bhartrhari on what cannot be said, parsons

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Bhartṛhari on What Cannot Be SaidAuthor(s): Terence Parsons

Reviewed work(s):Source: Philosophy East and West, Vol. 51, No. 4, Nondualism, Liberation, and Language: TheInfinity Foundation Lectures at Hawai'i, 1997-2000 (Oct., 2001), pp. 525-534Published by: University of Hawai'i PressStable URL: http://www.jstor.org/stable/1400166 .

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BHARTRHARI ON WHAT CANNOT BE SAID

TerenceParsons

Department f Philosophy,University f California t LosAngeles

Introduction

Ina seminalwork, Hans G. Herzberger nd RadhikaHerzberger rguefor the fol-

lowingpoints:

1. Bhartrhari iscussesclaims thatcertain relationscannot be signified.Exam-

ples are supposed to be the significationrelationitself,and the inherence

relation.

2. Bhartrhari as aware of theparadoxical

natureof these claims.

3. Bhartrharictuallyendorses these paradoxicalclaims.

4. These claims can be supportedby twentieth-centuryrguments.'

Mygoal is to clarifywhat Bhartrharictuallyclaims,to improveon the Herzbergers'

arguments n supportof Bhartrhari,nd to note some limitationson the extent to

which the claims underdiscussion may be supportedby twentieth-century evel-

opments. I will follow the followingoutline:

* Clarificationf the claims underdiscussion.* The Herzbergers'wentieth-century efense of the claims.

* Qualm #1: Gaps in the reasoning.* Qualm #2: Semanticparadoxversus ontological paradox.An improvement

on the Herzbergers' rgumentaboutsignification.* Qualm #3: A difficultyabout thatness.* Qualm #4: Limitations n what can be shown.* Qualm #5: Inherence s different!

* Qualm #6: Are we misinterpreting hartrhari?

Bhartrhari'sext is longandcomplicated,and one cannotpossiblydo justiceto it

ina shortdiscussion.Fortunatelyorourpurposes, he Herzbergers ase almostall of

theircommentaryon a small numberof sectionsfromBhartrhari'sext.Theyare asfollows:

(SS 1) Fromwords which areuttered, he speaker's dea,an externalobjectand the form

of the word itselfare understood.Theirrelation s fixed.

(SS3) "This s the signifierof that;that is the signifiedof this."

Thusthe thatnessof the relation s signified.

Philosophy East & West Volume 51, Number 4 October 2001 525-534 525

? 2001 by University of Hawai'i Press



(SS 4a) Of the relation there is no signifyingexpressionof the basis of a property

belonging o it.

(SS 19) The relation called inherence,which extends beyond the signifying unction,cannotbe understoodhroughwords eitherbythe speakeror bythe person o whom the

speech is addressed.

(SS20) That which is signifiedas unsignifiable, f determined o have been signified

through hatunsignifiability, ould then be signifiable.

(SS21) If'unsignifiable's beingunderstood s not signifyinganything, hen its intended

statehas not been achieved.

(SS22) Of somethingwhich is beingdeclaredunsignifiablehat condition(ofbeing sig-nifiable) annotreallybe deniedbythosewords,inthatplace, inthatway, nor inanother

way, norinany way.

The Herzbergersfind in these sections seven claims, R1-R7, which they discuss.

The claims are:

R1 Thesignificancerelation s unsignifiable.R2 Thesignificancerelation s undenotable.

R3 Thesignificancerelation s unnamable. B1)R4 Thedenotingrelation s unnamable.

R5 The inherencerelation s unnamable. B2)R6 The inherencerelation s undenotable.

R7 The inherencerelation s unsignifiable.B3)

By 'denotation' they mean signification by a noun:

x denotesy meansx signifiesy andx is a noun.

