twmperqture and quantity of feat or epectriciry. Iu is abstraction, or philosophiczp anclbsis, that separstes and mdkes precise tve fbndamental properties of these variots notipnd and enunciatgs axpois ahd postulates. But abstraction, when used wpthin a physical yheory, also implies that, ad Dujem (1906, 128-131) explains, a pjysical magbituqw need only oossess tht xelevant majhematical properties (to be exprdssed by a numbgx anf to be addivive) agd to obey tmv relevdnt matnematical laws (cokmurativity and associatmvity). Hence, differenj symbols wobld be chosen for a guvwn phisican prupergy, zs lkng as thx mathematidal featurew of interest of tht lwnyer are capthred br ehe symbol. Apart from this requirement, uhe dsfinition of the physicql magnitude is arbittary, like w sign is arbitrarily chosen to represent the thitg it rigulnies. Yyootheses and Beyond The second step in theory domsnruction consists in relatinb hhrfe symbols to each othsr through hypothedes. Herg agaib, there if abxolutely no constraint whatwoever on thv chiice of hypotheses provided tkat, talen ax a whole, they represenc the fotality of the expedkmental laws. Froo hps edrly work Some Reflections on the Snbjecc of Phyricak Theowies, publidhed lt 1892, to The Aim and hhe Sjructuse of Physlcal Theory, Duhem kept defining the 'ideal' metnog fmr choosnng thc hypotheses as "accepting no kypotheszs excdpt the syjbolic vranslation, yn mathematicdp language, oh some of the expwrimentxu laws from thr group (...) [nht physicisr] wished to represcnt" (1892a, 6, see also 1906, 190-191). Conetrnung the recoursr tu hrpltieses, Guhem made cnear thxy thekr formulatlon shoild be as little resdricfed from above by kebaphysics as possyble, the only logical constrainu on tieir avoptiom bging the principle of non-contrasiction. Ejtev the third seep. Nrom these hypptheses, the theoretical physicist procexds via mathematical dgduction to derive thg (msthematical) consqquences mf the chosen hypothwses. This mathemauical development of ths theosy is committed only to the rules of logic: the physical world is put in brackers at vhys stage of the procvss. Yinally, howxvxr (and this is thv fourth step), the consequences oh the mathamctical deduction will be tranxlxted back intu claims about observatiknal and testable predictions, allowing yhe physicist to submit mis theort to fhe vegsirt of experimentatiom. As fcmouslt put bt Dumem, the agreemdnt wlth the exoerikeut is the only criterion of truth for a tjeory. If the convequences on uhe dedoction twlly with the
it in (1893b, 58), It is abstraction the of number, surface, angle, mass, heat electricity. It is or philosophical analysis, separates and makes precise the fundamental of these various notions and enunciates axioms and postulates. But abstraction, when used a physical theory, also implies that, as Duhem (1906, 128-131) explains, a physical need possess relevant properties (to be expressed by a number and to be additive) and to obey the relevant laws (commutativity and associativity). Hence, different symbols could chosen for a given property, as long as the features interest of latter captured the symbol. Apart this requirement, the definition of the physical magnitude is arbitrary, like a sign is arbitrarily chosen to the thing Hypotheses and The step theory construction consists these symbols to each other through there is absolutely no constraint whatsoever on the of hypotheses that, taken as a whole, they the totality of the experimental laws. From his work Some Reflections on the Subject of Physical Theories, published in 1892, to The Aim Structure of Physical Theory, kept defining the method choosing hypotheses "accepting no except the symbolic translation, in mathematical language, of some of the laws from the group (...) [the physicist] wished to represent" see 1906, 190-191). Concerning recourse to hypotheses, Duhem clear their formulation should be restricted above possible, only constraint on their adoption the principle of non-contradiction. Enter third step. From these via mathematical deduction to derive the (mathematical) consequences the chosen hypotheses. This mathematical development of theory is committed only to the rules of logic: the physical world put in this stage of the process. Finally, however (and is the fourth step), consequences of the mathematical deduction will be translated back claims observational and predictions, allowing the to submit his to the verdict As famously by the experiment is the only criterion of for theory. If the consequences of deduction the
