unger - no people

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Why The re Ar e N o People PETER UNGER I agine, if you will, a somewhat uncom monly shaped object, one whose shape is not very irregular or bizarre, perhaps, but which is at least sufficiently s o that we have no common name or expression for an object with a shape of that sort. Following this instruction, then, you have not imagined a pyramid, or cylindrical object, for those are readily spoken of in available terms. I shall call your imagined object a nudnick, which term you are to apply also t o such various other objects as you deem suitably similar in shape to the first. In this way, we have invented a new word together: 1 have given you the form of the inscription, ‘nacknick’, and some instructions which help t o delimit the meaning. But only you have enough of an idea of the word t o p ut i t t o much use. That is because, according to this little story, you have not revealed your imagined shape t o me, o r done much else t o give me a useful idea of it. Let us change the story a bit. In this version, you do not first imagine any object. Rather, I now actually place before you an object of the sort which, we have supposed, you imagined in the first version. Pointing to this uncommonly shaped thing, I then say to you, “This object i s a nacknick, as are various others that are suitably similar in shape to it.” To be emphatic and explicit, in both ver- sions I may go on t o add these following words to my instructions: “Don’t think that an object must be exactly the same as this one in shape t o be a nacknick. Rath- er, while such exact sameness is amply sufficient, any object that differs in shape from a nacknick only minutely will also be a nacknick. There is, then, no particular limit on shapes for nacknicks. At the same time, however, many objects will differ from nacknicks, as regards their shape, substantially and significantly, and these will not be nacknicks. These remarks apply, of course, not only t o actual objects, which might be found in reality, but also t o such merely possible objects as might be only imagined.” I do not think that, in adding these explicit instructions, I would be changing the learning situation in any substantial way. Rather, I would 17 7

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Why There Are N o People

PETER U N G ER

I ag ine , i f yo u wi ll , a som ewha t uncom mon ly shaped ob jec t , one whose shape is

no t very i r regular or bizarre , perha ps, bu t which is a t least suffic iently so t h a t

we have no com mo n name or express ion fo r an ob jec t wi th a shape of tha t so r t .

Fo l lowing th i s ins t ruc t ion , the n , you have no t imagined a pyramid , o r cy l indr ica l

object , for those are readi ly spoken of in avai lable terms. I shal l cal l yo ur imagined

o b j e c t a n u d n i c k , which te rm you a re to apply a l so to such var ious o the r ob jec t s

as you dee m sui tably s imilar in shape t o th e f i rs t . In this way, w e have invented a

new word toge ther : 1 have given you the form of the inscr ipt ion, ‘nacknick’ , and

som e ins t ruc t ions which he lp to de l imi t the meaning . B ut on ly you have enough of

an idea of t h e w o r d to p u t i t to much use. That is because, according to this l i t t le

s to ry, yo u have no t revealed yo ur imagined shape to m e , o r d o n e m u c h e ls e to give

me a useful idea of i t .

Le t us change th e s to ry a b it . In thi s vers ion , you d o no t f i r st imagine any

objec t . Ra ther , I now ac tua l ly p lace before y ou an o b jec t o f the sor t which , we

have suppo sed, yo u imagined in the f i rs t vers ion. Point ing to t h i s u n c o m m o n l y

shaped th ing , I then say to you , “This ob jec t is a nacknick , as are var ious others

th a t a re su i tab ly s imi lar in shape to it.” To be emphatic and expl ici t , in both ver-

sions I m a y g o o n to add these fol lowing words to my ins t ruc t ions : “Don’ t th ink

t h a t a n o b j e c t m u s t b e exac t l y t h e s a m e a s t h i s o n e i n s h a p e to be a nacknick. R ath-

e r , whi le such ex ac t sameness is amply suf f ic ien t , any ob jec t tha t d i ffe rs in shape

f rom a nacknick on ly minu te ly wil l a l so be a nacknick . T here i s, then , n o par ticu la rl imi t on shapes fo r nacknicks . A t t he same t ime , however , many ob jec t s will d i f fe r

from nack nicks, as regards their shape , substa nt ia l ly and s ignif icant ly , and these

wil l no t be nacknicks . These remarks app ly , o f course , no t on ly to actual objects ,

which might be foun d in rea li ty, b u t a lso to such mere ly poss ib le ob jec t s as m i g h t

be only imagined.” I d o no t th in k th a t , in add ing these exp lic it ins t ruc t ions , I

would be changing the learn ing s i tua t ion in any subs tan t ia l way . R a ther , I w o u l d

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178 PETER U N G E R

only be mak ing expl icit w hat wou ld otherwis e be learned implici tly . E xce pt for this

r a t h er m i n o r m a t t e r , a n d t h e f a c t t h a t w e s e t o u t in t e n ti o n a ll y to inven t a new ex-

press ion , the word you have jus t come to unders tand i s o f a p iece wi th muc h tha t

you learned a t your mother ’ s knee. T he newness and th e exp l ic i t charac te r o f th i s

experience with ‘nacknick’ , however , let us ref lect prod uct ively on w hat logical fea-

t u r e s a r e c o m m o n to both the inven ted te rms and the express ions lea rned in ch ild -

h o o d .

1. THE ARGUM ENT FROM INVENTED EX PRESSIONS

What reflection reveals, I sugges t , i s tha t a com mo n fea tu re o f ‘nacknick’ and so

man y o t he r t e rms i s tha t they a re a ll logical ly incons i s ten t express ions . On a par

with ‘perfectly squar e t riangle’ , th e supposi t io n t ha t any thin g satisfies ‘nack nick’

implies a logical contradict ion. The instruct ions that served expl ici t ly to i n t r o d u c e

‘nacknick’ , and that now serve to govern th e te rm, were so devised as to ensure th i s

surprising resul t. Because of this , we can br ing ou t the incons is tency in th e term by

reflec ting o n those ins t ruc t ions , wi th n o need fo r us to e n t e r i n t o l e n g th y , c o m p l e x

a r g u m e n t a t i o n as to wh at th e word really means.

Our ins t ruc t ions endow ed ‘nacknick’ wi th such a meaning tha t i t is now gov-

e r n e d b y a t l e a st t h e s e t w o c o n d i ti o n s :’

( I n ) f s om e (ac tua l o r on ly poss ib le ) en t i ty sa ti s fies ‘nacknick’ , then any (ac -

tua l o r on ly poss ib le ) en t i ty tha t d i f fe r s m i n u t e l y , in shape , f rom tha t

putat iv e sat isf ier also satisfies th e expression.

( 2 n ) f s o m e ( a c t u al or only possible) ent i t y sat isf ies ‘nacknick’ , then ther e are

som e (ac tua l o r on ly poss ib le) e n t i t i e s each of w hich d i f fe r s substant ial ly ,

in shape , f rom tha t pu ta t ive sa t i s f ie r and each of which does no t satisfy

th e express ion .

As stepwise reasoning shows, because it is governed by these tw o cond i t ions , ‘nack-

nick’ is an incon sis tent term.

We may begin by consider ing some shaped objec t , i f only a possible one , that

is not a nacknick ; fo r , accord ing to my ins truc tion s, an d (2x1). if ther e are nack-

n icks , the re mus t be som e such . Having don e th i s, we want now to reason that , ac-

cord ing to these same ins t ruc t ions , the cons idered ob jec t also is a n ackn ick. Well ,

le t US n o w t h i n k a b o u t a n a ll eg ed n a c k n i c k , p e r h a p s ev e n t h e o b j e c t f r o m w h ic h ,

presumably , 1 t aught you the express ion . I f th i s i s a nacknick , then , accord ing to

my ins t ruc t ions , and to ( I n ) , so too i s an ob jec t on ly minu te ly d i f fe ren t in shape

f rom i t , in par r icu lar , on e th a t is minute ly m ore a l ike in shape to t h e o b j e c t t h a t w e

have agreed is not a nacknick . Now, as th i s n e w , minute ly d i f fe r ing ob jec t i s a l so a

nacknick , as my ins t ruc t ions have ind ica ted , so too is another objec t tha t d i f fe r s

f r o m i t , i n t h e s a m e d i r e c ti o n , b y a t l e a st r o u gh ly t h a t s a m e m i n u t e a m o u n t . I t is

n o t h a r d to see , then , th a t a sequ ence of reason ing takes us to t h e s t e p w h e r e a n o b -

jec t , on ly minu te ly more a l ike in shape to our “parad igm” nacknick than i s our

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W HY T H E R E A R E N O P E O P L E 1 7 9

considered non-nacknick, wil l be declared a nacknick. Then, f inal ly , the object

that , we agreed, was no t a nacknick will also be a nacknick. Acc ording to m y in-

s t r uc t i o ns , t h e n , t h e r e a r e o b je c t s t h a t b o t h a r e n a c k n ic k s a n d a r e n o t . T h e w o r d

‘nacknick’ , the relevant aspects of which these instru ct ions de termin e, is an incon-

sis tent expression.

I t might be ob jec ted aga ins t th i s reason ing tha t the re a re sequences of m inu te

differences that wil l not take us to our agreed non-nacknick , bu t ra ther wi l l ap-

proach a l imi t tha t is sa fely wi th in the range where p rope r nacknicks may b e recog-

nized. If this is so, t h e o b j e c ti o n c o n t i n u e s , th e n w e c a n n o t d r a w t h e c o nc lu s io n

t h a t , as the ins t ruc t ions have i t , the re a re ob jec t s tha t b o t h a re and a re no t nack-

n icks . But u nfor tuna te ly fo r th i s ob jec tion , the ex is tence o f such l imi ted sequences

will no t p reven t the inco ns i s ten t conc lus ion f rom be ing drawn. F or our ins t ruc t ions

explicit ly sqated tha t there is no p ar t icular l imit on s h a p e f o r n a c k n i c k s , a n d so t h e y

ensured t roub lesome seq uences to be avai lab le fo r our s tepwise reason ing . Fo r ex-

ample , on e avai lab le sequence is p resen ted when we con s ider on e b i ll ion roughly

equa l s teps o f d i f fe rence spanning the range f rom our parad igm to o u r cons iderednon-nacknick . Th is sequence means a long a rgum ent fo r us, i f things are spelled o u t

in de ta i l , bu t the incons i s ten t conclus ion is fo rced upo n us a l l th e same. I t is pret ty

clear, I suggest , tha t because of ou r devised instruct io ns, ou r inven ted expression

‘nacknick’ , desp i te its uti l i ty and natura l appear ance, is indeed a logically inconsis-

tent expression.

I shal l employ this observat ion of inconsis tency as a premise in an argument ,

th e Argum ent f rom Inven ted Expressions:’

( I ) The inv en ted expression ‘nacknick’ is logical ly in consis te nt .

The conc lusion of o ur a rg ume nt is to b e t h e p r o p o s i t io n t h a t t h e r e a r e n o p e o pl e.

To ge t i t f rom our p remise ab ou t ‘nacknick’ , we need a goo d dea l more . Mos t o fthis remaind er wil l be contained in this second premise:

(11) The ex pression ‘person’ is logically on a par w ith ‘nacknick’; if th e la tte r is

incons i s ten t , then so is t h e f o r m e r .

A great deal of this essay wil l be spe nt in supplying sup po rt for this crucial secon d

premise. There wil l be great resis tance, of course, toward its a c c e p ta n c e . F o r i t is

qu ick ly qu i te obv ious tha t , in con junc t ion wi th th e eminen t ly a t t rac t ive f i r s t p rem-

ise, i t logical ly yields th e s tar t l ing conclu sion:

(A) Th e expression ‘person’ is logically inconsistent.

Before a len gthy discussion o f th e claimed logical par i ty is ente red in to, a few briefremarks are in order to motivate (11), so tha t th e length ie r , m ore ana ly t ica l d iscus -

s ion may appear wor th th e e f fo r t .

Now, as I have se t th ings up here , the on ly th ing impo r tan t to an object’s be-

ing a nack nick is the s hape it has , though even th i s ma t te r , o f course , evapora tes in

inconsistency. So, in th is regard, o ur invented word paral le ls cer ta in ord inary ex-

pressions: for exa mple , ‘cubical object’ , in co ntra st to ‘perfec t cube’. F urth er , while

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180 PETER UNGER

I have specified only shape as important for nacknicks, I cou ld have easily specified

additional requirem ents for o ur putative objects, for example, that a nacknick be a

certain sort of nicknack. Any such additional requirement could not, of course,

have rendered the word consistent: given the determinative instructions regarding

shape, nothing could have don e that. With only shape in the picture, our example

has a certain purity and s implicity. But as regards the basic question, th at of incon-sistency, our invented word might be the same as expressions that cannot be SO

neatly described.

