What Early Husserl Can Tell Us About Mathematical

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CEU eTD Collection the biggest workisthe at toappreciating impenetrable times earliest Husserl’s obstacles both by contemporaries Husserl’s and aremisguided. recententirely themore critics realists introducingepistemology his in thatof contemporary intuition resembles mathematical knowledgemathematicala body of of truths. concrete perceptions has been the work of a intuition, unwarranted that correspondence and Husserl that Fregeconclude was it preciselyFrege’s of tendto criticism Arithmetic since Husserl mathematics which Husserl’s offering original i he isreproducingofhisteachers, and Carl rather Brentano, theideas Franz Stumpf than immature influenced toreject turn Husserl and psychologism

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Here I will take the early period to be Husserl’s writings from the preparation of his Habilitation Thesis to the the to Thesis hisHabilitation of fromthe preparation writings be Husserl’sto willperiod the early I take Here )

primarilyfinding focus phenomenological general,Husserl’s in theroots on of method further bothGermanin the developmentand existentialism, French developments of in Husserl’s earliest work Michael onceFrege Dummett withthe observedand that “maycompared Husserl be Logical Investigations Investigations Logical one 2.

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Here it ought to be noted that it is not entirely clear what was Mill’s position on the relationship between logic logic between the relationship on position Mill’s was what thatclear it isnot entirely noted be it ought to Here Husserl main target corresponded What is characteristic is What At least defense thatHusserl tohasdowithhis part isreferring ofthe naïveté of notthe There thisdismissal, areleastreasons for ofwhich many Givenearly thatHusserl’s areexclusively interests and mathematics, in philosophy of

in his in his of apprenticeship, is to showthat theis to introduction ofapriori psychologisminto such disciplines as and himself has an an of become approach. such ardent critic that was a Tagebuch Wilhelm Wilhelm 40 insufficientl beginner, withoutknowledge proper ofphilosophical problems,and with reasonnot without publication troubleI its my did a conscience… wasmere How immature,workseems howalmost hownaïve, this me;and childish to

the thought of arguments against arguments such views, part ). –

the period before the

with and with of psychologyand beof should thus

more po more Jerusalem

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commented on scholars such as Stuart suchJohn Mill scholars pular among philosophers.However,analytic pular the evaluation 921

influence on his earlyinfluence work onhis .

, June 4th , June

philosophical s LI LI and the revolutionaryandphenomenology the methodof is unsolvable contradictions :

Frege, wouldno it 5

outlined inPart Twooutlined of

things kills” (Husserl kills”

continentalanalytic and philosophers

the contention studied app LI LI . asand misguided immature. He Indeed, by thetime ofwriting , t be unreasonable toexpectt beunreasonable 2

Theodor Lipps,Theodor Gerardus – ropriately. has Husserl’s

quoted from Bell The objective ofhis objective The

that logic is in one that logic is

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199

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proceeding section ibid There amongstthat it analytic isanoldtale philosophers However, thiswas Nevertheless, ge’s Cursege’s abstract . the rejection of hiswork,based Frege’sthe may solelycriticism on unwarranted be , 51 led by psychological the led rules, PA - 54 .

objects such asobjects numbers, thework nature psychologistic ofthe may ). I will

46 it is not clear isnot it whether ). (2) contrary psychologya). The priori, laws are notknown of to coupled with coupled elaborate more on this inthefollowingchapters,elaborate however, onthis more

I will Frege’s llyIn a failure. to order show

Husserl’s main task in Husserl’s in maintask reading of

the latter’s how Fregemight have misinterpreted ogical ratheran orientation, than

former would have as former tobeasthelatter. vague the criticism

PA 6

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that that this is notnecessarily is that this thecase, in

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See Beth (1965, 353), Dummett 353), (1965, Beth See

rather was, as Tieszen accuratelyrather as “an was, Tieszen it, conditions putsthea for investigationinto priori

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ssues - psychologism is a is characteristicpsychologism ofhis mark philosophy. PA that contribute to the perception of contribute t tothe perception that sal applicability? These and similarconsiderations applicability?and Thesesal lead Frege to

is plagued with obscurities in argument, poor withobscurities choice inargument, terminologyis plagued of ,

Fregemistakenlygeneral takes aimofHusserl’sphilosophy the of to (1973, 158), Follesdal (1994, 3 (1994, Follesdal 158), (1973,

psychologism, often howevermost theand are ones thatreoccur

is essentiallyclaiming it is both amistake isboth it and a LI . 3

Given Vorstellungen 7 this

ideal objects,ideal andobjective. thatareuniversal

common conviction the nature of - 47), Sluga (1980, 39 Sluga (1980, 47), Philosophy ofArithmetic” ) that areinherentlywhile subjective, the same things rl’s earlyworkbeen has so viewed he work as atte a misguided

large

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Frege He provided and

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CEU eTD Collection 5 4 Frege ismore c they be to answering seem twoutterlyquestions different points. the conceptF” artificial istoo concepts appear. concepts concrete be can traced cases, orphenomenal to experiences thenumber inwhich ordersoun todemonstrate the be inaconcret thought foundation without ofHusserl, number, contesting states: approach thelogicist “noconcept can tothe definition carefully, of one lengthy passage in notes that canfound inthe be nature ofdescriptive psychology isentirely (Bell: 1990,61). motivated” ofconstrainsDavid themethodological “adoption determine Bell which inpart notes, the definitely th nomentionthat their ontology giveattempting an to epistemological account of careful attention enough and with patient is processes units, conviction was thatnumbers were but nothing the possibility 108).consciousness andknowledgeMill’s ofnumber” ofthe (Tieszen: 1994,

See (Husserl: 1990) 1990) (Husserl: See 1970) (Husserl: See and thatsuchour andinturn representations, concepts,are thepsychologicalcrafted by While they attempting aretogivean both account ofthe However Husserl of studied theworks

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Maddy’s theory primarily deals with sets, rather than elementary numbers, numbers, elementary than withsets,rather deals primarily Maddy’stheory epistemic abilityepistemic to Before move we Surely work Husserl’s in (Steiner: 1975) , to the extent thatFrege’s influenced, tothe extent work thatofandHale Wright its

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CEU eTD Collection 169 (2003, Hintikka 7 ( domain towhichitcouldnevertheless “theand world mental applied of acts” be is our ideas and subject’s relation longer theperceived objects to one, asan couldno thought be immediate unspoken 2003,170 and ones.” unconscious even (Hintikka: perceptions inrealitycom is a mechanical the of vision world a ofearly like sciencedirect what modern showed looks that broad scholastic philosophers came knowledge intuitive toequate waytaken is tobe ofintuition present( true.” is ormorenot athingnot acontingent or broadly,whether aboutth exists, proposition of cognition virtueof in can which ofa one isthat evident have thing knowledgewhether or of existing of the andexisting object present(ii) are as caused inthe andperceiver by the directly intuition of the scholastics. 3.1.

ibid. The historical reconstruction of the use of intuition from the scholastics to Locke here is in large part based on based part large isin here Locke to scholastics from the useofintuition of the reconstruction historical The

thus Historical to Introduction ), as Although the severelywas scope this it generally thatthe ofintuition, limited taken characteristic is What thatknowledge toalloftheseis arrived uses toby ofthe term LatinThe term and present (Adams:In intuitive object” Ockham’s 1987,501). “an thought the attr is broadits In scope. cognitions Scotus thework “intuitive of are arewhich (i) those 3. we directandunmediat dohave

M ATHEMATICAL ibution of intuition to objects to ofperceptio ofintuition ibution notion of intuition was intuition of notion - ibid 173) As Jaakko Hintikk As Jaakko ., .

