"The analytic breakdown of language, 
which was first rigorously performed hy 

Frege, is the unique and essential 
philosophical move of the analytic 

tradition." 



FREGE A N D W I T T G E N S T E I N 

The Limits of the Analytic Style 

C H R I S T O P H E R S H E R I D A N 

T H E A N A L Y T I C T R A D I T I O N I N P H I L O S O P H Y S T E M S F R O M T H E W O R K O F G E R M A N 

M A T H E M A T I C I A N A N D L O G I C I A N G O T T L O B F R E G E . B E R T R A N D R U S S E L L B R O U G H T 

F R E G E ' S P R O G R A M T O R E N D E R L A N G U A G E - P A R T I C U L A R L Y S C I E N T I F I C L A N G U A G E -

I N F O R M A L L O G I C A L T E R M S T O T H E F O R E F R O N T O F P H I L O S O P H Y I N T H E E A R L Y T W E N -

T I E T H C E N T U R Y . T H E Q U E S T T O C L A R I F Y L A N G U A G E A N D P A R S E O U T G E N U I N E P H I L O -

S O P H I C A L P R O B L E M S R E M A I N S A C O R N E R S T O N E O F A N A L Y T I C P H I L O S O P H Y , B U T I N -

V E S T I G A T I V E P R O G R A M S I N V O L V I N G T H E B R O A D A P P L I C A T I O N O F F O R M A L S Y M B O L I C 

L O G I C T O L A N G U A G E H A V E L A R G E L Y B E E N A B A N D O N E D D U E T O T H E I N F L U E N C E O F 

L U D W I G W I T T G E N S T E I N ' S L A T E R W O R K . T H I S A R T I C L E I D E N T I F I E S T H E K E Y P H I L O -

S O P H I C A L M O V E S T H A T M U S T B E P E R F O R M E D S U C C E S S F U L L Y I N O R D E R F O R F R E G E ' S 

" C O N C E P T U A L N O T A T I O N " A N D O T H E R S I M I L A R S Y S T E M S T O A D E Q U A T E L Y C A P T U R E 

S Y N T A X A N D S E M A N T I C S . T H E S E M O V E S U L T I M A T E L Y F A I L A S A R E S U L T O F T H E N A -

T U R E O F L I N G U I S T I C M E A N I N G . T H E S H I F T A W A Y F R O M F O R M A L L O G I C A L A N A L Y S I S 

O F L A N G U A G E A N D T H E E M E R G E N C E O F T H E C U R R E N T A N A L Y T I C S T Y L E B E C O M E S 

C L E A R E R W H E N T H I S F A I L U R E I S E X A M I N E D C R I T I C A L L Y . 



I 

Gottlob Frege (1848-1925) a i m e d to formal ize the language 

o f science such that the n o t a t i o n by w h i c h science ex-

pressed i t se l f corresponded to the r igorous objectivity o f 

the scientific worldview. O u t o f mathematics—speci f ical ly 

the concepts o f f u n c t i o n and equality—Frege derived a log-

ical system i n w h i c h ord inary language is represented by 

" t r u t h funct ions , " and m e a n i n g is represented by equality. 

This novel representat ion o f language as a f o r m a l syntacti-

cal system purpor t s to account for semantics as we l l . 

Frege's f o r m a l , objective systematization o f language 

marks the b e g i n n i n g o f the analytic t r a d i t i o n . 

The "conceptual n o t a t i o n " 1 is made possible by two paral lel 

deconstructions o f ord inary language: (1) the r e d u c t i o n o f 

ord inary g r a m m a t i c a l s t ruc ture—that is, the sentence— 

i n t o subject and predicate, and (2) the b r e a k d o w n o f ord i -

nary semantics i n t o sense (Sinn), reference (Bedeutung), 

and idea. Subsequently, Frege correlated mathemat ica l 

funct iona l i ty w i t h l ingu i s t i c predicat ion and mathemat ica l 

equality w i t h l ingu i s t i c " t r u t h va lue"—"the c ircumstance 

that i t [the sentence] is t rue or false." 1 1 The phi losophica l 

path by w h i c h Frege arrives at his " f o r m a l language" 1 " con-

sists generally i n these two steps. 

I w i l l refer to the reduct ion o f ord inary syntax to predicat ion 

p e r f o r m e d i n paral lel w i t h the pars ing o f ord inary seman-

tics as the analytic breakdown. I w i l l refer to the corre lat ion 

o f l ingu i s t i c c o m p o n e n t to logico-mathematica l symbols as 

the formal correlation. The analytic style—as i t was or ig i -

nal ly conceived—fundamental ly consisted o f these t w o 

phi losophica l moves. 

Briefly, the f o r m a l corre lat ion consists i n ascr ibing f o r m a l 

n o t a t i o n and syntax (a f o r m a l system) to an i n f o r m a l sys-

t e m . This usual ly involves the m a t h e m a t i z a t i o n o f n o n -

mathemat ica l content , b u t the f o r m a l system appl ied need 

n o t be str ict ly mathemat ica l . Frege's "conceptual n o t a t i o n " 

is an example o f a f o r m a l system that is n o t str ict ly mathe-

mat ica l , t h o u g h i t conserves the p r i o r i t y o f logical relations 

between symbols . l v 

"The analytic breakdown 
ultimately fails to achieve a 

total reformulation.... 
Language ultimately resists 

complete formalization." 

As p o i n t e d out by E d m u n d Husser l (1859-1938) i n The 

Crisis of European Science, the phi losophica l move that I 

have called the f o r m a l corre lat ion has been a n d continues 

to be cr i t ical to the success o f the scientific worldview. 

