E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) The BertrandRussellResearchCentre,McMasterU. russell: London arealsorecorded. or later,istranscribedhere.Theirjoin issues inRussell’sphilosophythathedi potential useoftopologyinphysics. Ru to followed upwithtwolongletters published somepenetratingcriticismsof when Newman Themostsubstantialoneoccurredin1928, cian MaxNewman. This articlereviewsthe interactions and relationshipsthatarenotdiscussedinthetext. tion is o and fromhismanyacquaintances.Thegainininforma- to letters of tions lifetime, paddedoutintothreevolumes(1967–69) by extensive transcrip- and organizations of the1960spromptedhimtohave it published in his B A particularly striking exampleisaletterthatRussellwroteinApril striking A particularly LOGIC, TOPOLOGYANDPHYSICS: POINTS OFCONTACTBETWEEN mously. However, the to bepublishedposthu- times from1931onwards,intendingit wrotehisautobiographyatvarious (1872–1970) ertrand Russell h ora fBrrn usl tde n.s.32(summer2012):5–29 the JournalofBertrand RussellStudies T set byalossincohesion,sincemanylettersinvolveactivities Centre forPhilosophyofNa BERTRAND RUSSELLAND i. w russell MAX NEWMAN Hendon, London I. Grattan-Guinness Middlesex U. Business School U.Business Middlesex London ivor2 ’ s philosophizedlogic W between Russell andtheEnglishmathemati- nancial demandsofhismanyactivities @ wc mdx.ac.uk Theexchange,whic rticles t involvementswiththeRoyalSocietyof tural and Social Science, Science, tural andSocial d not fully copewitheither atthetime not d 2 ssell onlogicalknowledgeandthe ssell a Russell’sphilosophyofscience,and nw 2 ae, uk ae, 4 bt , uk issn 0036-01631; online1913-8032 h openedupsome l.s.e. E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) to acorrespondent as “avery valuable critic”( mathematical objects, starting outwithde not justproofmethodsandderivationsbutalso needs: mathematical all to createabodyofknowledgesu sets of Cantor’s theory Georg and seppe Peano,andboltedontoithisownlogicofrelations ofGiu- logic mathematics. Around1900helearntofthemathematical fello bridge, hesoonwonaresearch ing inmathematicsand philosophy in 1894fromTrinityCollegeCam- including intheautobiography,anda few details su issues. thereisnoexplanationofthesource in anarticle;but,typically, made had agreed withsomecriticismsofhisphilosophythatNewman in whichhe mathematician”, 1928 to“MaxNewman,thedistinguished i. grattan-guinness 6 and individual items are cited in thestyle“ in arecited items and individual Anderson, indigital form muchof at itis available Russell ments. Thesignedholographoriginalsofletters sell’s Philosophy the philosophy, refreshing isP.Hager, through RusselltoGödel Cantor Mathematics from The SearchforMathematicalRoots, 1870–1940: tion ofthecontextsandotheraspectstheirrelationship. two letters each,istranscribedattheendofthis article, after an explana- markable lettersthatNewmansent writings.Nordidhereplytotwolongandre- his laterphilosophical Russell’s philosophythatRussellneverfullysorted out eitherthenorin construction of mathematicsmuchmoredi which renderedthere- paradoxes, serious logic andsettheoryadmitted sets.However,hesoonalsofoundthatboth of integers ascertainsets started a programme later called “metamathematics”, inwhichaxiom- started aprogrammelatercalled“metamathematics”, Around1900DavidHilberthad tics inthe1910sbutnotonlyone. most prominentgeneralphilosophyofmathema- the “logicism”. Itwas Principia Mathematica of hisformertutorA. tion 3 2 1 hasbeenwelldocumented, career Russell’s logicalandphilosophical Following the philosopher Rudolf Carnap,theirpositionisnowcalled philosopher the Following
On the mathematical sidesofRussell’sma the On Newman’s modest archive is kept inSt. Jo Auto 1 W In fact, Newmanhadpointedtosomemajordi In . 2: 176–7. Inalaterletter(25Aug. le, 2/15,containsbothsidesoftheex (Dordrecht:Kluwer,1994),a (three ofanintendedfourvolumes,1910–13). y N. Whitehead,theyputforwardtheircasein Continuity andChangeintheDevelopmentofRus- him laterin1928.Thefullexchange, na 1940 to L. Silcox)Russell praisedNewman to 1940 wship toseekanewphilosophyof lthough Newmanisnotnoted. Logics, SetTheoriesandtheFoundationsof change andseveralotherpertinentdocu- hn’s CollegeCambridge;thankstoDavid , [box]a-[folder]b-[document]c”.The Auto thematical logic seeI.Grattan-Guinness, 10.2 z (Princeton: PrincetonU. P., 2000). On . 3:39). W and http://www.cdpa.co.uk/Newman/ U nitions of the cult. Securingthecoopera- 10.4 are in the Russell Archives. theRussell in are U ce here. U W cient toful 2 nite cardinal U 3 Graduat- culties in W l , E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) case oftheDutchmanL. at that time tootherlogics,eithercomplementclassical logic or, in the is eithertrueoruntrue.Someattentionwasgiven asserted proposition by lawoftheexcludedmiddle,inwhichan two-valued logiccovered andmetamathematicswasthe“classical” logicism at all.Commonto the fewmathematiciansandphilosopherswhotookanyinterestinthem eclipsing allotherfoundationalstudiesamong By themid-1920sitwas properties ofconsistency,completenessandthe independence ofaxioms. atized mathematicaltheories,andalsoformal logic, werestudiedfortheir methods inmathematics. tionistic logic in which the lawwas rejected,alongwithallindirectproof “Neumann” in Britain duringtheGreatWarwasahandicapsu Britain in “Neumann” However, carryingthesurname year. mathematics triposinthefollowing in1915andtookpart Cambridge arship toSt.John’sCollege their onlychild,MaxwellHermann Alexander Neumanngainedaschol- Born inLondon1897toaGermanfatherandanEnglishmother, when hereturned surname to“Newman”,andMaxhadleavehiscollegeuntil1919, for hisfathertobeinternedasanenemyalien;thefamilychangedits terested instudyingRussell’smathematicallogic;upon but wentwithtwofellowJohnians. of theacademicyear1922–23atViennaUniversity.Hedidnotgoalone, distinction intheadvancedtopics. friends iftheywantedtogoalso. their colleagues;itseemslikelythathe FreudandKarlBühler decided togoViennameetSigmund o psychoanalysis, subjectsonwhichthetripos interested in the bearing upon logicandmathematicsofpsychology and Hebecame tripos(!). cal logic,whichwasabsentfromthemathematics close friends,anddoubtlesshedrewNewman’sattentiontomathemati- triposbyW. science(s) 1916, he specialized in traditional versionsoflogicastaught in the moral sell hadbeendismissedbyTrinityCollegeforhispaci As an undergraduate enrolling in 1919, Lionel Penrosehadbeenin- As anundergraduateenrollingin1919,Lionel careerwasveryunusual:hespentmuch Newman’s of The nextstep The otherJohnianwasRolfGardiner,thenoneyearintothelan- The 2. w and completed part Logic, TopologyandPhysics:RussellNewman newman y E. Johnson.HeandNewmanquicklybecame y E. y J. Brouwer,toreplaceitwith his own intui- ’ s unusual ii initiated ofthetriposin1921,witha “ bildung T ered severalcourses.He the visit, and asked and thevisit, ” W nding thatRus- W st activitiesin i U ofthe cient 7 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) down thestreetplayingachessgameintheirheads. town” ofVienna,wherePenrose and Newman would walkside-by-side aboutthattimein“the stilldeeplyimpoverished reminisced alittle in herautobiographyshe Bernal; Desmond a companiontothebiologist Gardiner’s youngersisterMargaret,whowastobecome an artist andalso Sir JohnEliotGardiner.Thethreeyoungmenwereaccompaniedby 8. Wirtinger; ordinaryprofessorWilhelm from only awelcomingletterofJuly1922 Nazis, the for and asanenthusiast guages tripos.Laterhebecamewell known inecology,organicfarming i. grattan-guinness 8 and Countryside”, Countryside”, and principal research interest wastoturntopology,which principal researchinterest mathematics wasdecisiveinchangingthedirectionofhisresearches.His 1984)”, forthcoming. 