502). ‘ intuitio

plex processplex albeit involving often all sortsofinferences, immediate ’

the Notion of Intuitionthe Notion of first gained the mainstream attentionin philosophical works I NTUITION IN a notes,what remarkable is scholastics’about use the of short

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viewsDescartes’ ofthose as hile Descartes mentionstheanalogywith perception often he when it, defining if we ofsomemathematical an have property, intuition we invirtu it have representation ofsomefigur IwheneverI corporeal of think a my may thing, in construct a mind confused imagingI somethingwheneveram thehabit in ofimaging something them as ifthey wereItI present before me.since trueof is that am thehabit in three consistingI aswell ofasidesjust as thousand thetriangle understand tobe IBut of think a if to chiliagon, want althoughI isafigure thatit understand not invented by me and ofthetrianglenature, immutable essence, eternal, whichand orform or is or has anywhere existed ever outsideofmy thought, I forWhen, example, aeven triangle,figureexists, imagine ifperhaps nosuch - sided figure,I thesame in waysided se thethousand donot sides imagine or

takes objectsbetakes to independent ofour intuition of for example from sensation: -

or dependent onmyor mind independent Descar objects, byway of

raises araises further e .

(Descartes: 1985, 50/ AT72) (Descartes: 50/ 1985, 12 Intuitive knowledgeIntuitive

innate ideas,innate

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ke: e of e CEU eTD Collection properties (whether di is between Kant 2009).(Janiak, each out, points of objects, affairs represent dosodistinctly properties but both orstates general, andwhile concepts are and singular. intuitions As mediate immediate are Janiak ( of Kant’s Husserlis Edmund mathematics” (Parsons: [who] nineteenthParsons notes, inthelate centuries andearly twentieth 3.2. AKantian defi 2003, 171). of thebecame it idea until more little ofintuition thana synonym for immediacy” (Hintikka: of fashion Descartes’ philosophy, Anschauung)

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the epistemic ability

offered aparadigm kindofa of conception intuition ofa applied philosophical to Infirst of chapter the the T The passage introduces he use of . . This way, as observes,. Thisway,Hintikka and similarcriticisms these“eroded thecontent

scholars, and concept ( concept and without concepts can yield conceptswithout a 193) can cognition. (Kant: 1999, concepts intuition corresponding without insomeway, nor tothemintuition concepts therefo Intuition the latter thoughtthatrepresentation.[…] itis to and relation in (spontaneity through concepts); givenan is object theformer of tous,through secondcognizing thefaculty forofthese anmeans by object representations whichrepresentations isthereception of (thereceptivity ofimpressions), fundamentalOur two cognition thefirst arises inthemind, sources of from While the While mathematical intuition mathematical , even thoughdeviates, even considerablyapplication intuition his of nition of Intuitionnition of rectly, or through imagination); (ii) therectly, orthrough epistemic imagination); ability of

the followingare the were 2007, 2007, precise of Begriff “pick heavily damaged byempiricisheavily 193). A philosopher whofalls193). Aphilosopher decisively thisparadigm under theelements cognition, thatneither so constitute re ofall our two centraltwo Critique ofPure ReasonCritique

relation between these two between relation ing ).

The most relevant distinction betweenThe relevant thetwoisthat most distinction

out” a singular out” a singular

the most common way most the gains prominence its notions 13

of Kant’s epi of Kant’s concrete X with all its perceptibleX withconcrete all its (henceforthwrites: Kant CPR) t criticism and criticism terms

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CEU eTD Collection 10 9 8 stems from experience the questionwe of howare toknowanything objects T ofintuition. beingform ofand beingof all outside thesubject, time ofall the objects possible form the through intuitions aregiven, which forms theintuitable objects on imposescertain (Kant: sensation information i aboutthesubject’s states. However, intuition representabout something “ (Kant though can intuition be applied and “immediate cognition”kinds of that allows therecognition thata belongs particularconcept singularrepresentation, tothis an singular both asingular Throughout issue. this concern with himself much been a to it. immediately

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Kant Parsons,

: 1999,155

( 1999, 172). matter of dispute matter 1999, 155/ 1999, This leads one to ofthe carefulIt is benoted notto must thatKant beconsideredThe should question whether to intuition

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representation A19

). the use of intuition as immediatecognitionof intuition the use dominant is

Intuition from sensationdistinct is alone, - B33). ing his all knowableobtains to objects andissupposed tobethe answerto . - In the introduction tothe

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, , and

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proposition is true. is proposition inferential knowledge; Intuitiveyieldsmediate,immediate as is that knowledge opposedto from intuition theycorrespond; instancesth ofobjects with Intuitionancapacity is epistemicinvolved inconnecting primarily thatis concrete Intuitionprimarily is as intuition understood The same will hold to thecontemporary holdto will The thataddress same I ofwill intuition views in those philosophers who emphasize the analogy philosopherswho emphasize andperceptual the betweenthose intuition that st prominent difference Husserl is betweenand Kant Representazion)

Husserl and the contemporary , where theformercognitive of processingrasping involved a ispart that is –

of some proposition. Contemporarysome proposition. of epistemology pays muchmore

), and respect heismuch inthis closerpre ), tothe that the e is a process involved incoming e isaprocess toknow involved

which e abstract quasi (or following three arefollowing aspectsintuition ofKantian

in Husserl’s terminologyin Husserl’s a issimply 17 uses ofintuition uses

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Intuition that is modeled on perception may, for example, yield in fau yield may,example,for perception onmodeled is Intuitionthat general but the ofpropositions, not allow intuition for do or theories Parsons’ Husserl say isthat not to This ughand careful ledge. Intuitiongenerally is tobeattaken play incasesofimmediate c 11 Herewith the contemporaryHusserl ways parts approaches Finally, before

What is characteristic is ofallWhat ofthesethatdespite thedifferences views intheir is

p. is taken t

Do these propositions that we arrive to by satisfyDo these intuition way propositions criteria? these of hat dependent the degree is ofreliabilityintuition on of treatment than II than her. cantreatment provide

turning to Husserl’s particular conception of intuition, Iturning toHusserl’s particularconception of intuition, should

- factiveness thesis remains: intuition, howeverfactiveness intuition, competent remains: the thesis

. 12

This, of course, is understandable,course,for isattemptingThis, of Husserl is The , degrees vary will ofreliability ofintuition greatly from namely the mathematicalnamely the epistemologyofCharles , 13

and thus is does not, in itself, guaranteeand isdoesinitself, thus not, 18 n the

part This question deservesThis question a muchmore

- factive

t will t will p of contemporary of of philosophy just incasejust a one true justified, has lty propositions for my perception may myfor perception propositions lty -

have t concepts. Giv

– intuition

o considerably suffice tosay at suffice that, ognition

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CEU eTD Collection ofnumber knowledge analyze our to mainis aim itself.Husserl the concept of thethan origin rather concept, ofthe knowledge 15 theref and composed, which it is of parts separate usthe leads to representation ofa of the origin question insofar as the related, methodologically are two questions these However weit?’. have once content, knowledge its ‘What is question, fr clearly be distinguished to […] is ofcourse representation?’ a arises ‘Whence question “The 14 and requireobvious will nofurther considerations of ourconcept knowledge concept the theessence isilluminated, be ofthis ofnumber will of ‘origin theconcept o of methodological Husserl thusclaims thatthe major taskof provisions, knowledge ess the question of the Carl Stumpf ontology orsemantic the question of 3.3 place. be turnsoutto that ifone’swrong,genuine intuition a had never inthe first one intuition IThus all can a provide dois perception,as such latermuch attention career paystothe issues Husserl arising from knowledge on based Iif clearlyandperceive distinctly that immediate cognition ofsorts,