Galileo, Descartes, N e w t o n , and others have used the for-

m a l corre lat ion to describe shapes and physical bodies 

mathematical ly . Leibniz even proposed the idea o f a u n i -

versal nota t ion , capable o f accommodat ing everything 

w i t h i n one f o r m a l system. v Therefore, the f o r m a l correla-

t i o n p e r f o r m e d by Frege—although an interest ing inter-

pretat ion—does n o t const i tute a new k i n d o f phi losophica l 

move. I quite admire the i n g e n u i t y o f Frege's appl icat ion 

o f the f o r m a l corre lat ion, b u t I w i l l n o t fur ther discuss his 

"conceptual n o t a t i o n " and the corre lat ion o f a r g u m e n t and 

f u n c t i o n w i t h subject and predicate, re su l t ing i n the " t r u t h 

f u n c t i o n " f o r m u l a t i o n o f language. 

The analytic breakdown o f language, w h i c h was first r igor-

ously p e r f o r m e d by Frege, is the u n i q u e and essential ph i lo -

sophical move o f the analytic t r a d i t i o n . Th i s move a ims to 

t r a n s f o r m language—already a complex syntactical and se-

m a n t i c s y s t e m — i n such a way as to a l low the appl icat ion o f 

the f o r m a l corre lat ion. 

A p p l y i n g Husserl 's m e t h o d o f r e m e m b e r i n g forgotten 

phi losophica l steps, I w i l l trace the moves that Frege made 

i n p e r f o r m i n g his analytic breakdown. Th i s Husser l i an 

analysis reveals that the analytic b reakdown u l t i m a t e l y fails 

to achieve a total r e f o r m u l a t i o n — t h a t language f u n d a m e n -

E L E M E N T S S P R I N G 10 



tally resists complete f o r m a l i z a t i o n . ^ The specific nature 

o f this fai lure l i m i t s the analytic t r a d i t i o n such that , at most , 

i t prescribes a phi losophica l style, w h i c h , l ike Socratic dis-

course, is a useful too l , b u t far f r o m a strict phi losophica l 

m e t h o d . I n short , the general u t i l i t y o f the analytic break-

d o w n for addressing phi losophica l problems is severely 

constrained by its fai lure to clarify language to the p o i n t 

where i t is suff iciently objective to be formal ized . 

I I 

Language as we k n o w i t has b o t h syntax and semantics. 

Specifically, the words and phrases we use have b o t h g ram-

mat ica l m e a n i n g according to the i r f u n c t i o n i n correctly 

f o r m e d sentences (syntax) and i n t r i n s i c m e a n i n g (seman-

tics). The r e d u c t i o n o f g r a m m a r to subject ion and predica-

t i o n concerns the syntax o f language, w h i l e the pars ing i n t o 

Sense (Sinn), Reference (Bedeutung), and m o r e broadly 

Idea concerns semantics. 

Consider a s imple sentence: "The boy is G e r m a n . " Th i s is 

a g rammat ica l Engl i sh sentence, for the article ("the") , the 

n o u n ("boy"), the adjective ("German") , and the verb ("is") 

p e r f o r m funct ions w i t h i n the i r linguistic jurisdiction as art i -

cles, nouns , adjectives, and verbs. F r o m the g rammat ica l 

f u n c t i o n o f each w o r d i n the sentence—the syntax—I can 

te l l that the verb involved is be ing , the boy is the subject 

since he "does the be ing , " so to speak, and G e r m a n is the 

subjective c o m p l e m e n t — t h a t w h i c h the boy is. 

I n a d d i t i o n to b e i n g grammat ica l , the sentence makes 

sense because i t is reasonable to say, "The boy is G e r m a n . " 

W h y is this the case? The short answer is that the sentence 

has proper ly coordinated semantic content. We k n o w what 

a boy is, h a v i n g seen t h e m r u n n i n g a r o u n d our neighbor-

hoods (some o f us once were boys ourselves!). I n the same 

way, we k n o w what i t means to be o f G e r m a n o r i g i n , a n d we 

k n o w what the act or state o f " b e i n g " is. Consequently, we 

k n o w that a boy is subject to any n u m b e r o f states, that the 

G e r m a n nat ional i ty is one such state, and that " to be" is the 

COTTLOB FRECE PROPOSED A SYMBOLIC LANGUAGE FOR EXPRESSING FORMAL LOGIC, S H O W N I N TH E M I DDLE COLU M N. 

Basic concept Frege's notation Modern notations 

Judging h -A, IK A p(A) = 1 
p(A) = i 

Negation — i - A - A ; -A 

Conditional 
(implication) 1 A 

' B 

B-+A 
B = A 

Universal quantification 
— & — * 0 0 

Vy: «(y) 

Existential quantification — r ~ \ i ' — ^ * (u) 3y: <&(y) 

Content identity (equal sign) A = B A = B 

F R E C E A N D W I T T G E N S T E I N 



proper verb for expressing a state or characteristic. 

Therefore the sentence is reasonable. 

We can see f r o m this s imple example that a l t h o u g h syntax 

and semantics are related, they are two dif ferent aspects o f 

language. Th i s d i s t i n c t i o n necessitates at least t w o ph i lo -

sophical moves—one addressing syntax a n d another ad-

dressing s e m a n t i c s — i n order to prepare ord inary language 

for f o r m a l i z a t i o n . Frege recognized n o t on ly the necessity 

o f this "pre- formal izat ion , " b u t specifically that this step 

m u s t result i n b o t h a r igorous s i m p l i f i c a t i o n i n g r a m m a t i -

cal syntax and an e l i m i n a t i o n o f i n t u i t i o n f r o m semantics 

" to keep the cha in o f reasoning free o f gaps . " v n O n l y such 

a step w o u l d enable the ass imi lat ion o f ord inary language 

i n t o conceptual nota t ion . T h u s Frege conceived the ana-

lytic b r e a k d o w n as a syntactical reduction accompanied by a 

semantic deconstruction. 