1984)”, a logicianseeI.Grattan-Guinness,“Dis (now “algebraic”) topology,likeNewmanhimself;thejuniorsta “algebraic”) (now Reidemeister,whowastobecomeaspecialistin“combinatorial” Kurt university gaveanextraordinarychairto the 1922 topology ofsurfaces;in represented atVienna:someofWirtinger’sownwork interacted with the speciality ofBritishmathematics.Bycontrast,itwasquiterespectably who however was rather ill at the time and may nothavemetNewman. and time the at ill who howeverwasrather KarlMenger, included cluded LeopoldVietoris;andthestudentbody inars on years heldtwofullsem- later tory seminaron“algebraandlogic”,in cation. Inparticular,duringNewman’stimeintownheranaprepara- a topicforundergraduateedu- also but not onlyasamatterofresearch of hisdaywhotookformallogicseriously,andmoreover mathematicians the veryfew of one also was he only aspecialistinthetopologyofcurves, the incompletability of ematik undPhysik and aseditorofthe identity, with tional calculus ofthe doctoral studentworkingonthecompleteness 6 5 4 Of Newman’scontactswiththemathematiciansinViennawehave But theoutstanding M.Gardiner, R. TheWirtingerletterisat y J. Moore-Colyer, “Rolf Gardiner, Englis J. Gardiner, Moore-Colyer, “Rolf Principia Mathematica 6 but it seems clearthatNewman’sexperienceofViennese butit A Scatter of Memories A Scatterof The AgriculturalHistoryReview he published both that paper and a sequel of 1931 on 1931 of sequel hepublishedboththatpaperanda W W rst-order arithmetic(whichwastoberegistered na gure wasordinaryprofessorHansHahn:not , 2–1–2. For2–1–2. more, details of Newman’s emergence as . Soonhe was to have Kurt Gödel as a z (London: Free Association Books,1988),pp.61– (London:FreeAssociation covering theLogician MaxNewman(1897– covering 4 and also the fatherofconductor also and h Patriot and theCouncil fortheChurch Patriot h 49(2001):187–209. Monatshefte fürMath- 5 W rst-order func- not T in- z a E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) 1991). Medvedev, engage with Russell’s philosophy;surelyoneseesheavyViennesein with aseriousinterestinlogicandeducationreadinessto Newmandevelopedasa(pioneer)British topologist, return After his chair inthe1890s)andRussell’sphilosophy. in acknowledging major advocatedpositivismandempiricism, strongly Hahn andlaterCarnap no agreedphilosophyamongallitsmembers,Schlick, had the Circle Verlag anannotatededitionofBernardBolzano’s member. leading Circle”, inwhichHahnwasa “Vienna created whatwastobethebest-knowndiscussiongroup,so-called in1923Schlick appointment and philosopherMoritzSchlick;after oftheGermanphysicist philosophy pointment tothechairofnatural hetooktheleadingroleinap- mathematics in1921.During1922 he returnedtoViennaUniversityasafullprofessorof several years, surrounded certainchairsintheuniversity.Afterteachingelsewherefor in 1905hetookpartsomeofthephilosophical discussion groups that to hishigherdoctorate mid-1890s the from student atViennaUniversity information onoccasion. endowedwithhistorical mathematicslecturesinthe1920s, Hahn’s of Popper admiredthequality as Gödel’shigherdoctorate).StudentKarl schaften Philosophical Society lungen axioms of choice in developing the theoryoffunctionsarealvariable, axioms ofchoiceindeveloping the of acollegefellowship,andsubmitted apaperontheavoidance for Soon ences here,especiallyfromHahn. Circle”, Circle”, Philosopher’ “A and wer, 1995),pp.235–45; Debate”, inW.DePa York: Springer,2001).OnHahnseeK. Rosenthal, “Integration und Di 9 8 7 Hahn alsosawhimselfasaphilosopher.Throughouthistime Our guide to the Vienna Circle is F. Stadler, F.Stadler, is Circle totheVienna Ourguide M. K. , Vol. 1 (Vienna: Springer, 1995), pp. 1 pp. 1995), Springer, , Vol.1(Vienna: y (Leipzig:Teubner), Vol. 2, pt. y R. Popper, “Zum Gedenken an Hans Hahn”, in Hahn, H. The MathematicalIntelligencer y A. Newman, “On Approximate Continuity”, Scenes from theHistoryofRealFunctions Scenes 3. w 23(1923):1–18.Onthecontextsee uli-Schimanovich, ed., uli-Schimanovich, newman Logic, TopologyandPhysics:RussellNewman X T 7 uences fromErnstMach(whohadheldthat erentiation”, in in erentiation”, ’ s viennesephilosophy? C (1923),pp.1031–1135[article z 17,no.4(1995):16–19. Sigmund, “HansHahnandtheFoundational Sigmund, s Mathematician: Hans Hahn and theVienna and Hahn Hans Mathematician: s –20. In 1920 Hahn publishedwithMeiner In –20. The Foundational Debate Encyklopädie dermathematischen Wissen- after hisreturnin 1923 he applied The ViennaCircle Paradoxien desUnendlichen , trans. R. Cooke (Basel: Birkhäuser, R.Cooke (Basel: , trans. Transactions oftheCambridge passim in P.MontelandA. in Gesammelte Abhand- 8 (ViennaandNew Further,while iic (Dordrecht: Klu- (Dordrecht: 9b]); andF. (1851). X y u- A. 9 9 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) 178–91). 88 (1922):151–65(repr.in Newman”, although occasionallyhealludedtoitsconcerns;anditmustbeamajor the fellowship.Heneitherreviseditnorseemedtoseek its publication, of theRoyalSociety 1984”, Alexander Newman7February1897–22 hiswrote obituaryofafterhe Newman, inwhichitis notmentioned (“Maxwell Herman H. Cunninghamand than Cantabrigian.Hiscollegereferees,Ebenezer Viennese more far thinking of for amathematician,andinvokingways a readinesstoputlogicsat the centre of the answer—bothmostunusual asource; matical paperbyHilbertas metamathe- draw onthetwo-valuedlogic,forwhichhecitedarecent thatthey used logics ent He distinguished between these two kindsofphilosophizingby encounters andonwhichhewishedtofocus. one physical objectsthat the worldofreal not applicabletothoseofrealphysicalobjects”with […] moving invacua,andsoon),“certainideals,orabstractions bodies mathematics(smooth stances thatwascustomarilyadoptedinapplied any watermarks. essay donotcontain the of his essayinVienna;unfortunatelytheleaves the futureVie of several members point of Physics”,namedatopicthathecouldwell have heard aired by in August. Itstitle,“TheFoundationsofMathematicsfrom the Stand- a longunpublishedessayinthephilosophyofsciencethat was completed some unspeci i.grattan-guinness 10 1923, manuscript, St. John’s CollegeArchives,item John’s 1923, manuscript,St. Hermann Weyl. on whichhecitedpapersbyBrouwerand logic, constructive to go would pen teAmsterdamsect.1,12 von ausgeschlossenenDritten”, (repr. in die neueGrundlagenkrisederMathematik”, Works, 12 11 10 We seeherenotonlyaconcernwithphilosophicalquestionsbutalso andcircum- In itNewmancontrastedtheworldofidealizedobjects y F. Baker, didnotmakemuchofth D.Hilbert, L. Newman, “The Foundations of Mathemat Vol. 1 [Amsterdam: North-Holland Vol.1[Amsterdam: y E. Gesammelte Abhandlungen, y J. Brouwer,“BegründungderMengen Bulletin oftheLondonMathematicalSociety
W “Die logischen Grundlagen der Mathematik”, ed itemconcerningsolutionsofLaplace’sequation,and 31[1985]:436–52). 10 12 Gesammelte Abhandlungen, (1918–19) . Theidealizingappliedmathematicianswould Verhandlingen derKoninklijkeAkademievanWetenschap- Vol. 2 [Berlin: Springer Vol. 2[Berlin: , no. 5 (43 pp.), no.12(33pp.)(repr.in pp.), (43 5 no.