What is meant here by ‘origin of the concept’ should be understood as a question about the origin ofthe the question about as a understood be should ofthe concept’ ‘origin by here meantis What In ence only theitis concept, for of attendance careful through tothe the origin . Th On the Psychological Origin of Space Representations, Representations, Space of Origin Psychological the On

e Role of Intuition in Husserl’se Intuition in Role of As weanalysis see thenumberanswering will conceptisfirstaimedat Husserl’s of of The thatintuitions is biggest problem this with

of the concept thatof thewe about are able the content tobring of it , underhestudied whom

how numberThe conceptsepistemology focus known. are on rather than,say ore yields a more precise grasp of its content” (Stumpf: 1873, 3 1873, (Stumpf: ofitsgrasp content” more precise yieldsa ore - concepts, rather concepts, knowledge knowledge the s, in Husserl’s earlywritings wass, in highlyhisworkwith influenced by fallibility ofourfallibility f number’ (Husserl:f 2003,311)andconvinced is once theorigin that

guess are fallible evidently often very

of the concept has priority over the question of theconcept the contentof the priority over questionor has

than h than

that he, followingthat he,Brentano, Descartes,Kant andassumes in Halle from 1887 to 1901 in Halle 1887to from ow concepts are created. created. are concepts ow p

perceptions. However ispresentperceptions. ofit notalk in it does not seem guarantee to of doesit not thetruth Philosophy ofArithmetic 19

15 a book studied closely by Husserl, Stumpf writes: Stumpf closelyHusserl, by studied abook .

, even ifthey are definedmerely as

. Toput . It. idea that was Stumpf’s

it PA -

4) in other words, e

is is 14

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PA. PA. ven ven CEU eTD Collection certain simplify Andwhile to themental theintuition. apparatus activities involved in perceptual exp parallel to generation arithmeticelementary thatthese concepts is mental ofprimitive activitiesappear singular whole.given ofcomplex a parts example, ignoring whole;given of ordisregardingcomplex combining a parts orunifying of intuition the simple are, the agentget where allable features, theirrelevant to hastobesuchas, ridof the say, of graspnumber.of this,let usconsiderconcept Asan a theagent’s of basic example perception has toactively perceptual “purify” the cases w concept ofnumber, previous section, conceptsheaccommodate can andinsodoing sophisticated more arithmetic. limitation, Husserlthis concepts more builds complex theelementary ofnumber from experience,approach canof we arithm theelementary only truths through representation. Since authentic symbolic representationsrequire directperceptual concept direct isgenerated perceptual ofnumber inthemindwithout evidence objects get andbyintuition way theconceptIn of to ofnumber.contrast, an Inconceptsshort, w ofnumbers. two cups onthe table what color they are colorwhat they What is specific is What toHusserl’s In whataddition to hasbeenmentioned Husserl by begins analysis his distinguishing betweenand authentic in here we immediatelyhere perceive/experiencean

intuition. Sinceintuition. grounds Husserl analysisconcept ineveryday number his ofthe of eriences, assumes that he

one

or, more precisely, how do we come toknownumbers, precisely,or, more howdowe further two , that one of them has a oneofedge, chipped themhas, that . H .

usserl toarrive order concept claims‘ thatin at the numerical obje

clarification must be made. Since Husserl’s goalmade. todefine is clarification Since bethe must Husserl’s cts. The mind could arriveatcts. Themindcould e form an early representations aside from beingaside to intuit able from

views on the sort of intuition involved in involved of intuition the onthe sort views authentic 20

about useof Husserl’s intui

concept directly by countable perceiving instance of

of the inorder irrelevant to content such an

and soon,u it etic way. inthis Tosurpass . In cases. many themind

intuition by, intuition for , the have must mind a ntil shearriventil

tion he isinterested in ina

authentic authentic

– in the uthentic

for example for cups

s at two’

CEU eTD Collection inquestion” (Husserl:2003, concept 19). 17 See (Husserl:with imagination. 17) 2003, are, say,involved merely imaginarymind our andmateriallyor not in us. Direct perception to he presented 16 graspedIcollectionobjects ofasa the unifiedwhole am the numerical able property tointuit multiplicity typedistinctive is ofwhole am intuitions. a waymindreduces perceptual initial inwhichour representa the of number concepts is number activities, and ofprimitivemental theone inth to them, anditis Iconcrete objects, instanceabstract thata of certain intuit be numericalcan property ascribed numerical preciselyand is this value, plays whereaBy intuition crucial role. perceiving a Ihowever, grasp be must able of the to collection obje the particularof the perceived properties In objects. at the toarrivenumerical order concept, determinate objects of includingspecific collection and all ofits features,ascontext its such in Husserl’s analysis them and recognizing thus certain nu thata three booksstacked by myI the forgroupingcan objects actuallybedside, without perceive oftheenoughformation conceptfor of,say, the to know do notappearand t separately simplifying canconceptually theintuition be they intuition, distinguished from nevert

This need not actualThislimited experience need be to Husserlperceptual i.e. considers also cases where of counting objects the “Disregarding the properties the “Disregarding thatare different,we that areas all, thosethose commonwhich retain may to the to belong

ableas tosee belonging toonesort them As Though awarenesscrucial not perceptual is a concept indefining ofnumber, is it number concepts. What is crucial is What hereII a objectsgrasp certain isthatwhile collection of distinct noted above,early goes conceptionof Husserl’s intuition with a hand inhand –

a concrete unity numbera ofobjects” ofx concrete (Willard: 200 is noting thattheagent hasa is wayarrive thatweat ofdistinct numbers. knowledge c ollective

[…] […] hus arean integral ofwhich theprocesswe part through come

present mewith my to aconsciousness: totality field ora of connection mber be can attributed tothem. 17 ( kollektive Verbindung 21 . As Willard puts it, “in it, such puts . AsWillard a case,aand new

‘ the number three the perceptual representation that cts asa having unifiedwhole a distinct

plays thegenerationcentral role a in tions to more to tions basic ’ , that I am ableI toperceiveam , that ). Collective connectionis ). Collective 3, xviii). OnceI3, xviii). have Thus thefirst step 16

of a

reis replaced heless heless CEU eTD Collection contentof rather,presentation that isnot authentic, aan symbolic but (Husserl:193). one” 18 series becorrelatedwith the must authentic ofnumber concept (Bell: 1990,56). term theseries in basis ofearlier terms. onthe One (3) signs the ormore the in earliest of recursively,is aneffective inthat there procedure, of numeralsplacea generated thatthe series unique series, is inthis has and so ofnumerals representations perceptible can written whether conten items; they be or the spoken theory features: symbolicrepresentationthemselves hasthreeessential are (1) The of signs signsconcepts via he which definesas presentations ofnumber, Innotice issue,Husserl on. this introduces orfocusattention totackle inauthe order our numerical there thenumber can to concepts,of since items we isalimit explicitly distinct merelynumber, intuition connectswith such concepts. theparticulars arerequiresbe Hisalready equipped created. analysis thatone multiplicity.It impor is byto us andcollective intuition viewed combinationas and by Husserl is ‘something’ 123). numerical(Husserl: Adistinct 2003, given quantity,other hand, onthe is thata is numberthis initself isprimarilya cer perceived until which numerical property) that canmultiplicityapplied units. betoa ofperceived presentthus to an thewith consciousness o that oughtto them. The be role to ascribed ofcollectiveis combination along with intuition