Again, our learning situation involved just one paradigm nacknick, imagined

or presented, and this artifice also gives our examples a certain simplicity and pur-

ity, perhaps one not often found in the more ordinary course of things. But we

could have made things m ore ordinary with out importantly altering ou r examples:

For example, originally, I could have asked you to imagine several shaped objects,

each to have a quite similar unfamiliar shape. In the second story, I could have pre-

sented you with several similarly shaped objects. And, then, when things were to be

ma de exp licit, I could have alter ed my instr uctio ns, slightly,to

suit.So,

whetherwe have a single paradigm or a multiplicity is no t crucial to th e logic of t h e expres-

sion learned.

At this point, our second premise will have a certain plausibility at least. As

our first premise, (I), is so hard to den y, ou r conclusion fro m it an d (111, th at is, th e

startling (A), will now also be a t least plausible. But however surprising it may be,

(A) does no t directly concern th e existence, or nonexistence, of persons. It is, afte r

all, ab ou t an expression, ‘person’, and is no t directly abou t any putative people. T o

get a conclusion directly to concern our desired subject matter, however, is now

qu ite easy. We need only ad d to wh at we have, this final premise:

(111) If th e exp ress ion ‘per son ’ is logically inconsistent, then th ere are n o people.

In conjunction w ith (II I), our oth er premises validly yield o ur intended final con-

clusion :

(B) There are no people.

An d, this final premise, (I ll) , really is a logically uno bjectio nable proposition.

T o deny the idea t ha t an inconsistent expression does no t apply to anything,

one must be involved in a confusion. For what is inconsistent expression? I t is an

expression fo r which the s upposition th at it d oes apply leads to a contradiction.

But, then, th at supposit ion can not be true. Thus th e expression does no t apply. But

wh at confusion might be responsible for such an absurd d enial?

The chief culprit, I suppose, will be a failure to distinguish between, first, ourusing an expression to refer to certain objects and, on t he o ther hand, an expression

actually applying to, or being true of, those objects. You and I, for examp le, may

agree to use th e expression ‘perfectly s quar e triangle’, even given w hat i t now m eans,

to refer to such tomatoes as are both yellow and sweet. With normal suppositions

in force, including th e existence of people, th ere may well be such toma toes and we

may well usefully refer to them w ith th at expression. But we may be confid ent that

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W HY THERE AR E NO PEOPLE 181

those tomatoes are not perfect ly square t r iangles , even though we refer to t h e m as

such , and tha t the re a re n o such tr i ang les anyw here . We may be jus t as conf ide n t ,

then , tha t wha tever use we a re pu t t ing i t to , ou r chosen express ion , be ing incons is -

ten t , is t ru e o f n o ex is t ing en t i t i e s a t al l. So muc h, then , fo r den ia ls o f ou r f ina l

p r e r n i ~ e . ~

We have much to discuss , how ever , a s regards o ur o th er two premises, in par-ticular, premise ( I I ) , whe re logical par i ty is c la imed f or ‘person’ and ‘nacknick’ . My

suppor t fo r th i s idea , which wi l l a f fo rd some suppor t to ou r f i r s t p remise as well,

wil l com e largely in terms of an acco unt o f ’person ’ as a vague discriminative ex -

press ion . On this account , a l l such expressions, including the invented ‘nacknick’ ,

are logical ly inconsis tent . Briefly and rough ly, we m ay provid e som e idea of these

expressions: Firs t , in tha t they are vague, these terms contrast with, say, ‘ inch’ ,

whic h, we m ay al low, precisely pu rpo rts to disc r imina te the inch f rom a l l o ther

lengths . Secon d , in th a t they a re discriminative, these te rms con t ra s t wi th th e vague

express ion ‘en ti ty’ , which does no t pur por t to disc r imina te any th ing f rom anyth ing

e lse, suppos ing th a t we may a l low th a t any th ing a t al l i s an en t i ty . And , f ina l ly , the

vagueness of these terms is essentially involved in their purported discr iminat ions.

So, they wil l contrast with ‘ent i ty which is l ess than two’ , suppos ing tha t th i s ex-

pression is ab ou t as vague as ‘en t ity ’, bu t th a t th i s vagueness doe s no t en te r in to i t s

purpo r ted d i sc r imina tion (o f some numbe rs f rom o thers ) .

I a m a b o u t to exhib i t my account , which , whi le i t is incomplete , should be

de tai led enough to ind ica te th a t i t s main l ines a re adequa te . Before I d o so, l e t m e

remark tha t I am well aware of a f law that my account of these expressions is

b o u n d to have: I f th e accou nt is r ight , then , as ‘perso n’ is incon sis tent , there are

none of us , and so n o s t a t em e n t s , a c co u n t s , o r a r g u m e n t s t h a t w e p r o d u c e o r u n d e r -

s tand . The a ccoun t impl ies a paradoxica l s i tua t ion . But th i s paradox , I shall argue,

does no t nu l li fy the account . Ra ther , i t bespeaks i t s comprehens iveness an d tha t o f“an in te l lec tua l need to begin anew.”

2. AN ACCOUNT OF SOME COMMON VAGUE EXPRESSIONS

The inconsi s tency of ‘nacknick’ may be c rude ly charac te r ized as s temming f rom th e

fo llowing tw o rough condi t iona l s ta tements :

If som ethi ng differs f rom a nack nick minute ly , t h e n it also is a nacknick (n o

m a t t e r i n w h a t w a y i t thu s differs).

I f some th ing i s a nacknick , then there a re th ings th a t d i f fe r f rom i t in certain

ways by a l o t , so m u c h so t h a t t h e y a r e n o t nacknicks.

If som eon e, n o t a philosopher , were asked to express tha t incons i stency wi tho ut

any specif ic referen ce to shape , I th ink h e would express i t , we l l enough for h i s pur -

pose , in these te rm s or t e rm s s imi la r to them. No w, if we wan t , as philosophers , to

give a general cha racter iza t ion of the inco nsis tenc y, we too shall avoid any refer-

ence to any specif ic property. But we shal l t ry to be a b i t c lea re r abou t th e o f fend-

ing d i f fe rences tha n th e obscure re ference to a w a y . According ly , th e condi t ions we

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182 PETER U N G E R

should exh ib i t will no t be th e sor t a typ ica l l ea rner would be l ike ly to ar t icu la te .

Still , in learning the express ion in ques t io n , he m ay lea rn such under ly ing condi -

tions.

I sha ll endeavor , then , to presen t two condi t iona l s ta tements tha t charac te r -

ize ‘nacknick’, as well as ma ny ordina ry vague expressions. T he terms I m e a n t o

c h a r a ct e r iz e m a y b e r eg a rd e d a s f o rm i n g a n i m p o r t a n t , b u t n o t e x h a u s t iv e , g r o u p

among the vague discr iminat ive ones: those that are (purely) qual i ta t ive expres-

sions. To ind ica te these express ions , we may d i st ingu ish , we ll enoug h f or th e pur -

pose , be tween th e qua li ta t ive o r in te rna l p roper t ies o f an en t i ty a nd , in con t ras t , i ts

ex te rna l p roper t ies , o r re la tions. Thus , we sha l l say th a t tw o b lue rec tangula r so lids

may be t he sa me as regards al l the i r qua l i t a t ive p roper ties bu t d i f fe ren t as regards

cer tain of t heir re lations, f o r examp le, as regards their spatia l re lat ions to o t h e r o b -

ject s . W hether an express ion is vague o r no t , we sha l l say tha t i t is (purely ) qual i ta-

t ive just in case i t is governed by this fol low ing con dit io n: If an ent i ty sat isf ies th e

express ion , then so too does any ent i ty which shares that sat isf ier’s qual i ta t ive

proper t ies , that is, which is qual i ta t ively ident ica l with th e sat isfier . Th us , the ex -pression ‘ perfect cu be’ , while n ot vague, is qual i ta t ive, as are a lso th e vague expres-

s ions ‘cubical object ’ and ‘nacknick’ .

Am on g vague discr iminat ive term s, t he qual i ta tive ones sat isfy this s t rong er

condi t ion : I f a n en t i ty sa ti s fies th e express ion , then so d o e s a n y e n t i t y t h a t e i th e r

(a) is quali ta t ively ident ica l to th a t sa ti s fie r or else (b ) is minute ly d i f fe ren t f rom i t.

I t is to be unders tood , as is mo s t n a tu ra l , th a t the minu te d i f fe rences a l luded to in

(b ) a re in respec t o f qua l i t a t ive p roper t ies , r a ther than re la t ions . As is eviden t f rom

ou r p rev ious reason ing , t he impo r tanr p rob lems w i th these express ions der ive f rom

(b); thus , in o u r subseq uent d i scuss ion we may in genera l sa fely igno re (a ) , and

focus on th is p rob lemat ic aspec t .

Focus ing o n (b ) , w e may presen t o ur charac te r i s t i c condi t ions as fo llows ,w i t h t h e h e l p o f s o m e t e r m s to be c lar i fi ed la te r , namely , dimensions of difference

a n d direct ions a long them, which a re here to concern on ly the in te rna l p roper t ies

of t he en t i t i e s involved, as oppose d to the i r ex te rna l relation^:^

(11 With respect t o a ny qual i ta tive vague discr iminat ive expression , ther e are

d imens ions o f d i f fe rence , wi th d i rec t ions a long them, such tha t i f some

(actual o r only possible) ent i ty sat isf ies th e expression, the n al l minute dif-

f e r e n ce s f r o m t h e e n t i t y w i t h r e s p e ct to any one of these d imens ions wil l

f ind other (ac tua l o r on ly poss ib le) en t i t i e s tha t sa t i s fy , and wi ll f ind n o

(such) en t i ty tha t does no t sa t i s fy the express ion , p rov id ing tha t such a

f o u n d e n t i t y d o e s n o t d i f f e r m o r e t h a n m i n u t e l y i n a n y o t h e r s u c h r e ga rd .(2) With respect to any qual i tat ive vague discr iminat ive expre ssion, if so me

(ac tua l o r on ly poss ib le ) en t i ty sa t i s fies i t , then a mon g the d imen s ions and

di rec t ions tha t su f f ice fo r sa t i s fac t ion under (l), t h e r e is a t l e a st o n e d i -

mens ion of d i f fe rence and a t l eas t one d i rec t ion a long i t such tha t , wi th

respect to these , the re a re (ac tua l o r on ly possib le ) en t i t i e s each of which

differs substantially f rom tha t pu ta t ive sa t i s f ie r and each of which does

no t sat isfy t h e expression.

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W HY T H E R E A R E N O P E O P L E 1 8 3

The condit ions given in these two statements , a long with such discussion as c lar i -

f i es and suppor t s them, fo rm the hear t o f my account o f vague d i sc r imina t ive ex-

press ions. Now th is accou nt would , o f course , be un in te res t ing should there be

many expressions, but none which are qual i ta t ive vague discr iminat ive ones. But

this is not so. On the c on t ra ry , p rov id ing th a t the re a re any express ions a t a ll , the re

are a s ignificant numb er of this sort, nclud ing ‘bum py’, ‘ ta l l man ’ , ‘s tone’ , and ‘per-

son’.

The second of these condi t ions , in (2), is to t h e p u r p o r t e d e f f e c t t h a t t h e s e

expressions are to discriminate their satisfiers f r o m other en t i t i e s . Th is condi t ion ,

which indicates som e objects as falling outside an expression’s range, we shall call

t h e discriminative condi t ion . The f i r s t condi t io n i s to t h e e f f e c t t h a t , s u p p o s i n g a n y

en t i ty does , va r ious ones toge ther a re to s a ti sf y t h e e x p r e s si o n , b u t n o d e f i ni t e

bound i s to be p laced o n those t o be inc luded . Thus , w e sha ll cal l th i s condi t ion t he

vagueness condi t ion fo r the express ion in ques t ion .

While b o th o f these tw o c ondi t ion s a re requ i red to g e n e r a te o u r n o t e d i n c o n -

sis tency, i t is the vagueness cond it ion over which mo st discussion is l ikely to arise.Accordingly, le t us f i rs t t ry to ge t a n idea o f i ts impor t . To d o so, w e m a y c o n t r a s t

‘bumpy’, a qual i tat ive vague discr iminat ive term , with ‘f la t’ (o r with ‘absolutely

f lat’) a nd ‘no t fla t’ , which ar e relevant ly precise . If a surface is bum py , tha t is, sat-

isfies ‘bumpy’, and is n o t j u s t n o t f l a t , t h e n , j u s t as our condi t io n d i rec ts , so too is

any sur face tha t i s no more than minute ly d i f fe ren t f rom i t , even as regards shape.

