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Carnaps Conception of Explication:

From Frege to Husserl?

Michael Beaney

The task of making more exact a vague or not quite exact concept used in everydaylife or in an earlier stage of scientific or logical development, or rather of replacingit y a ne!ly constructed, more exact concept, elongs among the most importanttasks of logical analysis and logical construction" #e call this the task ofexplicating, or of giving an explicationfor, the earlier concept """ $%arnap 1&4', ()&"*

1 Introduction

+udolf %arnap is a key figure in the history of analytic philosophy, for he not only

played a central role in the !ork of the ienna %ircle in the decade from 1&2- to

1&.-, ut he also, in his susequent move to the nited tates !ith the rise of ai

3ermany, marked the shift in the centre of gravity of analytic philosophy from a point

in the orth ea to the mid)tlantic" %arnap !as influenced y 5rege, +ussell and

#ittgenstein, the three main founders of the analytic tradition, and in turn !as a

crucial influence on 6uine, 3oodman and other ma7or thinkers in merica" 8ut

although in many !ays %arnap !as the archetypical 9analytic: philosopher, he !as

also influenced y philosophers outside the analytic tradition" ;n recent years the neo)

usserl" ?y aim in this paper is to explore some of these

influences and relationships y considering %arnap:s methodology, and in particular,

the development of his vie!s on analysis"

The idea of explication is central to an understanding of %arnap:s

methodology= yet the term 9explication: itself did not appear in %arnap:s !ork until

1&4- $in 9The T!o %oncepts of @roaility:*, and the idea did not receive a full

discussion until 1&-0 $in the first chapter of theLogical Foundations of Probability*"3iven that %arnap:s notion of explication ears a striking resemlance to the

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conception of analysis that 5rege articulated in his 1&14 lectures on 9Aogic in

?athematics:, !hich !e kno! %arnap attended, and !hich %arnap himself mentions

in his 9;ntellectual utoiography: in discussing 5rege:s influence on him, this

deserves explanation" #hy did it apparently take %arnap over thirty years of active

!ork in philosophy to reflect upon the central methodological conception that, it

seems, he took over from 5regeB nd !hy did %arnap choose the term 9explication:

$9Cxplikation:*B ;f his o!n remarks are to e elieved, it !as motivated y usserl:s uses of the term" et his o!n use seems very different from either of theirs"

o did %arnap move from a 5regean to a >usserlian conception of analysisB Er

should he e seen as offering some kind of synthesis of othB Er does %arnap:s

mention of >usserl simply reveal their common neo)ere he examined critically some of the customary conceptions and formulations inmathematics" >e deplored the fact that mathematicians did not even seem to aim at theconstruction of a unified, !ell)foundedsystemof mathematics, and therefore sho!ed alack of interest in foundations" >e pointed out a certain looseness in the customaryformulation of axioms, definitions, and proofs, even in !orks of the more prominentmathematicians" s an example he quoted #eyerstrass: definitionJ H numer is aseries of things of the same kindI $H" " " eine Reihe gleichartiger DingeI*" >e criticiedin particular the lack of attention to certain fundamental distinctions, e"g", thedistinction et!een the symol and the symolied, that et!een a logical concept and

1%arnap:s notes on these t!o courses have no! een pulished, edited y 3ottfried 3ariel, inistory and Philosophy of Logic, 1&&'= see 5rege !""

2%f" 5rege #$= and for a discussion of this,

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a mental image or act, and that et!een a function and the value of the function"nfortunately, his admonitions go mostly unheeded even today" $1&F., F"*

%learly, !hat takes centre stage here is 5rege:s critique of mathematicians:

conceptions of their discipline, and the !ider philosophical implications of 5rege:so!n reconstructive activities !ere not, at least in %arnap:s eyes, addressed" This is

confirmed in the paragraph that immediately precedes the one 7ust quotedJ

lthough 5rege gave quite a numer of examples of interesting applications of hissymolism in mathematics, he usually did not discuss general philosophical prolems";t is evident from his !orks that he sa! the great philosophical importance of the ne!instrument !hich he had created, ut he did not convey a clear impression of this to hisstudents" Thus, although ; !as intensely interested in his system of logic, ; !as not

a!are at that time of its great philosophical significance" Enly much later, after the first!orld !ar, !hen ; read 5rege:s and +ussell:s ooks !ith greater attention, did ;recognie the value of 5rege:s !ork not only for the foundations of mathematics, utfor philosophy in general" $1&F., F"*

This is reinforced later on in the autoiography, !hen %arnap !rites that H#hereas

5rege had the strongest influence on me in the fields of logic and semantics, in my

philosophical thinking in general ; learned most from 8ertrand +ussellI $1&F., 1.*"

5rege may have provided the logical instrument for %arnap:s o!n !ork, then, ut it

!as +ussell !ho !as credited more !ith its philosophical motivation"

This suggests an ovious ans!er to our question" The notion of explication that, ineffect, is adumrated in 5rege:s 9Aogic in ?athematics: lectures !as simply not

appreciated y %arnap at the time= and it took many years of his o!n reconstructive

activities, utilising 5regean logic, efore he reached the point at !hich a conception of

explication could e adequately conceptualised" 8ut could !e then argue that there

!as a delayedinfluence, prompted perhaps y the later $re*reading of 5rege:s !orks

that %arnap mentionsB 3iven that the 9;ntellectual utoiography: !as pulished in

1&F., !ell after the discussion of explication, the ans!er might again seem to elargely negative, for %arnap does not mention 5rege:s influence in this regard" ;n any

case, 5rege:s 9Aogic in ?athematics: lectures remained unpulished, and although

%arnap:s notes on these lectures have survived, there seems to e no evidence that

%arnap later reread these 9!ith greater attention:" $; return to this in the next section"*

>o!ever, !hether or not there !as any direct influence of 5rege:s conception

of analysis in 9Aogic in ?athematics: on %arnap:s later notion of explication, there is

still a striking similarity, !hich suggests that a deeper explanation is required" ;n KK 4

and - !e !ill examine %arnap:s early notions of 9rational reconstruction: and 9quasi)

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analysis:, efore turning to his account of explication in KF" 5irst, ho!ever, !e must

outline the conception of analysis that 5rege articulates in his 1&14 lectures"

! Freges Conception of "nalysis

Ene !ay to approach the conception of analysis that 5rege offers in his 1&14 lectures

on 9Aogic in ?athematics: is y considering the response he provides there to !hat is

essentially the paradox of analysis" The paradox of analysis is often associated !ith

the !ork of 3"C" ?oore, and the name 9paradox of analysis: !as indeed first used, y

%">" Aangford $1&42*, in discussing ?oore:s !ork" 8ut the prolem itself has a much

longer history, and really goes ack to the paradox of inquiry formulated in @lato:s

Meno" 8ut even in its linguistic form, it can e found articulated long efore it !as

named as such, appearing explicitly, for example, in 5rege:s o!n !ritings" The

paradox can e stated as follo!s" %onsider an analysis of the form 9%is C:, !here%is

the analysandum $!hat is analysed* and C the analysans $!hat is offered as the

analysis*" Then either 9%: and 9C: have the same meaning, in !hich case the analysis

expresses a trivial identity= or else they do not, in !hich case the analysis is incorrect"

o no analysis can e oth correct and informative"

o! the ovious response to this is to disamiguate the notion of 9meaning:,so that an analysis can e deemed correct at one level of meaning and informative at

another" This is 7ust !hat 5rege did in the first t!o of the three responses that can e

discerned in his !ork, corresponding to his early, middle and late philosophy" ;n his

early !ork, taken as including his"egriffsschriftand &rundlagen, 5rege distinguished

et!een 9content: $9;nhalt:* and 9mode of determination: of content" %onsider 5rege:s

key example in KF4 of the &rundlagenJ

$Da* Aine ais parallel to line b"

$D* The direction of line ais identical !ith the direction of line b"

ccording to 5rege, $Da* and $D* have the same 9content:, ut 9split up: that content

in different !ays" This is seen as analogous to the relationship et!een the follo!ing

t!o propositionsJ

$a* The conceptFis equinumerous to the concept &" $There are as many o7ectsfalling under conceptFas under concept &, i"e", there are 7ust as many Fs as

&s"*

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$* The numer ofFs is equal to the numer of &s"

The equivalence et!een these t!o propositions, asserted in !hat has come to e

kno!n as 9>ume:s @rinciple:, underlies 5rege:s logicism" Gust as $Da* is offered as a

!ay of contextually defining direction terms, through its equivalence to $D*, so $a*

is offered as a !ay of defining numer terms, through its equivalence to $*"

lthough 5rege came to re7ect contextual definitions themselves, >ume:s @rinciple

!as retained, eing underpinned in his later !ork y his notorious xiom , in !hich

an analogous equivalence !as asserted" The equivalences involved here, at the time of

the &rundlagen, !ere understood as involving sameness of 9content:" En this early

vie!, then, the follo!ing response can e given to the paradox of analysis" n

analysis of the form 9% is C: is correct if 9%: and 9C: have the same content, andinformative if they 9determine: or 9split up: that content in different !ays"

;n his Philosophie der %rithmetik, >usserl o7ected to 5rege:s &rundlagen

definitions on the grounds that !hilst they may e extensionally equivalent, they !ere

not identical in 9content: $9;nhalt:*, !hich >usserl understood intensionally $1(&1,