“If a content is not “Ifis not directly a content one A perceptual One

bracket all the remainingofthebracket collectionconcreteconcrete allthe ofobjects parts

arrive . (2) comprise They a sothat any combination recursive possible progression, he

s arrive

at a fullyabstractat a object

by performing yet procedure,by performing mental another account of knowledge issurelyaccount ofnumber ofdealing incapable withall

given to as whatto in us, fact given it onlybut is, uniquely given that via our characterize signs then it, tant to notehere to describing isnot tant thatHusserl concepts hownumber s

at multiplicity. aconceptfrom follows of an indeterminate What

bjective representationa numerical of property (i.e. a quantity stripped of evena(i.e. quantitystripped of distinct its 22 tain multiplicitytain ofunits,a merefeatureless

whichgenerate enablesany usto later

with a certain conceptwith a . 18

that of

As Bell t ofconcrete

abstraction property ofthat notes ,

Husserl’s , by

of ntic CEU eTD Collection that in takes be themto ideal objects, does to account knowledge of for our independent fa especially important notbe should alone. of crucialthat we is arriveofintuition way toby importance. Inproposes. non sense, this the comeof the a tograspthatFrege concept,the description than formal like rather one it, above, s number separately cognitive processes from i the numerals 57). arithmetical signs and their (Bell: 1990, understanding oflarg to recognize their place intheofsigns arithmeticalas notes,my Bell and, system multiplicity.this other handgrasp ability my larger Onthe numbers ability toonmy isbased aggregatethat this a of multipl is objects IIintuition: theminthat with direct contact can have immediately and assuredly both say conceptsdeterminate and are ofnumbers numericalperceptual quantities arrived at by

not touch uponontological numbers concerning issues Indeed, isapplicable thatit in he stresses LI. LI. Because ( Husserl It Husserl’snot is notethat use important to ofintuition is thatwe Husserl’softheWhat tois cannot analysisconceptpoints ofnumber define mayWe of definition summarizeHusserl’s uch a However, IHowever, isplausible tostatethat it think we see can the

confined definition becomes which in aofwe morea specification priori of conditions culty and, one categoricalexplicitlyculty ofitsforms,is and, namely, intuition, intended to e numbers reaches no further thanfurther e reaches myability numbers no tocorrectly identify

to the context ofour thecontext knowledgeto ofnumbers his later work perhaps dueinsistence tohis up perhaps

we cannot - in all ferential and immediate knowledgeferential concepts number andimmediate of ideal objectsideal .

In icitythat thepropertyand appliesn units’ ‘having to LI LI fully and i onwards 23 equate equate anycase of

, whetherotherwise, mathematical or n which we come to grasp it. whichit. we tograspn come

number as follows. Both as authentic number follows. his conception of intuition in in his conception of intuition

on thepriorityepistemology) of ntuition gets intoan ntuition developed , that is, , thatis, immediate cognition immediate

limited . Thisobservation be will it isunclearit whether he

headwaters of this headwaters ofthis

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and surely it PA .

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CEU eTD Collection mathematical of with the discussion variety, Husse over stroked characterizationof themain features of beyond th scope the of thoroughand attentive analysis approaches ofthe of variety topsychologism of scholars w noted that there noagreement was univocally topsychologism by thosesympathetic phenomena way istheonly concepts analyze toproperly reduction psychology of philosophyand the to scene psychologism, for characterization of of thework himself to howpsychologismjust and defined was wha better,thought behelpful position itwill his lookacloser and,inturn,tounderstand into were ofthe figures one leading of needs be to mentioned,namely 3.4 cognitionis ofsorts, and it orientation already inthe . Varieties of Psychologism. Varieties of - generalized rl’s thought and we should keeprl’s should andwe thought front it ofus. It characterization of commontostart psychologism, is one’s especially The ( term ‘psychologism’ Before leave for early Husserl we more thetime being, hisproject one feature of .

ho canexclusively considered betobelongho truly tothis . However our task is to reconstruct the motivation andbackground our the motivation reconstruct . However taskisto of is thesis, thus here thus is thesis, havemerely we tobesatisfied a will with broad as PA.

as essential toourknowledge in ofnumbers it is in his works his that isin weit findthe It is Eduard BenekeEduard(Erdman 1870). p : Mill, : sychologism. His His sychologism.

Psychologismus the defined in a similar fashion, immediate an namelydefined inasimilar as neither overneither

trend, thus In ordertrend, what tosee thus motiv

Wundt Wundt

t version of it, if any, did Husserl commit ofifany,commit it, t version didHusserl the work of John Stuart Mill, as Stuart Mill, of John the work his 24

and claim that geneticclaim mental analysis of the definition of psychologism, definitionof psychologism, the it

, which, of course, isatthe, riskof being . ) However teachersand Franz Brentano Carl Stumpf Brentano was c was

: an attitude shared almost : anattitude shared oined byas Erdmann a Johan , while we are, whileweat it,

first

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explicit explicit position. position. PA insistence ated Husserl’s as isin it is unfortunately Providing a

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- CEU eTD Collection “everything againthat, it vastlyFrege how shows mis (Frege:are ofobjects” notheaps num predicates multiplicities of we cons (Husserl: 2003,169 the extreme endsfaulty ofa ofnumber definitionof theconcept (the accountHusserl Mill’s quotesandtakes as criticizes onmoreand it thanone occasion psychologism inthe Germanspeakingand academia toHusserl’sinparticular. position over andsay, as“two” name being, nothingnumber, isthus accordingother toMill, butacollectiongeneralize we of objects, that psychological thatare procedures for establishmenta of responsible the such concept. directthe most ofnumber, way concept wouldbe the,say, ofdefining t the outside space ind arithmetic are have they necessary. ofgeometry input, more verbal Thusthetruths thanjust arenot and thus According theonly toMill, isessential position are thatthe tohis truthsofmathematics tobenecessary. notconsidered psychologism is wellcharacterized by geometry hisviews and on arithmetic. Logic uctively. bers, nor their fully Here necessity. agrees insaying Husserl that“numbers withFrege (1843)the main was one of Hu approachMill’s important was ider numbers ider numbers sserl’s criticism of Mill sserl’s criticism ofMill to be M - time, first empirical andforemost established thepremises truths, are ofwhich athematical truths and truths principles areathematical

shunted off the subjective” into ( shunted

- but induc 171). His 171). to beempirical createdan throughto observa by , weproper are theobjecti left aaccount without ofneither

necessity necessity; isverbal tivegeneralizations ofthe empirical wo central remarks critical 1970 inspirations ofthe German Mill’s psychologism. may be (Mill: 1843, (Mill: ,

8). both interpreted by him Husserl intends claiming that

quite telling of his own position and morehis ownposition than of quite telling

to 25 the

56 more generalmore ibid., ). not mind

bring

9). Husserl’s ofMil views as thetruthsofmathematicsclearly

to mind - independent objects existing

further of developments tion of the numerical oftion

that of Frthat of rld around us. This way, us.This rld around other other is Frege’s o look into the o lookinto

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A CEU eTD Collection psychology, whic philosophical of issues epistemology, andthanempirical philosophy ofmind metaphysics note, that Brentano, though a self Brentano’s all these objects ofknowledge” (Wundt: knowledge, thestart theeye towards ofphilosophy isdirectedfrom the interrelation between various approaches]great separate a knowledge into number of objects individual Insteadtogether.saw itas Wundt s (Kusch: 1995,127).However,note,that important to itis philosophy seen was as not sciencesbased philosophyofthesegone; tobeontheresults instead was sciences” were “the days making philosophical research psychologygive make philosophy more will it “scientific” authority aswill it philosophy in positions Itseen departments. was often as noshockascenturyend themajority ofthe theXIX originally psychologists had that mentioned more rarely is Psychology the father psychology experimental of whom with Wilhelm Wundt, heworkedLeipzig often is andBerlin. in Wundt credited tobe Fregeintends number concepts belongclearly and to thatheobjectivity. totheof realm treatmentconcepts ofnumber omething meaning loseits thatshould be consideredventure a orshould doomed all Along withWundt’s characteristicAs Martin most Kusch viewsthat notes,the featureofWundt’s was Another significant influence

when philosophy would figure as the foundation of the natural and of of thehuman philosophy thenaturaland when foundation wouldfigureas the

Psychology from Psychology (1902) marks thebirth marks ofpsychology(1902) as an independ h was much more h was Wundt’s

Principles, and Empirical Standpoint and Empirical Standpoint Wundt shows thathe only isnot thathe thisbut awareagrees with of

more credible. more - a branches unionofthe “[whereas various ofscience: the proclaimed psychologist,wasproclaimed interested muchmore in

on Husserl’s early thought earlythought on Husserl’s primarily

and the publication ofand his thepublication another 1902 focus 26 , 48). , 48).

held achairheld inphilosophy.

essential .