I l l 

I n order to b r i n g l ingu i s t i c syntax d o w n to size, Frege re-

duces the complex g rammat ica l syntax o f language to pred-

icat ion. M o r e specifically, he makes the case that al l con-

crete statements can be re formula ted i n t o a 

subject-predicate structure, w h e r e i n the predicate art icu-

lates a " j u d g m e n t " about the subject mediated by the verb 

"to b e . " v m Th i s j u d g m e n t can either be t rue or false de-

p e n d i n g o n the subject, and th is j u d g m e n t becomes the p r i -

m a r y i n f o r m a t i o n c o m m u n i c a t e d by the syntactical struc-

ture . T h e impor tance o f the verb—part icu lar ly w i t h regard 

to tense, b u t also w i t h regard to voice and n u m b e r — i s 

downplayed dramatically. Given the large n u m b e r o f verbs 

i n any language, this r e d u c t i o n is s t u n n i n g . A g a i n , an ex-

ample can clarify this cr i t ica l shift toward predication syn-

tax. 

I t is n o t so di f f icul t to see h o w "The boy is G e r m a n , " fits i n t o 

predicat ion syntax. The boy comprises the subject, a n d the 

predicate contains a j u d g m e n t about German-ness related 

to the boy mediated by a f o r m o f " to be." But h o w can a 

grammat ica l ly syntactical sentence c o n t a i n i n g a transit ive 

verb be accommodated by predicat ion syntax? Consider 

the sentence, "The boy throws the ba l l . " I n order to express 

"The boy throws the ba l l , " i n predicat ion syntax, the sen-

tence m u s t be re formula ted to , "The boy is t h r o w i n g the 

ba l l . " The act ion o f the transit ive verb "to t h r o w " is con-

verted i n t o a j u d g m e n t about the boy mediated by " is . " I n 

an i m p o r t a n t sense, act ion is converted i n t o a state or char-

acteristic, a n d the subject is converted f r o m an agent per-

f o r m i n g an act ion i n t o an object u n d e r g o i n g j u d g m e n t . 

The sentence above is, o f course, a s imple example d e m o n -

strat ing the pr inc ip le o f convert ing g r a m m a t i c a l syntax 

i n t o predicat ion syntax, b u t Frege dedicates a large p o r t i o n 

o f the chapter ent i t l ed "Sense a n d M e a n i n g " to ar t icu la t ing 

the m e t h o d by w h i c h even complex sentences—sentences 

i n w h i c h whole phrases contr ibute to i n g r a m m a t i c a l syn-

tax—may also be converted i n t o predicat ion syntax. Frege 

proposed that the m e t h o d sketched above can restate a sig-

ni f icant p o r t i o n , i f n o t al l , g rammat ica l ly syntactical state-

ments i n predicat ion syntax. The result is that even the 

m o s t complex sentences can be expressed as a subject and 

a j u d g m e n t about that subject, achieving the requisite s i m -

pl i f i cat ion o f g rammat ica l syntax. 

I V 

W h i l e the syntactical r e d u c t i o n o f Frege's analytic break-

d o w n is essential, the semantic deconstruct ion is at once 

m o r e di f f icul t and m o r e controversial . As we w i l l see, the 

success—or fai lure as I a r g u e — o f the analytic b r e a k d o w n 

depends o n the success or fai lure o f the semantic decon-

s t ruct ion . But let us f irst trace the deconstruct ion before 

analyzing i t . 

As stated above, Frege's semantic deconstruct ion involves 

pars ing the semantic content o f l ingu i s t i c u n i t s or 

" s igns " l x —usua l l y words , b u t sometimes "several words or 

other signs " x — i n t o two d is t inct aspects o f m e a n i n g : Sense 

(Sinn) and Reference (Bedeutung). H e later dist inguishes 

between Sense a n d Idea, b u t the cr i t ica l importance o f this 

d i s t i n c t i o n cannot be clarif ied u n t i l the o r i g i n a l d i s t i n c t i o n 

is traced. Therefore to unders tand Frege's phi losophica l 

move, we m u s t f irst examine Sense and Reference. 

E L E M E N T S S P R I N G 10 



The Sense o f a s ign is the part o f its m e a n i n g " w h e r e i n the 

m o d e o f presentat ion is conta ined. " 5 " T h i s concept is d i f f i -

cult to define precisely, and Frege h i m s e l f can only i l lus-

trate i t by examples, most p r o m i n e n t l y that concern ing the 

names " m o r n i n g star" and "evening star" for the planet 

V e n u s . x " The Sense o f " m o r n i n g star"—a heavenly body 

appearing as a star i n the early m o r n i n g — i s qui te di f ferent 

f r o m that o f "evening star"—a heavenly body appearing as 

a star i n the evening. I n a s imi la r way, the p r o n o u n s " I " and 

" m e " are b o t h names for myself, b u t the i r Sense is dist inct : 

" I " acts as a subject i n a sentence whereas " m e " acts as an 

object. Therefore the Sense o f " m o r n i n g star" differs f r o m 

that o f "evening star" as a result o f the adjectival modif ica-

t i o n o f the m o d e o f presentation; the Sense o f " I " differs 

f r o m that o f " m e " as a result o f the funct iona l m o d i f i c a t i o n 

(change i n g rammat ica l f u n c t i o n i n the sentence) o f the 

m o d e o f presentat ion. Even t h o u g h i n b o t h cases the signs 

represent dif ferent names for the same t h i n g , b o t h the two 

signs for Venus and the two signs for the first-person s in-

gular differ i n m e a n i n g by d i f fe r ing i n Sense. 

I m p l i c i t i n our discussion o f Sense is the second aspect o f 

m e a n i n g : Reference. Reference is the property o f signs as 

designators o f objects—that is, "any des ignat ion . . . has as 

enced object is relatively def ined, i t serves perfectly we l l . 