If a surface is (absolutely ) f la t , how ever , there wil l be m inutely differing surfaces,

in shape, tha t wi ll n o t be (abso lu te ly ) f l a t . They wi ll have on ly a few t iny bum ps o n

them, in some cases , bu t no t so m u c h a s to be b um py. Likewise, i f a surface is no t

(abso lu te ly ) f l a t , it will no t fol low th at a l l minutely differing surfaces are also no t

f la t . Consider a near ly f la t surface. Th ere will b e a (possible) surface who se sha pe,

whi le minu te ly d i f fe ren t f rom i t , is d i f fe ren t in jus t such a way tha t it will be flat.In tu i t ive ly , I suggest , of these expressions, only ‘bu mp y’ wou ld be regarded as a

vague te rm. T he fa c t tha t on ly i t is governed by our f i r s t condi t ion , then , he lps

show th e in tu it ive po in t o f th a t requ i rement . s

To u n d e r s ta n d b o t h o f our condi t ions , we should exp l ica te our t a lk o f dimen-

sions of dif ference, fo r tha t i s a some wha t t echn ica l express ion whose con nec t ion

with our ordinary vague thinking can not be evident . We ma y begin ou r expl ic at ion

by no t ing tha t th ings do no t jus t d i f fe r as such , bu t a lways differ in o n e o r m o r e

w a y s or respec t s . Fo r example , a heavy red s to ne d i f fe r s f rom th ings tha t a re no t

red in respect of co lor , and f rom th ings t ha t a re no t heavy in respect o f w e i g h t .

Now , wi th m any such respec ts , we ma y , to a c e r ta i n e x t e n t a t l e a s t , s p e a k c o m p a r a -

t ive ly o f h ow muc h th ings d i f fer . In respec t o f co lor , fo r example , we say tha t our

red s tone d i f fe r s m o r e f rom th ings tha t a re b lue than f rom those tha t a re purp le .

In respect of weight , i t di ffe rs mor e f rom th ings , or a t l eas t s tones , tha t a re very

l igh t than f rom those o f a mod era te or in te rmedia te weigh t . Thus , we th ink of a

dimension of color , and also a dimens ion of weight, as a dimension of difference.

All of this is qui te ordinary to th ink . What i s l e ss common, bu t I th ink s t i l l qu i te

avai lable, is t he idea tha t ma ny things vary, too , with regard to stoniness , that is ,

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In respec t o f he igh t , he re the re levan t d imens ion , two men may d i f fe r by a f oo t

a n d w e d e e m t h e o n e a taII m a n a n d t h e o t h e r n o t . F o r e x am p l e , o n e m a y b e s i x

fee t s ix , p lus o r m inus a thousan dth o f an inch , and th e o ther f ive fee t s ix , p lus o r

minus tha t . In the downward d i rec t ion , th i s d i f fe rence of a f oo t would b e re levan t -

ly subs tan t ia1 ; in l ine wi th our seco nd cond i t ion , th e man of f ive fee t s ix would , thu s ,

n o t be a t a ll man . In th e o the r , upward d i rec t ion , n o d i sc r imina t ion of the sa ti s fie r

f r o m a n y t h i n g is p u r p o r t e d , a n d so n o prob lem s a r i se . Ju s t a s a man of s ix fee t s ix

is tall, so any man of g rea te r he igh t i s a t a l l man , o r so we com mon ly bel ieve. The

subs tan t ia l d i f fe rence o f a foo t , then , means no th ing in the upward d i rec t ion : un-

l ike a man of f ive fee t s ix , a man of seven fee t s ix is ( supposed to be) a ta l l man .

This purpor ted d i scr imina t ion in the dow nwa rd d i rec t ion is e n o u g h to pro-

v ide an a rgum ent th a t tu rns o n the inconsi s tency of ‘ t a ll man’. We choose a man

somew here d own there in he igh t , fo r example , a man of f ive fee t s ix , wh o is sup-

posed no t to b e a t al l m a n . A n d , w e ca n s h o w , b y t h e c o n d i t i o n o f ( l ) , h a t h e a l s o

is a ta ll m an ( if any m an i s) . F or if the m an of s ix s ix is t a ll , then so is a ma n min-

utely less in heigh t , say, a thou san dth of an inch less , plus or minu s a small f ract ion

of that . And if he too, then a lso ano ther , whose he igh t is a b o u t a t h o u s a n d t h o f a n

inch less. And, so, by s tep s, if the re is any ta l l ma n, the n o ur ma n of f ive-six is on e

of these . But , a s we have supposed , he is not . And , whi le we might seek to avoid

th e con t rad ic t ion b y say ing tha t , con t ra ry to w h a t w e s u p p o s e d , t h e m a n o f f i v e s i x

is af te r a ll on ly a t a l l on e , th i s is n o avo idance bu t on ly a fu t i l e pos tpon emen t . F or

accord ing to o u r s e c o n d c o n d i t i o n , t h e r e m u s t b e some (actual or only possible)

m a n d o w n t h e r e w h o is n o t t al l. B ut , whomever we choose , our f i r s t condi t ion th en

forces us to d raw the oppos i te conc lus ion about h im as wel l . Thus , the purpor ted

d iscr imina t ion cann ot b e m ad e ; th e express ion is a n i n c o n si s t en t o n e .

There is a po te n t ia l source o f ambigu i ty which , whi le I d o n o t t h in k I have in-

v i ted i t , can be p laced be yond se rious ques t ion ra ther qu ick ly . I t m i g h t b e th o u g h ttha t , accord ing to our second condi t ion , so long as the d im ens ion and d i rec t ion a re

a p p r o p r i a t e , a n y substan t ia l difference from a sat isf ier wil l rake us to objec t s , ac tua l

o r o n ly p o ss ib l e, t h a t d o n o t s a t is fy . T h is w o u l d b e a n u n f o r t u n a t e i n t e r p r e t a ti o n ,

as th e fo llowing exam ple makes c lea r : If th e d i f fe rence be tween a s ix-six man and a

five-six one is subs tan t ia l , then so i s tha t be tween a m a n o f e i g ht f e e t a n d a s i x s i x

man . But , whi le th e la t t e r i s, then , a subs tan t ia l d i f fe rence , and can be tak en in the

r igh t d i rec t ion , i t doe s no t t ake us to a m a n w h o , b y c o m m o n j u d g m e n t , is no t t a l l.

B u t o u r c o n d i t i o n d o e s n o t sa y t h a t j u s t an y en t i t y tha t thus d i f fe r s f rom a sa ti s fie r

wil l no t sa t is fy th e express ion in ques t ion ; ra ther , i t impl ies on ly th a t th e re mu s t be

at least some such. In the present case, there is indeed a pleni tude of re levant pos-

sible cases . Fo r exam ple, a ll th e possible me n w ith heights less tha n f ive fee t s ix will

d i f fe r suf f ic ient ly f rom th e e igh t fo o t man . Thu s , these m en , who a re no t t a l l, wil l

allow us to d e ri ve a c o n t r a d i c t i o n fr o m t h e a s s u m p t i o n t h a t t h e e i g h t - f o o te r is a tall

m a n .

In disarming a potent ia l source of a m b i g u i ty , w e h a v e e n te r e d u p o n t h e f i n e r

po in t s o f our ac coun t . In th i s ve in, we may no t ice th e f ina l , or ‘providing’, clause of

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186 PETER U N G E R

ou r vagueness condi t ion . Now , tha t c lause may seem to m a k e m a t t e rs c o m p l e x , b u t

i t is on ly a way of p rov id ing fo r wh a t would usua l ly b e unders tood an yway. Fo r we

a re to unders tand th a t such a m inu te d i f fe rence , by i t se lf , wil l no t make t he d i f fe r -

ence be tween sa r is f ie r and nonsat is f ie r , no t tha t the p resence o f one such smal l d if -

fe rence wi l l ensure a second sa t i s f ie r , no mat te r how d i f fe ren t f rom the o r ig ina l

th a t second e n t i ty migh t o therwise be . By th e same tok en , even wi th th i s “provid-

ing” c lause , our vagueness cond i t ion can be app l ied , in s tepwise fash ion , any nu m-

ber o f t imes . Fo r whi le var ious o th er d i f fe rences may add up so tha t they a re even-

tua lly m ore th an m inute ones , even by co mmo n-sense reckoning , in any one s tep no

such large differen ce wil l ever b e enco untered .8

Because our condi t ions d o no t spec i fy o r me nt ion any par ticu la r d imens ions

of d i f fe rence , o r d i rec t ions a long the m, bu t ,on ly requ i re , fo r sa ti s fac tion , th e ex ist -

e n c e o f s o m e , w e c a n n o t s t a te our c o n d i t i o n s i n a m u t u a l l y i n d e p e n d e n t f o r m . T h u s

our re fe rence in (2) to what i s requ i red in (1). We need this to m a k e s u r e t h a t t h e

d i ffe rences added u p by repea ted app l ica t ions o f (1) are comparab le to t h o s e f o r

which (2 ) ind ica tes an oppos i te c la im, so th a t a con t rad ic t ion wi ll a ri se , suppos ingt h e r e is any sat isf ier . With ‘nacknick’ , sha pe was specif ied as relevant ; by specify-

ing i t once in eac h , independent ly speci f ied con di t ions cou ld be given fo r the te rm.

A similar s i tuat ion occurs with the ordinary vague expression ‘ ta l l man’ , where we

m a y m e n t i o n height as the d imens ion , and spec ify t he downward di rec t ion a long i t .

B u t o f t e n t i m e s , we shal l be in n o pos i t ion to prov ide such speci f ic , independent ly

specif iable condit ion s.

O u r c o n d i t i o n s m a k e r e f e r en c e to poss ib le en t i t ie s tha t may no t be ac tua l . By

th i s dev ice , we may exp la in , fo r exam ple , our ready judgme nt tha t s ix - inch men

w o u l d n o t b e t a ll m e n , e v e n s up p o s i n g t h e r e a r e n o a c t u a l m e n o f t h a t he ig h t. F o r

we a re very read y to withhold ‘ ta ll man’ f ro m such an imaginary case. Now, if such

an exp lana tory re fe rence to possible ent i t ies is avoidable , the n we may just consid-e r i t a conven ience here , fo r b rev i ty . I f , on th e o the r han d , an impl ica t ion of such

dubio us ob jec t s is requ i red , tha t sho uld me an t roub le fo r these vague express ions .

Bu t even if such a p rob lem means , a ll over aga in , th e wors t fo r these te rms , 1 shall

n o t d w el l o n t h e m a t t e r n o w . F o r t h e s a m e d i ff i c u lt y , if t h e r e is o n e , w o u l d a p p e a r

q u i t e as damaging to various expressions that are not vague: i f something sat isf ies

“ is n o t a p er fec t cube ,” th en there a re ob jec t s , ac tua l o r on ly poss ible , th a t d i f fe r

f r o m t h a t s at is fi er i n s h a p e , a n d t h a t , t h u s , d o not sa ti s fy th e express ion . In o th er

words , such prob lems a re no t pecul iar to o u r t o p i c.

L e t us t u r n n o w to discuss some of t he l imi t s o f o ur of fe red condi t ions , fo r

t h e y a r c n o t m e a n t to cover every conceivable to pic . We may begin by not i ng a

vague express ion tha t i s no t governed by our second , o r d i sc r imina t ive , condi t ion ,

n a m e l y , the expre ssion ‘par t of physical reali ty’ . N ow , rhis term is , of course, a

qual i ta t ive on e; if an ent i ty is pa r t of physical real i ty , the n so too i s any o ther qua l-

i t at ive ly jus t l ike i t . A nd , sec ond , th i s express ion is a vague o ne ; if an y th ing , i t i s

even more vague than ‘ s tone’ . At the same t ime , i t i s governed by our f i r s t , o r

vagueness , condit ion: I f an ent i ty is a par t of physical real i ty , then so too is any

o t h e r t h a t , w i t h r e s p ec t to any d imens ion of d i f fe rence , is minu te ly d i f fe ren t f rom

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W H Y T H E R E A R E N O PEOPLE 187

it . An d, third , the expression is , qui t e obviou sly, a discr iminative one: it i s no t to

apply to such a pu ta t ive abs t rac t en t i ty as the number th ree . But , the d i sc r imina-

t ions i t m a k es d o n o t a p p e a r to involve i t s vagueness, a t l eas t no t in t he o rd inary

way we have been no t ic ing . Fo r it d o e s n o t s e e m t h a t t h e r e is a n y d i m e n s i on , or

spec t rum , o f g raded d i f fe rences , where par t s o f phys ica l rea l ity a re somew here to

l eave o f f and o the r en t it i e s a re to be newly encoun te red . So, ou r expression ‘p ar t of

physical real i ty’ does n ot seem to be of th e sor t we have ca lled vague discrimina-

rive. A t t h e s a m e t im e , i t is no t governed by ou r second condi t ion .