In letter toStumpf by deed, 1886 inhis , thatmerging philosophy with (1874). However, interesting itis to

text ofGermantext psychologism was was Principles ofPhysiological ent discipline the the teachings of teachings This should comeThis should , this way, this . W hat is of

CEU eTD Collection entirely is this of view” withacertain compatible ideal point empirical; experienc priori. Husserl’s ‘with ‘exact’, ‘apodictic’ and ‘self only probabilistic: yieldlaws ininductively ofpsychology whichbegeneralizations basedwill contingent and numberalrea can dissatisfaction of introduction of a priori truths philosophy primarily ofmind,for it isconcer psycholo phenomenology’ (Bell: 1990,6). Brentano liked tocall ‘descriptive psychology’,‘psychognosy’, ‘desc or or sometimes psychology, was most influenced“distinctively him which what philosophical discipline Davidalthough Husserl Bell was notes, undoubtedly work interestedinBrentano’s in yearsbeen coupleI’m of aglad for psychologist ofthe1976,16). And,as change” (Stumpf: Brentano notes: “ out induction’ (Bell:out induction’ 1990,6). This is well illustratedThis is “My dictum: by Brentano’sfamous is psychologicalstandpoint Brentano’sthe other approach, hand,at onaimedthe is It notethat important to is gyI an empiricalresearch. tobe ,

does the exclude not existence may ofidealobjects, knowledgewhich of be

and setsthe toneof this Husserl’s thought measurement. 1874,70). (Brentano: secondly, theintensity mental besubjectcannot phenomena of dependent influences physiological uponthe variable presences; ofunexplored o [There twofactors are] prevent acquiring which from us theexact conception f the highestsuccession: lawsof mental first,theyare empirical only laws dy be Iam nowcompletelyI a and metaphysician confess that after must having

e alone ismyI Yetalone teacher. e the share conviction withother thinkers that

found inBrentano, onmorewho claims found thanone occasion thatthe - evident’, and arrivesevident’, it at the laws immediately:‘atstroke’, one Mill’s Mill’s

neither Thus Brentano’s psychologism,Thus Brentano’s in the same way much radical tothe definitionof theessence empiricism of t is much better characterized much t is as b Brentano ned not with contingent with not with generalizations but ned 27

nor Husserl nor

. InHusserl’s. of hints deed,

(Brentano: 1874, 3) 1874, (Brentano:

a priori considered , “it’s results are elonging to descriptive ed to .

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of intuition is present is of intuition extent, theworkamong tosome in of,and, Kurt others,Gödel divergence ntemporary philosophical approaches to

rimarilygrounded inperception, either direct orimaginary. can be characterized by becan the negating ons philosophy ofmathematics, philosophy do notnecessarily

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, C which ONTEMPORARY may most thoroughlymost Parsons. intheworksargued offor Charles M ATHEMATICAL way ro intuition’s

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28 can al can

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I le , Old Distinctions, Old ‘see’ NTUITION However interesting itis tonote, that has been with that omeone whodefends the Kantian . , say,

mathematical objects; (ii)

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Application of Mathematical of Application Intuition

mostHusserl’sby notably canthat Tieszen, argued who has of notion Richard intuition help Parsons culties his theorywhenhis culties facedinfinities with potential encounters (Tieszen: work However 1984). has no rth in the rth ognitive relation thephysicaland a to perception”ognitive “something like world, begins his article “Mathematical Intuition”begins “Mathematical article his withthe claim faras anticipated Husserl an -

perception inourknowledgeperception ineveryworld day and latter, the

stating that the central feature of intuition is the analogy is thatthecentralstating ofintuition feature between sense will be will ofthe parallels betweenHusserl discussion andapplications Parsons’ PA,

Stewart Shapiro and Michael Resnikhave been

his his onlyphilosophywork solely mathematics.devoted ofto very inthe senseonly inscope, will thatit limited the cover

hematical structures objects (or (Balaguer: orpatterns)” 2001, relevant

to philosophy of mathematics, “it should playrole “it ofmathematics, should ato philosophy

application of intuition, of intuition, application 32 though the they prefer term

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CEU eTD Collection similarlyParsons, asserts toHusserl and is abodymathematical thatthere ofelementary good Hilbert’s illustrative exampleofthisis conceptionof finitary Hilbert, mathematics. certain structure the numbers. natural we numbers, however havequasi can of intuitions accessible byanyepistemic ofouriswhy of faculties. cannotintuition Thiswe an have are thequasi abstract objects which are concrete purely intermediary two? between the exactly does not leave ontologicalvery aside. considerations At theleast, mathematical concepts. find something for ofexplication a ourknowledge ofan prioriofelementa conditions mathematical intuition. grasp t concept thereverse work may inParsons’ we note ofnumber, while in Husserl’s, namely conception ofelementary of intuition arithmeticalconcepts casessimplest geometry ofelementary and arithmetic. hemeans are concept reconstructedasto of number A way to understand the distinction better seedistinction A wayisto the quasi tounderstand the Thus, ContraryHusserl, to The PA

manner in which Parsons present the notion of intuition is quite akin presentquite manner is to Parsons of the inwhich notion intuition thatof the use of intuition was evokedthe use as of intuition a - intuition provide accessintuition to

concrete, while abstractarewhile concrete,and not objectsthus tobecausally inert taken

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focusing mainly does onepistemological issues, 33

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CEU eTD Collection 20 asWhile, waspreviously, designate indicated to uses intuition Kant bothimmediate a objecta withanintuited directrelationship cognitive or,inthe case ofHusserl, Inelementary objects.uses ofthe bothoftheir term mathematical is parallel (as alike) collectivecombination intuition and to number inmuch morethan Parsons, detail the typeclear. immediately some object aa concrete ofperception, concept token,ofa with type its typeintuits (||). the process repetition. of |||,is atype ofI theform etc. thathas greatergenerate greater recursively can and numbers by could say by defined |, 1is of thathas that a theform type type thatha 2is definedI bywanted types.language, I Thus if inthis todefineelementary naturalnumbers compose given concrete tousin a perception. type makes What isaspecial geometrical up form types,instancesconcreteare while tokensand the ofthe as typesare objects understood the underlying anyconditions of sortof higher that theexistence and primitive ofsuch intuitivelyknown objects necessary,for is they are objects that

See certain object. defined in the same fashion. Itdefined inthe same a fashion. is (Parsons: 103) (Parsons: 1980, Furthermore,much closer is ofintuition Parsons’ toHusserl’s ofKant’s. use thanthat Though therole in of discusses intuition Husserl formation Bytoken ofconcrete perceiving thetype a cats (saythe f on two Parsons, following d of strokes. According to Parsons, purely abstract entities, such as numbers, purelyared ofstrokes.as Accordingabstractsuch toParsons, entities, are tousintuitivel known

erefore the role of intuition is,erefore intuition theroleroughly of immediately put,to connect