It is alsonotnotedinP. It nna Circle.Maybehewrotesomeof , 1975],pp.150–221).C. Mathematische Zeitschrift 11 e essay but agreed totheawardof essay e butthoseinterestedinreallife lehre unabhängigvomlogischenSatz ics fromtheStandpointofPhysics”, f Vol. 3 [Berlin:Springer,1935],pp. Vol. 33.1. ItwasgivenbyJ. z 18(1986):67–72. Biographical MemoirsofFellows , 1968], pp.143–80). Mathematische Annalen y J. Hilton,“M. y H. z y 10(1921):39–79 H. Weyl,“Über the di y F. Adams Collected y H. V er- y A. E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) 1 and26–8. ematics, but thenabandonedit. ematics, cus tology asconveyedintherecently published in especiallypsychologicalaspects,inwhichhewas mathematical logic, Vienna after for have continued, it. Thatcontactwill in interest Penrose’s have gainedatCambridgefrom source ofhisrecognitiontheimportancelogic. Oliver andSirRogerPenrose. eticist, psychiatristandstatistician,alsofatherofthe mathematicians London,andbecameadistinguishedgen- medicine atCambridgeand before developinglogicism.The thathehadadoptedin1899 losophy thesameempiricistapproach importance ofmakinginferences. In addition,he maintainedinthisphi- of types,thetheoryde logicism ormathematicallogicasmuchpossible, especially thetheory emulated techniquesfrom or philosophical programmeinwhichheused bridge UniversityPressin1909,Ru phy in1927and1928.Aftergetting Newman’s newspecialitiesweretolead him to criticize Russell’s philoso- ics by taking due noticeofquantummechanicsandrelativitytheory. taking ics by The Analysis of Matter infer similarstructuresaboutentitiesinthephysicalworld. could alloworforbidusto wondering ifthestructureofourpercepts the sensationsin the discussion ofitsunknowableentitiesthatarecausing cussed uponourperceptsorsensations of the external worldandreduced text ontheVienna Circle among manyothers.Russell’sempiricismfo- as aFieldforScienti philosophy wasmadeinthebook X 14 13 In thesewaysNewmanbuiltupon the awareness oflogicthathemust Russell appliedthisalternativeapproachcomprehensively in his book (1922) uenced by Russell and also by LudwigWittgenstein’snotionoftau- also and Russell uenced by In the Penrose Papers, Univ Penrose Papers, the In W W. Demopoulos andM.Friedman,“BertrandRussell’s rst place.However,inlaterworkheraisedthe status of entitiesby . He even worked on adissertationthepsychologyofmath- worked even He 4. w russell Logic, TopologyandPhysics:RussellNewman W c Method in Philosophy in c Method z (1927),inwhichhealsoallowedformodernphys- W nite descriptions,thelogicof relations, andthe ersity CollegeLondonArchiv ’ s logicizedphilosophy 13 W Penrose wroteseveralmanuscriptson From 1925 he studied for a degreein rst extended statement of this kind of rst extendedstatementofthis Our Knowledge of theExternalWorld ssell hadembarkedonanambitious Principia Mathematica Tractatus Logico-Philosophi- (1914), awidelyin The Analysis ofMatter es, see especially boxes20– es, seeespecially o T toCam- X uential y : Its 11 14 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) they were used ornot;forthenit“wouldhavetobe reckoned among the similarity into levels of “importance”accordingtothecontextsinwhich Russell soughttoobtain. He alsoqueriedRussell’srankingofstructure- structure alonecouldnotdeliverthe information abouttheentitiesthat external world; the properties suchascontinuityofourperceptsand on structuretobe excessive, and moreover questionably dependentupon tum though not asanecessity.However,Newman foundthisemphasis desidera- are theircauses,withstructure-similarityasa that ones ceived signi metaphysically moreprimitive”entitiescalled“events”. Russell tookthemtobe“alllogicallycomplexstructurescomposedof cluded, forexample,electronsand quanta and not juststicksandstones. candidate causalentitiesin- importance ofstructure-similarity,sincethe the The attempttoaccommodatemodernphysicswasonesourceof criticisms. in hisletter which Russellreferred that appearedinthephilosophicaljournal Club inDecember1927 Science ity inalecturetotheCambridgeMoral acutely criticizedRussell’sepistemologicalhandlingof structure-similar- Whenthebookcameout,he order. points inspaceandonspace-time pare forpublicationthetwoontological chapters ontheconstructionof autumn of1926;Newmanwasinthe audience, and helpedRussellpre- Tarner lecturesatTrinityCollegeCambridgeinthe the as delivered “The StructureofthePhysicalWorld”.Somechaptersbookwere on “PhysicsandPerception”, andanontological logical part three parts:“TheLogicalAnalysisofPhysics”,anepistemo- It fellinto i.grattan-guinness 12 L’analyse delamatière Materie losophie der Interest”, Contemporary Contextand Historical cized especiallyChap.20.Kurt Grelling 29ofthe 28and Chaps. with helpedRussell 48. Newman N. Gri andth Demopoulos, “Russell’sStructuralism 2003), pp.392–419;andHager(n.3),Chap.4. 16 15 Newman, “Mr. Russell’s ‘Causal TheoryofPerception’ Russell’s‘Causal “Mr. Newman, Thenonetoolucid W U cance was the inference from known perceived events to unper- cance wastheinferencefromknownperceivedeventsto n, ed., The Cambridge Companion to Russell to The CambridgeCompanion z 5. (Leipzig:Teubner,1929).Thereis , trans. P. Devaux (Paris: Payot, 1965). Payot, (Paris: P.Devaux , trans. w analysing russell Analysis ofMatter quickly translated thebookintoGerman: , p.9. of April1928acceptingNewman’s e AbsoluteDescriptionoftheWorld”,in Philosophy ofScience ’ s analysis Mind (Cambridge:CambridgeU.P., also alater French translation: Analysis ofMatter . z 15 ”, It was this this article to was It Mind n.s.37(1928):137– 16 z 52(1985):621–39; Of particular Of W , and criti- nale on Phi- E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) of arithmetic andanalysis. of theoriesalreadyavailable, preted soastobepartofappliedmathemat arithmetictenceunlike and analysis, “Geometry is because important, itcanbe inter- sees, mindiswhatthepatient later presentationofhisposi cism orelsedrivinghimbacktophenomenalism. to the fore,butsurelyatriskofeither radically modifying his empiri- when there isaregioncommontoallofthem”, it brought things more it fortheirexistence: ofamanifold,unavoidablydependentupon structures are“moments” hiscriticismbypointingoutthat strengthened Husserl, hecouldhave I think,absurd.” whichis, prime unanalysablequalitiesoftheconstituentsworld, Philosophia, 1982). chapters whereNewmanhadhelpedhim: oneofthe in temporal continuityandco-punctuality,thelatterarising and recognizedtheirsigni and alsoappearsbelowasletter temological contexts. ences”, ences”, Reasonable (ThoughPerhapsLimited)E I.Delhi: Grattan-Guinness, Anamaya,also 2003); “Solving Wigner’s and Mystery: the major signi skin oftheapple.Whilestructure-(dis-)similarityisarelationship the be consideredontheirown;forexample,themaincourseofmealor contrast tomoments,partsofamanifold In can beproperlyformed. extra-structuralinformationisneededbeforephilosophy and percepts, sell’s structuresare shirts, or the colour shirts, orthecolour as astructure standing. Hager (n.3),p.176,defendedRussell’spo 21 20 19 18 17 beenfamiliarwiththephenomenologyofEdmund Newman Had In his letter to Newman that he was toreprintinhisautobiography was In hislettertoNewmanthathe B. Smith, ed., CompareDemopoulosandFr See especially R. Seeespecially Newman(n.15),p.147, quoting
AMa, The MathematicalIntelligencer p. 299. Newman didnotcommenton th W cance when developing a (new)theoryunderthein of zz somethingorthings,liketheprice Parts andMoments:StudiesinLogicFormalOntology 17 y Logic, TopologyandPhysics:RussellNewman S. Kaushal, between 18 of wedonothavestructuresin isolation but always zz the diaryor the tion Russell assertedthat“Ma Russell tion is thinking” (“Mind and Matter”, is thinking”(“MindandMatter”, W things suchas(un)perceivedeventsand our cance. Omittedcategoriesincludedspatio- cance. 