Finally, let us look a t some l imi ts o f ou r vagueness con di t ion , and t ry to see

w h a t t h ey m a y , or m a y n o t , m e a n f o r us . T o w a r d t h i s e n d , w e n o ti c e t h e c o n t r a s t

be tween tw o k inds o f vague d i scr imina t ive express ion : those tha t a re (pure ly ) qual -

i ta t ive and those that are not . O nly th e f irs t of thes e wil l be governed by o u r vague-

ness condit ion, in ( l ) , o r t h e n o t i o n o f d i m e n si o n o f d i f f e r e n c e t h e r e e m p l o y e d

concerned on ly d i ffe rences as regards qua l i ti e s, o r in te rna l p roper t ies . Thus , fo r an

e as y e x a m p l e , t w o m e n m a y b e q u a li ta ti v el y t h e s a m e , b u t o n ly o n e m a y b e a r t h e

re la t ion to a wom an of be ing mar r ied . Thu s , on ly the o the r o f them i s a bache lor .Th e word ‘bachelor’ , then , is no t a qua l i t a t ive te rm. As s u c h , i t is no t governed by

ou r vagueness condi t ion : Scra tch th e mar r ied ma n a lone , so t h a t n o w h e i s m i n u t e -

ly d i f fe ren t f rom the bache lor as regards h is in te rna l p roper t ies . But though h e is

minute ly d i f fe ren t f rom an en t i ty tha t sa t is f ies ‘bache lor ’ , th i s mar r ied m an do es

n o t s a ti sf y t h e w o r d .

A le ss o b v io u s e x a m p l e is p ro v id e d b y J o h n T i e n ~ o n . ~e points to cer ta in

express ions fo r a r t i fac t s , fo r exam ple , ‘ t ab le to p’ and ‘door ’ . Cons ider two qual i-

ta t ively ident ical objec ts , each craf te d in diffe ren t areas by d ifferent people , qui te

i n d e p e n d e n t l y . T h e f i rs t is m e a n t t o s e rv e j u s t a s a d o o r , a n d d o e s so. T h e s e co n d is

m e a n t to serve just as a table to p, as i t does . I t seems c lea r tha t , suppos ing there a re

tab le tops , on ly one o f these is tha t . S cra tch ing one , which means a minu te d i f fe r -ence be tween them now, as regards in te rna l p roper t ies , wi ll , o f course , no t a l t e r the

si tuat ion. Upon ref lect ion, then, i t appears th a t the re wi ll b e m any vague d isc rimin-

a t ive te rms th a t a re no t qua li t at ive ones , and t ha t d o no t sat is fy the vagueness con-

d i t ion fo r our qua li ta t ive express ions . Con sequen t ly , to have a general account of

discr iminarive vagueness , we need a vagueness condit ion for these terms as well ,

a long wi th a match ing d i sc r imina t ive condi t ion . But , wha t does th i s mean fo r our

main top ic?

E v e n w i t h o u t m u c h t h o u g h t o n t h e m a t t e r , it is qu i te c lear that ‘person’ , un-

l ike ‘bachelor’ and ‘door’ , is indeed a purely qual i ta t iv e term. Perhaps som e creatu re

qualitatively identical to m e , b u t v er y f a r a w a y , m i g h t n o t b e a h u m a n b e in g s h o u l d

he lack cer tain relat ions, causal or otherwise , to a ll ( ea r th ly ) humans .” But he

would s ti ll be a person fo r a ll tha t . Cons equen t ly , as our chief interest here is in

‘person’ , and in puta t ive persons, i t is n o t m u c h to presen t purposes to provide such

mo re genera l condi t ions fo r d isc riminat ive vagueness as we now , adm i t ted ly , d o

desire.

St i l l, a suggest ion o r two seems to b e i n o r d e r , t o g iv e s o m e id e a of h o w o u r

acco unt o f vague te rms migh t be ex tended f ro m t he pure ly qua l i ta t ive ones to c o v e r

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vague discr iminat ive expressions generally . F or a s tar t , we ma y al ter our vagueness

c o n d i t i o n so th a t th e d imens ions o f d i f fe rence invo lved , and so the minu te d i f fe r -

ences wi th regard to them. wil l now concern external re lat ions as well as internal

propert ies . W ith this a l terat ion we may declare an ent i t y ob tained from an al leged

d o o r to be a doo r , shou ld th e change be a su i tab ly smal l one , such as wi ll , in fac t ,

be p rodu ced by th e n e t removal o f a per ipheral a tom. F or thi s ob ta ined ob jec t 's

relations to ot he r things will diff er only m inutely f rom those of the or iginal satis-

f ier , a ll th ings cons idered , whe th er o r n o t we regard i t as the very sam e ob jec t as

tha t o r ig ina l . Bu t w hi le we thus ach ieve some adde d exp lana tory pow er , thi s a l te ra -

t ion p rovides on ly a ra ther w eak , o r unambi t ious , vagueness condi t ion : A noth er

door , f a r away f ro m th e o r iginal , and wi th in te rna l p roper t ies on ly minu te ly d i f fe r -

en t , may well no t be declared a door . Fo r , al l things considered, th e extern al rela-

t ions o f th i s d i s tan t ob jec t may be so d i f fe r e n t f r o m t h e f i r st , i t s e em s , t h a t n o d e c -

la ra t ion concern ing i t will be available to us. To g r o u p t h e s e t w o d o o r s t o g e t h e r , a

s tronger vagueness condit ion is needed. A s u i ta b l e o n e m i g h t b e o b t a i n e d , I suggest,

if we d o no t speak of ex te rna l re la t ions genera l ly , bu t l imi t our re fe renceto

t h o s erelat ions the bear ing of which, by an object , are relevant to w h e t h e r o r n o t t h e

ob jec t is ( supposed to be) a sa ti s fie r, fo r exam ple , a do or. I f the se relevant re lations

a r e j u s t t h e s a m e o r m i n u t e l y d i f f e re n t f o r t h e t w o o b j e c ts , a n d t h e i r i n te r n a l p r o p -

e r ti es a re a l so t he sam e or m inu te ly d i f fe ren t , then they sha ll be g roup ed toge ther

as well . With these provisos, we may n ow have a sui table vagueness condit ion fo r a ll

discr iminat ive vague terms, as we have been understanding this category of expres-

sions.

F o r s u c h a n e x t e n si o n o f o u r a c c o u n t, I am inc l ined to th ink t ha t our o r ig ina l

d i sc r imina tive condi t ion will p rov e adequa te , wi th i t s re fe rence to t h e d i m e n s io n s

in th e pa i red vagueness condi t ion m atch ing th ings u p appropr ia te ly . B ut , if t ha t is

n o t q u i t e r i g h t , a s u i t ab l e m a t c h in g c o n d i t i o n s h o u l d n o t b e f a r t o s ee k . T h e s e ar em y sugges t ions , then , fo r ex tend ing m y accoun t f rom i t s p resen t exc lus ive concern

with purely qual i tar ive terms to cover vague discriminative expressions generally.

Having made them, I s ha ll n o t p u r s u e t h e m a t t e r h e r e , b u t w i ll o n l y n o t e t h a t m o s t

o f t h e r e m a r k s to be made about the qua l i t a t ive ones wi l l app ly as wel l to t h e

o thers . Hence , in wha t fo l lows , I ofte n shall spe ak indiscr iminately of vague dis-

cr iminat ive terms, in general , and those of them that are qual i ta t ive vague expres-

s ions .

3 . THE IDEA OF INCOMPLETE EXPRESSIONS

T h e m a in l in es o f o u r a c c o u n t a r e n o w b e f o r e us. O n th i s accou nt , vague d i scr imina-

t ive express ions a re incons i s ten t t e rms . Aga ins t our account , o thers may be p ro-

posed. Perhaps th e mo s t co mm on and appeal ing a l te rna t ive will be th e idea th a t

these vague te rms a re incomp le te express ions. Typical ly , a t least , this idea wil l de-

r ive f rom the thou ght th a t each of our vague express ions has borderl ine cuses, t h a t

i s , cases tha t ne i ther def in i t e l y sa t i s fy the te rm nor def in i t e l y d o n o t . T h e r e as on

for these cases , the idea wi l l then go , is tha t the vague express ion says no th ing

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Our s tatement with ‘def ini te ly’ , i t is t r u e , a t f i r s t a p p e ar s to suggest coheren t-

ly som e cases o f a th i rd logica l k ind , though th i s appear ance cannot be borne ou t . Ishould t ry to expla in th e i l lusory ap pearanc e here . Th e exp lana t ion , I think, fa l ls

in to t wo par ts : f i r s t , t a lk w i th ‘defin ite ’ can be used , coheren t ly , we may a l low, to

descr ibe ce r tain behaviora l s i tua t ions . An d , o nce th a t i s managed , the descr ip t ion

can lead to the inco heren t idea tha t , under ly ing th e described behav ior, th e re a re

logically bo rde rline cases. Let us d i sc u ss t h e f i rs t p a r t , f o r t h a t i s w h e re t h e t r o u b l e

star ts .

With regard to a typ ica l vague express ion , a norma l person will som et imes be

in a state of hes i tancy , uncer ta in ty , an d , pe rhaps , even confus ion . Wi th regard t o

cer tain (real or only imagined) objec ts , which he may cal l “bord erl ine cases,” he

will have n o def in i te disposit ion or t e n d e n c y to a p p l y t h e t e r m n o r a n y d e f i n i te

tendency to withhold i t . These ob jec t s wi ll co n t ras t wi th o thers , fo r which th e per -

son has such a t endency to a p p l y t h e term, as well as wit h s t i ll o thers , fo r which h e

has a def ini te disposi t ion to withhold the express ion . An d , these behav iora l con-

t ras t s can ho ld , n o t jus t fo r a s ing le ind iv idua l a t a m om en t , bu t fo r a soc ie ty dur -ing a long per iod of t ime . Where such a b road ly based p a t te rn o f d i spos i tions ex is t s ,

we m ay g ive a certain currency to t a lk o f “ border l ine cases .” But tha t t a lk , to re -

main coheren t , mu s t conf in e i tse lf to repor t ing upon the behav iors in ques t ion ; i t

cannot p roper ly en ta i l , to expla in the b ehav ior , s i tua t ions wher e an express ion do es

n o t a p p ly to a n o b j e c t a n d a l so d o e s n o t n o t a p p l y to i t .

Th e behav iora l con t ras t s jus t r em arked , i t may be apprec ia ted , wil l ho ld jus t

as well fo r invented inco nsis tent expressions, l ike ‘nacknick’ . A given individual wil l

be ready to apply “nacknick” to cer ta in ob jec t s , and to w i t h h o ld i t f r o m o t h e r s ,

bu t wi ll be uncer ta in ab ou t st il l a th i rd g roup . And , should th e te rm ga in cur rency ,

a mor e general behavioral pat te rn to t h e s a m e e f f e c t w o u l d d o u b t le s s en s u e . O b j ec t s

in the third gr ou p might well be regard ed, qu i te general ly , as borde rl ine cases. Solong as noth ing of muc h logica l im por t i s th us impl ied , such par lance may b e a l-

lowed . B ut , c lea r ly , no th ing much m ore tha n repor tage upon these d i spos it ions

could be coheren t ly conveyed by such ta lk o f border lines. For , c lea rly , ‘nacknick’ is

an incons i s ten t express ion , and ac tua l ly app lies to n o cases whatsoever . So i t is with

all vague discr iminative expression s, bo th inven ted and in heri ted .

Excep t in the i r re levan t behav iora l sense o f t he express ion , then , th e re can be

n o b o r d e r l i n e c as es . T h u s , t h e r e a r e n o n e to th rea ten ou r a c c o u n t ; t h e re i s n o c o m -

p e t i t i o n f o r us f rom th e idea o f vague express ions as incomple te . Fo r any incom -

pleteness will ar ise only over logical ly bord erl in e cases , an d so the suggest ion of in-

com ple te expressions i s no t a coheren t idea . Thou gh we have jus t made shor t work

o f the idea of i n c o m p l e t e e x p r es s i o n s, t h e r e w i ll b e s o m e , n o d o u b t , w h o w i ll b e

l o a t h e to par t wi th it . T h e r ea s on f o r t h e i r r e l u c t a n ce is s imple : t he idea can be

m a d e to appear very a t t rac t ive . For ou r reasonings to have maximum ef fec t he re ,

w e m u s t c o n s i de r t h e m o t i v a t i o n f r o m w h i c h s u c h a n a p p e a r a n c e c an d er iv e.

T h e m o t i v at i o n u n d e r l y in g t h e i d e a of incom ple te express ions i s due p r imar -

ily , I t h i n k , to a misplaced analogy between l inguist ic expressions and mathemati-

c a l f u n c t io n s . F o r a m a t h e m a t i c a l f u n c t i o n to yie ld a value fo r an ob jec t , tha t func-

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t ion mus t be def ined fo r , o r wi th respec t to , th a t ob jec t . Typica l ly , i t wil l be so d e -

f ined on ly if som eone , a mathemat ic ian , does someth ing , on ly if he def ines i t f o r

the ob jec t . I f no th ing is done , then th e func t ion is undef in ed for t h e o b j e c t, a n d i t

yields no par t icular value in the case. I f one thinks of a l inguis t ic expression as

yielding a posi t ive value fo r tho se objects i t appl ies to, and a nega tive one fo r those

it does no t , on e is wel l on h i s way to ward app ly ing th i s ana logy .