However, neither the word "denote" nor the idea, so far as I can see, occur in

Bhartrhari's ext. (This is apparent from inspection of the citations.) So I will ignore

any talk of denotation. I will also use 'signification' instead of the Herzbergers' 'sig-nificance' because the latter term is used today to mean "being meaningful," which

is not what Bhartrharimeant. So the claims I will discuss are

R1 The signification relation is unsignifiable.R7 The inherence relation is unsignifiable.

The Herzbergers' Twentieth-CenturyDefense of the Claims

The Herzbergersclaim that R1 R7 can be defended on the basis of twentieth-centurytechnical accomplishments in logic and metaphysics. The defense goes as follows:

Step 1. Paradoxes f set theory orce one to place limitson what setsexist.

Step2. These limitsentail that no relationmaybe one of itsown relata.

Step3. So significationcannot be signified.For if it were, it would be one of its own

relata.

526 PhilosophyEast& West



These maybe spelledout as follows:

Step 1

Consider he set R,which hasas membersexactlythose sets that are not membersof

themselves.Thatis:x E Riff- (xe x)

Ifyou plug in Rfor'x', you conclude:RE Riff- (RER)

This cannotbe true. So we must conclude that there is no such thingas the set that

has as membersexactly those sets that are not members of themselves. But this

conclusion cannotbe maintained n a completelyad hoc fashion;instead,we must

find a systematicway to limitthe assumptions hatwe make about sets so thatthese

assumptionsdo notyield the conclusion that such a set exists.

Step2

One way to limitour assumptionsabout sets and still have a usefulset theoryis to

adopt the Zermelo-Fraenkelet theory.This is an axiomaticsystemwhose axiomsfall into the following categories:

Axiom of Set IdentitySets with the same members are identical. Thatis, if x and y are sets with the

same members, hen x = y.

Axiomsof Set Existence

Empty et:Thereis a set with no members.

Unit sets:Forany entity,there is a set withthatentityas a memberand nothingelse.

Infinite ets: Thereis an infinitelybig set.And so on....

Axiom of Set Nonexistence(Regularity)No set has a member hat itself has a member hat itself

has a member,and so on, ad infinitum.

As a consequence of the axiom of regularity,no set s of orderedpairscan be a

memberof a pairthatis a memberof s itself.Buteveryrelationhas a set of ordered

pairsas itsextension.Itfollows that no relationcan be one of itsown relata.

Step3

Ifsignification tself were signified,it would be one of its own relata.This has been

ruled out. So signification annot be signified.I now proceedto some qualmsthatI

have about the Herzbergers'easoning.

Qualm #1: Gapsin the Reasoning

Thereare some gaps in the reasoningprovidedby the Herzbergers.First,he princi-ple of regularitys only one way among manyto avoid the paradoxes.So the argu-

Terence Parsons 527



ment in favorof regularitys inconclusive.Second, no reasonis given to attribute o

Bhartrharihe view that every relationhas a set of orderedpairsas its extension.

Without hisassumption he argumentbreaksdown. (Fregeoriginallyheldthateveryrelationhasan extension,but he abandonedthat view because it led to paradox.)

Qualm#2: SemanticParadoxversusOntologicalParadox

Since signification s a semantic relation,Bhartrhari'saradoxabout significationseems to be more akin to the semantic paradoxesthan the ontological ones dis-

cussed by the Herzbergers.TheOntological Paradoxes.These stem from naturalprinciplesabout sets, or

properties, r relations.The Russellparadoxgiven above is an example of an onto-

logical paradox.SemanticParadoxes.These stemfrom naturalprinciplesabout semanticnotions,

such as truth.Anexampleof a semanticparadox s the LiarParadox:

Consider he sentence: 'Thisverysentence is not true'.Ifit is true,then what it

says mustbe the case. But itsays that it is not true.So, by reductio, t cannot be

true.Ifit is nottrue,then what it says is the case. So it is true.So, by reductio, t

cannot notbe true.

So we have shown both thatthe sentence is not true and that it is not not true-a

paradox.

An Improvement n the Herzbergers'ArgumentRegarding ignification:

"SignificationCannotbe Signified!"