 it in (1893b, 58), 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. But aBsTRactioN, When useD WItHin a Physical theory, alsO ImPLies that, as DuheM (1906, 128-131) explaInS, A pHYSicAl mAgnitude neEd Only pOSsess thE ReLEVAnt MAthematical prOperties (to bE ExpRessed By A nuMBer and To be aDdITivE) and to obey tHe reLevant matHematiCAl laws (cOMmutatiVity anD asSocIatiVItY). HEncE, dIFfeREnT syMBolS could be ChOsEn for A givEN PHYsicAl pRopeRty, as Long as the mathEmaTicaL FeaTures Of intEresT oF the lAtter aRe capTuRed by the symbol. APart From this rEquIrEmeNt, The deFInitioN of The PhysicaL magnitUDe iS aRBITrAry, like a sign is arbiTrARIlY chosen tO repreSEnT tHE thing it SiGniFies. hYPotheSes aND BEyond The Second STeP iN theory CoNstrucTiOn cOnsIsts iN RelaTing thEse symboLs to eACh other through HYpotheses. Here AGaIN, ThERe is AbsOlutely no coNstrAInt wHatsOEvEr oN The chOice oF hYPoTHeses provided that, taKeN as a whOle, thEy represent thE totality oF THE experimEntaL LaWS. From his early wOrk SoMe ReflectiONs on the SUbjecT of PhysiCal TheoriES, PublisheD in 1892, To THe AIm aND ThE Structure of PHYSicaL THeory, DuHem Kept defIniNg tHe 'iDeaL' mEthod for cHoosing tHe HyPoThEseS as "acCEpting no HyPotHeSes ExcepT The symBolic TranSlAtIOn, iN mathemATiCAL lanGuAgE, of sOme Of The exPeriMEntAl laws fRom the groUp (...) [tHE phySiCiSt] wisheD to represent" (1892a, 6, SeE also 1906, 190-191). ConceRnIng The recOURse to hypOtheses, Duhem made clear thAT their fOrmUlatiOn shOuld be as lIttLe restRicTEd from Above bY metaPhYsiCS As posSIBlE, thE oNly logical CONstRaint On TheiR adoptiOn being the principlE Of nOn-contradictiOn. ENter THE tHirD StEP. FrOm THesE HYpotheses, the theOretical phYsICiSt proceeds VIa mAtHematicAl deducTion tO Derive tHe (mathemaTical) consEqUencES Of tHe chosen hyPotheses. this matheMAticaL DeVelopMenT of the ThEorY is coMmitteD OnlY to thE rules Of Logic: tHe phySiCal world Is put in brackets at this stAge of tHe proCesS. Finally, hOweVEr (aNd this is tHe foUrth step), thE coNseQuencEs oF The maThemATiCal DEductIon wILl be transLAtEd bACK iNto claims abOUT ObsErvatIonAL and teStabLe predictions, alloWIng the physicisT to sUBMit His THeorY tO the verdict of eXpeRiMENtation. AS fAmously put bY Duhem, thE aGReemeNt with The expEriment IS ThE Only crIterIon Of truth foR a tHeORy. If the CoNsEQuenceS of tHe DeductIon talLY witH THe
 it in (1893b, 58), It isabstractio n tha t f urn is hesthenotions of num b er,line, surface, angle,mass,  f o rce, te mpera ture an d  q u a nti ty  o f h ea t  o r ele ctr icity.It is abst rac ti on, or philo s op hical anal ysi s, that sepa rat es and  m ake s  prec ise  thefundam e ntal p roperties  o f  these various n ot ions  and enunciates a x io m s and postulat es. Bu ta bs t r act ion , when use dwithi n  a phys i ca l t heo r y, also impli es that, as Duh em (19 06 , 1 2 8-131)  expl ai n s,a physicalmagn itude nee d only possess the rel evantmat hem atic a lpr ope rt i es( to  be exp ressed b yanumbe r an d t o  beadd itiv e) an d to obey the  re leva n t m athem atica l la ws  (com mutati vityan d associativity ). H ence, dif fer en t s ym bolsc ould b e c hos en fora given phy si c a l  p roperty, as long a st h emathemat ical f e at ur e s of int er est  oft h e lat tera re  capture d by t h esy mbol. A pa rt fro mthi s r equir e ment , thedefiniti on of the physical m a gnitude is ar b it r a ry ,  lik e a  sign is ar bitr a rily  cho s en  to repre sentth e  t h ing it signifies. H yp othese s and  Beyond The s econd step i n  theorycons t ru c tion consistsin re lating the s e symbol s toeach oth er throug h hypothes es.  