V 

T h u s the m e a n i n g o f a s ign is d iv ided i n t o Sense and 

Reference. "The regular connect ion between a s ign, its 

sense, and what i t means is o f such a k i n d that to the s ign 

there corresponds a definite Sense and to that i n t u r n a def-

i n i t e t h i n g m e a n t , " x l v says Frege. Certainly b o t h are re-

q u i r e d to obta in "comprehensive knowledge o f the t h i n g 

meant , " x v b u t these two aspects o f m e a n i n g differ i n some 

i m p o r t a n t ways. For Frege, the cr i t ica l difference between 

Sense and Reference is this : Sense is subject to change 

based o n the part icular s ign and its use i n context, whereas 

Reference is u n c h a n g i n g w i t h i n the set o f signs re ferr ing to 

a given object. Put another way, a s ign w i t h a part icular 

Sense has only one Reference, b u t a Reference can have 

m a n y signs, each w i t h a dif ferent Sense. I can p o i n t to or at 

least state the specific Reference o f any s ign independent o f 

the context i n w h i c h that s ign appears, and that Reference 

never changes. W h e t h e r I use " m o r n i n g star" or "evening 

star," i f you ask m e what I m e a n , presumably I can say, 

"Venus!" or at least p o i n t i t out i n the sky. I f the object is the 

same for two signs, t h e n the signs share m e a n i n g w i t h re-

spect to Reference, b u t this shar ing does not affect the sin-

"Sense is subject to change based on the particular sign 
and its use in context, whereas Reference is unchanging 

within [its] set of signs...." 

its m e a n i n g a definite object (this w o r d taken i n the widest 

r a n g e ) . " X 1 H The signs " m o r n i n g star" and "evening star" 

may differ i n the i r Sense, b u t because b o t h refer to Venus, 

the signs are the same i n the i r Reference. Concordantly, 

because b o t h " I " and " m e " refer to the first-person singular, 

the two signs are the same i n their Reference. Notably, the 

object o f Reference may be either a physical object (Venus) 

or a concept (first-person s ingular) . So l o n g as the refer-

gular i ty o f the object referenced. There are not two planets 

called Venus because i t has two signs that reference i t . 

I n contrast, the m e a n i n g o f a s ign w i t h regard to Sense nec-

essarily changes depending u p o n the "mode o f presenta-

t i o n [i.e. the context]" o f the s ign. "Evening" is di f ferent 

f r o m " m o r n i n g " by d e f i n i t i o n ; thus , the two signs refer to 

dif ferent t imes o f day. Th i s modal dependence o f Sense re-

F R E C E A N D W I T T G E N S T E I N 



quires some interpreta t ion i n order to apprehend. I n m a n y 

cases, th is i n t e r p r e t a t i o n — l i k e k n o w i n g the difference be-

tween " m o r n i n g " and "evening"—is relatively easy for a 

person "suff ic iently fami l iar w i t h the language." X V 1 

This modal knowledge r e q u i r e m e n t for apprehending Sense 

provides a p o i n t o f entry for i n t u i t i o n and, therefore, for er-

rors i n d e t e r m i n i n g the precise m e a n i n g o f a s ign. I n other 

words , Sense becomes dependent, however slightly, o n the 

indiv idual ' s capacity to interpret the language be ing used. I 

w i l l not apprehend the Sense o f " m o r n i n g star" and 

"evening star" i f I do not k n o w the def in i t ions (again, i n the 

dict ionary sense) o f " m o r n i n g " and "evening." A n y pene-

t r a t i o n o f the subject's inherent l ingu i s t i c capacity i n t o the 

analytic b reakdown cannot be tolerated, for this subjectivity 

inso lubly resists the f o r m a l corre lat ion. 

V I 

Frege k n e w that i f the Sense o f a s ign cou ld be even partial ly 

observer dependent, he w o u l d not be able to apply the f o r m a l 

corre lat ion, and his conceptual nota t ion w o u l d be under-

m i n e d . Therefore, i n an at tempt to preserve Sense as a gen-

eral, objective concept, he in t roduced a d i s t i n c t i o n between 

the moda l ly dependent aspect o f m e a n i n g (Sense), w h i c h 

remains objective t h r o u g h its g r o u n d i n g i n the contextual 

use o f the s ign, and the observer dependent aspect o f mean-

i n g (Idea), " an i n t e r n a l image, ar i s ing f r o m m e m o r i e s o f 

sense [sensory] impress ions . . . b o t h i n t e r n a l and 

e x t e r n a l . . . [and] i m b u e d w i t h feel ing. " x v n 

I n order for his conceptual n o t a t i o n to be applicable to any 

statements at all i n ord inary language, Frege m u s t assert 

that Idea is n o t a universal ly s ignif icant aspect o f a sign's 

m e a n i n g . The decisive move o f the semantic deconstruc-

t i o n is the insistence u p o n Idea as a t h i r d and categorically 

d i s t inct aspect o f m e a n i n g and its subsequent subordina-

t i o n to Sense and Reference i n certain cases . x v m Frege's se-

m a n t i c deconstruct ion o u t r i g h t rejects the n o t i o n that the 

subject's (i.e. language user's) i n h e r e n t l ingu i s t i c sensibil-

ity is, i n al l instances o f language, inextricably l i n k e d to 

subject's l ingu i s t i c capacity. H e rejects that Idea always 

plays a role i n the use and unders tand ing o f language. 

Frege asserts that Idea plays a t r i v ia l role i n all b u t h i g h l y 

metaphor ica l forms o f language, l ike poet ry . x l x For h i m , 

the p r i m a r y difference between "The boy is G e r m a n " and 

"Let us go t h e n , you and I , / W h e n the evening is spread out 

against the sky/ Like a pat ient etherised u p o n a t a b l e " x x is 

that the semantic content o f the first sentence is accounted 

for by Sense and Reference, whereas that o f the second re-

quires Idea i n a d d i t i o n to Sense and Reference to be under-

stood properly. 