122*" There is some 7ustification for this vie!J since $Da* and $D* involve different

concepts, it !ould seem that they cannot e intensionally equivalent" The amiguity

in the notion of 9content: that this suggests, ho!ever, had already een recognised y

5rege in dra!ing his distinction et!een 9inn: and 98edeutung:" This distinction first

appears in 95unction and %oncept: $FC*, !hich !as given as a lecture on & Ganuary

1(&1= and in his letter to >usserl of 24 ?ay 1(&1, he states explicitly that this is a

disamiguation of his earlier notion of 9content:". ;n his 1(&4 revie! of >usserl:s

ook, he then uses this distinction in responding to >usserl:s criticism" ;n articulating

the criticism, he provides a clear statement of the paradox of analysis itselfJ

;f !ords and cominations of !ords refer to LbedeutenM ideas, then for any t!o of themthere are only t!o possiilitiesJ either they designate the same idea or they designatedifferent ideas" ;n the former case it is pointless to equate them y means of adefinitionJ this is 9an ovious circle:= in the latter case it is !rong" These are also theo7ections the author raises, one of them regularly" definition is also incapale ofanalysing the sense, for the analysed sense 7ust is not the original one" ;n using the!ord to e explained, ; either think clearly everything ; think !hen ; use the definingexpressionJ !e then have the 9ovious circle:= or the defining expression has a more

3'", &'/FR, 1-0= cf" C(, 1&(/FR, 1(F" 5rege:s letter to >usserl of 24 ?ay 1(&1 makes clear that

5rege did not kno! of >usserl:s !ork until >usserl sent him a copy ofPhilosophie der %rithmetik,!hich happened sometime in pril/?ay 1(&1" $>usserl:s preface is dated pril 1(&1, so it cannot haveoccurred efore then"* ;t !as not >usserl:s criticism, then, that had prompted 5rege:s distinction"

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richly articulated sense, in !hich case ; do not think the same thing in using it as ; do inusing the !ord to e explainedJ the definition is then !rong" $R, .1&/FR, 22-"*

;n reply, 5rege argues that for the mathematician N as opposed to the

9psychological logician: N it is only"edeutung, i"e", 9the thing itself:, that matters" o9coincidence in extension: is all that a definition need captureJ neither the senses of

the relevant expressions nor the ideas evoked y them are relevant $R, .1&)20/FR,

22-)F*" 5rege:s second response to the paradox of analysis can thus e stated as

follo!s" n analysis of the form 9% is C: is correct if 9%: and 9C: have the same

"edeutung, and informative if 9C: has a 9more richly articulated sense: than 9%:

$something that is not, strictly speaking, of concern to the mathematician*"

;n essence, ho!ever, 5rege:s second response is the same as his firstJ adistinction is dra!n et!een t!o notions of meaning" 9%ontent: has ecome

98edeutung:, and 9mode of determination of content: has ecome 9sense:" o is

5rege:s second response etterB The ans!er is 9o:, for analyses and definitions must

capture more than 7ust sameness of"edeutung" %onsider the follo!ing t!o examplesJ

$%>* cordate is a creature !ith a heart"

$%* involves sameness of sense N on some conception of 9sense: N and

not 7ust sameness of"edeutung" o too in the case of 5rege:s o!n definitions and

axioms, sameness of sense and not 7ust sameness of"edeutungis required" ;n some

places, 5rege seems to ackno!ledge this" ;n 95unction and %oncept:, for example, he

remarks that !hat, in effect, are instances of the t!o sides of xiom 9express the

same sense, ut in a different !ay: $FC, 11/FR, 1.F*" This sounds more like the9content:/9mode of determination of content: distinction, !ith 9content: no! eing

understood as 9sense:" ;n the &rundgeset)e itself, 5rege talks of the t!o sides of

xiom eing 9gleichedeutend: $&&, ;, K./FR, 21.)4*, ut !hat he means in this

case is sameness of "edeutung and sense, as his later use of the term

9gleichedeutend: sho!s $&&, ;, K2'/FR, 220*" Cven 5rege, then, !as a!are that

analyses and definitions require sameness of sense and not 7ust sameness of

"edeutung" 8ut if this is so, then the response to the paradox of analysis that is

suggested in his reply to >usserl is inadequate"

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;n his 1&14 lectures on 9Aogic in ?athematics:, 5rege makes his most

sustained attempt to resolve the issues involved here= and !e can regard these lectures

as offering his third and final response to the paradox of analysis" >e egins y

distinguishing et!een 9constructive: $9aufauende:* and 9analytic: $9erlegende:*

definitions" %onstructive definitions simply stipulate, for areviatory purposes, that a

ne! sign is to have the same sense as !ell as the same"edeutungas a more complex

sign" nalytic definitions analyse the sense of a sign 9!ith a long estalished use:= and

it is here that the prolems arise" ;f !e take an analytic definition of the form 9%is C:,

then there are t!o cases to consider" ;n the first case, 9%: and 9C: oviously have the

same sense, ut here, 5rege notes, !e should really talk of axioms, encapsulating !hat

Hcan only e recognied y an immediate insightI $LM, 22'/FR, .1F*" ;n the second

case, 9%: and 9C: do not oviously have the same sense" 8ut !hat !e do here, 5rege

argues, is introduce a ne! term 9": to replace9%:, !here 9": is defined in the !ay !e

!ant, y means of 9C:" ince 9"is C: is a constructive definition, !e in effect bypass

the question as to !hether 9%: and 9C: have the same sense" >aving done this, !e can

then reintroduce the sign 9%: if !e !ish, as long as !e understand that it is to e

treated H as an entirely ne! sign !hich had no sense prior to the definitionI" $LM,

22')(/FR, .1'"*

This strategy looks attractive as a response to the paradox of analysis" 5or ifthe original sense drops out of consideration in our constructive activities, then thereis no longer an issue aout capturing it" %onsider, for example, 5rege:s definition of90:J

$C0* The numer 0 is the extension of the concept 9equinumerous to the conceptnot identical *ith itself:" $%f"FR, 11("*

;t is clearly asurd to suggest that the ordinary person kno!s this definition" 8ut given

the amount of confusion that there has een aout our concept of ero, it !ould seem

equally asurd to expect an analysis to capture our ordinary understanding" ll that is

necessary for such definitions to count as oth correct and informative is that they

allo! us to derive Hthe !ell)kno!n properties of numersI, as 5rege put it in the

&rundlagen$K'0*"

>o!ever, this strategy merely avoids rather than solves the paradox" Cven ifour ordinary understanding is deficient, it still acts as a constraint on our constructiveactivitiesJ there remains something to !hich our analyses are ans!erale" t the veryleast, the paradox of analysis simply re)emerges at the level of the system as a !hole,

as 5rege:s appeal to the 9!ell)kno!n properties of numers: indicates" 5rege admits toa residual !orry here, ut according to him, !hat constraints there may e operate

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purely at the pre+theoreticallevel" Eur grasp of the senses of simple terms is oftenconfused, as if seen Hthrough a mistI, and the aim of logical analysis is to articulatethose senses clearly, in preparing the uilding stones for the susequent !ork ofconstruction $cf"LM, 22(/FR, .1')(*" 8ut again, this merely seems to displace ratherthan resolve the paradox of analysis"4

;t should e clear 7ust ho! close 5rege:s conception of analysis is to %arnap:slater conception of explication" 3iven that %arnap attended the lectures in !hich

5rege elaorated it, the ovious suggestion is that %arnap simply took over his

conception from 5rege" >o!ever, although %arnap:s notes on 5rege:s lectures have

survived, there are not, unfortunately, any interpolations or marginalia to indicate that

%arnap !as inspired y 5rege:s conception"-8ut even if there !ere, it !ould e to

miss the real point here" 5or !hat is important is the tension that underlies any

reconstructive pro7ect" En the one hand, the !ork of analysis is to elicit and clarify!hat !e already kno!, and !e cannot depart too radically from our ordinary

understanding, on pain of clarifying nothing at all" En the other hand, there must e a

certain amount of reconstruction and revision, since our ordinary understanding is

frequently confused and unreliale" 3iven that %arnap follo!s 5rege in using logic in

a programme of philosophical reconstruction, it is not surprising that the tension

underlies his thought too, and that it should eventually prompt him to reflect

45or further discussion of 5rege and the paradox of analysis, see 8eaney 1&&F, KK -"4, -"- and ("-"55or the record, here are %arnap:s notes on the relevant part of 5rege:s lecturesJ

Die Definition ist logisch OerflOssig, psychologisch !ertvoll"Die Definition hilft nicht nur aufauen, sondern auch, das Pusammengesette u erlegen, "8" umdie Pahl der xiom u verringern" Cine solche Perlegung lQsst sich nicht e!eisen= nur fOhlen,dass man das +ichtige getroffen hat, und e!ahren"CxacterJ #ir auen von neuem auf, indem !ir das Crgenis unserer Perlegung enuten" Pu!eilen!ird auch in einer Definition der inn eines schon frOher lQngst gerauchten Peichens festgesett"Dies kann man nicht e!eisen= es muss einleuchten= es ist keine !illkOrliche 5estsetung, sondernein xiom"Cs sei das alte Peichen= !ir nehmen an, ein estimmtes, usammengesettes Peichen stimmeOerein mit dem inn von " #enn !ir es nicht genau !issen, so verfahren !ir soJ !ir seten

