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Descriptionofmathematics
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–accordingtotheauthor’sintentions–aresupposedtosomewhatwidentheir
meaningand(implicite,atleast)illustratethem.
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Theaforementionedquotation:TheGodmadetherealnumbers,isoften
giveninaslightlydifferentform:TheGodmadetheintegers,thewholerest
ismadebymathematicians.
Butperhaps:TheGodmadetheformallogic...andthewholerestismade
bymathematicians?
Woulditmake(more)senseto(analogously)say:TheGodmadethe
musicalscale(basicsounds),andthewholerestismadebycomposers?Let
usnote,thatherewespeakofcomposing(henceinventing)ofmusicalpieces
(letusstress–pieces);henceinthiscontextweclearlyspeakofwhatwas
createdbycomposers.
Itseemsthatasimilarquestioncanbeaskedwithregardtoworksofart
createdbypainters,or,ingeneral,byallsortsofartists.Letusnote,thatthe
term“creating”itselfsuggeststhatweintuitively(but,really,justintuitively?)
areconvincedthatherewearedealing(more)withinventingthandiscovering.
Orisitperhapsthatbothinmusicandpaintingwediscoverthepossibilityof
invention(composition!)from(alreadyexisting)soundsorcolors?
Finally,isitthatthecreationinwritingisinsomesensesimilartothe
creationinmusicorplasticarts?Canweassumethatapoet,whowrotea
poem,discoveredthepossibilityofinventingapoem?
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Ishallriskhereadigressionregardingtheoriesspecificfornaturalsciences.
BeforedoingsoIshallremarkthatIintendtoremainona–primitiveone,
infact–intuitiveground,noteventryingtoconsiderwhether,forexample,
thereisadifference,orwhatsortofadifferenceistherebetweentheexistence
ofa“mathematicalentity”andtheexistenceofa“materialentity”.Iwould
onlyliketoshareanobservation(asuspicion?)regardinganalogiesbetween
thepossibilityofinvention(discoveryofsuchapossibility?)inmathematics
and,forexample,intheoreticalphysics.
Ifweagreethataphysicistdiscoversthestructureofthematter,the
questionremainshowdoeshedescribeit.Mostoften(Ithink)onespeaks
ofthisorthattheory,whichI–shallriskto–reducetotheconstruction
ofamathematicalmodel(mathematicalmodels).Couldwethensaythat
aphysicistdiscoversthepossibilityofinventingamodel?
Quiteoftenithappensso,thatamodeldoesnotcomplywithourex-
pectations(doesnotHreflecttherealitysufficientlywell”).Onetheneither
abandonssuchamodel,orHimproves”it,hencedefactoHproposes”(invents)
anewone.Isitnotyetanotherdiscoveryofthepossibilityofinventingof
a(“better”)model?
