Rend. Mat. Acc. Lincei s. 9, v. 16143-157 2005) Matematica.(5)

ABSTRACT. D ?i) The class of the axiomatic foundations mentioned in the title is called Ax Found; and its structure is treated in the introduction. ?ii) This consists of Parts A to G followed by the References. ?iii) In [17] Bressan's modal logic is treate

ONAXIOMATICFOUNDATIONSCOMMONTOCLASSICALPHYSICS...147

RemarkthatthisstronglyjustifieswhatIhavewrittenhere.Furthermore(ii)theaforementionedversionprintedin(D)belongstothearticlePitteri2003-seeAS1;3-printedinExtendPitt.(iii)LastlyInotethatitsmainpartwrittenbelowgivesusvarioususefulinformation(possiblynotdirectlyrelatedwithTruesdell'sletter)evenifitfailstobecompletedbyExtendPitt,sothatitisnotfullyunderstandable.

AS7,2(i)LetmespecifythattheMemoriamentionedinassertion(a)belowistheMemoriaLinceamentionedin[12]onp.24ofExtendPitt.Inhis1986-letterTruesdellstronglysupportedthismemoriaasastartingpointfortheextensionofMettocontinuousmedia(4).(ii)Truesdell'sappreciationofBressanappearsonp.259oftheworkPitteri2003-seeAS1;3-fromline-14toline-6,aswellasfrom(D)onp.21ofExtendPitt(mainlyfrom(D)'spart(e)).Furthermore(iii)forhisappreciationofBressaningeneral,onecanseeTruesdell1984-seeAS1;7-and,e.g.,item14intheContentsonitsp.503.There`FearofRealWorkinFormalLogic'ismentioned;andthementionedworkisperformedbyBressan.Incidentally,toseeN.Belnap'sobservationin10withinpagexxivofGIMC'sprefacemaybeusefultoo.(iv)LastlyTruesdell'sappreciationofBressanalsoappearsfrom(somepartsof)thepp.533to534inTruesdell1984.(Heknew,e.g.ftn.7onp.19ofExtendPitt).ThesocalledTruesdell'svolumeisthevolumeonwhichPitteri2003ispublished,i.e.thevolumecontainingthefollowing

SymposiumonrecentadvancesandnewdirectionsinMechanics,ContinuumThermodynamics,andKineticTheoryinMemoryofCliffordA.TruesdellIII,withinthe14thU.S.A.NationalCongressofAppliedMechanics,Blacksburg,June23-28,2002.

AS7,3Belowisourmainpart(a)to(h)ofTruesdell's1986-letter:themainpoints(a)to(f)(onwhichftns.(a)to(c)areplacedforexplanations)andTruesdell'sadditions,mainly(g)to(h).

(a)ThesubjectofthisMemoriabelongstoHilbert'ssixthproblem,`MathematischeBehandlungderAxiomederPhysik...',whichpresentlyisonlypartiallysolved.TruesdellmentionstheremarkablecontributionsgiventoitssolutionÏilhavybyNoll,Williams,Gurtin,Appleby,SÂ,Ziemer,Matolecsi,amongothers;thenheadds:(b)Allofthemhaveusedonlytheprocedureofmathematicalanalysis.Theiraxiomsareproposedasnecessaryconditionstoconstructmathematicalstructuresfitforconsistentandclearapplicationstophysicalsystemsandpresent-daytechnology...

(4)Onp.19ofExtendPittseethe1stparagraphofthetextandftn.3(where'[12]'justreferstotheaboveMemoria).