19 Structural Analogies in Understanding Nature Structural AnalogiesinUnderstanding iedman (n.14),pp.630–2. itcannotcarrythesameweightinepis- z 30,no.3(2008):7–17. AMa 10.1 T ics”, which surely cont ics”, whichsurely ectiveness of Mathematics in the NaturalSci- ectiveness ofMathematicsin , p. 5. The passage quoted includes thesen- includes quoted , p.5.Thepassage sition, ongroundsth of , Russell agreed withthecriticisms agreed , Russell zz theapple.InsamewayRus- 20 holding“between is bizarre structure-similarity. Ina tter iswhatthephysiologist 21 of radicts theapplicability zz themeal or PfM at surpassmyunder- , p.151).Recently W ve events (Munich: X of uence (New zz the can 13 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) a touch in the two parts di parts a touchinthetwo “Two partsofmybodyarecontiguousifthequalities by which I locate touch”, where and appealed to“contiguity”,“apropertygiveninsight in which two simultaneous parts of oneexperiencearerelated.”Healso ly”; thus “Twoeventsare‘compresent’whenthey arerelated in the way them simultaneous- experiences person one two ormorequalitieswhen thislatitudebyinvoking reduce 1928 had neverhappened! questioned”, asiftheeventsof be could tion treatedassomethingthat confessed to“havebeensurprised he replying tocriticismsfromErnestNagelintheSchilppvolumeof1944 itinlaterphilosophicalwritings.When about seems tohaveforgotten W. i.grattan-guinness 14 Analysis ofMatter a geometryisonehavingsubstantia from experience, thestat derived tion is de relation must bea one, suchasmight be apurelylogical is intended togiveempirica physics Since percept ble, NagelhadalsofailedtowarmRussell’sconclusionthatsincea such aswavesorparticlesinquantummechanics. wehaveimmenselatitudeintheinterpretationofoursymbols”, sense, the empiricallyknownrelationof‘neighbourhood’intopological knowledge of the physicalworldisonlyasto structure resulting from tion (butwithoutnaminghim)that“Inphysics,assumingour in particular,hisdiscussionof“structure”heechoedNewman’sposi- be in somenervethebrain, examining.” brain heis the he looksatabrainispartofhisownbrain,not y Russell did not publish a reply to Newman either then or later, and later, or Russell didnotpublishareplytoNewmaneitherthen 25 24 23 22 In T. Stace (p.355). T. Stace
Schilpp,pp.335–6(Nagel),p.702(Russell)
HK AMa HK Human Knowledge , pp.315,347. , p.273. of , p.383. z the world has to be also somewhere in theworld,whichmust theworldhastobealsosomewhere 23
z among theSchilpp critics was largely W ned in terms derived from expe derivedfrom in terms ned z (1948) Russell gave perceptionsomeattention: (1948)Russell 22 T Perhapsforrenderingbrainsurgeryimpossi- er verylittle.” therefore “compresence”, “whichholdsbetween l empiricalcontent,butifnot,not. be constructedinpuremathematics,but ement thatspace-timehassuch-and-such l truth, theorderingrelationmustnot z “what the physiologistseeswhen “what W ; see also p. 716. The reception ofthe ; seealsop.716.Thereception nd the causal theoryofpercep- 25 Thus,regardingspace-time, critical, comprehensivelysowith rience. Iftheorderingrela- 24 He attempted to Heattempted E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) true orneverinthesecondeditionof characterization oflogicalpropositionsasalways The Wittgensteinian beyond theoverallcommitmenttoempiricism. or relationsisunclear guage remainsmute; in particular, the status ofpropositionalfunctions relationship tolan- theory oftruth-functionspropositions,butthe characterizing logic;forexample,in devoted tologicalknowledge.Logiciansareoftencuriouslycoyabout reformulations ofhisreservations(letter Newman’s reply toRussell’sletter,sentinMay1928,contained elegant on Russell’sphilosophy. never beenincludedinanyofthebook collections of reprintsarticles has essay Newman’s and to attractmostofRussell’scommentators, not the book was reprintedin1954(andalsorecently),these issues continue ment (where Husserlisalsoomitted);theyarisein connectives andquanti ofpossibilitiesisincreasedbytheinterde choice veil. The in whichweknowthesesensibleexperience. notion of“ “Ishouldliketotakeasprimitive”the letter his in did Russell,since than and beliefs,Newmanstoodfurtheralongtheempiricistdirection metalogic asdistinctfromitshostlogic. hampered bythefailureofmostlogiciansexplicitlytorecognize was age Newman alsocharacterizedhispositionas“onethinghappeningafter example, For losophers, cuttingtheirownthroatswithOckham’srazor. categories ofknowledgethatoftena of paucity a pertinent contrastsbetweentemporal and spatial knowledge, onesenses clearly recollectedfromtheunpublishedessayof1923.Whilehemade terminating procedures,suchasmanipulationsofmathematical symbols, I suggest thattheorderingrelationis 26 These topicsdonotappearin Maintaining that logicisprimarilyconcernedwithhumanmeaning that Maintaining
HK (1959), butthe , pp.346–7. things happening Logic, TopologyandPhysics:RussellNewman Analysis ofMatter W 6. ers; the clarityofdiscussionin that pre-Gödelian w newman onlogic z ”. His examples of such“processes”included A HistoryofWesternPhilosophy contiguity orcompresence,inthesense is only mentioned once. Although is onlymentioned Principia Mathematica 10.2 Principia 26 My Philosophical Develop- My Philosophical ), but thebulkofitwas but ), T ects reductionist phi- ects reductionist z onlylightly lifts the W nability of z logicisa (1945) 15 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) speci soonafteritappeared”in1931onsomeun- proof you aboutGödel’s however, in 1966NewmanwrotetoRussellthat“I remember talking to for achat(letter Russell expressed surpriseatNewman’sapproachandinvitedhimdown cance ofGödel’stheorems. tinguished metalogicfromitshost logic and so never grasped thesigni while Russelladvocatedhierarchies of languages from1921,heneverdis- Positivist Hahn held thatlogicwasconcernedexclusivelywith which (a)logicisonesourceofknowledge. within theorizing subject to extra-logical perceptibleoccurrencesthatcanbe but such, as not logical pluralism ofthe1923essaywasmuchpreferable.Thingshappeningare dependent? Andissimultaneitybetw logicalwaystobetime require and have togothisoppositeextreme logichasbeenamajorhumanfailingformanycenturies,dowe poral torecognizetheimportanceoftem- failure another”. Grantedthatthe i.grattan-guinness 16 place graduallyfromthe1940s. his secondletter.Whatdidhehaveinmind? principal mathematicalinteresttobearhere,andalsoin He broughthis Logic may refer, expression,notwiththeentitiesoreventstowhichlanguage linguistic for about twenty years, under the name of Combinatorial Topology.” of for abouttwentyyears,underthename researches mathematical systems ofrelationshavebeenthesubject of ships requiredmoredimensionsintheir representation: “Suchproperties relation- complicated bouring dotsinacircle,andhenotedthatmore people representation ofaquartet between perceptionandtheexternalworlda similarity partial structural footnoteto his articlein a In In his reply of August 1928 from hissummerhomenearPenzance, In hisreplyofAugust1928 30 29 28 27 Envisionedbranch asa of mathematics by G. Newman,lettertoRussell,25September1966( Newman(n.15),pp.139–40.Thechange SeeGrattan-Guinness(n. F. Ablondi, “A Note on Ha 13(2002) W ed occasion. 7. 27 w alinethatNewmancouldhavepro : topology 37–43. 10.3 28 The conversationwouldhavebeencurious;for, The ). It seems not to havetakenplaceatthattime; to ). Itseemsnot ( 3), pp.327–8,388–91,592–3. not 29 hn’s PhilosophyofLogic”, ) Mind inbritishmathematics in which acquaintances wereneigh- in een events impossible? The logical events impossible?The een z Newmangaveasanexampleof of name to “algebraictopology”took to ofname na , 2–15–11; W y W. Leibnizunderthe tably followed. History and Philosophy of History andPhilosophy ra 1 710). means W of 30 - E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) neer he becametoanotableextent experience turned fromhisVienna British mathematics lay in point-set topology. ThuswhenNewmanre- rise oftopology;forexample,itsonlyplacein the in played majorroles name Another exampleisprovidedbytherectangle (lack of a mapofrailwaysystemwhenitrepresentsthe is topological object ofthecityKönigsberg;acommonkind rivers the bridges across oftouringtheseven familiar topologicalsituationsistheimpossibility its continuousdeformation.Among under unaltered below, thatremain inside oroutside,neighbouringdistant,above as such domain a of ena that manifestedinthevariable curvature of space. tributed aproposalto interpret matterandmotion aselectricalphenom- the theoryofknotsP. Kelvin, examples includevortexatomswithLord mathematics: in ing, especially “common-sense” philosophyhademphasizedspatial-topologicalthink- issurprising,forthetradition ofScottish This not intheBritishIsles. Oxford U.P.,2011). in R.Flood,A.Rice Victorian Scienti Foundations ofthe BC Join ing Europe (suchasVienna),Paris,the ing only onesideandedge. tain theMöbius-Listingband,whichmergesinsidewithoutsideandhas 32 31 Topology had been developing especially at centres in German-speak- in had beendevelopingespeciallyatcentres Topology z andgeta doughnut. Alternatively, join See See R. Olson, SeeR.Olson, researcher inalgebraictopologyBritain. D analysis situs z to passim zz W ) connections betweenstationsbutnottheirdistancesapart. ) connections A B elds of forces in the electromagnetism of Clerk Maxwell, and elds offorcesintheelectromagnetismClerkMaxwell, A z and in I.