L i ke t h e f u n c t i o n s of mathem at ics , i t ma y then be th oug ht , an express ion wil l

y ie ld a va lue on ly in th e case o f those ob jec t s fo r which i t is def ined . And , i t will

be def ined fo r an o b jec t on ly if some people have de f i n ed the express ion fo r the

objec t . Now, th i s th ink ing con t inues , the peop le may have def ined i t positively with

regard to a ce r ta in ob jec t : in th a t case, th e va lue there wil l be pos it ive , and the ex-

pression will apply to the ob ject . Or , they m ay have def ined i t negat ively: then, the

value ther e will be negative, and t he e xpres sion will no t apply. Or, as in mathem at -

ics, they m ay no t have def ined i t with regard to th e ob jec t . In th i s l as t case , th e ex-

pression will be undefined with respec t to t h e o b j e c t, i t will yield n o value the re ,

nei ther posi t ive nor negat ive; and, so, i t will nei ther apply to t h e o b j e c t n o r n o t a p-ply to i t . Ra ther , i t wil l f ind a border l ine case in th e ob jec t , thu s be ing an incom-

ple te express ion .

A c c o r d i n g t o o n e w a y o f v i ew in g t h e m a t t e r , a m a t h e m a t i c a l f u n c t i o n t h a t is

d e f i n ed f o r c e r t ai n o b j e ct s b u t n o t f o r o t h e r s m a y b e c o m p l e t e d , so t h a t it is the n

def ined fo r those o thers as well . Ana logous ly , th e idea o f incomple te express ions

ma y be fu r ther deve loped : A vague d i sc r imina tive express ion may b e made more

precise by complet ing i ts def ini t ion. So l o n g as th e previously posi t ive cases rema in

as such , and so with th e previously negat ive ones , a com plet ion wil l be admissible .

Th us, f or a typical vague expression, the re wil l b e a grea t , perha ps an inf ini te , vari-

e ty o f admiss ib le comple t ions , non e of which v io lates th e meaning wi th which the

express ion had been endow ed. Any such c omp le t ion wil l dec ide , whe ther pos it ive -ly or negat ively, each of the expression’s borderl ine cases . And, what can deter-

mine which complet ion we f ix upon, i f ever we desire to make precise a cer tain

vague express ion , wil l be the p urposss we t hen wish i t to serve. So, the accep t -

a b l e c o m p l e t i o n w e c h o o se n e ed n o t b e a n a r b i t ra r y c h o i c e .

Th e idea o f incomple te express ions i s th us a very a t t rac t ive idea. Accord ing to

i t , our express ions a re each cons i s ten t and more : th rough the i r a lready def ined

cases , they prov ide us wi th s tab le con t ras t s , wi th an in te l lec tua l anchor . A t th e

s a m e t i m e , t h r o u gh t h e ir b o r d e r li n e c as es , th e y p r o v i d e u s w i t h t h e o p p o r t u n i t y f o r

crea’ t ive conceptual choice. But , in addi t ion to r es ti ng o n a n i n c o h e r e n t n o t i o n o f

borde rl ine cases , this appeal ing picture rests upo n a we ak or misplaced analogy be-

t w e e n m a t h e m a t ic a l f u n c t i o n s a n d t h e e x p r e s si o n s o f o u r language.

What i s i t , in the spec ia l sense in tended , fo r an express ion to b e d e f i ne d ? O f

course , it is n o t f o r i t to be def ined in th e usua l sense , where a s ta tem ent i s ma de

th a t e luc ida tes the te rm’s meaning . For,ma ny preci se t e rms , comple te ly def ined in

our spec ia l sense , have never had the i r meaning thus e luc ida ted and , on the o ther

s ide , ce r ta in vague word s have had the i r mea ning ma de to le rab ly p la in. O n th e con-

trary, what is here al luded to is simply this: the e x p r e ss i o n h as b e e n e n d o w e d w i t h

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such meaning tha t , wi th respect to some ob jec t s a t l eas t , tha t meaning de te rmines

w h e t h e r o r n o t t h e t e r m a p pl ie s to those ob jec t s. On ce we rea lize th a t th i s i s wha t

this ta lk of def ini t ion comes to, w e c a n s e e t h a t t h e i d e a o f i n c o m p l e te d e f in i t io n

a m o u n t s to nothing. For , with respect to any express ion , and any ob jec t , unless we

def ine tha t express ion wi th respec t to t h a t o b je c t , t h a t is, unless soc ie ty has endow ed

it w i t h s u c h m e a n i n g a s d e t e rm i n e s w h e t h e r o r n o t i t a p p li es t o t h e o b j e c t , t h e e x -

pression will n o t apply to the ob jec t . If we ins i st tha t th e te rm’s no t app ly ing to a n

objec t means tha t i t yields a (negat ive) value for th at ob ject , th en a (negat ive) value

wil l be yielded even i f nothing has been d on e to produc e such a resu lt . Cons ider the

expression ‘ouch’. I t has no t been def ined wi th respec t to th e E mpire S ta te Build -

ing. Yet , i t does n o t apply to tha t en t i ty . If w e ins is t tha t th i s means ‘ouch’ y ie lds a

negative value fo r the Building, then so be i t . Of course , on e migh t no t insi st tha t

‘ouch’ yields a value here. Bu t , s t i ll , i t d o e s n o t a p p l y to th e Building. So, h o w e v e r

we describe mat te r s , we cann ot coheren t ly app ly t he o f fe red ana logy .

A func t ion , then , i f no t su itab ly def ined , may y ie ld n o value wi th regard to

a cer tain object , nei th er posi t ive nor negative. Bu t , wh eth er owing to w h a t is dic-

t a t e d b y its meaning or no t , an express ion wil l app ly to a given objec t o r e lse i t wil l

n o t d o so. Unl ike th e fun c t ion , wi th i ts va lues , the re is n o f u r th e r c o u r se f o r t h e e x -

pression to t a k e .

The idea of incomplete expressions is i tself inconsis tent . I t c a n o f f e r n o g e n u-

ine a l te rna t ive to ou r acc ount o f vague express ions as incons i s ten t te rms . Le t us in -

q u i r e s o m e w h a t m o r e d e ep ly now as to t h e n a tu r e o f t h e ir i n c o n ~ i s t e n c y . ’ ~

4. VAGUEN ESS AN D GROUND LESS INCONSISTENCY

I t is easy to assume th a t an y incons i s ten t express ion resu l ts f ro m a c lash be tween

ideas each of which is i tself qui te consis tent . O u r by n ow fam il iar expression ‘per-fec t ly square t r i ang le ’ may be reckoned an example o f th i s . As s u c h , t h a t e x p r e s-

s ion may be regarded as governed by tw o qu i te p rec ise condi t ions , which may be

expressed as follows:

( I t ) f s om e (actual o r only possible) en t i ty sat isf ies th e expression ‘perfect ly

square t r iangle’ , then (s ince that putat ive sat isf ier is a per fec t ly square

ob jec t ) the sa ti s fie r has exac t ly fo ur in te r io r ang les .

( 2 t ) I f so m e (ac tua l o r on ly poss ib le ) en t i t y sa t i sf ies the expression ‘per fec t ly

square t r iangle’ , then (s ince that putat ive sat isf ier is a t r iangle) t he sat is-

f ie r has exac t ly th ree in te r io r angles.

T he c lash here is be tween th e idea of having exa ct ly f ou r such angles , which implies

h a vi ng m o r e t h a n t h r e e , a n d t h a t of having exac t ly th ree , which impl ies no t hav ing

m o r e t h a n three. We m ight say th a t th e incons i s tency in ‘per fec t ly squa re t r iang le ’

is grounded in th e c lash be tween these tw o cons i s ten t concep t ions . I t is easy to as-

sum e, then , th a t every incons i s ten t express ion mu s t b e g round ed in a t l eas t one

such c lash as tha t . On the con t ra ry , however , it is a featu re o f vague discriminat ive

te rms tha t the i r incons i s tency is n o t t h u s g r o u n d e d , b u t is relevantly groundless.

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W H Y T H E R E A R E NO PEOPLE 193

A n d , it is a virtue of o u r tw o c ondi t ion s fo r such express ions tha t they se rve to

bring ou t this groundlessness .

The differences that f igure in o u r vagueness condit ion are referred to as mi-

nute ones , and those o f our d i sc r imina t ive condi t ion as substantial in a m o u n t o r

s ize. Whatever the mea ning of ‘minu te’ an d ‘substant ia l’ , we m a y t a k e i t t h a t n o t h -

ing sa ti sf ies bo th o f these a t o nce , wh e the r the th ing in ques t ion be a s li ce o f mea t ,

a num ber , o r a d i f fe rence . Th e te rms ‘minute ’ and ‘ subs tan t ia l ’, then , purpo r t to b e

mutual ly exclusive in their appl ica t ion; i f the y have any appl icat io n, i t m u s t r e s p e ct

this condit ion. I t is in v i r tue o f th i s exc lus iv i ty th a t these te rm s might appear to

underl ie successful discr imina t ions pur por ted by o ur vague discr iminat ive expres-

s ions. But ‘min ute’ an d ‘substantia l’ are themselves discr iminat ive vague terms. So,

both o f them are incons i s ten t express ions ; ne i ther has any rea l app l ica t ion a t a l l,

thus none which is exclusive of the other’s . Even so, the incons i s tency of o ther

d i scr imina t ive vague te rms may be unde rs tood in t e rms of th e incons is tency of each

of these two express ions . A t th e same t ime , the i r own incons i stency may a l so be

unders tood in t e rm s of themse lves . While these two te rm s a re thus ra ther deep lyp laced , they prov ide n o clash be tween con s i s ten t concep t ions . Accord ing ly , th e

inconsis tencies they serve to expla in are relevant ly groundless .

What is i t , a f te r a l l, fo r o ne ob jec t to di f fe r minu te ly f rom ano ther , in a ce r-

tain respec t, fo r tha t d i f fe rence be twe en them to be a minu te one? If th a t d i f fer -

ence i s minu te , then so is a d i f fe rence , a long the same d imens ion , which i s on ly mi-

nu tely g rea te r than it . This l eads to t h e c o n c l u si o n t h a t a c e r t ai n d i f f e re n c e , d e e m e d

subs tan t ia l , and so n o t min ute , mus t be deem ed as well a min u te one . Thus , the re i s

n o minute d i f fe rence in the f i rs t p lace .

L e t us recons ider o ur parad igm nacknick an d th e ob jec t we agreed to b e so

di f fe ren t f rom i t as to b e n o t a n a c k n i c k . T h e d i f fe r e n c e b e t w e e n t h e s e t w o , w e

supposed , was a subs tan t ia l one , and so n o t a m i n u t e d i ff er e nc e . B u t a n o b j e c t t h a twas ab out a b i ll ion th o f th e way f rom th e parad igm to t h e n o n - n a c k ni c k d i f f e r e d

minute ly f rom the parad igm. I f it did , then so d i d t h e n e x t o b j e c t i n t h e c o n s i d er e d

sequence , fo r th e ex t ra b i l l ion th of t h e w a y t h u s a d d e d w ill n o t m e a n t h e d i f f e re n c e

b e t w e e n a m i n u t e d i f f e r e n c e h e r e a n d o n e t h a t is n o t . B u t , t h e n , t h e d i f fe r e n c e b e-

tween th e paradigm and th e s t il l nex t ob jec t wil l a l so be a minu te one , o n the sam e

pr inc iple . By s tepwise reasoning , we sha ll thu s conc lude tha t th e d i f fe rence be tween

th e parad igm and th e cons idered non-nack is a min u te d i f fe rence . Th is l e t s us , in

t u r n , c o n c l u d e t w o t hi ng s : f i r s t , w e m a y c o n c l u d e t h a t t h e s up p o s e d n o n - n ac k n i c k

is a lso a nacknick , which he lps sho w ho w th e quan t i t a t ive te rm ‘minute ’ under l ies

‘nacknick’ . And , second , we deduce the re la ted con t rad ic t ion : tha t the s u p p o s e d

subs tan t ia l d i f fe rence , be twe en th e parad igm and t he agreed non-nacknick , is also a

m i n u t e o n e .