I thinkthat it is possible to improveon the Herzbergers' rgumentby giving an

analogueof the liarparadox.Itgoes as follows.

Step 1. Ifthere is a predicate hatobeys certainnaturalprinciplesof truth, hen

one is led to a contradiction.So there cannotbe such a predicate.

Step2. Ifsignificationwere signified,the predicate hatsignifiesit would obeycertain "principlesof signification."One could then define a predicatethat

obeys the principlesof truth, hus leadingto the contradictionn Step1.

Spelledout, the argumentgoes as follows.

Step 1

Supposethere is a predicate, true', hatobeys the followingtruthprinciple oranysentenceS:

S - 'S' is true

AbbreviatethesentenceIam now uttering'by 'a'. Then utter"ais nottrue."The a is

that sentence thatsays thata is not true:

528 Philosophy ast&West



a = '- (a is true)'

The reasoning hat leadsto a contradiction mploys two arguments.First,we show

thata is not true.Beginby assuming hat it is true:

Suppose:a is true

then '- (a is true)' s true substitutingor'a'then - (a is true) by the truthprinciple.

Butthiscontradicts he initialsupposition.Sowe have used a reductioad absurdumargumento establish -' (a istrue)'.The

second argumentproceedsfromthis.

We have: -(a is true) shownabove

so ('- (a is true)' s true) substitutingor'a'

so (-1 a is true)) by the truthprinciple.

Butthis contradictswhat was shown above.

Step2

Suppose that some relationalpredicate,'signifies',signifies signification.Then the

followingwill be true forany singular erm T:

[SIG] fthere is such a thingas T,then 'T'signifiesT.

Example:

If there is such a thing as the president,then 'the president' signifies the

president.

Ifwe concentrateon terms hatsuccessfullyrefer, he schema can be simplified o:

[SIG] T'signifiesT

Call this the "significationprinciple."The significationprincipleentailssome prin-ciples thatleadto the liarparadox.Thefollowingis a sketch of how thisgoes.

Using a well-known(twentieth-century)rtificialdevice, it is possible to makethe questionof whatentitya certainsingular ermsignifiesequivalent o the questionof whethera given sentence is true or false. Forexample, consider the concocted

singular erm:

the number hatis 1 if everyswan is white and that is 2 otherwise

Ifevery swan is white, this singular ermsignifies1; if not every swan is white, it

signifies2. So thereappears o be an equivalencebetween:

'thenumber hat...' signifies1

and

'everyswan is white'is true

Terence Parsons 529



Guidedby thisparallel, t is possibleto definetruth n termsof signification.That s,one can formulatea conditionusingthe predicate'signifies' hatsatisfiesthe truth

principlesdiscussed above. So the proofof a contradiction n Step 1 can be re-

peated.(Seethe Appendix o this articlefordetails.)This is a reductioad absurdum

of the assumption hat leads to the contradiction,which is the significationprinciple.

So the significationprinciplecannot hold. But it would hold forany relationalpred-icate thatsignifiedsignification.So it is impossible or a relationalpredicate o dig-

nifysignification.What has been shown? This argumentconcludes that significationcannot be

signifiedby a relationalword like 'signifies'.It does not address the questionof

whethersignificationcould be signified by a noun such as 'signification' r a noun

phrasesuch as 'theirrelation' SS1) or 'the relation' SS3, 4a).The Herzbergersocus on the questionof whethersignification an be signified

by a noun or noun phrase.Since Bhartrhariimselfuses such phrases o signifysig-nification(in SS 1 and in SS 3 and 4a), this makesBhartrhari'spracticeviolate his

own theory.But if the question is ratherwhethersignification an be signifiedby arelationalword like 'signifies',then his practiceseems to be consistentwith his

theory.