The conceptual n o t a t i o n cannot be used for language i n 

w h i c h Idea plays a s ignif icant role alongside Sense and 

Reference i n the d e t e r m i n a t i o n o f m e a n i n g precisely be-

cause a h i g h degree o f observer dependent ass ignment o f 

m e a n i n g precludes the objectivity necessary for semantic 

content to be formal ized . I n order for the semantic decon-

s t r u c t i o n — a n d consequently the analytic b r e a k d o w n — t o 

be even part ial ly successful, Frege must relegate observer 

dependent m e a n i n g only to certain forms o f language. 

Were he to a f f i r m Idea as equally d e t e r m i n a n t compared 

w i t h Sense and Reference, or to integrate Idea i n t o Sense, 

the analytic breakdown would fail to render any form of ordi-

nary language amenable to the formal correlation. The seman-

tic content o f all language w o u l d conta in a fundamenta l ly 

subjective aspect that cou ld not be e l iminated . 

T h u s , he insists that there are "three levels o f 

difference . . . at most the ideas, or the Sense b u t not the 

m e a n i n g [Reference], or, finally, the m e a n i n g [Reference] as 

w e l l " (SM i 6 i ) . x x l Sense and Reference, as Frege conceives 

t h e m , are def inite aspects o f a sign's semantic content. 

Th i s def init ive , objective nature allows t h e m to be rendered 

i n conceptual nota t ion by apply ing the f o r m a l corre lat ion. 

H e admits that where observer dependent Idea is s igni f i -

cant i n the d e t e r m i n a t i o n o f semantic content, the f o r m a l 

corre lat ion cannot be applied. H e contends, however, that 

i n a s ignif icant p o r t i o n o f l ingu i s t i c f o r m u l a t i o n s , Idea has 

a t r i v ia l effect o n the semantic content o f signs. I n this way, 

Frege i m p l e m e n t e d the first analytic breakdown o f lan-

guage and la id the foundat ion for the analytic t r a d i t i o n . 

E L E M E N T S S P R I N G 10 



V I I 

The propositional analysis o f language enabled by Frege's 

analytic b reakdown is i n m a n y ways carr ied to its logical 

conc lus ion i n L u d w i g Wittgenstein 's (1889-1951) f irst sem-

i n a l w o r k , the Tractatus Logico-Philosophicus (1921). 

Wit tgens te in fu l ly expounds the assertion that there is a 

d i s t i n c t i o n between certain issues that phi losophy can ad-

dress and others that i t cannot. The l i n e is d r a w n between 

what is art iculate—suff ic ient ly objective to be formal ized 

a n d analyzed—and what is inar t i cu la te—too observer de-

pendent to y ie ld to the analytic breakdown. We have just 

seen the o r i g i n o f this d i s t i n c t i o n i n the Frege's semantic 

deconstruct ion. 

After p u b l i s h i n g the Tractatus Wi t tgens te in re t i red f r o m 

philosophy, bel iev ing that he h a d clearly def ined this l i n e 

between w h a t k inds o f concepts and issues were "fair 

game" and w h i c h could n o t be addressed. Wit tgens te in 

t h e n served as a schoolmaster i n Austr ia , where he re-

m a i n e d u n t i l 1929, w h e n he r e t u r n e d to Cambridge w i t h a 

r e i m a g i n e d perspective o n the phi losophica l p o s i t i o n that 

he had been i n s t r u m e n t a l i n sol idi fy ing. The p o w e r f u l crit-

ic isms he leveled against his analytic contemporar ies—par-

t icular ly against what I have called the semantic decon-

s t ruct ion—are p u t fo rward as collected m u s i n g s i n 

Philosophical Investigations (1953). The a r g u m e n t w i t h 

w h i c h W i t t g e n s t e i n challenges the possibi l i ty o f the seman-

tic d e c o n s t r u c t i o n — c o m m o n l y referred to as the " f ami ly 

"Wittgenstein fully 
expounds the assertion that 

there is a distinction 
between certain issues that 

philosophy can address and 
others that it cannot." 

resemblances" a r g u m e n t — i s suff iciently c o m p e l l i n g to 

call i n t o quest ion the analytic breakdown, the o r i g i n a l 

phi losophica l move o f the analytic t r a d i t i o n . 

I t is notable that Wittgenstein 's m u s i n g s o n this p o i n t i n 

Philosophical Investigations appear as an i n f o r m a l series o f 

t h o u g h t experiments and observations, and n o t a f o r m a l ar-

g u m e n t . As a result o f th is presentat ion, phi losophers 

often get i n t o t rouble w h e n a t t e m p t i n g to interpret 

Wittgenstein 's w o r k , especially the concept o f m e a n i n g as 

" f ami ly resemblance." As I see i t , the " f ami ly resem-

b l a n c e s " ™ 1 a r g u m e n t is fair ly evident, so I a i m only to ar-

t iculate and n o t to interpret . I t is necessary, however, to do 

some " s t r i n g i n g together" i n order to clarify the nature o f 

Wittgenstein 's c r i t i c i s m o f Frege's semantic deconstruc-

t i o n . I n l i g h t o f the body o f l i terature o n the topic , i t is i m -

portant to make clear to the reader m y i n t e n d e d use o f 

Wittgenstein 's idea. 

V I I I 

I stated i n Section V I that the cr i t ical step i n Frege's seman-

tic deconst ruct ion—the step that allows the complete exe-

c u t i o n o f the analytic breakdown—is the separation o f ob-

server dependent m e a n i n g (Idea) f r o m b o t h Sense a n d 

Reference. The success o f this separation is p a r a m o u n t . I 

t h i n k that I have sufficiently explained w h y th is is the case 

and w h y Frege is so concerned w i t h the sequestering o f 

Idea to forms o f language w h i c h he does n o t a i m to formal -

ize. I t is precisely th is s i tuat ion that Wittgenste in 's " f a m i l y 

resemblances" a r g u m e n t questions. 