Hilbert, considers beHilbert, such to strings objects thathe ofstrokes calls

cognitive y, namely payingcareful attention tothe processes that come 34

- process order reasoning (see Hilbert: 2002 reasoningorder (seeHilbert: ,

immediately

that is essentialthat is acquisition forof the ,

in both oftheirin both . Furthermore, Hilbert insists . intuition puts theagent puts intuition into 20

of the concept of of the – ence) the cognizerence) the

to make theform of approaches s the form of ||,s theform of 3 a p , 376). roperty of

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CEU eTD Collection are ofandcollection countable alike. as about, a items such knowledge bycan thatwe isthatwhichcaused have theperceivable thato objects objectexisting affairs orstatewhich of addresses. thebelief order for version ofof knowledge causal theory back tosuch concepts knowledge we isthat have such counterintuitiveasHusserl’s claims thattheonly insistence mathematical true identical. Parsons’ evocation empirical be to an observations objectintuition. ofmathematical 2007, verypoint clear withcri his areexperienced notdirectly Therefore, assume that intuition mathematical objects objects representation. almost exclusivelyas immediatecognition, andvery rarely a used todesignate singular epistemology. the reverse and may We note Parsons inHusserl cognitiona muchmore singularrepresentation, thelatter and pr is 167) where he states that set theory is too complex and relies167) whereheavily thatsettheory too hecomplex states istoo onnon . Husserl ontheother and hand, Parsons, apply only it All that said, IAll that said, to donotintend For some belief considered hastobe tobe knowledge it

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of the term

of Maddy’sset to of application intuition theory(Parsons: . T claim that Husserl and Parsons’ use of intuition is andclaim Parsons’ that Husserl use ofintuition

he he is muchmore nuanced comm and does not bjects bjects main assumption behindassumption main 35

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CEU eTD Collection 21 the term. elementary concepts mathematical articulationexplicit ofthe tothe relevance mathematical intuition of Itof Parsons. inKant’s not or is Gödel’s early Husserl’s work find butin thatwe nevertheless thevein in anticipated conceptionand of application mathematical the intuition, mathematical (Parsons: knowledge 2007,152). such views,explicitly stating doesnotimply evocationof thathis intuition an account for all that we to

wards Among (1973, see 350 others Collier However, s Manycontemporary and philosophersof epistemologists are mathematics skeptical pl this view this

ausibly 21 consider to be knowledge. Parsons is thus cautious thus is not tobeconsider knowledge. Parsons etting this difference aside, Ietting isplausibletoassumethat difference it Husserl this think aside, . A mongreasons, other

in a sufficiently similar waycontemporaryof in asufficientlysimilar use tothe - 352). it cannot account cannot ait body for

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propositions propositions of the first CEU eTD Collection 22 merely aofthe description number address should essence ofnumber the suggestHusserl’s of inquirywouldkind this review of aThis is popular interpretation for several reasons.Firstly, influential isgiveninFrege’s it and are inthe thus abstractsense thatthey only term The primary questionhere issue; onerather toreconstruct from it foundall has controversialthroughout hints the book burdensomegiven task,especiallystance that Husserl nowherefully stateonthe does his challenge access c more pl issue already in p objects; (ii)knowledge can was 5.1. roblem,

Among others see Bell (1990, 23), De Boer (1978, 12), Miller (1982, 89 (1982, Miller 12), (1978, De Boer 23), (1990, Bell see Amongothers

Husserl and theAccessProblemHusserl and to uni ?

It as him stating tempting is that tointerpret applicationTo see couldbe of at Husserl’s whether intuition alluseful theaccess to Itasserted mainphilosophical objective Husserl’s often is that ausible, thenclaim ascan inpart, we thatappliesintuition Husserl, hallenge , we must must , we which, terms. seen, ashave we be can similar putin PA te twocompeting ideal about(i)knowledge involves assumptions knowledge: 5. ,

H which I paperwhich insection twoof this discussed PA, USSERL similarlyp to somecontemporary begin thequestion of with hisontological PA in commitments relating becomes tothe contemporary hisuse ofintuition even debates

AND THE ’ S is: didHusserl numbersis: consider conditions in whichconditions in we graspconcept.Husserl’s the Therefore, onlyarise experience from C

ONCEPTION OF C ONTEMPORARY

reading. all, After the 37 , a supposedly abstract, a supposedly and are generalizationsare

M latonists ATHEMATICAL numbers . 22

This D . EBATES . Secondly, the very. Secondly, the natureof to be

are craftedcounting, through If isaddressing Husserl this - resonates withthe access well 100). 100). ideal any in ofthe sense

inquiry into theconceptinto inquiry of over objects physical

throughout his career throughout his NTUITION objective entity,objective not

to answer the .

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. CEU eTD Collection 23 of nominalistfrom approaches harsh his criticisms tomathematics. what accused Fregefamously hasof. him representations. which they are directed, and definitions, Husserl’scan frustratingly prose be seldomoffers obscure, assharpclear distinctions he and knowledge i ofnumbers choice than ofHusserl’s an ofphrasing” conviction actual (ibid.) T 2003. xvii). not beingact of thepart existence the ordependent upontheact” foror(Willard: nature its intentionalitycarrying tothe totalitywhatever over are that things oftotalitycounted, being Husserl’sWillard, formation of number were thought earlierhe Husserl’s] andlanguage neverworks, [in different light particulars:an its objectabstracted all awayof that we from have closest hecomes toobjectivity,as seen, we already have calling isby a number as he calls followingBrentano, it without any connections further theobjective to The realm. definition, at leas

Among others see, Bell (1990, 59), Tieszen (1994, 97 (1994, 59), (1990, Tieszen Bell see, Amongothers Furthermore, that Husserl wasFurthermore, ta thatHusserl Italso be may However theearly tend vast ina scholars of tosee majority Husserl work hisearly hus Willard thattheterm holds ‘psychic’an was “incredibly misfortunate rather . 23 that of 2003,123) thesomething. (Husserl: those contents.is only But on there residemust inthe characteristic every common toeachand of one aIf number] isto have designationgenuine [i.e. this abasis, thenit

however Neitherdoes hemathematics tobe of psychology, consider an extension in any usual sensewordin any ofthe usual Accordingexample, to,for t onthe face it,suggeststhat the concept ofnumber of isa the case that Husserlthe case that s knowledgeabstract of obje it is clear is thatintend number not it hedoes be concepts to subjective

if we todistinguish are careful towards andobjects mentalacts of the conce

king some sort of a realistking of inferred can stance somealso sort be

pt of number points at points “on pt ofnumber

simply takes it tobeasimply it fact matter takes our of that Dallas Willard, Willard, Dallas 38 -

“psychical”’ (Willard: xxvii). 99), Miller (1982, 89 (1982, 99), Miller

e all cts, in - encompassing concept

one orthe sense other ofthe term thought despite “the many of confusions . -

100). 100).