y C M. James, ed., M. James, Scottish Philosophy andBritish Scottish and R.eds., Wilson, , topology focuses upon place and position,properties place , topologyfocusesupon Logic, TopologyandPhysics:RussellNewman z to B , and obtain a cylinder; thenjoinend y G. Tait.TheEnglishman W. W c Style History ofTopology z (Princeton:PrincetonU.P,1975);and Mathematics inVictorianBritain D C usa and theSovietUnion, Physics, 1750–1880: aStudyinthe D Figure 1 (Amsterdam:Elsevier,1999). z to B z and 32 Yettheyhadnot y K. Cli C z to AD A T z ord con- andob- (Oxford: z toend 31 passim but pio- 17 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) sequence of polygons polygons sequence of boundary edgesde not. Aclosedsequenceof is on eachedgeisrelevantbutthestraightness tices” terminate each edge, and no edgesintersect;theorderofletters linear programming. time alsointhegeometryofnumbers,mathematicaleconomicsand property ofasimplexwasconvexity,whichfeaturingstronglyat that a commonedge.Animportant with triangles could betakenasapairof on [London: O ( session Frank Ra same (1926): 222–7.Atthe “the simplex”,andcompoundsofthem“complexes”. and then to the“point”);foralldimensionsgeneric term was called in threethe“tetrahedron”,andsoonup(andalsodownto“edge”, curvilinear sides.Intwo dimensions thebasic“unit”was“triangle”, triangles withrecti-or by cal relationshipsofa“surface”bycoveringit to representthetopologi- various methodsthathedescribedpreferred Advancement ofScience. Associationforthe British the in August1926attheannualmeetingof 8i.grattan-guinness 18 in James[n.31],pp.1–24). 1877 (T.CrillywithD.Johnson,“TheEm Georg Cantorhadshowntheisomorphismbetw (Newman onpp.216–17). schiedenen ZweigederTopo in topologybythelate1920s:H.Tietze Wissenschaften sided; otherwiseitisone-sided,liketheband. such cases the surfaceseparatesitsinteriorfromexterior and so is two- cancel out;forexample,edge andso quence), andalltheinternaledgesareusedinbothdirections the sequence Report of the British Association for the AdReport oftheBritishAssociation for Figure 2,baseduponNewman’sdiagram,showsa surface. Two “ver- One of Newman’s actions was to expound the “combinatorymethod” expound to was One ofNewman’sactions 35 34 33 analysis situs Thede Newman,Combinatory“The Method inAnalysis Situs”, M. Dehn andP. Heegaar U W nability of dimension wasitselfama of nability , Vol.3,pt.1,pp.153–220(1907,article ce of the British Association, 1926],p.342). Association, ce oftheBritish EC z in the German mathematical encyclopedia, mathematical intheGerman , W CD nes anoriented“surface”.For example, the ordered ECF , DG logie”, Vol. 3, pt. 2, pp. 144–227 (1929, article article logie”, Vol.3,pt.2,pp.144–227(1929, 33 d, “Analysis Situs”, in in Situs”, d, “Analysis Taking as the basicguide an article of 1907 , , CDGF GF GJ , z in and L. Vietoris, “Beziehung der zwischen ver- JH ergence ofTopological Dimension Theory”, vancement ofScience,Ninety-FourthMeeting , CDGF GJHIEF , msey talkedabout“mathematicallogic” HI een the unitlineandsquarein een , jor researchtopicintopologysince z iiiab IE andedge Encyklopädie dermathematischen z z hasasitsboundaryedges (and alsothereversese- (and 3). An article updated progress 3). Anarticle Mathematical Gazette FG 35 z in Therectangle 34 GJHIEF amongthe iiiab . In 13) z 13 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) had recently explored in combinatorytopologyingeneral. in had recentlyexplored anapproachthat he of edgessimplexespossessingcommonvertices, relationshipsrenderedinterms with cally intermsofneighbourhoods, bestexpressed set-theoreti- be atomic dimensions”.Theselattermight of spacetime plication ofstatisticstoform“lawsaboutsmallpieces Koninklijke AkademievanWetens the intervalbetweentwopoints reconciling the topology with thespace-timemetricand relation of of sequencessimplexes.Buthewa odicity ofthesephenomenawasrepres The peri- drew atetrahedroncontainingsevenverticesforthepurpose. within space-timeasa“mosaic”of“4-dimensionalsimplexes” ible sion andabsorptionina“luminousevent”; both quantummechanicsandrelativitytheory. insomeofRussell’streatment topology for in detail,andsawscope had recently tivation wasthathe mo- His metamathematics). of Hilbert hadmadeastrongpresentation tending the International CongressofMathematiciansatBologna(where to Russell, which he sentfrom Italy in September 1928 soon after at- This material lay behind the proposals of Newman’s second letter ( second Newman’s of This materiallaybehindtheproposals Newman envisioned“the 38 37 36 One candidatefortopologicalinterpretationwasthetheoryofemis- Newman, “Onthe Foundations of Combinatory AnalysisSitus”,
AMa AMa I E J , esp. Chap. 35. , esp.Chap. , esp. Chap. 33. , esp.Chap. 8. H G D H F C w newman onthetopologyofphysics Logic, TopologyandPhysics:RussellNewman chappen teAmsterdamsect.1 W nal uni 37 W inrelativitytheory. nished readingthe s alsounderstandablyunsureabout W ented bycorrespondingrepetitions ed statementofphysics”asan ap- 36 Newmansawitasexpress- z 29(1926): Analysis ofMatter Figure 2 Verhandlingen der
38 611–41. Heintro- X 10.4 , and 19 ) z E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) British Association. British would comebackintoplay. connections withtopology.Maybesomeset-theoreticformulations emerges;theproposedrevisionofconvexitywouldweaken Figure 2, longing to of ( not feature prominently in the physics of the story” the prominently inthephysicsof feature not time orlater.Indeed,“topologydid that at either sure whattocookinit, duced thenotionof“ i.grattan-guinness 20 (at 308–9). constituent simplexes.However,he U developing.” geometry weare ‘straight’; straightnessisanotionwhollyforeigntothe example, “The‘lines’thatwearede Newman’s assistancemayhaveriseninplacestoghostauthorship;for onspace-timeorderwhere chapter the notably andnotaccidentallyin “Analysissitus”doesfeatureinRussell’sbook, physics wouldlooklike. edges, itisnottooclearwhathistopologicalrepresentationofmodern themsuchas absorptionasjoining vertices andrelationshipsbetween as particles cryptic: inparticular,beyondhavingelementary rather also is ity. made primitivesincetherewouldthenbenonecessity to invokeconvex- suggestedthatco-punctualeventsbe and should belogicallysimple”, rest. Hedemanded,rathercryptically,that“thecharacterizationof uponwhichthetopologywillpartly continuity, example, theneedfor events onwhichstructureisbasedandfromcausalityfollows:for theunderratedstatusof namely about yourtheory”ofstructure, space-time. a ‘4-array’(groupsof5)”in the tetrahedron that represented (relativistic) represented as“verticesof protons-, andquanta-at-an-instant”couldbe were appropriatelylabelled.Inqu , whose entries are de are , whoseentries 41 40 39 topological kitchen,butwasnot his out Newman seemstohavelaid “Please excusethisenormousletter”,endedNewman.Whilelongit grumble Newman concludedhisletterwithareturnto“mychief n C. Nash, “Topology and Physics—a Historical Essay”, in James (n.31),pp.359–416 James in Essay”, C. Nash, Historical “Topology Physics—a and