!illkOrlich fest, 8 soll den inn des usammengesetten Peichens haen" #ar dann die 1"Definition richtig, so muss der inn von mit dem von 8 Oereinstimmen" #ir vermeiden dasPeichen , und auen das gane ystem noch einmal auf, unter 8enutung nur von 8" #enn derufau des ystems gelingt, so kRnnen !ir aus P!eckmaessigkeitsgrOnden auch !ieder das altePeichen einfOhren= nur mOssen !ir es als neu eingefOhrt etrachten, als o es vor der Definitionkeinen inn gehat hQtte"Cin!andJ #ie kann es Oerhaupt !eifelhaft sein, o der inn eines usammengesetten PeichensOereinstimmen mit dem inn eines schon lQngst ange!andten Peichens, dessen inn schon lQngstfest steht" Ga, !enn dies der 5all istS er !enn !ir es nur H!ie durch einen eel erlickenIS$%arnap:s notes, 111)10)0., F)'"*

; am grateful to 8rigitte hlemann of the @hilosophisches rchiv der niversitQt

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systematically on his methodology in 7ust the !ay that 5rege did in his o!n later

!ork"

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# Carnaps Early $or%: &ational &econstruction

%arnap may not have introduced the term 9explication: until 1&4-, ut the central idea

that that term gave expression to !as present in some form from %arnap:s very

earliest !ork, and in particular, !as encapsulated in his conception of 9rational

reconstruction: $9rationale achkonstruktion:*, !hich formed the underlying

motivation of his first ma7or ook, Der logische %ufbau der 'elt, !hich !as

pulished in 1&2(" The connection et!een 9explication: and 9rational reconstruction:

!as made very clear in %arnap:s preface to the second edition of the%ufbau, !hich

appeared in 1&F2" fter noting that he !ould no longer put things in quite the !ay he

had earlier, he goes on to endorse the philosophical orientation of the ookJ

This holds especially for the prolems that are posed, and for the essential features ofthe method !hich !as employed" The main prolem concerns the possiility of therational reconstruction of the concepts of all fields of kno!ledge on the asis ofconcepts that refer to the immediately given" 8y rational reconstruction is here meantthe searching out of ne! definitions for old concepts" The old concepts did notordinarily originate y !ay of delierate formulation, ut in more or less unreflectedand spontaneous development" The ne! definitions should e superior to the old inclarity and exactness, and, aove all, should fit into a systematic structure of concepts"uch a clarification of concepts, no!adays frequently called HexplicationI, still seemsto me one of the most important tasks of philosophy, especially if it is concerned !ith

the main categories of human thought" $1&F1, v"*

%arnap:s call for ne! definitions of old concepts echoes 5rege:s famous passage in

the &rundlagen $vi)viii* !here he re7ects the 9historical: approach to understanding

our concepts and advocates precisely that conceptual systematisation that is here

called 9rational reconstruction:" 8ut !hat also deserves note is the lack of any mention

of the prolems concerning the relationshipet!een the old and the ne! concepts,

!hich %arnap:s later discussion of explication did at least attempt to address"

The %ufbau opens !ith a quote from +ussellJ HThe supreme maxim in scientific

philosophising is thisJ #herever possile, logical constructions are to e sustituted

for inferred entities"IF#e have already noted %arnap:s +ussellian motivation, and it is

clear that %arnap himself sa! his !ork as extending the +ussellian programme as he

understood it" ;n his 9;ntellectual utoiography:, he explicitly mentions the influence

of +ussell:s (ur ,no*ledge of the External 'orld, !hich he read in 1&21, and

endorses the !ords !ith !hich +ussell dra!s that ook to a conclusionJ Hthe study of

6+ussellR#P, 11-= cf"L%, .2F"

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logic ecomes the central study in philosophyJ it gives the method of research in

philosophy, 7ust as mathematics gives the method in physics"I'nd after quoting

+ussell:s impassioned call for a 9ne! eginning:, %arnap commentsJ H; felt as if this

appeal had een directed to me personally" To !ork in this spirit !ould e my task

from no! onS nd indeed henceforth the application of the ne! logical instrument for

the purposes of analying scientific concepts and of clarifying philosophical prolems

has een the essential aim of my philosophical activity"I $1&F., 1."*

8ut +ussell:s maxim is notoriously amiguous" Does it entail a programme of

ontological eliminati-ism, or 7ust of epistemological reductionismB +ussell:s theory of

descriptions lies at the root of the maxim, ut even if !e agree that +ussell:s theory

sho!s ho! definite descriptions may form part of a meaningful sentence !hilst

lacking meaning in themselves, this does not imply that the definite descriptions

9analysed a!ay: do nothave a referent" 8ut it is clear that %arnap himself interpreted

+ussell:s maxim epistemologically rather than ontologically, as permitting rational

reconstruction rather than ontological deconstruction" %arnap !as famously

dismissive of ontological endeavours, and it !as the pro7ect of conceptual

clarification !ith the help of modern logic that %arnap really sa! as important"

The fact, ho!ever, that %arnap attempts to reduce our kno!ledge to a 9given:

that is understood phenomenalistically has often led to %arnap eing interpreted as

more +ussellian than he !as" 5or it also true that %arnap offers the possiility of a

reduction to a physicalistic ase= and the possiility of alternati-e9reductions: sho!s

that 9rational reconstruction: is not regarded as part of an ontological enterprise N to

see !hat kinds of things are 9really: or 9ultimately: there" s %arnap himself explicitly

said in commenting on his%ufbaupro7ectJ H#ith respect to the prolem of the asis,

my attitude !as " " ontologically neutral" 5or me it !as simply a methodological

question of choosing the most suitale asis for the system to e constructed, either a

phenomenalistic or a physicalistic asis" The ontological theses of the traditional

doctrines of either phenomenalism or materialism remained for me entirely out of

consideration"I $1&F., 1("*

7+ussell (,E', 24.= quoted y %arnap 1&F., 1." +ussell goes on to sayJ H;t !ill generally e foundthat all our initial data, all the facts that !e seem to kno! to egin !ith, suffer from vagueness,confusion, and complexity" %urrent philosophical ideas share these defects= it is therefore necessary to

create an apparatus of precise conceptions as general and as free from complexity as possile, eforethe data can e analysed into the kind of premisses !hich philosophy aims at discovering"I $(,E',24-"* This too !ould have struck a strong chord in %arnap"

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#hat, then, is the point of 9rational reconstruction:, if not to engage in a

pro7ect of ontological pruning or sortingB @art of the point !as precisely to sho! the

futilityof ontological disputes, and this goes ack to %arnap:s first !ork, his doctoral

dissertation, Der Raum $1&21*, !hich had attempted to reconcile the different

conceptions of space of mathematicians, philosophers and physicists, y

distinguishing et!een formal space $understood as an astract logical system*,

intuitive space $interpreted in a

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the human mind are not only necessary in the sense of eing universal ut are also

constitutive of the !orld as !e experience it, i"e" the phenomenal !orld $!hich is

!hat opens up the possiility of the synthetic a priori*" 8ut !ork in the 1&th century

on the foundations of geometry, in particular, had cast dout on

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9+ational reconstruction:, then, might e etter named 9rational reconstitution:,

although the term 9rational: certainly suggests an epistemological rather than

metaphysical motivation" The point !as not to 9reconstruct: the !orld ut to

9reconstitute: our kno!ledge of it, and the aim of this !as to elucidate thestructureof

our kno!ledge to demonstrate its o7ectivity"12 The importance of structure can e

rought out if !e ask !hat the relationship is et!een 9ordinary: and 9reconstituted:

kno!ledge" #hat, more specifically,/ustifiesa rational reconstructionB %arnap:s later

principle of tolerance might suggest that anything goes, ut there must clearly e

some constraints on the adequacy of a reconstruction" ;n descriing his%ufbaupro7ect

in his 9;ntellectual utoiography:, %arnap !ritesJ Hlthough ; !as guided in my

procedure y the psychological facts concerning the formation of concepts of material

things out of perceptions, my real aim !as not the description of this genetic process,

ut rather its rational reconstruction N i"e", a schematied description of an imaginary

procedure, consisting of rationally prescried steps, *hich *ould lead to essentially

the same results as the actual psychological processI $1&F., 1-= italics added*" 8ut

!hat does %arnap mean y 9the same results:B The only example he gives is that of

material things, Husually immediately perceived as three)dimensional odiesI, ut to

e Hconstructed out of a temporal sequence of continually changing forms in the t!o)

dimensional visual fieldI $iid"*" The !ay that film and television !ork illustrates

very !ell !hat %arnap has in mind here, ut it is unclear ho! to generalise from this

case, and 9the same results: still needs further specification" >o!ever, if !e focus on

the role ofstructure, then an ans!er can e given" 5or if it is structure that !e are

primarily concerned to reveal, then preservation of structure must operate as the

essential criterion of correctness for rational reconstruction"

Ef course, 9preservation of structure: itself still needs further specification, ut at the

time of the%ufbau, %arnap did not suppose that there could e alternative logical

structures, and it is logical structure that is essentially at issue here" ;f !e recognise

once again the

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content" 3iven that the actual content $the intuitive 9;nhalt:* of human experience may

vary from person to person, or indeed from one time to another !ithin the life of a

single individual, then it is shared form or structure to !hich !e must appeal in

elucidating the intersu7ectivity that underlies the o7ectivity of our conceptual

practices"

To the extent that %arnap:s early conception of logical analysis, then, can e

characterised as involving 9rational reconstruction:, !e can extract from his early

thought a relatively clear ans!er to the paradox of analysis" %arnap may not have

explicitly addressed the issue in the !ay that 5rege did in his 1&14 lectures, ut his