The essence o f Wittgenstein 's c r i t i c i s m is th is : instead o f 

" p r o d u c i n g s o m e t h i n g c o m m o n to a l l that we call lan-

guage, I a m saying that these p h e n o m e n a have n o one 

t h i n g i n c o m m o n w h i c h makes us use the same w o r d for 

a l l — b u t they are related to one another i n m a n y di f ferent 

ways . . . and i t is because o f this re lat ionship that we call 

t h e m all ' l a n g u a g e . ' " ™ 1 1 H e makes three assertions here: 

(1) the Reference, n o t the Sense, is the p o i n t o f entry for 

subjectivity, (2) as a result , a g iven w o r d — o r s ign according 

to Frege's t e rmino logy—has n o concrete c o m m o n refer-

F R E C E A N D W I T T G E N S T E I N 



ence, and (3) relatedness based o n use (Sense), not common-

ality, is the f u n d a m e n t a l feature o f language. 

These three ambi t ious claims are best unders tood sequen-

tially, so f irst c l a i m first. Frege certainly unders tood the 

p r o b l e m o f the observer dependent aspect o f m e a n i n g , b u t 

he located subjectivity's p o i n t o f entry i n the Sense mean-

i n g o f a w o r d — w h a t W i t t g e n s t e i n calls use. Wi t tgens te in 

t h i n k s that this p o i n t o f entry is incorrect because—in con-

siderat ion o f h o w language is actually exercised—the same 

w o r d appears i n the same way i n the same sentence, re-

gardless o f the user. W h e n I say, "The boy is G e r m a n , " and 

w h e n y o u say, "The boy is G e r m a n , " we are b o t h u s i n g the 

words " the , " "boy," " is , " and " G e r m a n " i n the same way. 

Proper use—being a f u n c t i o n o f b o t h g rammat ica l syntax 

a n d proper u n d e r s t a n d i n g o f the w o r d s — c a n n o t be de-

pendent o n the language user, or there w o u l d be no stan-

dard g r a m m a r and we could use words however we 

pleased. This is n o t the case: " G e r m a n is the boy," is u n i n -

te l l ig ible because the speaker o f th is sentence has used the 

words improper ly . Therefore, i n order for any l ingu i s t i c ex-

press ion to be inte l l ig ib le to its speakers, n o t only m u s t 

there be proper uses and i m p r o p e r uses o f words , b u t the 

words c o m p o s i n g the expression m u s t c o n f o r m to stan-

dards o f proper use. I n other words , Sense cannot be per-

sonal, or no one w o u l d be able to c o m m u n i c a t e . 

I f even some words h a d a subjective Sense, th is w o u l d con-

stitute a private language. Wi t tgens te in extensively consid-

ers the possibi l i ty o f a private language a n d comes to the 

conclus ion that i t is imposs ib le by v i r tue o f its impract ica l -

ity. I w i l l n o t elaborate m u c h fur ther o n this po int , b u t I 

t h i n k the pr inc ip le is demonstrated by a s imple example. 

Consider the g ibber ish a y o u n g c h i l d w i l l concoct to com-

munica te w i t h i m a g i n a r y fr iends. The c h i l d understands 

this pseudo-language perfectly w e l l (and, presumably, so do 

his i m a g i n a r y fr iends!) , b u t i f he were to say, "Gaggle ben-

ner g ibblemony, " instead of, " I l ike water," I w i l l not have 

the foggiest idea what he means because I do n o t have ac-

cess to the Sense i n w h i c h those words are used. W h a t is 

i m p o r t a n t , again, is that each w o r d m u s t be used proper ly 

according to its standard uses (Sense) i n a language i n 

order for a va l id sentence to be f o r m e d . 

Let us r e t u r n to the example "The boy is G e r m a n . " Each o f 

these words has Sense i n that they are al l used properly, re-

s u l t i n g i n an inte l l ig ib le Engl i sh sentence. But what is 

m e a n t by the w o r d "German"? M o r e specifically, what is 

referenced by the w o r d " G e r m a n " and what actually hap-

pens w h e n I conjure that reference? Earlier, "German-

ness" sufficed as the Reference, b u t "German-ness" is quite 

nebulous . Does i t m e a n " o f G e r m a n descent"? or " f r o m the 

country Germany"? The same a m b i g u i t y exists w i t h "boy." 

A P H O T O G R A P H OF L U D W I G W I T T G E N S T E I N , PERHAPS THE 

MOST I N F L U E N T I A L PHILOSOPHER OF T H E TWENTIETH 

CENTURY. 

E L E M E N T S : : S P R I N G 10 



Does i t m e a n "a smal l male , " "a y o u n g male , " or "an i m m a -

ture male"? There does n o t appear to be any " b o u n d a r y " 5 0 ^ 

des ignat ing w h a t is referenced by " G e r m a n " or "boy": " the 

extension o f the concept is not closed by a f r o n t i e r . " ^ 

Reference, therefore, is not really concrete at al l . 

W h a t is m o r e , n o t only is m e a n i n g w i t h regard to Reference 

n o t concrete, i t cannot be concrete and specific. Here 

W i t t g e n s t e i n uses a h e l p f u l example. I f I a m s h o w n a se-

ries o f pictures o f leaves a n d t o l d , "These are leaves," I w i l l 

obta in a usable definition o f "leaf" such that I a m competent 

to identi fy another, di f ferent leaf as " l e a f . " x x v l H o w do I do 

this? One m i g h t say that i t is because I have an idea o f what 

"leaf" is, or m o r e clearly, a "schema" o f "what is c o m m o n to 

al l shapes o f l e a f . " x x v n I n order for th is to be the case, th is 

schema o f "leaf" m u s t appear i n m y m i n d " n o t as the shape 

o f a part icular l ea f . " 5 0 ™ 1 1 1 I f the "leaf" schema were specifi-

cally representative o f a part icular leaf, i f I saw any other 

leaf I w o u l d n o t be able to identi fy i t as "leaf." Th i s is n o t 

the case because I certainly can identi fy leaves o f m a n y 

shapes and colors as "leaves," and any language user can do 

th is as we l l . 

