Journal for the History of Analytical Philosophy Volume 2, Number 8Editor in ChiefSandra Lapointe, McMaster UniversityEditorial BoardJuliet Floyd, Boston University Greg Frost-Arnold, Hobart and William Smith CollegesHenry Jackman, York University Chris Pincock, Ohio State University Mark Textor, Kings College LondonRichard Zach, University of CalgaryProduction EditorRyan Hickerson, University of Western Oregon Editorial AssistantDaniel Harris, CUNY Graduate CenterDesignDaniel Harris 2014 Paola CantRichard Tieszen, After Gdel. Platonism and Rationalism in Mathematics and Logic. Oxford: Oxford University Press 2011, x + 245 pp. 44.00 (hardcover). ISBN 978-0-19-960620-7.Paola CantReview: After Gdel. Platonism and Rationalism in Mathematics and Logic by Richard TieszenPaola Cant Thisvolumeisaimedatdevelopinganddefendingatheoryof knowledge that would best explain our relationto theabstract ob-jects of mathematics and logic. This theoretical stance is developed inrelationtoGdel'sphilosophicalconception, butdoes not pre-tendtobefaithfuleithertoGdel'sintentionsortohis writings. The philosophical approach developed in thebook is called consti-tuted Platonism and is presented as a formof rationalism that com-binessomeaspectsof whatGdelcalledtherightwardtendency (the belief inthe cognitive roleof reason) withsome aspects of the leftward tendency(theimpossibilityof havingcognitiveaccess to noumena). This combinationof left and right is exactly what Gdel appreciated inHusserls work inhis 1961 essay on the modern de-velopment ofthefoundationsofmathematicsinthelight ofphi-losophy.Thevolumeisconceivedasaphenomenologicalessay aboutphenomenologyinmathematicsandlogic:constitutedPla-tonismappears asa Gdelianstrategyaswellasa consistent de-velopmentofaHusserlianperspectiveappliedtomathematics and logic, but alsoasanalternativeto Quinesholismandanan-swer to Carnaps conception. The rst and the last chapters, which set thestageanddrawsomeconclusionsontheroleof reasonin science, are perhaps themostinformativeand interestingparts of the book, because Gdels ideas arediscussed inrelationto differ-ent authors (especially Kant, Husserl, Carnap and Quine).Gdels distinctionbetweenaleftward andarightwardtendencyinphi-losophy of mathematics and logic drives theagenda, and is useful in understandingboth Gdels refusal of any formof reductionism andthephenomenologicalwayoutfromtheKantiandualityof phenomena and noumena.ConstitutedPlatonism isbasedontheideathattherearetwo notions of independencefromthemind(pp. 101102):someob-jects arestrongly independent fromthe mind because they arein-dependentofanypossibleexperience,whereasotherobjectsare independent fromthemindinthe sensethat they appeartous as invariant indifferent experiences and ourknowledgeof themun-dergoescertainconstraints(grammatical,formal,meaning-theoretic,structural, andsoon).ConstitutedPlatonism claimsthat mathematical and logical objects aremind independent inthe sec-ondsense,becausetheirobjectivityisconstitutedbyconscious-ness,andinparticularbytheoverlappinghorizonsofdifferent meaning-bestowingmonads (p. 96).Theauthordoesnotpretend thatGdelactuallyconsideredallmathematicalobjectsasinde-pendent fromthemind inthesecondsense. Forexample,hecon-cedestoMarkvanAttenthatGdelmighthavetakennatural numberstobeideasinthemindofGodandthusindependent fromany humanmind (p. 17). Settingasidecertain aspects of G-dels conception, in this and in several othercases, the author aims todevelopadefensibleformofPlatonisminmathematicsand logic. Strong mind-independence is takentobe incompatible with humanknowledge,andthussubjecttodenitivecriticismcon-cerningcognitiveaccessibilitytoabstractobjects.So,Tieszen chooses weak mind-independence, which allows us to understand theexperience ofabstract objects byanalogywithsensoryexperi-ence: abstract objects areknownby a rationalintuitionthat is not immediatebutallowsillusion,errorsandknowledgerevision. Thisexplainshowour knowledge ofabstract objects mightbein-complete, but objective. This is forexamplethe caseof settheory, whereconcepts areexact but ourintuitionofthemispartlyinde-Journal for the History of Analytical Philosophy, vol. 2 no. 8[1]terminate,andaclaricationofourintuitionoftheconceptsis neededinordertosolveproblems.Set-theoreticalparadoxesare not thesymptom of a cognitive impasse, but rather anexample of correctable illusions, because inthepresence of the contradiction (paradox), wecanshift to a new perspectiveonsets that does not appear to be contradictory (p. 162).Theauthorsintentiontodevelopacoherentphilosophical conception,withoutlimitinghimselftoaliteralreconstructionof Gdels ownthinkingiscertainlya veryinterestinganddifcult task,whichthevolumeachievesinaconvincingandsuccessful way. The exaltationof reasonis obtained through the emphasis on intentionality,andinparticular,onthedifferentiationofseveral intentionalactsinvolvingproof,justication,ideation,exactness, axiomatization,formalization,andthesearchfornecessities(p. 141).Abstractobjects aretheinvariantobjectsthat constitutethe correlativecontents of suchacts.Knowledgeof abstract objects is possiblebecausewearenotonlydirectedbyintentionstoward theinvariants that weconceiveinmathematics,but[] someof theseintentionscanbefullled,partiallyfullled,orfrustrated (p.157).Husserlsphenomenologicalapproachtoconsciousness and intentionality, as well as Gdels emphasis onthe capacities of reason, are used to develop a coherent theoreticalapproachtothe philosophyofmathematicsandlogic.Yet,thechoicetodepart fromsomeofGdelsideas,andmaybealsofromsomeof Husserlsideas,raisessomequestionsconcerningthemethodol-ogy of the research. Thevolumeis not based ona merelyhistoricalapproach,be-cause,astheauthorhimselfdeclares,theversionofplatonicra-tionalismadvocated inthe book doesnot "reect allthe elements of Gdel's ownview", yet one of theaims of the volume is that of informingthereaderabout thecontentof"Gdel's relevantwrit-ings orthe supplementary materials" (p. vii). And this latteraimis well achieved by a thoroughanddetailedpresentationof Gdel's remarksonPlato,Leibniz,KantandHusserlintherstchapter. Yet,therearenotasmanycommentsonPlatoasexpected,and those onLeibniz are related only to his project of a universal char-acteristicwithoutanyreferencestomonadologyortohismeta-physicalwritings.Theauthoracknowledgesthattherearesug-gestionsinsomeof Gdelswritingsthathewas preparedtogo Leibnizswayonthis matter, but adds that fora varietyof rea-sons,Iamnotgoingtopursuethislineofinquiry (p.11).This choiceisnot furtherelucidated, but oneshould considerthat G-deldid notmakefully explicitinhispublished writings orinthe consideredsupplementarymaterialshowdeeptheinuenceof Leibnizsphilosophywasonhisownwork.So,onewillhaveto wait fortheimminent publicationofthetranscriptionofGdels manuscriptsonphilosophy(theso-calledMaxPhil)byGabriella Croccosresearchgroup,inordertobetterevaluatetheroleof Leibnizs ideas on Gdels own thinking. A secondmethodologicalquestionconcernsthepossibilityof followingandbetrayingGdelat thesametime: ontheonehand the authorwants to start fromGdels own texts, and on the other handhedevelopsacoherentandwell-groundedphilosophical conceptionthat might notcorrespond entirelyto Gdels philoso-phy.ThisisthereasonforthechoiceofthetitleAfterGdel, which is very appropriate, because the author follows Gdel up to acertainpointthatseemsdefensible.ThesurveyonGdelsre-marks onphilosophyintherst partisveryinterestingandad-herenttoGdelstexts.RichardTieszendeclaresfromtheoutset thathewill steerclearof Gdels remarksonreligion,angels, de-mons,ghostsandthelike,becauseheaimstodevelopa formof rationalismaboutmathematicsandlogiconly(p.viii,204).This disciplinary boundary is of course a useful restriction, if one wants to build a theory about mathematical and logical objects. Yet, it has theeffectofsteeringclearofGdelsinterdisciplinaryapproach Journal for the History of Analytical Philosophy, vol. 2 no. 8[2]too, basedontheintegrationof metaphysics,logic,mathematics, history, theology and natural sciences.Athirdmethodologicalquestionconcernsthereferenceto mathematical practice in the arguments used to defend constituted Platonism, for examplewhen the authorclaims that mathematical objectsarenotconceivedasmoments ofrealentities.Theauthor rarelygives specic examples, and evenwhensomemathematical examplesarementioned (e.g.fromnumbertheoryorsettheory), theyareseparatedfromtheirhistoricalandculturalcontext. The interest formathematical practice is not only compatible with, but alsocrucialto a phenomenologicalapproachbased ontheinvesti-gationof appearances,but therearemany different mathematical practices and styles, some of which might be compatiblewith em-piricism,suchasthetraditionofusingrationalnumbersrather thanrealnumbersinmeasurementtheory.So,eithertheauthor mentions somespecicmathematicalpracticesthatarebasedon Platonism, or mathematical practice is not a sufcient argument in favorof Platonismagainst certainforms of strongempiricism. For exampleitisnotenoughtosaythatourpracticeshowsthat mathematicscannotbeasetofemptyhypotheses,conjectures, expectations, or problems, or that it cannot lack rational intuition. Suchcriticalremarksnotwithstanding,thebookis a veryin-terestingandstimulatingtextthatachievesarareanddifcult task: it connects ina new and fruitful way two traditions that have been separated and opposed forpoorreasons and fortoo long: the analyticalandthecontinentaltradition.Ontheonehand,the authormakesHusserl(andsomeofHusserlslanguage)under-standabletologiciansandphilosophersofmathematics;onthe other hand it invites Husserls scholars to take into serious account thecorrelations toGdelstechnicalresults,includingtheincom-pletenesstheoremsandtheremarksonTuringsmachines.The accuracyofthequotationsand therichnessoftextualreferences, togetherwith the comparisons withother authors of theanalytical traditionsuch as Quineand Carnap, do not only improve the clar-ityofthetext,butwillcertainlystimulatearevivalof studiesof Gdels philosophy.Oneofthemainmeritsofthevolume,from an historicalperspective, is exactlythat of tellingus what Gdels philosophy cannot be, destroyinga widespread but oversimplied understandingofhisPlatonism,andinvitingthereadertocom-pletetheframeworkbyathoroughinvestigationofGdelsun-published materials. Paola CantAix Marseille Universit / CNRS, CEPERC (UMR 7304) 29, avenue Robert Schuman, 13621 Aix-en-Provence Cedex 1 France. paola.cantu@univ-amu.frJournal for the History of Analytical Philosophy, vol. 2 no. 8[3]