!ork suggests ho! 5rege:s response might e refined" +ational reconstructions can e

regarded as correct in so far as they preserve structure, and informative to the extent

that, y astracting from content, the structure they reveal elucidates the o7ectivity of

our scientific practices"

' Carnaps Conception of (uasi)"nalysis

;n !hat !ay does rational reconstruction 9astract from content:B 3iven that in his

main $phenomenalistic* sketch of a 9

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N understood in the decompositional sense N could not yield these qualities, precisely

ecause they !ere not seen as constituentsof the elementary experiences $KF(*"14

%arnap:s ans!er !as that they are 9constructed: $in the sense of 9constituted:* 1- y

!hat he called 9quasi)analysis:, a method that mimics analysis in yielding 9quasi)

constituents:, ut !hich proceeds 9synthetically: rather than 9analytically: $KK F&, '4*"

;n essence, %arnap:s method of quasi)analysis is 7ust that method of contextual

definition or logical astraction that 5rege had introduced in the &rundlagen"1FThis

!as the example that 5rege had given to motivate his logicist 9constructions: $see K.

aove*J

$Da*Aine ais parallel to line b"

$D* The direction of line ais identical !ith the direction of line b"

line, !e might suggest, is also an 9indivisile: unit $at least in so far as it is intuited,

i"e", !here it is not seen as 9composed: of an infinity of points, or smaller lines*" et it

too has properties that can e ascried to it on the asis of the relations it has to other

geometrical figures" ;n particular, !e can talk of its 9direction:, !hich, !hilst not

literally a 9constituent: of it arrived at y $decompositional* 9analysis:, can

nevertheless e introduced contextually, y means of the relation of parallelism" otoo in the case of >ume:s @rinciple, !e have an equivalence relation holding et!een

things of one kind $concepts* eing used to define N or 9construct:, as %arnap !ould

put it N things of another kind $numers*J

$a* The conceptFis equinumerous to the concept &"

$* The numer ofF:s is identical !ith the numer of &:s"

umers too are not constituentsof the concepts to !hich they are ascried, ut are9constructed: from the appropriate equivalence relation"

>o!, then, does %arnap apply the method of astractionB lthough he

distinguishes et!een analysis and quasi)analysis, !hat he actually gives to explain

14; say more aout the decompositional sense of 9analysis: elo!"

153iven the !idespread use of 9construct: in this context, from no! on ; shall use it as synonymous!ith 9constitute:, unless other!ise indicated" 8ut it is to e understood that 9construct: does not mean9uild up out of parts:"

16%arnap himself talks of the 5rege)+ussellian 9principle of astraction: in KF&, and in K'. mentionsits source in 5rege:s &rundlagen" ;t should e noted, though, that 5rege did not himself see it as aprinciple of abstraction" %f" 8eaney 2000, K4"

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the operation of quasi)analysis is an example of analysis, involving colours, !hich at

least normally are thought of as properties rather than 9quasi)properties: of o7ects

$K'0*"1'The simplest case can e seen as ased on the follo!ing $seemingly trivial*

contextual definition, the term 9is equicoloured to: areviating 9has the same colour

as: $to ring out its connection !ith the examples 7ust given*J1(

$5a*E7ect1is equicoloured to o7ect 2"

$5* The colour of1is identical !ith the colour of 2"

ccepting such a definition as unprolematic,1&and given that eing 9equicoloured: is

an equivalence relation, !e can immediately proceed to form the equivalence classes,

!ithin the relevant domain, from !hich to $structurally* define the constituentcolours"

%onsider, for example, a domain of o7ects numered 1 to F, each of !hich

possesses one and only one of three colours, lue, green and red, symolised y 9:,

9g: and 9r:, respectively, as represented in the follo!ing taleJ20

ob/ect 1 2 . 4 - Fcolour g r r

*a+le 1

;magine, ho!ever, that !e do not kno! !hat these o7ects are $all !e kno! is that

there are six o7ects, !hich !e have numered simply for reference*, nor !hat colours

they have $or even ho! many colours there are*" 8ut !hat !e do have is the complete

list of 7udgements concerning the sameness of colour of each pair of o7ects,

kno!ledge that is exhiited in the form of a list of ordered pairs for !hich the

equivalence relation holdsJ21

173iven %arnap:s avo!ed ontological neutrality, it might seem surprising that %arnap presupposesthat colours are properties rather than quasi)properties" ; return to this shortly"

188oth the term 9equicoloured: used here and the term 9simicoloured: used elo! are my o!n"

19; take up the question of %arnap:s precise understanding of $5* shortly"

20;n !hat follo!s, ; dra! on the detailed discussions of quasi)analysis offered y 3oodman $1&'',ch" -* and +ichardson $1&&(, ch" 2*, from !hom the examples $!ith 7ust one minor change* are taken"

21; here follo! +ichardson $1&&(, --* in giving an orderedpair list" ince !e are dealing !ith an

equivalence relation $a relation that is reflexive, symmetric and transitive*, it might seem redundant togive e"g" oth 1, 2U and 2, 1U= ut in the case of the actual primitive relation that %arnap chooses forhis phenomenalistic construction, namely, 9recollection of similarity: et!een elementary experiences,

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1, 1U= 1, 2U= 1, .U=2, 1U= 2, 2U= 2, .U=., 1U= ., 2U= ., .U=4, 4U=-, -U= -, FU=

F, -U= F, FU"

lthough this may e all !e kno!, it is easy to derive from this the equivalence

classes, the classes of o7ects that have the same colourJ

V1, 2, .W= $4W= V-, FW"

%arnap calls these classes thecolour classes$K'0*" The first corresponds to the colour

lue, the second to green and the third to red, and !e can regard the colour of an

o7ect as eing structurally defined as the property that the o7ect has in virtue of

eing a memer of the relevant equivalence class" 5urthermore, one can see ho! such

a result is independent of !hether such properties are indeed genuine or merely

9quasi: constituents of the o7ects" #e have achieved the required division in the

domain of o7ects, according to their colour, y proceeding from the ordered pair list"

%learly, if every o7ect has one and only one colour, and !e are dealing !ith

an equivalence relation, then it is very easy to determine the colour classes from the

ordered pair list" 8ut !hat if every o7ect has one or more coloursB %onsider, for

example, the case represented in the next tale $!hich is the same as the previous

case, except that more colours have een added to some of the o7ects*J

ob/ect 1 2 . 4 - Fcolour r g g r gr

*a+le

;n this case, !e have to make use not of an equivalence or identity relation ut of a

similarityorpart identityrelation"22T!o o7ects are 9simicoloured:, let us say, if they

share at least one colour" The relevant ordered pair list !ould then e as follo!sJ

1, 1U= 1, 2U= 1, .U= 1, -U= 1, FU=2, 1U= 2, 2U= 2, .U= 2, FU=

the order of the terms is important, since the relation is asymmetric" ;t might also seem redundant tonote the pairs that indicate reflexivity, e"g" 1, 1U, ut this is nevertheless important for deriving any

equivalence classes that are unit classes, e"g" V4W in this case"22%arnap does not discuss first the simpler case of an equivalence relation, ut immediately gives theexample of the relation of 9colour kinship: $95arver!andtschaft:*, as defined here $cf" K'0*"

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., 1U= ., 2U= ., .U= ., 4U= ., FU=4, .U= 4, 4U= 4, FU=-, 1U= -, -U= -, FU=F, 1U= F, 2U= F, .U= F, 4U= F, -U= F, FU"

8ut ho! do !e get from this to the individual colour classesB En %arnap:sconception, a colour class must fulfil oth of the follo!ing conditions $K'0*J2.

$1*Cvery o7ect in the class stands in the relevant relation to every other o7ect in theclass"

$2* o o7ect outside the class stands in the relevant relation to every o7ect in the

class $i"e", the class is the maximalclass*"

5rom the first line of the list, !e might hypothesise the follo!ing classJ V1, 2, ., -, FW"

8ut this violates the first condition, since 2, -U and ., -U are not on the list"

Dropping -, !e might then suggest V1, 2, ., FW" This does satisfy the t!o conditions=

and !e have our first colour class $corresponding to the colour lue*" Dropping 2 and

. yields V1, -, FW, !hich forms another colour class $corresponding to the colour red*"

ince the second line of the list also yields V1, 2, ., FW, if !e then consider the third

line, similar reasoning yields oth this class yet again, dropping 4, ut also the further

colour class V., 4, FW, dropping 1 and 2 $corresponding to the colour green*" o ne!

colour classes can then e found, and !e have our three classes corresponding to the

three colours"

There is no dout that %arnap:s procedure here is ingenious, and if it !orks,

then it certainly opens up the possiility of defining all properties on the asis of a

similarity relation otaining et!een the o7ects of the chosen domain" The task is

then to choose the right o7ects and the right relation" s !e have noted, the o7ects

%arnap chooses are 9elementary experiences:, and the relation he chooses is that of

9recollection of similarity:, from !hich he then proceeds to 9rationally reconstruct: our

other notions" o! the details of this construction need not e given here= 24!hat !e

23The conditions must otain not 7ust for colour classes, ut for any 9similarity circle:, to use thegeneric term that %arnap introduces here N since !e are not necessarily talking of equivalence classes,and !e no! have a case !here transitivity fails" #e should also note that !hen the similarity relationinvolved ecomes not apart identityut a similarity relation that allo!s of degreesof similarity$!ithin a defined limit*, then a gap opens up et!een the similarity circles and the colour classes,requiring further manoevres to ridge $cf" K'2*" ince my main concern is !ith the underlying method,; do not discuss these complications here, ut for detailed accounts, see Cerle 1&'-= 3oodman 1&'',

ch" -= +ichardson 1&&(, chs" 2).= and +unggaldier 1&(4, chs" 11)1."245or further discussion, see 3oodman 1&'', ch" -= +ichardson 1&&(, chs" 2).= +unggaldier 1&(4,@art ;;"

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are primarily interested in is the method itself" %an it actually !orkB The ans!er is

that it only !orks if certain circumstances obtain, as %arnap himself recognises $K'0*"

To see this, consider the follo!ing case that differs from the last case solely in that

o7ect - is lue as !ell as redJ

ob/ect 1 2 . 4 - Fcolour r g g r gr

*a+le !