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entity,

. CEU eTD Collection method in ideal objects, namely geneticthat taskof ofarithmetic a howwe be account will toexplain mayhave of knowledge famously “The itin therelevance mentions Origin of ofGeometry” number asseea an work attemptgeneticanalysisconcept Husserl’s inPA toprovide ofthe of space by he means thetime ofwriting be them PA, to purely 5.2. Brentano. of relation in Husserl’s to ontologicalthe access commitments problem (Tieszen: 1994,99) 2000,95) Hill: that he in isaPlatonist later inhiscareer Husserl, ofthoseneither whoinfluences from thepositions force actual textual evidence notfrom from either oftime was Husserl advocating actually of time writing by the of symbols tothat concept“nominalism both loses has nowayelucidatingand andessence, oftherelationship full Husserl as a FullHusserl asa - - time blown Platonism Tieszen has argued only not intend doesnumber that Husserl be concepts to objective The vastare earlyscholars majority toclaimHusserl thatalready of inclined by the . PA This sort of This sort

(Tieszen: 1994,98 (Tieszen: Husserl is sufficiently similar to his later works, where the notion of geneticis sufficiently where tohis later similar thenotionof works, analysis is , Guillermo Rosaddo Haddock

arguesfor thus, alsoassume some radical reason we Platonism, should

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takes up atakes up - 100) . He

: B crucial part ofcrucial Husserl’s part philosophy, later and he grounds his etween Maddy and Parsonsetween and Maddy

39 (Haddock: 200,199) (Haddock:

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Husserl indeed - blown Platonist byblown Platonist thetime ofwriting P - of four thing I andit, notonanything individual. am not species statement ‘FouraI prime number is toseven’, relatively the am meaning It is… time, immutable andtime, 98). acausal” (ibid, PA. intend

evident evident Four, them andhave intuitivelythem in space them presentand arelocated time considers numberconsiders tobe ideal objects s ( I have that when Ithat whengeneric ‘Four’ sense,e.g., say inthe inthe as, Husserl: 2001, 239 Husserl: 2001, Frege’scriticism was utterly Husserl since was misguided

it Charles Parsons but also but Parsons Charles before my logical regard, and ambeforeon passing logicaland my regard, judgment PA.

Having this in mind it difficult not inmind is this Having tose 40 LI, LI,

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), s CEU eTD Collection aggregate is impossible it does second, not; readilymost are thefollowing:aa determinate toMaddysetmembers, has of an number matter. view for Mill’s has famously been many criticized thetwowhichreasons, but apply of collapsing Stuart proposal Mill’s see John to into sets asn stancePlatonist However inthe first place? indanger if Platonism, is Maddy’somits it view we knowledge cansuch as why ofentities unproblematic setsvia have perception, a take I‘abstract’. Sobeit; attach noimportance tothem”(Maddy: 1980 writes: “Onconventions, some means terminological this that setsnolonger count as we cannotinafinite cannot univer or perceive which exist have be should able how anytodemonstrate we plausibility,ofsets knowledge have she that good ofthisproblemissupposed tobe.If A an example set. infinite views Maddy’s are to wetime, seem withoutanatural ofwhat be to left certain account mathematica not seemanswer have intospace to clear once bring isthis: ofmathematics atheobjects we mathematical object ofsorts, way th ofintuition, painting by a collection picture: concrete perceiving similar aof mathematicalmerely object, ourrepresentations ofthem. not that of Kant that intuition by directperception or byimagination); byperceiving a by intuition. perceptual herspatio claim thatsetsare is Furthermore whether thefirst in ask a place. one Platonist shebe may to needs She The urgentthatcan most and objection betheorytowhichshe toMaddy’s raised does A spatio and Gödel’s: perception is necessary for it, but it puts us in directus in puts and perceptionit it,but Gödel’s: necessaryfor is contact to

it a is set containing threeelements. - temporally located set is any aggregate of objects that Itemporally objects setany located is aggregate that(either can of perceive at acertainwhich numerical property,

canattributed tothem. be - temporally and thatknowledge given is located ofthem tous

to distinguish3 elements anaggregate from of 41

Intuition hereIntuition isunderstood as a

stack of three books I grasp ofthree books stack by is also se. othing of physical butaggregates We couldWe Husserl see as

objects I toknow,by come objects consideredas a , 59 ). If, Mad ). as l objects are dyclaims, hybrid of - CEU eTD Collection least theabstr with Seen light, answer thatwe inthis access Husserl’s is are causally tothe problem at connected abstract entities problem a in vaguely way Maddian perceptual intuition. answerchallengewould simply tothegras isimpossible thatit be authenticallyacquiredand conceptsofthem. manipulations ofnumbers Thus rests ontheauthentic concepts.allowsfor number This symbolicof representations isarrivedcomplex at bymy recognitionthat the number belongs tothealgebraic system that knowledge isstrictly and ofnumbers limited, knowledge thatare concepts ofnumber representation,As wefrom direct of seendiscussion have symbolic Husserl’s perceptual direct set.infinite seems Husserl’s be account to preferable toMaddy’s, that doesnothold inthatit set theory, he ataccount can the least first for challenge, namely perceive cannot thatwe an ofset theory.axioms Maddy to deal for are problems has notapplicable with such largely view, tohis stemfrom case of ismerely aggregates, thatHusserl problems abouttalking that then cardinalities the does Husserl explicitly connectconceptIf settheoryofnumber. withthe ofsetsMaddy’s in intuition again Howeverforare here sense. inconfusion, wenowhere left Intuition doesunits seemvery of ascome numbers to aggregates close understood to of set containing thatset. the “aggregate” a very set containing is from thataggregate,butit distinguish important to a perceptuala experience condition isalwaysnecessary for theknowledge numbers. of Thus, On the other hand, ha ifit At first be glance, equally these seems criticismsapplicabletoHusserl would it that if Husserl – without succumbing to all of the problems succumbingwithout whichMaddy’s plague theory. toallofthe act formal propertiesformal andact we thus ofmultiplicities, knowledge have of

is afull - blown Platonist, he blown Platonist, ppens thaton Husserl hisaccountofnumbers modeling is – namely,

42 by postulating that we are causally thatweby postulating are connected to

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- body dualism ues thatGödel andMaddystruggled realm is still leftrealm unaccounted for. isstill Parsons ofmathematical theory - Peano axioms” (Parsons: the 2007,188), how axioms” butjust Peano As we there seen, crucial have difference isonewhich , nor does his theory, nor andoes intuit his presuppose - abstract mathematical unclea abstract objects remains an issue with Husserl’san ap issue 43

ncrete and quasincrete m in virtueofm in knowing theelementary numbers as formal propertiesnumbers as formal Ifc we

with - abstract entities, but that is thatis but abstractentities, - abstract entities. This way This abstract entities. – onsult the rulesonsult of he has neither to proach.

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answer to this is thetheory is answer tothis of the quantit t all possible conceptst allpossible given are tous

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of the force - 180). e CEU eTD Collection 99). 1998, (Brentano: sense” common sum of The evident. being their without term the outit turnsthat synthetic hecalled which principles deman science that Kant claimed Reid. that ofto similar very essence 24 Brentano’s ontologythe external,world say bracketed, material isto is isthat which that opposed tonoumenal ones,touseKant’s terminology. human onthethingsis not existing inthemselves, but inspiration from that ofKant’s. The onBrentano’sstudy focus ofontology all ourknowledge claims. issimply orsoBrentano nonsensical, that one cannot evidence. ‘b their ‘see’ Accepting such could agree not Kantwith in was the not evident, at and,af least according Kant, to, they form with Reid’sjudgments common sense. of Such judgmentscertain, appearthough synthetic 2012, predecessorscontemporaries, and “Kantundoubtedlya occupies place ofhonor” (Frechette: viewsBrentano, are of towhom those sympathetic,with certain provisos, if contemporariescriticized havevarious aspectsKant’s thought of while still arithmetic, andturnof nor hisepistemology.Indeedevery twist Husserl’s many of enumerating’ (Husserl:aresame?” 2003,34). notthe the processenumerating.But notclear ‘number’ it of is that ‘representation of and

“InGermany

1). eye However thisdoesnotstop As Guillaume Frechettenotes, inallofthe criticisms Brentano against made his has However