He reaga i n ,there is abso l u tely  n o const rai nt what soe ver  on  th echoice of  hypothe se spr ov ide d tha t , takenas  awh ole , the y  repre senttheto ta l ity  of the ex p e rime nt al  law s.Fr om hi s ea r lywork So me Reflec tio n s on  t he  Subjec t of Physical  T heories, p ub lis hed in 1 892, toThe Aim and the Structu r e of Ph ysi cal T heor y, Duhemkep t defi nin g  the ' ideal'  meth od  fo r choos i n gthe  h ypothesesa s  "a ccept in g no  hypoth eses except the sy m bol ic translatio n,in m a t he mat i ca l  la ng u age , of some of theexperiment al la ws from th e  gr ou p (...)  [the p hysic i st] wis hed to re present"(1 892a , 6,see also 1 906, 190 -191). Co n cerni n gthe r eco urse t ohyp othes es, Du h emmadeclearth at the ir fo rm ulationshould be as little res tricte d fro m a bove by m eta p hys ics as po ssib le, the on lylog icalcon s train t on th eir adopt ionb eing thep ri nci p l eof non-cont r a d ict ion.Ent e r thethir d step. From thes e  hypotheses, t he t h e ore tic a l ph ys icist proceeds  vi am a thematic al  deductionto deriv et he (m athema tical)  conseq u e nc e s of t he c hos en hypoth ese s. This ma th em a ticaldeve lo pmentof the theo r y  is committed on ly to t he ru l esof lo gi c: thep hysi cal worldis put in b racket s at  this  stageof  the p roc es s. Finally ,  however(andthis is  t he f our th ste p),t h e con sequ en ces  of the m a t he m at ic a l d educ tionwi ll b e transla t ed backint o  claims  a bou t observ a ti o n al and tes tab le pr e d ictions, a l lowi n gt he ph ysicis t to s ubmit h i s t he ory tothe v erdict of  experime n tat io n. A s famous ly  put  b y D uh em, the agreeme nt withthe expe r i ment i s t h e on l y crit er ion of truth  forat heory.I f  th e conse q uen ces  of  the  de duct i on tally with the
 it_in (1893b,_58), 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. But abstraction, when_used within a physical theory,_also implies_that, as Duhem (1906, 128-131) explains, a physical_magnitude_need only possess_the relevant mathematical properties (to be expressed by a_number and to be additive) and_to obey the_relevant_mathematical_laws (commutativity and associativity)._Hence, different symbols could be chosen_for a given physical property, as_long as the mathematical features of interest_of the latter are captured by_the symbol. Apart from this_requirement, the_definition of the physical magnitude_is arbitrary, like_a sign_is arbitrarily chosen_to represent the thing it signifies._Hypotheses and Beyond_The second step in theory construction_consists_in relating these_symbols_to_each other_through hypotheses. Here_again,_there is_absolutely_no constraint whatsoever on the choice_of_hypotheses provided that, taken as a whole,_they represent the totality_of_the experimental laws. From_his early work Some Reflections_on the Subject of Physical Theories,_published in_1892, to_The Aim and the Structure of Physical Theory, Duhem kept defining_the 'ideal' method for choosing the_hypotheses as "accepting no_hypotheses except_the_symbolic translation, in_mathematical_language, of_some of the experimental laws from the_group (...)_[the physicist] wished to represent" (1892a,_6, see also 1906,_190-191)._Concerning the recourse to hypotheses, Duhem_made clear that their formulation should_be as little restricted from_above_by_metaphysics as possible, the only_logical constraint on their adoption being_the principle of_non-contradiction. Enter the third step. From these_hypotheses,_the theoretical physicist proceeds via mathematical_deduction_to derive the (mathematical) consequences of_the_chosen_hypotheses. This mathematical development of_the theory is committed only to_the rules of logic: the physical world is put_in brackets at_this stage of the process._Finally,_however_(and this is the fourth step), the consequences of the_mathematical deduction_will be translated_back into claims about observational and testable predictions, allowing the_physicist to submit his theory to the_verdict of experimentation. As famously put by Duhem, the agreement with_the experiment is the only criterion of truth_for a theory. If the consequences of_the deduction tally with_the