In general , we may say tha t wh en ad d ing a min u te d i f fe rence to a n o t h e r , t h e

resul t i s a l a rger d i f fe rence th a t is s ti ll a minu te one . Supp ose som eone to ok excep -

t ion to t hi s g e n e r a li t y , t h i n k in g t h a t t h e r e m i g h t b e t w o big di f fe rences for minu te

o n e s , so t h a t w h e n they were added t he resu l t fa i led to b e a m i n u t e d i ff e re n ce . L e t

us consider one of these: i t is supposed to be la rge f o r a min u te d i ffe rence . L e t us

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cons ider as well a d i f fe rence , the sam e in d im ens ion and d i rec t ion , tha t i s on ly one

millionth of its mag nitude. This la t te r d ifference wil l no t be a large one , even for a

minute d i f fe rence ; it will be minu te fo r a minu te d i ffe rence . But if i t i s minu te fo r a

minute d i f fe rence , then so is one t ha t i s on ly tw o mi l l ion ths the magni tude o f th e

l ar ge m i n u t e d i f fe r e n c e, f o r t h e e x t r a m i l l i o nt h c a n n o t m e a n t h a t w e h a v e g o t t e n toa m inu te d i f fe rence o f some o ther sor t . By s tepwise reason ing , we may even tua l ly

conc lude t ha t ou r o r ig ina l minu te d i f fe rence , supposed ly la rge fo r such a d i f fe rence ,

is a l so minu t e fo r a m inu te d i f fe rence . An d , we m ay d o as much fo r th e la rge mi-

nu te d i f fe rence to which i t migh t b e added . A dding tw o such d if ferences , each of

which may thus be reckoned min ute even fo r minu te d i f fe rences , canno t , then ,

y ie ld a d i ff er en c e t h a t is n o t m i n ~ t e . ’ ~

Th e idea o f a subs tan t ia l d i f fe rence is re levan tly on a par w i th tha t o f a mi -

nu te one. If a given differen ce is substa nt ia l , then so i s one th a t is only minu te ly

less. Bu t however small we re quire a difference to b e so tha t i t f a i l to be subs tan t ia l ,

we may eventual ly reach i t . Thus , any such d i f fe rence wil l be dec la red subs tan t ia l ,

as well as n ot sub stant ia l .

Th e po in t s w e have mad e abo ut ‘m inu te ’ and ‘ subs tan t ia l ’ can a l so be mad e

ab ou t o the r pairs of s imilar terms, ab o ut ‘small’ an d ‘ large’ , fo r exam ple. Each

me mb er o f such a pa i r wi ll be a quantitative vague discr iminative express ion; on e of

them wi l l purpor t to d e n o t e t h i n g s w h o s e m a g n i t u d e is less than an y to which the

o t h e r c a n p r o pe r l y a p p l y , t h e o t h e r to d e n o t e to opp osi t e effect . Of course, a term

ma y be quan t i t a t ive in th is sense and a l so be a pure ly qua li t at ive express ion in the

sense we previously defined. In every case, I hypothesize, the inconsis tency of

vague d i sc riminat ive expressions may be u nders to od in t e rms o f some such quan t i -

t a t ive pa i r o r pa ir s . When a pa i r is su i tab le fo r such unders tand ing , we m ay ca ll i t an

underlying pair fo r the express ion in ques t ion . So, each typical vague expression h asa t l eas t o ne such u nder ly ing pa ir .

In giving my condit ions, in ( 1 ) a n d ( 2 ) , for qual i ta t ive vague terms, I e m -

ployed th e te rm ‘minute ’. Th is was a measure in th e d i rec t ion o f cau t ion . For whi le

a more co mm on wo rd l ike “smal l” appear s su i tab le to underl ie m any such expres -

s ions , fo r which o f course “min ute” wil l a lso serve , the re ma y be som e for which

only th e la t t e r t e rm wi ll p rove adequa te . I t i s wo r th no t ing , I t h i n k , t h a t w i t h m a n y

v a gu e t e r m s t h e s o r i t e s a r g u m e n t s t h a r s p el l t r o u b l e c a n b e q u i t e sh o r t . F o r e x a m p l e ,

I thi nk we regard a m an of s ix- two as ta l l , b ut on e of five-eleven as no t a ta ll man.

B u t h al f a n i n c h w i ll n o t m e a n t h e d i f fe r e n c e b e t w e e n a t a ll m a n a n d n o t . So, a n e x -

p l ic i t b u t qu i te sh or t a rgum ent wil l y ie ld n o ta l l me n a t a ll. I suggest tha t this help-

fu l shor tness is due largely to th e fac t th a t ‘ smal l’ i s enough to underl ie th e f i r s tc o n d i t i o n f o r ‘talI man’. Consequent ly , ‘minu te ’ here g ives us, with a longer argu-

m e n t , a l ux u r y o f c a u t io n .

This g roundless incons i s tency , charac te r i s t i c of vague discr iminat ive terms,

i s no t to b e c o n f l a t e d w it h t h e f a c t t h a t t h e n o t e d s t e p w is e r ea s on in g e x p o se s t h e

inconsistency of th e expressions in quest ion . To c la ri fy th is po in t , we m ay inven t

expressions whose inconsis tency is e x p o s e d i n t h a t s t ep w i se m a n n e r , b u t t h a t d o

no t have the fea tu re o f g roundless incons i s tency . In one respec t , tha t o f hav ing

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their inconsis tency grounded in precise , consis tent concepts , such expressions wil l

be l ike ‘perfect ly squa re t r iangle’ . In an oth er , th at associated with th e s tepwise rea-

sonin g, they wil l b e unl ike such an obviously inco nsis ten t expressio n, and will be

like our typical vague ter ms. B ecause of this la t ter l ikeness , such an invente d term

wou ld , unde r su i tab le c i rcumstances, p rove usefu l to ma ny norm al people . Le t me

proceed to inven t such a useful expression.

A t inkergrid, w e m i g h t s a y , is s o m e t h i n g t h a t o n e m i g h t e n d e a v o r to bui ld ou t

of the mos t typ ica l i t ems found in a t inker toy se t . These i t ems a re o f two k inds :

s t icks and wheels . N ow, the term ‘s tick’, as well as ‘wheel’ , is a vague discr iminative

o n e , a n d so i t has g roundless incons is tency . Thus , w e d o no t wa nt o u r inven ted

’ t inkergr id ’ to be def ined in t e rms of s t i cks and whee ls , fo r then th e inven ted te rm

would also have groundless inconsis tency. Let us b e t t e r s a y , t h e n , t h a t w h a t o n e

w o u l d e n d e a v o r to bui ld wi th a t inker toy se t would be , no t a t inkergr id i t se lf , bur a

physical real ization of a tinkergrid. Th e t inkergrid itself would be a mathem atical

en t i ty , comp osed of o ther m athemat ica l en t i t i e s , which a re i t s basic parts : line seg-

men ts o f u n i t l eng th , which o ne might use s t i cks to endeavor to realize , and nod es,where l ine segments can con nec t a t r ight ang les , fo r which a whee l m igh t be used .

Th e idea of a t inkergr id , then , is tha t o f a ce r ta in mathem at ica l s t ruc ture . But , o f

course , the re mig h t be no mo re possib il ity o f such a s t ruc tu re than of a s t ruc ture

tha t is a perfect ly squ are t r iangle .

N o w , to def ine the general co ncep t ion of a t inkergr id , we beg in w i th th e

more par t i cu la r idea o f a parad igm t i n keg r i d . A parad igm t inkergr id , we sha ll say ,

is in t he fo rm of a c ube , with ten-unit l ine segm ents to each of i ts twelve edges;

each edge , th en , con ta ins e leven nodes , tw o a t i t s ends and n ine in te rna l ly . Th is

t inkergr id is comp osed of a thousa nd un i t ce ll s, each in the fo rm o f a cube com -

posed of twe lve segments and e igh t nodes . Th e ce ll s a re a r ranged in such a way th a t

they d o no t over lap , bu t a re su i tab ly ad jacen t , so th a t th e w hole t inkergr id is pe r-fec t ly cons t i tu ted o f them: ten layers each wi th ten co lumns and ten rows of un i t

cells. I t should appear c lea r how, us ing th e s tandard t inker toy i t ems , one would t ry

to realize a paradigm tinkergrid. So mu ch f or parad igm t inkergr ids ; wha t o f tho se

t h a t a r e n o t p a r a di g m s?

As our def in i t ion i s to have i t , a pa rad igm t inkergr id i s bu t one s or t o f t inker -

gr id; re lated to it are o ther sorts,which are al l sui tably related to each other . We

shal l no t p ut this by mea ns of any quanti t ive vague discr iminat ive expression fo r

tha t wo uld involve ‘ tinkergrid’ in groundless inconsis tency, which w e are to avoid.

T h u s , w e d o n o t have as a second c lause o f our def in i t ion a ny such condi t iona l as

th is o ne : I f someth ing is a t inkergrid , the n any th ing t ha t d i f fe r s f rom i t by a f i t t l e

bit is a lso a t inkergr id . Ra ther , we shal l pu t ou r second c lause more su i tab ly in som e

such te rm s as these : I f someth ing is a t inkergr id , then any th in g tha t di f fe r s f rom i t

b y t h e r em ova l o r add i t i on of o n e or t w o basi c par t s is a lso a t inkergrid.

While we thus m o v e to avoid g roundless incons i s tency , we have n o t y e t en-

sured any incons is tency a t a ll f o r our inven ted te rm , bu t o n ly a ce r ta in b izar reness.

Fo r wi th ou t any fu r ther c lause in o ur def in i t ion , ou r t e rm a l lows a tinkergrid to

have n o basic par ts a t a l l. Such a “nul l r inkergrid” w ould b e a mo st pecu lia r en t i ty ,

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of cours e; s t i l l, according to the def ini t ion’s progress SO far , there they will be. B ut

insofar as null tinkergrids are claimed by o u r inven ted express ion , and no c laim i s

mad e in the oppos i te d i rec t ion , ‘ t inkergr id’ wil l be qu i t e un l ike mo s t o rd inary te rms .

To m a k e i t more l ike them , we ad d th i s l as t c lause to ou r def in i t ion : Any t inkergr id

is composed of a f in i te pos it ive num ber o f bas ic par t s. Now , ou r inven ted expres-

sion will have it tha t the re a re n o “nu ll t inkergr ids ,” an d i t wil l indeed be much

more l ike our o rd inary te rms . For , wi th th i s l as t c lause , we have ensured tha t o ur

invente d expression wil l be an incon sis tent one.

Th e inconsis tency of ‘ t inkergrid’ ma y be exh ibi te d as fol lows: Firs t , a para-

digm t inkergrid is a t inke rgrid, ind eed , one having a cer tain f ini te posit ive num ber

of basic par t s , say , N of them. B ut , then , so will be an en t i ty tha t , may be ob ta ined

f rom i t by the removal o f on e par t , which wi ll have N-1 basic parts. By stepwise

reason ing , we mus t conc lude tha t the re wi l l be a t inke igr id wi th N-N asic par ts ,

tha t i s, wi th none a t a ll . But o ur express ion a lso requ i res th a t an y t inkergrid have

som e posi tive num ber o f such par t s. Th us , th i s las t i t em, wi th n o basic par t s , bo th is

a t inkergr id and a l so is no t one .While this invented term is thus inconsis tent , I h a ve l i t tl e d o u b t t h a t i t could

be easi ly l ea rned and pu t to use by m any norm al people , in var ious su i tab le c i rcum-

s tances. In t he f i r s t p lace , few w ould no t ice tha t th e re was any incons i stency here.

Indeed , few would no t ice rh a t , wi tho u t the f ina l clause , the re would b e nu ll t inker -

gr ids . Desp i te th e te rm’s hav ing ground ed incons i s tency , mo s t peop le would ge t the

idea th a t a t inkergr id was ava i lab le on ly a t l evel s “wel l above” t ha t where no bas ic

parts remain. So l i r t le , the n, will these ideas be related to ou r expression’s meaning.

A n d , p e r h a p s m o r e i m p o r t a n t , e v en o n c e t h e i n c o n s i st e n c y is p o i n t e d o u t , a s w e d i d

here , th e p rob lem is shunted as ide .

Insofa r as I have bee n successful, ‘ t inkergrid’ , while incon sis tent , has n ot b een

defined by using an y discr iminative vague term in an essent ia l role . Accordingly, t heinconsis tency thu s genera ted is no t re levantly grou ndless ; i t i s no t l ike tha t observed

with typical vague expressions. L ike th e inconsis ten cy in ‘square t r iangle’ , the in-

consis tency in ‘ t inkergrid’ involves a c lash betw een ideas th at are each precise, con-

s i s ten t ones . Bu t o f th e t wo , on ly ‘ t inkergrid ’ has g round ed incons is tency of a sor t

th a t a l lows fo r a qu i te use fu l express ion , po ten t ia l ly , a s use ful as typ ica l vague ones .

5 . PARADIGMS IN PERSPECTIVE

W e began w i th a pu ta t ive parad igm of a nacknick , imagined o r rea l, wi th someth ing

t h a t w a s to sa ti s fy th e expression . Bu t as fu r ther im posed condi t ions de te rmined

mat te r s , th e beg inn ing ob jec t cou ld n o t poss ib ly sa ti s fy th e inven ted te rm. For , a s

t h a t e x p r e s s i o n w a s t h u s d e t e r m i n e d to be logica lly incons i s ten t , n o ob jec t a t a ll

could sat isfy i t . By par i ty o f reasoning, we have suggested tha t a logical ly s imilar

s i tu at ion h olds f or ou r ordinary vague discriminat ive expressions. Against this sug-

g e s t i o n , o n e m i g h t t r y to s t reng then th e ro le o f parad igms in t he lea rning s i tua t ions ,

n o t o n l y as regards o ur o rd inary express ions , bu t also as concerns such expl ici t ly

inven ted ones as ‘nacknick’ . The ob jec t ion to our reason ing would then proceed

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along som e such l ines as these: When I i n s t r u c t e d y o u t h a t a n y o b j e c t m i n u t el y d if -

fe r ing f rom a nacknick (as regards shape) would a l so be a nacknick , wha t yo u rea lly

accep ted , and had as a de te rminan t o f your new usefu l express ion , was no t qu i te

w h a t I ins t ruc ted you . Ins tead , i t was this ra ther s imilar sounding, but logical ly

qu i te d i f fe ren t , condi t ion : I f someth ing is (n o t jus t an y o ld nacknick , bu t ) a paru-

d igm nacknick . then any o b jec t d i f fe r ing f rom i t minute ly ( in shape) is a nacknick .