The tale suggests that !e ought to e ale to form the colour class V1, -, FW,

representing red, ut this class violates the second condition, since there is at least oneo7ect outside the class $e"g", 2* that is simicoloured to every o7ect in the class"

3oodman calls this the 9companionship difficulty: $1&'', 11'*, since it arises

!henever one of the colours $here red* is al!ays accompanied y another colour $here

lue*, though the latter may occur separately"

second difficulty arises if !e consider the follo!ing alternative case, !here o7ect 2

is red as !ell as lue and o7ect - is green as !ell as redJ

ob/ect 1 2 . 4 - Fcolour r r g g gr gr

*a+le #

This tale suggests that !e ought to e ale to form oth the classes V1, 2, ., FW,

representing lue, and V1, 2, -, FW, representing red, ut oth violate the second

condition" The class !e can form is V1, 2, ., -, FW N every o7ect is related to everyother o7ect, and there is no o7ect outside the class related to every o7ect in the class

N ut this is not !hat !e !ant" 3oodman calls this the 9difficulty of imperfect

community:, ecause in the latter class, there is no one quality that all its memers

share"2-

%learly, !hat these difficulties sho! is that there may e no one)one correspondence

et!een the qualities to e represented and the constructed classes" ;n the case of the

25Cven if !e allo! 9dis7unctive: properties, e"g", red)or)lue, !e have still failed to represent red andlue individually"

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companionship difficulty, there are classes that !e !ant to form ut !hich cannot e

formed, and in the case of the second difficulty, there are classes that can e formed

ut !hich !e do not !ant to e formed" ;n the first case, there is a property for !hich

there is no corresponding class= and in the second case, there is a class for !hich there

is no corresponding quality" This latter !ay of putting it suggests that there are t!o

further possiilities hereJ that there is a property for !hich there is more than one

corresponding class, and that there is a class for !hich there is more than one

corresponding property" 3iven that classes are extensional entities $if t!o classes have

the same o7ects, then they are the same class*, the first possiility is ruled out= ut the

second possiility !ould arise in a case of !hat might e called 9mutual

companionship: N !here t!o properties al!ays accompany one another" The class that

!e may e ale to form !ould represent oth properties $7ust ecause classes are

extensional entities*"2F

;n response to the companionship difficulty $!hich !e can here understand in oth its

forms*, %arnap suggests that the more o7ects there are and the smaller the average

numer of colours that an o7ect possesses, the less likely this difficulty !ill arise

$K'0*" 8ut as he himself also recognises, this presupposes that there are no systematic

connections et!een colours, and as 3oodman remarks $1&'', 11'*, this threatens to

make the ruling out of 9unfavourale circumstances: circular N %arnap:s method is to

e restricted to those cases !here it !orks" >o!ever, in defence of %arnap,

+ichardson has argued that the companionship difficulty is only a prolem if the

method of astraction is used in analysis rather than quasi)analysis $1&&(, -&)F4*" ;n

quasi)analysis, !here there are no actual constituents to pick out, there is no

independent reality against !hich to 7udge the resulting constructions" ;f it is only

structural properties !ith !hich !e are concerned, then these are indeed only

ans!erale to the relations on !hich the constructions are ased"

This defence is clearly in keeping !ith the neo)

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constructions not arising N e-en in the case of 0uasi+analysis" >o!ever, almost as an

afterthought, he concludes this section as follo!sJ

a more detailed investigation, !hich !e have to omit for lack of space, sho!s that theseinterferences in the concept formation through quasi analysis can occur only ifcircumstances are present under !hich the real process of cognition, namely, theintuitive quasi analysis !hich is carried out in real life, !ould also not lead to normalresults" $K(1"*

#hat %arnap seems to e suggesting here is that similar 9interferences: occur in actual

psychological processes, so that it is to the credit of his account of quasi)analysis that

room is made for them" The difficulties, in other !ords, can e turned to his o!n

advantage" 5urthermore, this only reinforces the neo)e does not explicitly take the neo)

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$5* The colour $constituent* of1is equal to the colour $constituent* of 2"

5or if analysis yields constituents rather than quasi)constituents, and the !holes of

!hich the constituents are parts are themselves distinct $i"e", the o7ects 1 and 2 in

this case*,2' then the t!o colour constituents of 1and 2cannot, strictly speaking, e

identical ut only equal, in the relevant respect" o !hilst quasi)analysis can e seen

as yielding $5*, analysis should e thought of as yielding $5*"

>o!ever, if this account of analysis is right, then an infinite regress threatens" 5or if

t!o constituentsare uncovered, then there !ill e some similarity relation holding

et!een them, in !hich case the method of astraction $contextual definition* can e

applied again to uncover further constituents" o either !e need some different

account of constituent, !hich %arnap does not supply, or !e no longer have a cleardistinction et!een analysis and quasi)analysis" ll !e really have is quasi)analysis=

and this in any case might seem to e all !e have in $9pure: uses of* the method of

astraction, !hich, after all, is seen more as a 9constructive: process"

Ef course, if there is no viale distinction et!een analysis and quasi)analysis,

!here oth are seen as involving the method of astraction, then this might seem to

support the neo)is position !as inherently

unstaleJ he !as in the process of freeing himself from the +ussellian programme that

had to some extent inspired him, !hilst allo!ing his more neo)ere is one characteristic passage, in !hich %arnap summarises his vie! ofquasi)analysisJ

the analysis or, more precisely, quasi)analysis of an entity that is essentially anindivisile unit into several quasi)constituents means placing the entity in severalkinship contexts on the asis of a kinship relation, !here the unit remains undivided"$K'1"*2(

27This rules out iamese t!in cases, !here one or more constituent parts are shared y t!o larger!holes" gain, this reveals ho! ontological assumptions may underlie conceptions of analysis"

28The 3erman readsJ Hdie nalyse, richtigerJ 6uasianalyse, eines 3eildes, das seinem #esen nach

eine unerlegare Cinheit ist, in mehrere 6uasiestandteile edeutet die Cinordnung des 3eildes inmehrere er!andtschaftsusammenhQnge auf 3rund einer er!andtschaftseiehung, !oei dieCinheit unerteilt leit"I ; have slightly altered the standard Cnglish translation $y +olf " 3eorge*,

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%ompare this !ith %arnap:s characterisation of logical analysis in his 1&.4 paper,

9Die ?ethode der logischen nalyse:J

The logical analysis of a particular expression consists in the setting)up of a linguisticsystem and the placing of that expression in this system" $1&.F, 14."*2&

fter the pulication of the %ufbau, %arnap never talks of 9quasi)analysis: again,

except in referring to the ideas of the %ufbauitself, and !e can see !hy" 5or in the

contrast it suggests !ith 9analysis:, there !ere realist undertones of an ontological

kind that %arnap !as later keen to purge" ;t !ould e tempting to conclude y saying

that %arnap:s distinction et!een analysis and quasi)analysis turned out to e only a

quasi)distinction= ut it !ould e more accurate to say N as far as %arnap !asconcerned N that it !as only a pseudo)distinction, a residue of unreconstructed

metaphysical thinking"

, Carnaps -ater $or%: Explication

8et!een the %ufbauand the introduction of the term 9explication:, %arnap:s ideas

developed in important !ays" ;n 9The Climination of ?etaphysics through Aogical

nalysis of Aanguage:, !hich appeared in 1&.2, %arnap outlined a conception of

logical analysis in !hich metaphysical thinking !as not merely aandoned ut

explicitly repudiated" The aim of logical analysis !as, on the positive side, to clarify

the concepts of empirical science, and, on the negative side, to sho! that metaphysical

statements !ere meaningless 9pseudo)statements:" Aogic !as seen as the onlymethod

of philosophy, and as %arnap argued in his second ma7or !ork, .he Logical #yntax of

Language $1&.4*, this entailed the identification of philosophy !ith the logic of

scienceJ

The aim of logical syntax is to provide a system of concepts, a language, y the help of!hich the results of logical analysis !ill e exactly formulale" Philosophy is to be

!hich renders 9eines 3eildes, das seinem #esen nach eine unerlegare Cinheit ist: simply as 9of anessentially unanalyale entity:, !hich does not do full 7ustice in this context to the meaning of9unerlegar: and its echo in the use of 9unerteilt: that follo!s" ;t is !orth noting here that in an earlydraft of !hat ecame the%ufbau, %arnap did indeed talk of 9Perlegung: and 96uasierlegung: ratherthan 9nalyse: and 96uasianalyse:, !hich reinforces the suggestion that analysis !as originallyunderstood more in the decompositional sense"