One of a priori a priori . Which is to say isto Which Brentano’s that

it was Kant who undertook to save knowledge from Hume’s skepticism, and his method wasin method his and skepticism, fromHume’s knowledge save to undertook who Kant was it

Brentano’ in order to be a criticalin order a Husserl notaccept tobe realist need judgments is unjustified judgments is a priori priori a

s most frequentlys most is points stressed amounts for him to proposition that stand for us as true from the beginnin from the true usfor as stand that proposition himto for amounts

a priori priori a

a priori priori a him

judgments. On close inspection of what he means by this, however, however, this, meansby whathe of inspection close On judgments. to his proposedto his ontology PA

from taking an ontological stance judgments have the same character as Reid’s judgments of judgments as Reid’s character same have the judgments a priori a priori . is dedicated. 24 consideration be will ofphenomenal objects

He parallels Kant’s synthetic 48 on

character the claim but ofstatements, such things thewayare by perceived the they

oundation forBrentano What science.

lind’ judgmentslind’ asthefoundation of As ds as its foundations a number of number a foundations as its ds Bell notes,a criticalfeature of

. that

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CEU eTD Collection interchangeably. 25 to designate im Brentano often uses objectivity’, an object ‘existenceas something’ in andIt alike. note, that important to is givingmerelyexamples an Empirical Standpoint simply as the understood phenomena.IntentionalityBrentano’s relevant of ontology,is another feature can which be is ‘in’the(Chrudzimski, Smith:2004,205) mind theyare thecorresponding act, sense from andinthis inseparable theimmanent object mental note,Chrudzimski theimportant aspect most “imm ofthe ‘immanent orBarry andArkadiusz ‘intentional objects’, As correlates’. Smith ‘contents’ an 103) object” (Brentano: 1874, writes, tomental “what phenomena characteristic is isthemhaving so introducing in mental phenomena mental actsand physical andactivities, are phenomena contents acts. ofthe the said phenome reference us to,and no philosophical Brentano’sontology tendency; treatment ofhassolipsistic a pronounced “there isno namely,

In Brentano’s terminology all mental phenomena are acts are mental phenomena all terminology InBrentano’s Regrettably, Brentanoprovide not account an does instead explicit relation, ofthis Physical accordingBrentano, ‘intentionall thus, phenomena to A critical inBrentano’s distinction na. Mental phenomena arena. which nothingcontent” have Mental phenomena but“acts

something (Brentano: itself as within object thing), or immanentincludes objectivity.Every phenomenon mental directionan (which towardtobeun object isnot what weunambiguously,reference call, toacontent, notwholly might though AgesMiddle (or called mental) theintentional in Every mental phenome manent content present act. content amanent in mental objects External are therefore not object object and synonyms,as in ‘mental such

he famously writes: mental act’s necessaryreference toanobject and the

. ‘Physical are phenomena’ used thus interchangeably with Psychology from anEmpiricalView Psychology of Point from content of a mental actcontent ofamental e of denizens ofthee natural ofdenizens (Bell: 1990,9). world” non is characterized is thenon Scholastics by what ofthe ontology

. –

he uses ‘mental phenomena’ and ‘mental act’ ‘mental and ‘mentalphenomena’ he uses

drawn anence” objects that ofimmanent is - interchangeably, for he uses both

existence’, ‘immanent 1874,

between mental and physical derstood herederstood a as meaning - existence ofanand object,

88)

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CEU eTD Collection “an affirmation ofuniversals,sentences of Husserl’sstance, explicitly time ontological this AsRollingernotes,hePlatonist. saw itas consent. but remains an open question. categorizing and physical mental theminto phenomena. yield fromthe representations ourmakeup epistemic analyzed and that thatare by tobe objec mightadopted have weextension, mayBrentano’s thenthat Husserl, descriptive suppose psychology, along with mental phenomen contents’, namely theimmanent as thatmakes object something immediately presen the act intentionallyIntuition is directed.may ofan as be aempty understood ‘act fulfillment either per numerical ordistinct se, pro following: of Brentano’s ontology. if Husserl a is criti faculties. the objects that areby themselves,throughcognitive therepresentations save determined our constituents ofcognition,he remains tothe claim faithful that we nodire have heconsiderably departs Kant’s from of analysis the ofknowledge, and partition Kant’s grasped intheir original form. talked about,not phenomena asthey are

we attribute be should notto Brentano’s carefulontology to ts in whatever form they exist are whateverthey formts in exist real, wesave reach through them may however not However, whether this canWe safely thus Brentano’s say isthatofa that ontology realist While critical one.

It thatBrentano well known wastoHusserl’s is unsympathetic Brentano does not giveaccountBrentano anofthe conceptas does Kant, ofnumber, did however

The grasping of thegrasping conceptisanact/mentalThe ofnumber thenumber, phenomenon, on/act, this way yielding waythis on/act, inourrecognition ofnumber concepts. cal realist realist cal his critical realismHehis critical aswell. wouldthenbe A brief ofHusserl’s ofsuch sketch treatment Husserl’s heavily earlyprojectis Brentano influenced by his account of number c

interpretation thanth more is plausible perty, is the immanent objectan act, ofsuch isthe perty, which to - , rathernoumena, in - themselves and otherthemselves 50

oncepts would not goagainstoncepts theletter not would

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serl’s earlyserl’s ontological commitments

Husserl’s correspondence with Brentano,Brentano’sown reflections correspondenceHusserl’s oron with - LI, LI, impossible impossible then wethedark as remain were muchin we be

to establishthe legitimacyother over of one the onist interpretationonist 51 , which,

it remains be to

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was , it may, it see important to be what was - iently similar way similar iently tothe Kantian tradition Kantian 6. nterpretation, I nterpretation, certain considerations needed toset to provide

C ONCLUSION 52 ecauseI what as primarywas saw my to task

a thorough its Husserl’s

corresponding concept.

However, i

and especiallyBerlin, histeacher in

I not only does Husserl t ried tosteer awaya more from

epistemological treatmentepistemological of yet contemporary contemporary

conciseof overview n just whatn just way does he Platonist (save placesPlatonist from . II have what provided Husserl’s authors However weare epts thefirst in defineand

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was CEU eTD Collection relevant thecontemporary to itdoessoin ofmathematics, philosophy remains: matter H of further research. Husserl antici Philosophy ofArithmetic criticism andIdeas headwatersofhisphenomenologicalproject. thatare being in developed Husserl’s earlyphilosophyHusserl’s only ofmathematicsnot issues thatare with deals pated them . are Determining are is,again extent ideas these towhat plausible owever whatever the result ofsuchthefactowever whateverresult an theinvestigation,

very much alive today and it is generally muchalivevery and that is notrecognized it today 53

much the same way. , a

CEU eTD Collection Hintikka, J. 1969 Hintikka, J. Hilbert,das Unendliche”, D.2002.“Über Hale,2002. B.and Wright, C. Gödel, Follesdal, D. Frege, ofArithmetic;Foundations G.1980.The trans. J.L. Austin, Northwestern Evanston: Frege,of Dr. G.1970.ReviewArithmetic. Husserl‘s in Philosophy of Frechette, G.2012. Erdman, B. 1870. Dummet, M.1994. Dummet, Descartes, 1985. R. Descartes, 1985. R. De Boer, T. 1978. 1973.“ContraCollier, K.W., of Knowing” An theCausal Studies: inPhilosophical Theory Chudnoff, E. Forthcoming. inMathematics” “Intuition in A.,Smith, Chrudzimski, B. 2004.“Brentano’s Ontology”, in Brentano, F. Brentano, F. Benacerraf, P. Bell, A. Balaguer, M. Adams, M.M.

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