But , the ob jec t ion con t inues , th i s “parad igmat ic” condi t ion , even in con junc t ion

w i t h o t h e r l ea r ne d c o n d i t i o n s f o r t h e t e r m , c a us e s n o t r o u b l e s o m e i n c o n si s t en c y .

As th i s was t he t rue s i tua t ion even wi th ‘nacknick’ , we may b e qu i te conf iden t th a t

chis sort of th ing occurs wi th our typ ica l vague inher i ted expressions. Consequent -

ly , th e obje ct ion con clude s, they ma y b e sat isf ied by their paradigm cases , as .well

as by var ious othe r objects .”

A good dea l l a te r on , in Sec t ion 9 , 1 shal l d i scuss th e ques t ion of “what you

really go t out of my instruct ions.” An d I shal l there argue that whatever e lse you

may have go t ten , o ne th ing you go t was the vagueness condi tion , wi th no re fe rence

to paradigms, that I actual ly offered to y o u . A n d , so, 1 shal l argue, that t rouble-

some con di t ion he lped t o de te rmine ‘nacknick’ fo r you , wha tever e lse may a l so

have played such a determinin g role . I f this is so, then you r ‘nacknick’ wil l be a n

incons i s ten t express ion , s ince y o u were given o ur ot he r , discr iminat ive con dit io n

f o r i t . For once those tw o condi t ions govern a t e rm , t ha t t e rm will be an incons is -

ten t one , however m any fur ther condi t io ns may a l so govern i t. But fo r now , rea liz -

ing tha t our recen t ob jec t ion m ay poss ib ly be def ic ien t in som e such o the r respec ts

as w e have jus t in d ica ted , let us f o c u s on l y o n t h e c o n d i t i o n t h a t it claims is so read-

ily learned. Is this paradigmatic c ond it ion q ui te f ree fro m diff icult ies , and sui table

for an ob jec t ion to o u r a c c o u n t? I shal l a rgue tha t , fo r a t l eas t th ree reasons , i t i s

no t : f i r s t , it is unlikely t ha t we learn i t (unl ikelier s t il l th at w e learn i t w i t h o u t

lea rn ing the s imple r o f fe red condi t ion) ; second , i t would invo lve us in inconsis-t e n c y a n y w a y , a n d , t h i r d , sh o u l d t h e f i r s t t w o r ea s on s b e d i s c o u n t ed , t h e c o n d i t i o n

would have our apparen t ly vague te rms be p reci se and no t vague a t a ll .

Th e Ers t a rgum ent p roceeds f rom th e recogni tion th a t ‘parad igm nacknick’

wil l be just as muc h a vague discr iminat ive te rm as ‘nacknick’ i tself. S upp ose th at

we have an al leged paradigm nacknick before us . After a while , even less than a

secon d , the ob jec t loses som e a toms , genera l ly mo re than an y it m i g h t h a v e t h e n

gained. This wil l have var ious effects upon the object . As regards var ious dimen-

sions, general ly including th at of sh ape , th e object wil l be minu tely differ ent f ro m

th e way i t was. But desp i te these minu te d i f fe rences , we regard the ob jec t now be-

f o r e u s as being a paradigm nacknick. N ow , as relevant expressions with the word

‘parad igm’ will thus a l so be vague d i sc riminat ive ones , t he so r t o f condi t ion t ha t i s

to govern ‘nacknick’mus tgovern them as wel l. To den y this is to i m p o s e a n e n t ir e l y

ad h o c rest r ic t ion on th e s i tua t ion , and one which , we have jus t seen , runs coun te r

even to c o m m o n ~ e n s eu d g m e n t s . So, we mu s t n ow have th is c ondi t ion as well : if

som ething is a paradigm paradigm nacknick, h e n a n y o b j e c t t h a t d i ff e rs f r o m i t m i -

nutely ( in sha pe) is a paradigm nacknick. B u t , o f c o u r s e, m a t t e r s d o n o t r e s t h e r e ,

fo r th e expression ‘paradigm paradigm nack nick’ is a lso a vague discr iminat ive one.

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Thus, an inf ini te chain is es tabl ished. Do we learn , with ‘nacknick’, such an in f ini ty

of govern ing cond i t ions? I f ind the Suggestion qui t e incredible .

O n t h e v ie w I am advoca t ing , each of these in f in i te condi t ions does ho ld t rue .

Indeed , in each case , a S t ronger condi t ion ho lds t ru e , f rom which on e of these fo r -

m e r m a y b e d e d u c e d . F o r e x am p l e , I advoc a te th a t th i s con di t ion ho lds : I f an ob-

jec t is a paradigm nack nick , then any ob jec t th a t d i f fe r s f rom i t minu te ly ( in shape)

is also a parad igm nacknick (and so, of co urse , i t is a nacknick) . But , on my v iew, a

person , a smal l ch i ld , fo r example , can lea rn an d u nders tand on e of the condi t ions

wi thout hav ing to l earn an in f in i ty o f th em. On th e ob jec tor ’ s v iew, in f in i te ly m ore

lea rn ing mu s t be d on e by such a person .

As a n a d d e n d u m to t h i s f i rs t a r g u m e n t , w e m a y n o t e t h a t , f r o m a n i n tu i t iv e

perspec tive , th i s ob jec t ion ge t s th ings backw ard . T he o b jec t ion would have i t t h a t

ou r Understanding o f ‘nacknick’ , o r ‘ s tone’, is depen dent o n th a t o f ‘parad igm nack-

n ick’ , o r ‘parad igm s tone’ . But , in tu i t ive ly , in o rd inary s i tua t ions , the co n t ra ry

s e e m s to hold. We f i rs t learn ‘s tone’ an d only t he n und erstand longer expressions

o f w h i c h it is a par t , l ike ‘expens ive s tone’ , ‘poor example o f a s tone’ , or ‘paradigmcase of a Stone’ . Returning to ou r smal l ch i ld , we can be lieve tha t he migh t under -

s tan d ‘ s tone’ wi th ou t ye t unders tand ing a ny of these longer express ions . But he

could no t a t t ach much s ign i f icance to any of the m w i thou t f i r s t unders tand ing

‘stone’.

A s e c o n d a r g u m e n t is r ea d il y a t h a n d s h o u l d i t b e n e e d e d . N o w , f o r t h e s a k e

o f a r g u m e n t , k t us suppo se tha t , fo r all we have jus t sa id , “parad igm nacknick” and

i ts associated inf ini ty may al l be learned qui te easi ly even by t iny tots . But even

s u p p o s i n g t h i s, w e n o w h a v e to con f ron t t he p rob lem of g roundless inconsi s tency .

For i t seems tha t i f someth ing i s minu te ly d i f fe ren t f rom a parad igm nacknick ( in

shape) , the n som eth ing which i s , in th a t sam e d i rec t ion , on ly a t iny , minu te b i t

mo re d i f fe ren t , wi ll also be minute ly d i f fe ren t f rom th e parad igm nacknick . But , byreason ing fami lia r f r om th e p revious sec t ion , we sha l l then have to c o n c l u de o f a n y

shaped ob jec t t ha t i t is minu te ly d i f fe ren t f rom a paradigm nacknick . So, o n o u r

n e w p a r a d ig m a t i c c o n d i t i o n , i t m u s t b e a n a c k n i ck . B u t b y o u r d is c ri m in a ti ve c o n -

d i t ion fo r ‘nacknick’ , some such ob jec t s wil l no t b e nacknicks . So, our paradigmat-

ic condi t io n wi ll n o t p rov ide us wi th a Cons is ten t express ion .

In reply t o th i s , the ob jec t ion migh t have i t tha t a s imila r parad igmat ic condi -

t ion app lies t o our under ly ing quan t i t a t iv e vague express ions , fo r exam ple , t o ‘mi-

nu te ’ . B ut i s the re a ny p laus ib il i ty t o th e idea th a t we have a parad igm of someth in g

m i n u t e ? W h a t w o u l d t h i s p u t a t iv e p a r a d ig m b e ? B u t , p e r h a p s , t h e n , w e s h o u l d e x -

p a n d t h e q u a n t i t a t i v e e x p r e s si o n t h a t n o w is KO have a paradigm. What is i t t o b e :

‘minute ly d i f fe ren t ’ , ‘minu te ly d i f fe ren t f rom som eth ing as regards shape’ , ‘minu te-

l y d i f f e r e n t f r o m a p a ra d i g m n a c k n ic k as regards shape’; or w h a t ? T h e c h o i c e s e e m s

h o pe le s s. F o r t h e r e s ee m s n o p a r a di gm t h a t w e h a v e f o r any of these expressions.

M o r e o v e r , the express ions tha t have ‘nacknick’ as a com pon ent seem t o get ordi-

n a r y l e a rn in g t h e w r o n g w a y r o u n d , as before , whi le those t ha t lack such a comp o-

n e n t s e em too genera l to h a ve m u c h b e a r in g o n t h e case a t h a n d.

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Even i f both o f th e p revious two a rguments a re d i scoun ted , and we p r e s u m e

tha t ou r paradigmatic con dit io n is both easily learned an d also results in no incon-

s i s te n c y , t h a t c o n d i t i o n w o u l d n o t s e e m to se rve th e purposes fo r which i t was in-

t roduce d . For , a s a th i rd a rgument shows , the condi t ion would then have i t tha t

ou r apparent ly vague expressions were actual ly precise one s, and so not vague a t a ll :

We begin by remem bering , f ro m Sect ion 3 , o u r t ruism th at a given expression ei ther

applies to a ce r ta in ob jec t o r does no t app ly . Th is wil l ho ld t rue fo r ‘paradigm nack-

nick’ . Thus, this expression wil l apply to just those cases in a perfect ly def ini te

range , and to any o thers i t will no t apply . So, ‘paradigm n acknic k’ will b e a precise

express ion . By th e same reason , ‘minu tely d i f fe ren t in shape f rom a parad igm nack-

nick’ will also be a precise expression. So, both ind i rec t ly and a l so qu i te d i rec t ly ,

we may reason tha t p rec ise ly the same wil l ho ld fo r th e s imple r ‘nacknick’ i t se l f: i t

will be a p rec ise ex press ion and , as such , no t a vague one . So, cont ra ry t o a ll appear -

ances, ‘nacknick’ , as well as ‘s tone’ , will be absolu tely precise , and th us will n ot b e

vague at all . This final failure of o u r parad igmat ic condi t ion sugges t s a thought

w h o s e i m p o r t a n c e g o e s b e y o n d our in te res t in reb u t t ing ob jec t ions to o u r a c c o u n t.

The on ly way fo r o u r apparen t ly vague te rms to be vague is for t h e m to be inconsis-

ten t . Were they n o t incons i s ten t , they should have to b e precise , which they are not .

6 . SORITES ARGUMENTS, COUN TERFA CTUA L REASONING,A N D OBSCURE DIMENSIONS

Th e s tepwise reason ing we have recen t ly g one th rou gh , to exhib i t the inconsis tency

in o u r inven ted ex pressio ns, ‘nacknick’ an d ‘ t inkergrid’ , is hardly new to philosophi-

cal discussion. Su ch reasoning is ch aracter is t ic of sorites arguments, which, fol low-

ing the classical case of the alleged heap, or soros , seek to sho w tha t ce rta in en t i t i e s ,

ordinarily alleged to ex is t , in fac t do no t . In Sec t ion 2, w e e n c o u n t e r e d o n e s u c hargument , aga ins t the ex is tence o f t a l l men . Tha t a rgument , fo l lowing t rad i t ion ,

was exhi bi te d in a highly realis tic form. W ith norm al supp osi t ions in force, the in-

s tances in the sequence over which reasoning ranged were al l to b e f o u n d i n t h e a c -

tual world. The real ism was avai lable for us, we migh t say , because o f t he relevunt-

ly gradual na ture o f t he ac tua l wor ld . Th is g radua lness, and the a t tend an t rea li sm,

is in one way all to t h e g o o d : I t makes sor i tes a rgum ents hard to dismiss, if no r to

i g n o r e, b y s e r i o u s t h i n k er s w h o e n c o u n t e r t h e m . B u t i n a n o t h e r w a y , 1 th ink , a con-

cen t ra t ion o n rea li st ic examples can be un for tuna te : i t can b l ind us t o t h e c o n c e p-

tual basis of the arguments . So, to help i l luminate this basis , le t us engage in som e

suitably cou nter fact ual reasoning.16 T he appro pria te reasoning, as wil l sho rt ly ap-

pear , is more thoroughly counte r fac tua l , or h y p o t h e t i c a l , t h a n t h a t u s u al ly e n c o u n -tered in p hi losop hy, as well as in everyday thinking. I t requires us to imagine people

l iving in a world d iffer ent f rom ours wh o are themselves imagining a world diffe rent

f rom the i r s , in par t i cu la r , a wor ld jus t l ike ours. I n a w a y , t h e n , w e m i g h t t h i n k o f

th is reason ing as doubly counte r fac tua l . Bu t I c a n n o t s e e t h a t t h e e x t r a i m a g in a t i on

involved causes any ser ious diff icul ties .