Alternatively,Newmanmighthavehadin AMa, AMa, z +1)-simplexes to which they belonged; for example,theseptetbe- for +1)-simplexes towhichtheybelonged; p. 307. X z was “made into a 2-array” when the verticesofitstriangles when 2-array” a into was“made 39 But no surface of a topological analysis of matter,suchas analysis topological Butnosurfaceofa W ned in terms of the topological relationships betweenits relationships ned intermsofthetopological n -array” of vertices,speci 40 had notpresentedthisappr antum mechanicstalkof“electrons-, mindthe incidence matrix ofacomplex W ning arenottobesupposed W oach in his lecturetothe 41 ed bythe collection forsomedecades; points E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) same shiptothe tember 1927,whenthey(and logician) Oswald Veblen. logician) Oswald withthe topologist (and ton, wherehespenttheacademicyear1928–29 Within weeksofhissecondlettertoRussell,Newman was o topological too (repr. closed down, perhapsbecauseofdisa closed 1933–34,heranitonlyforthe twosucceedingyearsbeforeitwas year academic axiomatic theoryandintuitionisticmathematics.Readyforthe ematical logic and logicism butalsometamathematics,Gödel’stheorems, mathematical tripos;itcoverednotonlymath- Cambridge the into insert course onthe“Foundations ofMathematics”thathemanagedto new buthisinterestinlogicwasevidenta ready dominatedbytopology, physics”, publishedinMay1928,hestated,ratherinaccurately,that later writings;inparticular,apo lay beyond hiscompetence.However,topology features occasionally in may guessthatitscontents one letter; this seems nevertohavereplied Mathematics Research, 1896–1939”, in Asp on thepuretheory. of Di techniques. nent context,anditdrewmostonset-theoretic the roleofdi of AlgebraicandDi Among hislaterphilosophical books, former university,butIcannotguaranteethatthereplywillbeintelligible. wishes toknowwhatacageis,Iadvise othe versities, onethatofPrinceton,the mathematics calledtopology,whichison To de among students. However, during the years 1938–41hewas somehow years among students.However,duringthe 44 43 42 Russell,“PhysicsandMetaphysics”, See,forexample,R.Penrose(son W. Aspray, “The Emergence ofPrince Emergence “The W.Aspray, V Papers erential Topology inRelativity W ne a cage is a most complicated problem in a very modern branch of ne acageismostcomplicated probleminaverymodern 10: 273). He will have had chances to 10:273).Hewillhavehadchances (Minneapolis: U. of Minnesota P.,1985),pp.346–66. U.of Minnesota (Minneapolis: T usa erential topology in relativity theory was the most promi- erential topologyinrelativitytheorywasthe V T erential Topology1900–1960 . er. Logic, TopologyandPhysics:RussellNewman 9. w newman ray and P. Kitcher, eds., ray andP.Kitcher, the RussiantopologistP. 44 Hiscareerinmathematicalresearchwas al- (Philadelphia: of LionelandstepsonNewman), ’ s latercareer Saturday Review ofLiterature him to writeProfessorVeblenof the pular articleon“PhysicsandMeta- pular r that of Moscow.If anyofmyreaders that r ton asaWorldCenterforMathematical Human Knowledge ly properlyunderstoodintwouni- (Basel: Birkhäuser, 1989),concentrates Birkhäuser, (Basel: T ection amongsta discusstopologywith Veblen in Sep siam History andPhilosophyofModern y S. Alexandro , 1972).J.Dieudonné, Tz (1948) haslittle ) travelledonthe z 4(1928): 210–11 T T aswell toPrince- 42 Techniques Russell A History 43 21 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) example, J. 1983), esp. pp. 90–4. Amongthelargeliterature to timelater. sion onlogicforwhichRussellhad hoped, contacts occurred from time Mathematics atManchester. of onlogicattheSchool,andthenheadofDepartment author even co- and colleague time: versity. Newmanwasalongsidemuchofthe Laboratory andthenatManchesterUni- Physical National the puting at theSecond WorldWar,andpostwarinvestigatorincom- during Park School atBletchley extraordinary atthegovernmentCodeandCypher Turing’s lifeweremomentous:expe theory, ofwhichNewmanwastheonlyBritishstudent.Thee 1935 andlearntofmetamathematicsrecursion foundations coursein threeyearslaterhesatinonNewman’s uate, andaftergraduating e papers. tocontinueplacingquestionsonfoundationsintheexamination able i.grattan-guinness 22 a memorialmeetingmountedbytheRationalistAssociationinJune the task.However,hecontributedapleasantsurvey of Russell’s logicin himself inhis70sandnotabletoful was he then by but Society; Royal forthe obituarist heagreedtobethechief when Russelldiedin1970 in1962,and a messageforthecelebrationsofRussell’s90thbirthday sent Newman successful. Member in1966;eachnominationwas Foreign Gödel as of ination ofTuringasFellowtheRoyalSocietyin1950and andRussellsecondedboththenom- Russell’s backing:heproposed a FellowNewman furtheredthecauseoflogicthere,with As 1939. in Society, secondedbyJ. Royal History ofComputing ofComputing”, Pioneer and Codebreaker, Topologist, Newman: hisplaceincomputerscience but lacking, Newman’s activities of P., 2006).Thedetails questions, seeGra questions, T ects upon his later career. In 1931 Alan Turing arrived as an undergrad- an as upon hislatercareer.In1931AlanTuringarrived ects 47 46 45 RussellandNewmanneverseemed tohaveheldtheirdiscus- While Newman’s secondaryinterestinfoundationswastohavemajor But FordetailsofthisphaseNewman’s Documentsonbothsides A.Hodges, 45 y M. Copeland, ed., M. Copeland, 47 Alan Turing:theEnigma In 1936 Hardy hadproposedNewmanasFellowofthe In1936 ttan-Guinness (n.6). z 29(2007):76–81. Colossus: the First Electronic Computer Colossus: theFirstElectronic are gathered together in togetherin gathered are 46 y E. Littlewood, andtheelectiontookplace (London: BurnettBooksandHutchinson, rtise in computability, code-breaker rtise incomputability, is nicelysketchedinD.Anderson,“Max career, includingtran attheSchoolstillseemtobesomewhat on the early historyofcomputerssee,for the on na , folder2–15. (Oxford:OxfordU. scriptions ofallhis IEEE Annalsofthe T ects on W l E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) in 1970. 10.1 and unusualcareerhasstayedintheshadows. na 49 48 nuity of perceptsandnon-perceptswassoaxiomaticinmy of nuity that spatio-temporalconti- was realise did my metaphysic.WhatI would weakentheplausibilityof it your criticisms,noryethowfar aloneinaddition tostructurewouldprotectmefrom punctuality perceptible. garded as a relationwhichmightexistamongperceptsandisitself from oneendofthe universe to theother.Andco-punctualityIre- compresentwithit) another number ofsteps(fromoneeventto percepts andnon-percepts, even thatonecould passbya had assumed thattheremightbeco-punctualitybetween I is tosay, assumed spatio-temporal continuitywiththeworldofpercepts,that had always I known aboutthephysicalworldexceptitsstructure. that say, did I fact in had notreallyintendedtosaywhat to laystress).Itwasquiteclearme,asIreadyourarticle,that involved is improbable, thecardinalnumber not is as as itwouldseemtobe,if, the wayisnotquitesotrivialanassertion dinal number.