Qualm#3: A Difficultyabout Thatness

The semanticparadox ust discussed can be solved by supposingthatsignificationcannot be signified.However, Bhartrhariays that the thatnessof the significationrelationcan be signified.Unfortunately,his reinstates he contradiction hat was to

be avoidedby notsignifying ignification.Here is how:

Duplicatethe reasoningabove, but replace'signifies'by 'is a signifierof'. This

makesno difference o the patternof the reasoningabove.

So we have not been successfulin defendingBhartrhari'shole view, only the partof it minusSS3.

Qualm#4: Limitations n WhatCan Be Shown

Ifsomething0 is not signifiable, hatmaybe because of the nonexistenceof 0 or

because of a semantic failure.Thatis, it is not signifiableeither because it does not

existor because it does exist,but the signification elationcannot connect anywordwith it(see fig. 1).What hasbeen arguedabove, by both the Hezbergers nd myself,is that there isn't a significationrelationthat is signified.To supportBhartrhari e

need to supportthe strongerclaim that there is a significationrelationthat is not

signified.Butthere is no twentieth-centuryonsensus on the existence of relations

(cf. Frege).Whatfollows is a modest attempt o supportBhartrhari'sption (thatsignifica-

tionexists,but it cannotbe signified).Suppose hata relationexistsifyou can specify

exactly what things it does and does not relate.Assume a languageLwith some

530 PhilosophyEast&West



wora w rd

Figure1

words nit,andsupposehatyoucanspecify xactlywhateachword ignifies.Thenthere s a relationhatrelates ach word o what tsignifies.Call hatrelation Z."Nowsupposehatwetry osignifyZbyaddingo La relationalredicate signifies."Question:an'signifies'ignify ignification?nswer:tdepends. tcaneasily ignifyZ,andZ was hesignificationelationorL.But f'signifies'sadded o L, herewillnow bea newsignificationelation,nditis impossibleor signifies'o signifyhat.

Insummary,here ruly s a significationelation,Z;this relation elates ach

word owhat hatwordsignifies.Andthatrelation, , couldbe signified.But fyoudidthat,Z wouldn't e thesignificationelation nymore!Thiswasargued bove.)So there sa significationelation,ndalthoughtcouldbe signified,"the ignifica-tionrelation"annotbe signified.

Qualm#5: Inherences Different!

TheHerzbergersakesignificationo be a specialcaseof inherence,ndtheyargueon this basis hat nherence annotbe signifiedorthe samereasons hatsignifica-tion cannotbe signified.Their laim hatsignifications a specialcaseof inherence

is basedentirely n the claim orm SS19)that nherence extends eyond hesig-nificationunction." his nterpretationf SS 19 is far romobvious.

What s inherence?Whatever lse it is, it seems o include he relation etweena universalndanentityo which hatuniversalpplies.For xample, n individualcow is a cow byvirtue f the factthat he universal owness nheres n it.For im-

plicityofdiscussion,willassume hat nherencesexactly hisrelation.Setsarespecial ortsofuniversals;heyare"extensional"niversals-universals

thatare denticalfthe same hingsnherenthem. Karl otterrgueshat heNyayatook universalso be extensional.)2o there s littledifference etween he inher-ence relation nd the set membershipelation.nparticular,heontologicalpara-doxes nfectbothsettheory ndpropertyheory;his s because xtensionalitys notrelevanto the paradoxes. o, forthe purposes f thisdiscussion,we cantake set

membershipo be a modern ersion f inherence.Nowineveryknownwentieth-centuryettheoryhere snosetthatcouldserve

as the extensionof a membershipelation.This includeseven non-well-foundedset theories hatreject he axiom of regularity.o there is a sense in whichthe

twentieth-centuryainstreamejectsheexistenceof an inherence elation, nd soitrejectsBhartrhari'siew that here saninherence elationbutone thatcannotbe

signified).