Fur thermore , w h a t is t rue o f "leaf" is t rue o f "boy" a n d 

" G e r m a n , " and I see no reason w h y i t cou ld not be t rue o f 

any word ' s usable d e f i n i t i o n . A n d i t m u s t be so, for 

Reference m u s t be suff iciently non-specific to accommo-

date al l instances o f a word 's use—even previously u n -

k n o w n use. But i f b e h i n d each w o r d lies an u n b o u n d e d 

m e n t a l schema o f what that w o r d means that is necessary 

for proper use o f the w o r d , t h e n Reference is inherent ly ob-

server dependent. This is because " i f someone were to 

draw a sharp boundary I cou ld n o t acknowledge i t as the 

one that I too always wanted to draw, or h a d d r a w n i n m y 

m i n d . ' , x x l x 

This "unbounded-ness" may seem odd, b u t consider the 

way we actually use language. We do n o t have a w o r d for 

every specific leaf i n the w o r l d , as w o u l d be the case i n a lan-

guage w i t h concrete Reference. Even efforts to make refer-

ence concrete only go so far. A l t h o u g h "We can draw a 

b o u n d a r y — f o r a special p u r p o s e , , , x x x n a r r o w i n g "boy" to 

" J im S m i t h " only narrows boy so far because there is m o r e 

t h a n one boy n a m e d J im S m i t h (I k n o w at least t w o person-

ally). Therefore, a certain subjectivity is i n h e r e n t to 

Reference and cannot be e l i m i n a t e d w i t h o u t deny ing c r i t i -

cal features o f the way i n w h i c h we actually use language. 

I X 

Accept ing the subjectivity o f Reference " w i t h b l u r r e d 

edges," X X X 1 W i t t g e n s t e i n h i m s e l f asks the key quest ion: "Is 

i t only other people w h o m we cannot te l l exact ly? ' , X X X 1 1 Put 

another way, " i f the concept . . . is u n c i r c u m s c r i b e d l ike 

that , y o u don ' t really k n o w what y o u m e a n . " ' 0 0 0 1 1 Th i s is ap-

parently false, for I certainly k n o w what I m e a n w h e n I say, 

"The boy is G e r m a n " even i f I cannot specify the exact ref-

erence o f each w o r d . Were i t n o t the case that I h a d work-

i n g def in i t ions o f these words , I w o u l d n o t be able to use 

t h e m correctly. I t is clear that I k n o w what I m e a n because 

correct use impl i e s a correct usable d e f i n i t i o n . 

The first quest ion is m o r e interes t ing and m o r e di f f icul t . 

H o w do other people k n o w what I m e a n w h e n I proper ly 

use words i f that proper use is based o n a usable d e f i n i t i o n 

o f the w o r d derived f r o m a " b l u r r e d edge" Reference. 

Wit tgens te in employs the concept o f "game" to explain th is 

p h e n o m e n o n i n terms o f " f ami ly r e s e m b l a n c e " 5 0 ™ ^ be-

tween each person's usable def in i t ions o f a w o r d . Chess is 

di f ferent f r o m tennis , a n d yet they are b o t h " g a m e s . " x x x v 

They are b o t h games n o t because there is " s o m e t h i n g com-

m o n to all, b u t [because] s imi lar i t ies , re lat ionships , and a 

whole series o f t h e m at that " l i n k chess a n d t e n n i s . x x x v i I n 

passing between games, " m a n y c o m m o n features drop out , 

and others appear," b u t w h a t remains are "correspon-

dences w i t h the f irst g r o u p . " x x x v n 

Such is the case w i t h a w o r d . W h e n passing between i n d i -

vidual 's usable def in i t ions o f a w o r d , there is no one t h i n g 

i n c o m m o n , b u t m a n y correspondences. W h e r e m y usable 

d e f i n i t i o n o f " G e r m a n " m i g h t inc lude m y f r i e n d Matth i s 

(who is German) , the spoken language ("scheissekopf" 

c o u l d be m y favorite w o r d i n any language), Faust a n d 

F R E G E A N D W I T T G E N S T E I N 



"The strength and incredible utility of language lies .. .in 
the very capacity of a word to accommodate richness in 

meaning." 

Goethe, Nietzsche, Ber l in , etc. whereas m y f r i e n d M a t t h i s ' 

usable d e f i n i t i o n m i g h t inc lude dif ferent people, sounds, 

l i terature , phi losophers , places, etc. w h i c h are nonetheless 

o f the categories people, sounds, etc. By these correspon-

dences " G e r m a n " is c o m m u n i c a b l e i n any proper use be-

tween Mat th i s a n d I , even t h o u g h we do n o t have a com-

m o n usable d e f i n i t i o n o f " G e r m a n . " T h u s the proper 

concept ion o f language is not a set o f def ined proposi t ions 

as Frege asserts (at least i n certain areas), b u t rather "a com-

plicated n e t w o r k o f s imi lar i t ies over lapping and criss-

c ross ing . " 5 ™™ 1 1 1 The s t rength and incredible u t i l i t y o f lan-

guage lies not i n universality, b u t " i n the over lapping o f 

m a n y f i b r e s " — i n the very capacity o f a w o r d to accommo-

date richness i n m e a n i n g . x x x i x 

X 

Wittgenstein 's c r i t i c i s m o f Frege's concept ion o f Reference 

as specific and concrete—"an area" w i t h clear b o u n d -

ar ies x l —is quite power fu l . I t reveals that the semantic de-

c o n s t r u c t i o n — t h e cr i t ical step i n the analytic b reakdown o f 

language i n t o propos i t ions—is executed by means o f a 

false premise . I n d o i n g so, W i t t g e n s t e i n calls i n t o quest ion 

any t rans format ion , analysis, and conclus ion about lan-

guage and about phi losophica l issues p e r f o r m e d o n the 

shoulders o f the analytic breakdown. As a result , this ap-

proach to analytic phi losophy cannot serve as the basis for 

a system able to address a wide range o f press ing phi lo-

sophical issues; i t makes assertions about l ingu i s t i c f o r m 

and m e a n i n g that are demonstrably false. 