29HDie logische nalyse eines estimmten usdrucks esteht in der ufstellung eines prachsystemsund in der Cinordnung des usdrucks in dieses ystem"I The paper !as !ritten for a conference in@rague in eptemer 1&.4, ut !as not pulished until 1&.F"

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replaced by the logic of scienceN that is to say, y the logical analysis of the conceptsand sentences of the sciences, for the logic of science is nothing other than the logical

syntax of the language of science" $1&.', xiii"*

;n his susequent !ork, %arnap came to recognise that logical syntax needed to e

supplemented y semantics, and it !as the aim of the t!o volumes of his #tudies in

#emantics$1&42, 1&4.* to provide this supplementation" There is a great deal to say

aout these developments, and their relationship to the !ork of other philosophers and

logicians, most notaly, #ittgenstein, 3Rdel and Tarski".0 8ut there remained an

underlying methodological unity in these developments, and for the purposes of the

present paper, !e can concentrate on the more systematic account of methodology

that %arnap later provided"

The term 9explication: first appears in %arnap:s !ork, in print, in Gune 1&4-, in

a paper entitled 9The T!o %oncepts of @roaility:" %arnap makes clear in the

opening paragraph that his main goal is to offer explicationsof our pre)scientific

conceptions of proaility, although he concentrates in this paper on providing

9clarifications: of the t!o explicanda that he claims to find in ordinary language" $The

detailed explications !ere to e pulished in 1&-0*" %arnap also pulished another

paper on a related topic in pril 1&4-, 9En ;nductive Aogic:, !hich, though it refers to

his forthcoming Gune paper in a footnote, makes no mention of explication" This may

not in itself signify that %arnap did not have the concept of explication in mind !hen

he !rote the paper, except that, in the final section of this paper, he does indeed offer

some methodological reflections, in terms not of 9explication: ut of 9rational

reconstruction:, !hich, as !e have seen, !as his original term for his philosophical

method" o !e can conclude that at some point et!een the !riting of 9En ;nductive

Aogic: and 9The T!o %oncepts of @roaility:, !hich !ere pulished in pril 1&4-

and Gune 1&4-, respectively, though oviously !ritten earlier, %arnap introduced theterm 9explication:"

;n his 9;ntellectual utoiography:, %arnap !rites that H5rom 1&42 to 1&44 ; had a

research grant from the +ockefeller 5oundation" During this time, !hich ; spent near

anta 5e, e! ?exico, ; !as first occupied !ith the logic of modalities and the ne!

semantical method of extension and intension" Aater ; turned to the prolems of

proaility and induction"I $1&F., .F"* The former resulted inMeaning and $ecessity,

305or discussion of %arnap:s development in this period, see %offa 1&&1, chs" 1-)1'= %reath 1&&&=5riedman 1&&&, @art Three= ?ormann 2000, chs" -)'= +icketts 1&&F= eel 1&&2, ch" -"

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pulished in 1&4', and the latter in Logical Foundations of Probability, pulished in

1&-0" ;n the preface to the first edition of Meaning and $ecessity, %arnap confirms

that HThe investigations of modal logic !hich led to the methods developed in this

ook !ere made in 1&42, and the first version of this ook !as !ritten in 1&4.,

during a leave of asence granted y the niversity of %hicago and financed y the

+ockefeller 5oundationI $1&4', iv*" 3iven that the underlying idea of rational

reconstruction !as already in place at this time, !hat can have stimulated talk of

9explication:B T!o particular pulications are relevant hereJ firstly, the appearance in

1&42 of the volume on ?oore in 9The Airary of the Aiving @hilosophers: series,

edited y @aul chilpp, in !hich %" >" Aangford has a paper on the paradox of

analysis= and secondly, the pulication also in 1&42 of the Dictionary of Philosophy

edited y Dagoert +unes, in !hich %arnap himself makes a numer of contriutions"

Aet us consider their possile influences y turning to the t!o main pulications that

presented %arnap:s !ork in the period from 1&42"

The notion of explication is introduced very early in Meaning and $ecessity"

;n K2 %arnap !ritesJ

The task of making more exact a vague or not quite exact concept used in everyday life

or in an earlier stage of scientific or logical development, or rather of replacing it y ane!ly constructed, more exact concept, elongs among the most important tasks oflogical analysis and logical construction" #e call this the task of explicating, or ofgiving an explicationfor, the earlier concept= this earlier concept, or sometimes theterm used for it, is called the explicandum= and the ne! concept, or its term, is called anexplicatumof the old one" $1&4', ()&"*

t this point there is then the follo!ing footnoteJ H#hat is meant here y

9explicandum: and 9explicatum: seems similar to !hat Aangford means y

9analysandum: and 9analysans:= see elo!, n" 42, p" F."I $1&4', (, fn" '"* 5ollo!ing

up this further footnote, !e find a reference to Aangford:s paper on ?oore and the

paradox of analysis, at the point in %arnap:s o!n ook !here he offers his conception

of intensional structure as a solution to the paradox of analysis" s !e have noted,

Aangford:s paper !as pulished in 1&42= and the ovious suggestion is that it !as this

paper that prompted not only %arnap:s o!n response to the paradox of analysis, as

illustrating his conception of intensional structure, ut also his conception of

explication, as modelled on Aangford:s conception of analysis"

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;n illustrating his conception of explication in K2 ofMeaning and $ecessity,

%arnap takes the example of 5rege:s and +ussell:s logicist 9explication: of numer

terms such as 9t!o: N Hthe term 9t!o: in the not quite exact meaning in !hich it is

used in everyday life and in applied mathematicsI, and their different explications of

phrases of the form 9the so)and)so:" 8ut %arnap:s introduction of the idea of

explication precedes his discussion of 9A)truth:, !hich is offered Has an explicatum

for !hat philosophers call logical or necessary or analytic truthI $1&4', '*, and other

such 9A)concepts:" >o!ever, %arnap says little aout !hat constraints there may e

on the adequacy of an explication" >e does indeed say that explication Hconsists in

laying do!n rules for the use of corresponding expressions in language systems to e

constructedI $1&4', (*, ut on the relation et!een the explicandum and the

explicatum, all he says is thisJ H3enerally speaking, it is not required that an

explicatum have, as nearly as possile, the same meaning as the explicandum= it

should, ho!ever, correspond to the explicandum in such a !ay that it can e used

instead of the latter"I $;id"*

%arnap provides a much fuller discussion of explication in the first chapter of

Logical Foundations of Probability, pulished in 1&-0" Ene of %arnap:s main aims in

this ook is to clarify our various conceptions of proaility" ince these conceptions

have only a vague articulation in everyday life, %arnap sees his task as that of making

these conceptions more precise, that is, of providing an explicationfor them $cf" 1&-0,

1)2*" >e thus first offers some general methodological remarks concerning

explication" ince these also develop, to a considerale extent, the rief remarks he

makes aout explication in 9The T!o %oncepts of @roaility:, !hich, revised,

formed the second chapter ofLogical Foundations of Probability, ; shall concentrate

on the fuller discussion here"

K2 of %arnap:s first chapter is entitled 9En the %larification of an

Cxplicandum:, and after offering a characterisation of explication similar to that

provided inMeaning and $ecessity$quoted aove*, %arnap goes onJ

The term 9explicatum: has een suggested y the follo!ing t!o usages"

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#hat ; mean y 9explicandum: and 9explicatum: is to some extent similar to !hat %">"Aangford calls 9analysandum: and 9analysans:J Hthe analysis then states an appropriaterelation of equivalence et!een the analysandum and the analysansI L1&42, .2.M= hesays that the motive of an analysis His usually that of supplanting a relatively vagueidea y a more precise oneI L1&42, .2&M"$@erhaps the form 9explicans: might e considered instead of 9explicatum:= ho!ever, ;think that the analogy !ith the terms 9definiendum: and 9definiens: !ould not e useful

ecause, if the explication consists in giving an explicit definition, then oth thedefiniens and the definiendum in this definition express the explicatum, !hile theexplicandum does not occur"* The procedure of explication is here understood in a!ider sense than the procedures of analysis and clarification !hich usserl, andAangford have in mind" The explicatum $in my sense* is in many cases the result ofanalysis of the explicandum $and this has motivated my choice of the terms*= in othercases, ho!ever, it deviates delierately from the explicandum ut still takes its place insome !ay= this !ill ecome clear y the susequent examples"

#hat !e have here is a reference oth to Aangford:s paper on the paradox of analysis,

and also to usserl:s notions of explication as %arnap found them

descried in a dictionary of philosophy pulished in 1&42".2 usserl:s

conceptions, ho!ever, are quite different" 5or usserl:s notion is much closer to

%arnap:s, as involving a precisification of an everyday concept" ;ndeed, %arnap

recognises in the second paragraph that there is an important difference here, in

distinguishing et!een 9analysis: in !hat is clearly the usserl scholar, readsJ H$3er"%uslegung* ;n>usserlJ ynthesis of identification et!een a confused, non)articulated $internally indistinct,unseparated* sense and a susequently intended distinct, articulated, sense" The latter is the explicate$Explikat* of the former"I nder 9Cxplicative 7udgment:, !ritten y ernon G" 8ourke, !hichimmediately follo!s, !e readJ H$Aat" explicatio, unfolding* mental action !hich explains a su7ect y

mentally dissecting it= $

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9Aogic in ?athematics: lectures*" 8ut !e clearly need to say something aout the

explicandum if the explication is to e understood at all, and it is here that 9analysis:

in the sense of 9clarification: takes place" Cven though the terms to e explicated may

e imprecise, %arnap !rites, Hthere are means for reaching a relatively good mutual

understanding as to their intended meaning" n indication of the meaning !ith the

help of some examples for its intended use and other examples for uses not no!