Terence Parsons 531



Inanother ense, however,there is an inherencerelation,but it is a differentypeof thingfromordinary elations;n one approach t is a kind of class as opposedto a

set; in the Frege-Russellheoryof types it is of a higher ype of thingthanordinaryrelations.Inall of these theories,it is not possiblefor inherence o be one of itsown

relata.The question then arises: is this signifiable?This seems to amount to the

question:is there a two-place predicate,say, 'is a memberof', that holds betweentwo termsexactlywhen the firstsignifiesa thingthat is a memberof (that"inheres

in")whatever he secondthing signifies.And all twentieth-century orkinset theoryassumes that there is a meaningful wo-place predicatethat works in this way-

contrary o Bhartrhari.

Qualm#6: Are WeMisinterpretinghartrhari?

The Herzbergers sk whetherthere is a noun, such as 'signification',hatsignifies

signification.I have asked whether there is a verb,such as 'signifies', hatsignifies

signification.But in Bhartrhari'swritings,quoted above, he seems to be askingwhetherthere can be an adjective,such as 'unsignifiable',hatappliesto significa-tion. Ifthis is what he means,then neither he Herzbergers orI have addressedhis

view. Thus,further esearch s called foron this matter. nparticular,t seems to me

to be important otjustto establishwhat Bhartrhari'siews are on thismatter,but to

find out why he held such views. That is, insteadof seeking a twentieth-centuryvalidation orrefutation)f hisviews, it would be far better o discoverhis own rea-

sons for thinkingwhat he thought. Unfortunately,he text, although lengthy,does

notappear o shed much lighton this. So "deeper"scholarshipmaybe called for.

APPENDIX: DETAILS OF HOW TO GET THE LIAR

PARADOX FROM SIGNIFICATION

Supposesignification beys the principle hat foranytermT which actuallysignifies

something:

'T'signifiesT.

Then:

'the numberthat= 1 if S and that= 2 if -S' signifiesthe numberthat= 1 if S and

that= 2 if - S

Becauseof the way that definitedescriptionswork:

(thenumber hat= 1 ifS and that= 2 if - S)= 1 ifandonly ifS.




' (Thedefinitedescriptionbtainedby writinghefollowingdown inorder:

'the numberhat = 1 if'the sentence nthe boxandthat= 2 if '

thesentence nthe box

signifies1)

Figure

So:

'the number hat= 1 ifS and that= 2 if - S' signifies1 if andonly ifS.

Anotherway of expressing his is:

The definitedescriptionhatyou get by writing hese inorder:

'the number hat= 1 if' + 'S'+ 'and that= 2 if ' + 'S'

signifies1 ifandonly ifS.

As a result, he following"truth"principleholds:

S _ The definite description'the numberthat= 1 if'+ 'S'+ 'and that= 2 if -' + 'S'

signifies1

I call this the "truth"principlebecause it mimics perfectlythe truthprincipledis-

cussed in the text, ifwe simplydefine 'x is true'to be:

[**]x is true= the definitedescription the numberthat= 1 if'+ x + 'and that= 2 if

-' + x signifies1

It is now possible to formulatea liarsentence, and duplicatethe reasoningof the

liarparadox.We get a version of the liarparadoxby writingthe following, which

is equivalent to 'the sentence in this box is not true' (see fig. 2). To get the liar

paradox,simplyduplicatethe proof given in the text, substitutingor 'x is true' the

following:

Thedefinitedescriptionthe number hat= 1 if'+ x + 'and that= 2 if -' + x signifies1

Andsubstitutingor 'a':

the sentence in the box

Now replace every appeal to the truthprinciplewith an appeal to [**]above, andthe proofgoes exactlyas before.

Terence Parsons 533



Notes

1 - Hans G. Herzberger nd RadhikaHerzberger, Bhartrhari'saradox," ournalof

IndianPhilosophy9 (1981): 1-17.

2 - KarlPotter,"AstitvamJneyatvaAbhidheyatva,"n Beitrage urGeistesgeschichte

Indiens:FestschriftorErichFrauwallner,rsg.von G. OberhammerLeiden:E.J.Brill,1968), pp. 275-280.


bhartrhari on what cannot be said, parsons

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