I w o u l d l ike to say i n conclus ion that I do n o t w i s h to belit-

tle the as tounding inte l lectual effort displayed by Gott lob 

Frege i n the f o r m u l a t i o n o f his conceptual n o t a t i o n . Nor 

a m I asserting that his w o r k is useless because o f the u l t i -

mate fai lure o f the semantic deconstruct ion. The analytic 

style i n its cur rent c o n c e p t i o n — e m p h a s i z i n g the use o f r i g -

orously clear language a n d f o r m a l logic i n a r g u m e n t — h a s 

proven invaluable i n considerations o f language, aesthet-

ics, science, a n d even phi losophy itself. I n a d d i t i o n to his 

cont r ibut ions to philosophy, i t should n o t go u n n o t i c e d that 

m o d e r n c o m p u t a t i o n has its roots i n Frege's w o r k . I n fact, 

Frege h i m s e l f i n t e n d e d his n o t a t i o n to be a phi losophica l 

tool . H e says as m u c h : " m y 'conceptual notat ion ' , fur ther 

d e v e l o p e d . . . can become a useful too l for p h i l o s o p h e r s . " x l 1 

I believe the lesson o f the fai lure o f the analytic b reakdown 

is th is : the task o f phi losophy is to articulate, clarify, and ex-

a m i n e those p h e n o m e n a that are the case. The task is not , 

as Frege puts i t , " to break the power o f the w o r d over the 

h u m a n m i n d . . . f reeing t h o u g h t f r o m that w h i c h only the 

nature o f the l ingu i s t i c means o f expression attaches to 

i t . " x l i l I t is n o t generally the case that we experience t h o u g h t 

detached f r o m language, a l though this is certainly t rue for 

some forms o f t h o u g h t — l i k e prayer. To assume otherwise 

cannot lead to c lar i f icat ion o f phi losophica l issues, for one 

is p e r f o r m i n g operations o n art i f ic ial constructs that do n o t 

exist i n "the l i fe w o r l d , " x l m as Husser l w o u l d say. W h e n 

these constructs become complex and compel l ing—as a 

f o r m a l n o t a t i o n encompass ing language certainly i s — i t re-

quires the clear t h i n k i n g o f a L u d w i g Wit tgens te in to b r i n g 

us back to the w o r l d i n w h i c h we live. 

E N D N O T E S 

i . Frege 2000 (104) 
i i . Frege 2003 (163) 
i i i . Frege 2000 (104) 
iv. Frege 2000 (111) 
v. Frege 2000 (105) 
vi . Husserl (57-59) 
vi i . Frege 2000 (104) 

E L E M E N T S S P R I N G 10 



v i i i . Frege 2000 (111) Wittengenstein, Ludwig. Philosophical Investigations. Trans. G. 
ix. Frege 2003 (158) E. M . Anscombe. 3rd ed. Blackwell Publishing, New York: 2001. 
x. Ibid. 
xi . Ibid. 
x i i . Ibid. 
x i i i . Ibid. 
xiv. Frege 2003 (159) 
xv. Frege 2003 (158) 
xvi. Ibid. 
xvii. Frege 2003 (160) 
xvii i . Frege 2003 (161) 
xix. Frege 2000 (104-105) 
xx. Eliot (w 1-3) 
xxi. Frege 2003 (161) 
xxii. Wittengenstein (67) 
xxii i . Wittengenstein (65) 
xxiv. Wittengenstein (69) 
xxv. Wittengenstein (68) 
xxvi. Wittengenstein (73) 
xxvii. Ibid. 
xxviii. Ibid. 
xxix. Wittengenstein (76) 
xxx. Wittengenstein (69) 
xxxi. Wittengenstein (71) 
xxxii. Wittengenstein (69) 
xxxiii. Wittengenstein (70) 
xxxiv. Wittengenstein (67) 
xxxv. Wittengenstein (66) 
xxxvi. Ibid. 
xxxvii. Ibid. 
xxxviii. Ibid. 
xxxix. Wittengenstein (67) 
xl. Wittengenstein (71) 
xl i . Frege 2000 (106) 
x l i i . Ibid. 
x l i i i . Husserl (48-53) 

R E F E R E N C E S 

Eliot, T. S. "The Love Song of J. Alfred Prufrock" i n The 
Complete Poems and Plays: igog-1950. Harcourt Brace & Co., 
New York: 1980. 

Frege, Gottlob. "The Conceptual Notation." I n The Conceptual 
Notation and Related Articles, trans. TerrellWard Bynum. 3rd ed. 
Oxford University Press, New York: 2000. 

Frege, Gottlob. "On Sense and Reference." i n The Frege Reader, 
trans. Michael Beaney, 151-171. Blackwell Publishing Ltd., New 
York: 2003. 

Husserl, Edmond. The Crisis of European Sciences and 
Transcendental Phenomenology. Trans. David Carr. Northwestern 
University Press, Evanston, I I : 1970. 

F R E G E A N D W I T T G E N S T E I N