intended can help the understanding"I $1&-0, 4"* #hat is required is 9elucidation:

$9CrlQuterung:* rather than explication proper, !hich requires a theoretical system in

!hich rules for the use of the corresponding expressions are laid do!n $cf" 1&-0, .,

-*"..

ccepting, then, that an everyday concept has een 9elucidated: sufficiently to engage

in explication, !hat are the criteria of adequacy for explicationB ;n K., %arnap lays

do!n four requirements for a concept to e an adequate explicatum for a given

explicandumJ

$1* similarity to the explicandum=

$2* exactness=

$.* fruitfulness=

$4* simplicity"

s far as the first is concerned, %arnap !ritesJ HThe explicatum is to e similar to the

explicandumin such a !ay that, in most cases in !hich the explicandum has so far

een used, the explicatum can e used= ho!ever, close similarity is not required, and

considerale differences are permittedI $1&-0, '*" s an example, %arnap takes the

case of a iologist explicating our pre)scientific concept of a fish, replacing it y the

iologically defined concept, !hich %arnap suggests !e call 9piscis: to avoid

confusion" ?ost of !hat !e used to call 9fishes: still come out as 9pisces:, ut !hales

are oviously one exception" There is enough similarity, even though there are

important divergences"

o !hat 7ustifies the divergences from ordinary languageB The ans!er, of

course, lies in the advantages of the scientific system in !hich the explicatum is

located, and this is !hat is rought out y the other three requirements that %arnap

formulates" s far as the second is concerned, %arnap !ritesJ HThe characteriation of

the explicatum, that is, the rules of its use $for instance, in the form of a definition*, is

33gain, there is an echo here of the distinction et!een elucidations and definitions that 5rege dre!in his 9Aogic in ?athematics: lectures=LM, 224/FR, .1."

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to e given in an exactform, so as to introduce the explicatum into a !ell)connected

system of scientific conceptsI $iid"*" The requirement of exactness lay at the core of

the idea of rational reconstruction, and talk of 9!ell)connectedness: here highlights

once again the importance of a clearly revealed structure in the system that is

constructed"

#ell)connectedness also lies at the asis of the third requirement" HThe

explicatum is to e a fruitful concept, that is, useful for the formulation of many

universal statements $empirical la!s in the case of a nonlogical concept, logical

theorems in the case of a logical concept*"I $;id"* nd in explaining this, %arnap

!ritesJ H scientific concept is the more fruitful the more it can e rought into

connection !ith other concepts on the asis of oserved facts= in other !ords, the

more it can e used for the formulation of la!sI $1&-0, F*" Taking %arnap:s example

once again, fishes as scientifically defined $pisces* have more properties in common N

have more connections !ith one another N than fishes as pre)scientifically understood

$animals living in !ater*, allo!ing more general statements to e formulated $iid"*".4

The requirement of fruitfulness that %arnap formulates here is a clear echo of the

emphasis that 5rege placed on the fruitfulness of definitions in his early !ork, and in

the &rundlagen, in particular" ccording to 5rege, the definitions of numer that he

offers are fruitful precisely to the extent that they allo! him to derive 9the !ell)kno!n

properties of numers: $see K. aove*= and here too, !e might say, the value of the

reconstructed system lies in the connections that it exhiits et!een the concepts

defined and the statements formulated".-

%arnap:s final requirement is simplicityJ HThe explicatum should e as simple as

possile= this means as simple as the more important requirements $1*, $2*, and $.*

permitI $1&-0, '*" The simplicity of a concept is to e measured, %arnap states,

according to the form of its definition and the forms of the la!s connecting it !ith

other concepts, ut he rightly emphasises that any simplicity considerations are

suordinate to the other three considerations $iid"*"

The central example that %arnap discusses to elucidate his account of

explication is the concept of temperature, !hich %arnap offers as an explicatum for

the concept of !armth" %arnap first distinguishes et!een classificatory, comparati-e

34>ere there is an analogy !ith the use of colour classes, in !hich every o7ect is related to every

other o7ect, to define colours in the%ufbau"35%f" 5rege, &L, K2J HThe aim of proof is not only to place the truth of a proposition eyond alldout, ut also to afford insight into the dependence of truths on one anotherI $FR, &2*" %f" &L, ix"

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and 0uantitati-econcepts" To concentrate on the simplest cases $monadic properties

and dyadic relations*, classificatory concepts, such as *arm, classify things into t!o

mutually exclusive kinds $*arm and not+*arm*= comparative concepts, such as

*armer, express a relation et!een t!o things ased on a comparison, given in the

form of a 9more $in a certain respect*: statement= !hilst quantitative concepts, such as

that of temperature, descrie things y the ascription of numerical values $cf" 1&-0, ()

&*" %arnap !ritesJ H%lassificatory concepts are the simplest and least effective kind of

concept" %omparative concepts are more po!erful, and quantitative concepts still

more= that is to say, they enale us to give a more precise description of a concrete

situation and, more important, to formulate more comprehensive general la!s"I

$1&-0, 12"* The concept of temperature, %arnap then argues, may e regarded as an

explicatum for the comparative concept *armer, in that it makes more precise !hat

the latter expresses" Things may indeed e ordered y means of the relation *armer

than, and therey assigned a numer representing their position in the series, ut

assigning them a numer representing their temperature grants them some more

9asolute: value"

>o! then does the explication of 9!armth: y means of 9temperature: satisfy

%arnap:s four requirementsB #e may readily grant that the explicatum is exactJ there

are clear rules governing the use of the concept of temperature, and a thermometer, for

example, can e easily used to measure temperature" The explicatum is fruitful, as

there is indeed a !ell)connected scientific system in !hich the concept of temperature

plays a central role in the formulation of la!s and general statements" The explicatum

is also relativelysimpleJ it is oth easily defined $or at least permits straightfor!ard

measurement* and readily incorporated into scientific la!s" ll three requirements

concern the nature and role of the explicatum !ithin the scientific theory" The

interesting N and prolematic N philosophical question concerns the relation et!een

the explicatum and the explicandum, precisely the question raised y the paradox of

analysis" ;f 9considerale differences are permitted: $cf" 1&-0, '*, then !hat constraint

at all does the requirement ofsimilarityimposeB

;n the present example, %arnap interprets the requirement of similarity as

follo!sJ HThe concept Temperature is to e such that, in most cases, ifx is !armer

thany$in the prescientific sense, ased on the heat sensations of the skin*, then the

temperature of x is higher than that of yI $1&-0, 12*" To see the connection !ith5rege:s examples of 9fruitful: definitions, particularly as given as contextual

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definitions in the &rundlagen$and xiom of the &rundgeset)ehas the same form*,

and %arnap:s o!n use of the method of astraction in the %ufbau, let us set this out as

follo!sJ

$Ta* xis !armer thany"

$T* The temperature ofxis higher than the temperature ofy"

$Tc* There are numerical values nand d, !here dU 0, such thatxhas a temperatureof $nXd*Y andyhas a temperature of nY"

Gust as in 5rege:s examples, an equivalence relation holding et!een o7ects of one

kind is offered as a !ay of defining an identity statement concerning o7ects of a more

astract kind, so too here a comparative relation holding et!een t!o o7ects,

expressed in $Ta*, is used as the starting)point for an explication that involves a more

theoretical concept, captured in $T*".F $Tc* 7ust makes explicit the quantitative

measurement that the appeal to temperature allo!s" ;n each case, there is at least a

hope that the definiens and the definiendum, or the explicandum and the explicatum,

are 9equivalent: in some appropriate sense= ut in so far as one relies on ordinary

language and the other uses concepts precisely defined !ithin a scientific system,

there may e cases !here discrepancies arise" %arnap himself descries a case in

!hich a discrepancy occursJ

uppose ; enter a moderately heated room t!ice, first coming from an overheated roomand at a later time coming from the cold outside" Then it may happen that ; declare theroom, on the asis of my sensations, to e !armer the second time than the first, !hilethe thermometer sho!s at the second time the same temperature as at the first $or evena slightly lo!er one*" Cxperiences of this kind do not at all lead us to the conclusionthat the concept Temperature defined !ith reference to the thermometer is inadequateas an explicatum for the concept #armer" En the contrary, !e have ecome accustomedto let the scientific concept overrule the prescientific one in all cases of disagreement"

;n other !ords, the term 9!armer: has undergone a change of meaning" ;ts meaning !asoriginally ased directly on a comparison of heat sensations, ut, after the acceptanceof the scientific concept Temperature into our everyday language, the !ord 9!armer: isused in the sense of 9having a higher temperature:" $1&-0, 12)1."*

The example is instructive" 5or it is not 7ust that !e can allo! the odd

discrepancy !ithout invalidating the explication, ut that the explication may actually

have value to the extent that it opens up and explains discrepancies N and indeed, not

36There are also differences here, particularly !ith regard to the direction of explanation" 5or 5rege,in the numer case, $a* is offered as a !ay of defining $*" 5or %arnap, $T* is used to explicate$Ta*"