(Thisby assertionaboutitscar- an ceptible tosuchandastructureis assertion aboutthe physical world involved in sayingthatitissus- myself. somewhat ashamedatnothavingnoticedthepointfor ial, andIam about thephysicalworldexceptitsstructure are either false ortriv- ly obviousthatmystatementstothee me in“Mind”. w Newman’spieceappeared untitled in Published byRussellin Published , 2–15–20,22and32. Many thanks for sending me theo sending Many thanksfor Russell, 24April1928,fromPeters I havenotyethadtimetothinkouthowfartheadmissionofco- you pointout,thattheonlye as It isofcourseobvious, entire- it make You read itwithgreatinterestandsomedismay. I 48 He died in 1984, in his 88th year, and much of hisremarkable W nite. This,however,isnotapointuponwhichIwish Logic, TopologyandPhysics:RussellNewman 10. Auto. w the fourletters 2:276–7. New Humanist W eld T T -print of your article about y 49 ect that nothing is known is ect thatnothing z 1 (Dec.1972):321–2;materials nothing T ective W nite z is 23 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) 10.2 4i.grattan-guinness 24 out—has somebearingontheproblem. have heldforsomeyears—andhopetimeorothertowork the foundationsoflogic thatI on I have.Butthegeneralposition system at least roughlyoutlinedinmyhead,andIcannotpretend I thoughtitwouldbefoolishtodosowithouthavingacomplete stract speculations. questionsleaveslittletimefor moreab- making upexamination you doso. butIdonot quiteknowhowde voured phenomenalism, youthatfa- with your ownpositionis.Igatheredintalking fromyourarticlewhat merely negative,sinceitdoesnotappear arenot which know whetheryouhaveanyideasonthematter thought, butIshouldbegratefulifyoucould it. thoughts thatIfailedtonotice my statementsappearedtodeny “ I thinkto an altogether more rudimentarysetofideasfromwhich the pagebeforemetheprocesswillterminate,belongs on the letters statement, the beautiful economy,but an unde than because they are truly primitive. Theadoptionof than becausetheyaretrulyprimitive. convenience place ratheronaccountoftheir their won have science tion. cessarysigni assured ne- the have to me between unperceived“events”doesnotseemto beyonddoubt,butIconfessthat“causalproximity” places think That the beliefssigni whose terms ofconcepts refer in some wayorigin ofthesolarsystem—andproblemistoanalyzethemin to structure[,]the world—e.g.about of parts unperceived edly connectedwith your analysis I sentially oneof '
w In the I madenopositivesuggestionsin my articlein“Mind”because I hopeyouwillexcusemylongdelayinanswering your letter— I am at the moment much too busy to give the matter proper The conceptsordinarilyregardedasfundamentalinlogicor ” shouldbe constructed when Newman, 29May1928,fromSt.John’sCollege W W ned symbolallowsformallogictobedevelopedwith rst place you will probably agree that the problem is es- rst placeyouwillprobablyagreethattheproblemis z
meaning W cance, atanyratewithoutfurtherexamina- z —we have certain beliefsthatareundoubt- —we have meaning W cance we feelassurepossible. cance e.g. z isthequarry.Thenotion , thatifI “count” through W nd time to let me nd timetolet ' x
W . z f nitely x z as E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) I sh[oul]d like to take as primitive is that of of I sh[oul]dliketotakeasprimitiveisthat certain given process terminates withanumberthatsatis certain givenprocess certain equationmeansthata a of solution a ment thatthereexists ofsymbols,andthestate- rows going throughandmanipulating ofmathematicsconsistin will cometoanend.Theoperations kind typeofpropositionisthatacertainprocessthis primitive arowofthings”,andthemost to thenotionof“goingthrough This leads individualized to“onethinghappeningafteranother”. logic weareconcernedwithperceivedhappenings,whichcanbe caseI am afraid you will not make much of this rather confused caseI amafraidyouwillnotmakemuchofthisrather same place”)issu events. unperceived to applied my perceptsandcannotbedirectly notion ofspatialseparationisdirectlytraceabletoqualities the (unperceived) thingshappeninginsuccession;whereas meaning of direct apprehensionofthe a have I present. Anditseemstomethat is quitedi just past,over,gone.TherelationofLondontomy present location about past events—they are past, not“relative”tothepresent,but absolute something from thosethatarenot.Thereis happening are the Th[eor]y of Relativity, whichdoesnotdistinguishevents May, hasnoexactspatialanalogue,anddoesnotappearas a fact in that weare E.g. theimportantfact all. at touch not does pects oftimewhichit itself distinguishtime-likefromsp the th[eor]y by theGeneralTh[eor]yofRelativity.Notonlydoes of spaceandtimerequired assimilation the easy tostresstoomuch of “thingshappeningoneafteranother”(inthesame locality). It is less. it; thequestionwhetherit “exists” between thechangesismeaning- from theset of “happenings”—quantumchanges—associatedwith abstracted on myviewanatomistobe example, For entities. static consists ofevents”,butI conceive of your events as in awaymore underlying ourbeliefsabouttheexternalworld. theprimitiveone is that it isthisnotionof“thingshappening” thefoundationsofmathematics,butIinclinetobelievethat with chie idea equation. Ihavehithertopursuedthis Whether this notional theme is happening in succession (“atthe in happening is Whether thisnotionaltheme We may, I think,gofurtherandadmitassigni may, We It is possibly just this that you mean by sayingthat “the world T erent in this respect from the relation of the pasttomy erent inthisrespectfromtherelationof now Logic, TopologyandPhysics:RussellNewman z in the year 1928, andno other, in the month of U cient to make a world I don’t know.Inany I world cient tomakea ace-like vectors, but thereareas- vectors, ace-like things happening. things X W y inconnection cant the notion cant the W es the In 25 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) 10.4 10.3 6i.grattan-guinness 26 dor tains onepageofhisowncopytheletter. (2-dimensional “mosaic”) cared tocome. chance nearhereforthevacation? supposeyouarenotbyany dearly lovetodiscussthematter—I feel thatsomethingofthesortmaywellberight.Ishould I but di very gest onlogicis me verymuch.Thepointofviewyousug- interested which May, with youifeverhavethetimetospare. tomediscusstheseideas pleasure account. Itwouldbeagreat 50 dim.) and sional simplexes (a 4-dim-simplex is the analogue of sional simplexes(a4-dim-simplexistheanalogue sort of“mosaic”4-dimen- a were space-time riodicity. Suppose pe- of that “quality” isreallynecessaryfortherecognition sure quite I amnot tifying matterfromconsiderationsofstructurealone. spherical disturbances, and so your analysisgivesamethodofiden- themselves simplycentresof are quanta and ger Theoryelect[ron]s connecting emissionandabsorption. On the deBroglie–Schrödin- “luminous event” analysis ofperiodicityandtheideasingle just had time to read it through. I am very pleased if you found the found you if pleased list ofpapersIsentyouuseful. very am I through. it read to time had just T [Presumably Newman was referring to Russell’s citations of Vietoris, Felix Haus- Felix ofVietoris, toRussell’scitations referring was Newman [Presumably w , P.
w Two thingsIfoundparticularly Any time during the next fortnight Icouldputyouupif Any timeduringthenextfortnight 29 was onlyforlackoftimethatIdidn’tansweryourletter It It was very kind of you to send me your new book—I have only have book—I new your me send to you of kind very was It Russell, 10August1928,fromCarnVoel Newman, 2September[1928],fromLugano,Italy.Hisarchivecon- y S. UrysohnandMengerin tetrahedron T (3-dim.)) erent from what I havebeenaccustomedto, what from erent AMa, AMa, 50 Chaps. 28 and29.] interestingwerethegeneral z
triangle (2- E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) namely, thatthe W possible listeningtolectures,it is hard to doubt thatthe question. sary to commit oneselfeitherto to sary your bookisdevoted.My feeling but thishardlytouchesthedeeperproblemstowhich equations, and otherstogettensorforms of thequantum made byEinstein W attack beforeon the problem of therelationbetweenquantumand space timeofatomicdimensions.Therehasreallybeennoserious lawsaboutsmallpiecesof must allbederivedstatisticallyfrom ible as relation[s] between ible asrelation[s] statements aboutsuchapatternareexpress- all that notice You will and havewonderedifeverythingmightcomeoutofitsstructure. a 4-dimensional patternofsimplexesthe kind mentioned above, rangement. prove adequate,tosomemore de should former ite “converging”sequences;andif,asonehopes,the list isgivenofthetriosselected from lection ofthings two commonvertices.Anycol- have common edgemeansthatthey sis[t]ent witha(3: con- ing ofdomainsfromasetcoveringthespace-timecontinuum vance tode jects ofatmost3di towards explainingeverythingintermsofthe intervals of along acertainchainofsimplexesthesamearrangementrecursat mean that periodicity are structural,notqualitative.Nowmight any “continuous structure”oftheinterior the simplexes, but yet ofanychoice ofco-ordinates,orindeed erties areindependent dimensions arealvarietyofarrangementsispossible).Theseprop- The microscopic character of sp[ace] timeatapoint The microscopiccharacterofsp[ace] can vary is thenumberofsimplexescontaining allthat dimensions incidences betweentheirothervertices.(In2 pend onthewaysimplexes ed statement of physics,whenitcomes,mustbeontheselines, ed statement eld physicssofaras I know.Somehalf-heartedattempts havebeen Now that I have a clearer view of thewholetheorythanwas view Now thatIhaveaclearer With regards to “luminous events”, it would be a very greatad- a be would it With regardsto“luminousevents”, Ihaveforsometimethoughtthatspace time might be W p ne interval length bycounting,butistheactualcount- interval ne simplexes?Thetendencyofphysicsdoesseemtobe Logic, TopologyandPhysics:RussellNewman E y W 1)-quadratic formfords y becomes a 2-dimensionalpatternor a becomes eld laws and thequantitiesinvolved inthem and eld laws T erent sorts(electrons,protons,quanta). vertices W W tted togetherthere—i.e.ontheco- nite neighbourhood[s] ortoin W is, however, that itwillbeneces- , e.g.,that nite assumptionsabouttheir E z whicharetoberegardedas z 2 ? Itseems a complicated abg arrangement a , but in 3ormore but , and a agd mightde- array W nal uni- havea ofob- , ifa W ar- n- 27 E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) percepts ofotherpeople”,andthen“eve 8i.grattan-guinness 28 of p.388 credible eveninthe“third degree”, accordingtoyour “trichotomy” arguing; butisit rock-bottom solipsistwaywithwhichthereisno understood inthe be domains insp[ace]-time.Idon’tmeanthisto di events hard toseewhatreasonthereisforbelievinginthe existence of the W help. For one thing thatdoesseemclearisthe thing help. Forone to example ofpercepts,—eventsinone“speciouspresent”—seem thing resemblingthesefavouredtraitsinphysics;nordoesthe ing the nullinterval[,]should there not besomepropertydistinguish- cal property correspond[ing]to“b ly applicabletothem.(In this theory there w[oul]d be somephysi- course, “in of tices” arenot, simple object[s]whichareunanalysedinphysicaltheory;the“ver- (groups of 5). Thishypothesishastheadvantageof making logically be “vertices”ofa“4-array” may protons-, andquanta-at-an-instant tain things—the of cer- grouping the ties ofsuch“manifolds”arereallyproperties are into a “triangles” orunits.Thusthe collection 52 51 could bedistinguishedfromotherarraysof this kind. Amsterdam paper,how my I havesuggested,in not? For the statement to containthematerialforan by asingleevent,while connected are electrons it mean tosaythatemittingandabsorbing does what happenings weperceivetodon’t.But ence from to be plausible it must be capable of statement as such—an infer- still somesortofgeneralizationexperience—atleastIthinkthat [Newman(n.38).] [Namely, “the three grades of certainty”: “the highest,percepts”,“the myown then ned relation to the phenomena theyexplain?Icannot phenomena ned relationtothe T This bringsmetomychiefgrumbleaboutyourtheory.I erence (on which so much depends) between events andother erence (onwhichsomuchdepends)betweenevents events on which it is based, and especially to understand what is the is what understand to especially and based, is it which on 2-array 52 z from other portions of space-time, other thantheirde- fromotherportionsofspace-time, —as credibleascausality?Theargumentforcausalityis —as z (“pictured”inp.1[above]) by specifyingthatits abg vertices. , agd Itistemptingtosupposethatelectrons-, W , nitesimal”—the notion of size is hard- is size of notion nitesimal”—the ade nts whicharenotperceptsofanybody”.] , aez elonging tothesamesimplex”.) some otherpairsofp[oin]tsare , azb a , b , , edh g , manifolds orspaces d continuity , e explanation , 51 z Allproper- , h W ismade nd any- ofour W nd it units of E:\CPBR\RUSSJOUR\TYPE3201\russell 32,1060 red.wpd June 25, 2012 (9:21 pm) debted to Roger and Oliver Penrose, Joseph Kouneiher, andthereferees. Kouneiher, debted toRogerandOliverPenrose,Joseph in- also toUniversityCollegeLondonArchives.ForadviceIammuch trand Russell Archives atMcMasterUniversityin Canada.Iamindebted andtheBer- the MasterandFellowsofSt.John’sCollegeCambridge, For permissiontoreproducetheseletters I thank William Newmanand subset isco-punctualwithaneventnotbelongingto think youusethemafterwards. these needbebroughtinsoearly:Idon’t why see don’t I but “line” about convexity.Thereremainthede reservation w[oul]d, Ithink,besatisfactorywithoutanyprivate tuality is“pictured”ashaving a common domain, thisdef of theworld? causal theoryof perception, whichclaimtodealwithrealproperties opposed totheories,likethe as phenomena, governing complicated kept intheirplaceasapparatusforenunciatingcompactlythelaws be schemes theory, innouncertainway.Butshouldnotallsuch appear asentitiesinphysical rience, electrons,etc.,at-an-instant,do improvement, forthoughithas little contact withimmediateexpe- arbitrary. The“vertex”theoryI mentioned above is perhaps aslight act ofanalysis,andtosomeextent an is presents”) (“specious parts stream of perceptsasitisoriginally“received”;any separation into set ofevents, exists a set of exists aset without assumingthat,given course of events?Of by takingasprimitive“copunctuality”betweenany culty, withoutcommittingyourself to any disagreeable hypothesis, di whole the of yourfundamentalconcepts.Couldyounotavoid tion whichunderliesyourde be logicallysimple.Thiscanhardly be said of the convexity condi- events, itseemsimportantthatthecharacterisationof Please excusethisenormousletter[.] With regard to With regard a N , ofwhichevery Logic, TopologyandPhysics:RussellNewman y co-punctualevents.Thenapointwouldbe[the] topology: acknowledgments whateverthemetaphysicalstatusof W nition, whenitiswrittenoutinterms W nite subset isco-punctual,butno nite W nitions of “between” and nitions of“between” N , thereactually a W points nite number . Ifco-punc- z [inition] should U - 29