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only discrepancies et!een our ordinary language and the scientific language, ut

also !ithin ordinary language" T!o people may disagree over !hether the room, say,

is !armer or colder than it !as a fe! minutes ago, and an appeal to the thermometer

reading may settle the question" nd furthermore, as %arnap points out, our ordinary

use of language may change as a result, and ecome more refined in its o!n

application" t the very least !e !ill ecome more sensitive to possile discrepancies,

and all these advantages may e seen as contriuting to the value of the explication"

Cxplications, !e might say N and !e might see this as revealing a further usserl !as highly sensitive"

. Husserls Conception of Explication

s !e sa! in the last section, according to %arnap himself, his introduction of theterm 9explication: !as partly motivated y >usserl:s talk of 9explication: as Hthe

synthesis of identification et!een a confused, nonarticulated sense and a

susequently intended distinct, articulated senseI $%arnap, 1&-0, K2*" lthough it

seems that %arnap:s kno!ledge of >usserl:s conception !as derived solely from

Dorion %airns: definition in +unes:Dictionary of Philosophy$1&42*, and no genuine

influence can e detected, it is instructive to compare %arnap:s conception !ith

>usserl:s"

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>usserl:s most sustantial discussion of explication occurs in chapter 2 of @art

; ofExperience and 3udgement, a !ork that !as edited $!ith >usserl:s authority* y

Aud!ig Aandgree and pulished in 1&.&, the year after >usserl died" >usserl here

distinguishes et!een 9simple: or 9immediate: apprehension $9schlichte Crfassung:*

and 9explication: $9Cxplikation:*, and does indeed talk of a 9synthesis of

identification: $K22*" >is concern is !ith the different levels of reflective perception

of an o7ect" 9imple apprehension: is the lo!est level, !hen all !e are a!are of is the

o7ect 9as a !hole: $iid"*" 8ut as >usserl had explained earlier in the ook $K(*, every

experience of a thing has its 9internal horion:, delimiting an area of possile

kno!ledge eyond that core that constitutes our immediate apprehension" Cxperience

has a 9retentional: and 9protentional: structureJ in oserving an o7ect, our experience

is informed y our existing kno!ledge and expectations" #e may recall previous

perceptions or already have in mind a type that the o7ect instantiates, for example,

and !e may imagine !hat the o7ect !ould look like from a different angle or

anticipate ho! it might change" t the second level, then, our kno!ledge is enriched

as !e elucidate further aspects of the o7ect" This is explication"

Explication is penetration of the internal hori)on of the ob/ect by the direction of

perceptual interest4 ;n the case of the unostructed realiation of this interest, the

protentional expectations fulfill themselves in the same !ay= the o7ect reveals itself inits properties as that !hich it !as anticipated to e, except that !hat !as anticipatedno! attains original givenness" more precise determination results, eventually

perhaps partial corrections, or N in the case of ostruction N disappointment of theexpectations, and partial modaliation" $E3, K22"*

;n so far as this process reveals aspects of the o7ect that are there to e

revealed, talk of 9explication: seems appropriate N appropriate, that is, if something

like the

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o7ect of explication need not e 9intuitively given: $K2F*" 98rother: can e analysed

as 9male siling:, for example, !ithout any rother eing present= ut it is not

conceptual analysis that >usserl has in mind" Cxplication is an enrichmentof sense

operating throughout *ithinthe domain of intuition" evertheless, >usserl does allo!

that our expectations may e disappointed, and that partial corrections may occur, and

this rings him closer to %arnap" %arnap may conceive of rational reconstruction or

explication as abstracting from intuitive content, ut oth >usserl and %arnap see

explication as a process of precisification, y means of !hich our ordinary

understanding is refined, and if necessary, transformed"

s !e have seen, ho!ever, %arnap is not particularly concerned !ith the

relationship et!een the explicandum and explicatum, requiring merely that they e

9similar:" 5or >usserl, on the other hand, it is the movement of explication itself that

is of central concern, and he descries its essential structure in K24" Taking an o7ect

#, !ith internal properties or 9determinations: $98estimmungen:* 5, 6, etc", >usserl

characterises explication as a process in !hich the determinations are referred to a

9sustrate: !hich serves as the locus for the 9synthesis of identification:"

The process of explication in its originality is that in !hich an o7ect given at first handis rought to explicit intuition" The analysis of its structure must ring to light ho! a

t*ofold constitution of sense L#inngebungM is realied in itJ Ho7ect as sustrateI andHdetermination 5ZI= it must sho! ho! this constitution of sense is realied in theform of a process !hich goes for!ard in separate steps, through !hich, ho!ever,extends continuously a unity of coincidenceN a unity of coincidence of a special kind,

elonging exclusively to these sense)forms" $E3, K24a"*

Cxplication not only reveals properties of an o7ect, ut also opens up the very

distinction et!een 9sustrate: and 9determination: on !hich the integrity of the

process depends $K24*" s >usserl !rites, Hfter the explication of the 5, the #

ecomes #5= after the emergence of the 6, $#5*6, and so onI $K24c*" The movement ofexplication consists in Ha continuous internal transformationI, !herey the properties

of the o7ect that are precipitated out are rooted in Ha permanent synthesis of

coincidenceI $iid"*"

>usserl goes on to discuss various complications, in further explication of theprocess itself, ut the essential conception is clear" lthough >usserl focuses onreflective perception of an o7ect, the account can e readily extended to other casessuch as the mathematical and scientific ones that occupied 5rege and %arnap" >ereexplication involves opening up not 7ust logical distinctions such as that et!een

su7ect and predicate ut also function)argument forms, causal structures, and so on";ndeed, !e can regard the !hole panoply of science as a tool in opening up the

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structures of experience in 7ust that enrichment of our understanding that >usserl !asso concerned to conceptualise"

Developing this >usserlian account offers a !ay of supplementing andpartially correcting the 5regean)%arnapian conception of reconstructive explication"To see this, let us return to the paradox of analysis, and consider ho! it might e

resolved y ringing together elements from 5rege:s, %arnap:s and >usserl:s thought";f !e egin !ith 5rege:s first t!o responses, then !e can agree that a good analysismust 9split up content: in a 9more richly articulated: !ay, ut there is no single

ifurcation of meaning that provides a general ans!er" Cxplication may open up morethan 7ust one distinction= the full resources of a roader conceptual frame!ork ormore po!erful theoretical system may e required" #e can agree !ith all three that ananalysis should not e regarded as simply trying to capture our pre)existingconceptions, confused as they often are, although our ordinary understanding does actas a constraint, at the level of structure" The aim of analysis is to elucidate thisstructure, and to refine rather than replace our ordinary conceptions, !hich does notrule out revising them !herever necessary"

This can e illustrated y taking a simple example from chemistry, involving

the analysis of a process rather than an o7ectJ

$#* alt dissolves in !ater"

$>* 2>2E X a%l >.EX X %l X aX X E>"

$#* represents a familiar process $an everyday phenomenon of our 9life)!orld:*, and

$>*, !e could say, provides its 9chemical analysis: $a translation into the language of

science*" There is also a sense in !hich, for the purposes of chemistry, $>* does

replace $#*, in that it is this equation that represents the reaction and that plays its

part in more complex analyses of chemical processes" evertheless, in no sense does a

chemist discard its informal characterisation, as captured in $#*" #hatever

manipulation of chemical formulae a chemist may perform, the informal

characterisations remain in the ackground, presupposed in our scientific activity" ;n

offering $>* as the analysis of $#*, then, the chemist is refining rather than

replacing ordinary language, for certain scientific purposes"

There is an extent to !hich correct and informative analyses do involve

9splitting up content: differently" #hat makes $>* a correct analysis of $#*, for

example, is that they oth refer to the same 9content: N in this case, the same chemical

process" >o!ever, even this requires qualification" 5or 9!ater: as !e ordinarily

understand it N the !ater that !e drink and !ash in N is not 7ust > 2E, ut also

contains 9impurities:= and 9salt: too can refer to more than 7ust a%l" o the 9content:

of $>* is itself an idealised refinement of the 9content: of $#*" 8ut !hat tends to

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happen in such cases is ad7ustment of our ordinary notions to reinforce the analysis"

$>* makes us interpret $#* as Hodium chloride dissolves in 9pure: !aterI= and

once the ad7ustment is made, then !e do have sameness of 9content:" ameness of

9content: is indeed a constraint on the adequacy of an analysis, ut this is not to say

that the 9real: content of the sentence of ordinary language is properly grasped prior to

understanding the theory in !hich the analysis is offered" >usserl talks of the results

of explication as 9precipitates: $9iederschlQge:*, and the metaphor is apt" 5or

contents or senses too should e seen as crystallised outin analysisJ the material is

already there in the fluid of our everyday life, ut it needs the seed of a theoretical

concern to precipitate them out".';n the end, !hat makes an analysis a good one is its

success, as part of some overall theory, in convincing us that our ordinary discourse is

indeed imprecise, and requires refinement for scientific purposes"

>o! informative an analysis is !ill depend on !hat !e learn in this process"

ltimately, there is no ahistorically positioned ans!er as to !hether an analysis is

oth correct and informative" 8efore the theory is developed in !hich the analysis is

offered, the analysis, if it is understood at all, !ill seem incorrect= and after it is

developed, !ith the necessary transformation in our understanding effected, it !ill e

correct ut uninformative" To talk of 9correctness: is to make a move *ithina system=

yet informativeness arises in the process of developing, learning and using a system"

n analysis is 9informative:, in other !ords, y eing transformati-e" 5rege and

%arnap may have developed systems in !hich 9correctness: !as located, ut it !as

>usserl !ho reco

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