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200 PETER U N G E R

S u p p o s e , t h e n , t h a t a c c o r d in g to s o m e l a w of na ture , a ll o f the men who ever

l ived , and w ho ever wi ll , were e i ther exac t ly t en fe e t in he igh t or else nine fee t , and

tha t they were aware o f the i r he igh ts . Now, let u s suppose as well that , even with

th is k nowledge , these m en ha d t he sam e express ion ‘ ta ll man’ as we now do , com-

ple te wi th t he sam e meaning ; they m ight even speak Engli sh , or a n e x a c t c o u n t e r-

par t . S uppo s ing thi s , i t w o u l d b e c o m m o n f o r t h e m to judge th a t a l l men were ta l l

m e n . A n d , s u p p o s in g t h e m to be aware o f th e law govern ing the i r he igh ts, they

would judge fu r ther tha t a l l men would a lways be ta l l men , as indeed , in a sense ,

t h e y m u s t . T h e s e m e n c o u l d imagine a m a n of f ive fee t s ix , of course , jus t as we

can imagine o ne o f s ix inches . But fo r them , such men would be on ly imaginary .

C o u l d a p h i l o s o p h e r a m o n g t h e m , w h o w a n t e d to cons t ru c t a so r i t es aga ins t

th e ex is tence o f t al l me n , deve lop a n e f fec t ive sor i t es? I t seem s clear to m e t h a t h e

c o u ld d o as well as we n ow can . I t is jus t th a t h is a rgu ments , by our p rev ious sup-

p o s i ti o n s , w o u l d b e c o n d u c t e d i n a c o u n t e r f a c t u a l m a n n e r . T h e p h i l o s o p h e r w o u l d

bid his fe l lows to cons ider a wor ld jus t l ike ours in fac t i s , where th e d i s t r ibu t ion of

ac tua l he igh ts would thus be g rea tly inc reased in numb er and a lso sh i f ted dow n-

w a r d . T h e y w o u l d a g re e t h a t a m a n o f s i x f e e t si x would still be t a ll , bu t a man of

f ive fee t s ix would not be. Our philoso pher wo uld the n have avai lable a pr inciple , in

c o u n t e r f a c t u a l f o r m , c o r r e s p o n d in g to o u r f i rs t cond it ion fo r qual ita t ive vagueness:

If a m a n o f a cer ta in he igh t would be a t a ll man , then so t o o would be a m a n w h o s e

he igh t would be n o m o r e t h a n a t h o u s a n d t h o f a n i n ch le ss . T h u s , o u r p h i l o so p h e r

c o u l d c o n c l u d e t h a t if t h e r e are any ta ll me n , th en a man of f ive fee t six would be

a ta l l man and also would not be one . S ince he n ow could reason tha t the re real ly

are no t any ta ll m en in th e f i rs t p lace , ou r ph i losopher would have cons t ruc ted an

ef fec t ive sor i t es aga ins t ta l l men , tho ugh he emplo yed counte r fac tua l reasoning in

t h e p r oc e ss . T h u s , w e h a ve s u p p o r t e d t h e i d e a t h a t a sor i tes a rgum ent aga inst t a l l

men i s essen t ia l ly a conceprua l a rg ume nt , which f i t s in so well with our a c c o u n t o fvague disc r imina t ive expressions.

J u s t as our acc oun t o f vague express ions has i t , o u r counte r fac tua l so r i t es

against ta l l me n served to indicate th at ‘ tal l ma n’ is inconsis ten t . I ts inconsis tency is

g e n e r a t e d b y our t w o c o n d i ti o n s f o r q u a l it a t iv e v a gu e t e r m s . T h e s e c o nd c o n d i t i o n

s a y s t h a t a n e x p r e s s i o n o f t h a t sort wil l purpor t to dist inguish, with respect to at

least o n e r e l e v a n t d i m e n s i o n of di f fe rence , those en t i t i e s tha t sa t is fy i t f rom those

t h a t d o n o t . T h i s c o n d i t i o n , b e in g q u i t e ge n er a l, d o e s n o t sp e ci fy or charac te r ize

t h e d i m e n s i o n s to be invo lved . I t is u p to us in a ny par t icu la r case to p ic k o u t a

r e l e va n t d i m e n s i o n , as a basis for our stepwise reasoning, or e lse to c o n d u c t t h a t

reason ing in s uch a way tha t , we can b e conf iden t , i t wi ll cover a t l eas t one such d i -

m e n s i o n . In th e case o f ‘ ta ll man’ , our u n d e r s t a n d i n g o f t h e e x p r e s si o n a ll ow s US to

b e c o n f id e n t t h a t h e i gh t is relevant. With ‘s tone’ , as a lready ind icated, n o such rele-

van t d imens ion i s ready to b e so clearly specified: Size itself is not c ruc ia l . If y o u

po ur an Al ice - in -Wonderland po t ion on a s tone , i t wi ll ge t mu ch smal ler , bu t wi ll

s t i l l be a s ton e ( i f on e before ). Perhaps , ‘size n re la t ion to s t ruc ture ’ i s more l ike i t ,

b u t I c a n n o t s a y e x a c t ly w h a t t h a t m e a n s , m u c h le ss h o w i t is to b e t r e a t e d a s a

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W HY T H E R E A R E N O P E OP LE 201

dime nsion of difference. But we may bui ld co nfiden ce, nevertheless , tha t ‘s tone’

is a logically incon sis tent expression.

T o w a r d t hi s e n d , w e m a y l o o k f o r a v a ri at io n or grada t ion in things tha t wil l

h a v e s s o c i a t e d w i t h i t a re levan t g rada t ion in a t l east o ne d imens ion tha t p lays a

discr iminat ive role with ‘s tone’ . Our actual world, with its considerable divisibility

of “mate r ia l com plexes” suggest s to us a sui table procedure. By removing a s ingle

per iphera l a tom gen tly f rom an a lleged s tone , and the n toss ing i t r andomly awa y ,

on e will progressively prod uce a se que nce of en t i t ies , going dow n to a s ingle atom ,

whose p roper t ies , wi th regard to a relevant dime nsion, will vary qui te gradual ly .

Wi th th i s p rocedure , we remain qu i te in the dark as to w h a t dimensions of differ-

ence (a re supposed to) form the basis of our term’s discr iminat ions. But whatever

ones they may b e , we can be con f iden t th a t a t l eas t on e is covered by a sequence of

en t i t i e s , man y m i l lions in num ber , ob ta ined in th is sys temat ic manner . Le t us con-

s t ruc t , then , a su i tab le sorites of d e c o m p o s i t i o n by minute removals.

By hav ing re levan t p roper t ies vary g radu a l ly wi th ou r minu te removals , na tu re

conspires to suggest to us an effect ive sor i tes against s tones, in a ra ther real is t icf o r m . F o r i t is easy to f ind accep tab le each o f these tw o condi t iona l p ropos i t ions ,

a t l eas t as t rue in fac t :

( i ) F o r a n y t h i n g t h e r e m a y b e , if i t is a s tone , then th e ne t removal f rom i t o f

a s ingle at om , in a way mo st preservative of there being a s ton e in th e s i tu-

a t ion , wi ll no t mean t he d i f fe rence as to w hether or not the re i s a t l eas t

one s tone in th e s i tua t ion .

(ii) For anyth in g there may be , if i t i s a s ton e , then it cons is t s o f mor e than a

h u n d r e d a t o m s b u t o f a f in i t e n u m b e r o f t h e m .

These tw o premises , we ma y no t ice , wil l y ie ld us a con t rad ic t ion f rom th e

rath er common-sensical asser t ion

There is a t l eas t one s tone .

For, cons ider any p lausib le cand ida te fo r s ton eho od: T ha t en t i ty wi ll cons is t o f a

f i n i t e n u m b e r o f a t o m s , s ay N , w h e r e N is g rea te r than on e hundred . T ha t is assured

US by our second premise . But , by o u r f i r s t p remise we a re to ld tha t by tak ing away

an a tom , we shal l s ti ll have a s tone , now o ne wi th N-1 a toms . Accord ing to t h a t

same premise , then , by s tepwise reason ing , we shal l have a s tone even when w hat i s

before us is on ly an ob jec t cons is t ing o f t e n a tom s , or , indeed , even when we have

n o a to ms a t a ll . But th i s con t rad ic t s wha t ( ii ) t e l ls us : as the re a re no t m ore than a

h u n d r e d a t o m s t h e r e , t h e r e is n o s t o n e i n t h e s i t u a t i o n .

N o w , it is, o f c o u r s e , n o t p a r t o f t h e m e a n i n g o f ‘ s to n e ’ t h a t a n y s t o n e s h o u l d

c o ns is t o f a t o m s , l e t a lo n e m o r e t h a n a h u n d r e d b u t s o m e f i n i te n u m b e r o f t h e m .

I n d e e d , so far as I can d i scern , i t is n o t e v e n re q u i re d b y o u r t e r m t h a t a n y p o r t i o n

of a s tone should be phys ica lly removable f ro m th e remainder . Fur ther , p rov id ing

th a t some is thus removable, and even removed , the re’s no th ing in ‘ s tone’ which

says that the rest wil l not suddenly van ish , or suddenly se rve to c o n s t i t u t e s o m e -

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202 P E TE R U N G E R

th ing u t te r ly d i f fe ren t , fo r example , an exo t ic p lan t . Tha t none of these things hap-

p e n , a n d t h a t o u r a r g u m e n t p r o c e ed in w a y o f a g r a d ua l s e q u e n c e o f s u i ta b l e e n t i -

ties is, we m ight sa y , whol ly a mat te r o f wor ld ly , con t ingen t fac t . But as p resen ted ,

our sor i t es agains t s tones migh t seem to depen d o n these suppos i t ions . Th is appear-

a n c e is eas ily d i spe l led , however . Fo r we may c omb ine the idea o f counte r fac tua l

reasoning, previously discussed, with th e system atic pro ced ure used for obsc ure di-

mens ions jus t deve loped . W i thout go ing in to mu ch derai l, we may imagine a phi los -

opher , wi th ou r sam e language , l iv ing in a very d i f fe ren t wor ld f rom ours , where h is

a lleged s ton es ca nno t b e decompo sed . Bu t , if he were imagina tive enou gh , he cou ld

contem pla te a w or ld jus t l ike ours,where s tone s can be appropr ia te ly p icked ap ar t .

If h i s wor ld con ta ined s tones , then so too w o u l d ours, he cou ld reason . Then he

could show h imse l f tha t ours w o u l d n o t a n d , t h u s , n o n e a n y w h e r e .

We a re nex t to pass to a direct discussion of ‘person’ , and of putat ive people .

Pursuing the ideas so fa r deve loped , we sha l l a rgue tha t th e express ion canoo t be

sa t i s f ied , and th a t the re rea lly a re n o such en t i t i e s as people . Before we do so , I

should n o t e b r ie f ly th a t man y ob jec t ions have been ra i sed aga ins t so r i tes a rguments ,even aga ins t w ha t migh t be regarded as the m os t rea li s ti c so r t . Whi le I t h i n k t h e r e is

l i t t l e mer i t in any of these ob jec tions , i t is n o t a m a i n p u r p o s e o f m i n e h e r e to m e e t

t h e m . To t h e e x t e n t t h a t m y p r e s e n t a c c o u n t is well a rgued , o f cou rse , tha t p ro-

v ides so me sup por t fo r so r i t es a rguments . Thus , ind i rec t ly , th e acc oun t gives a rep ly

to al l object ions to these reasonings. But I leave to other p laces the mat te r o f de-

tailed responses to part icu lar object ions.”

To give you an idea , however , o f w ha t o ne m us t accep t if one is to reject

sor i tes a rguments , I s ha ll ju s t m e n t i o n t w o p o i n t s t h a t I discuss elsewhere.’* F irst,

to re jec t o ur sor i t es aga ins t s tones , we mus t accep t th i s: the re wi ll b e ce r ta in s tones ,

c o m p o s e d o f m a n y b il li on s o f a t o m s , w h o s e c o n t i n u e d e x i s t e n c e, w i t h n o a t o m s re -

placed , req uires every s ingle on e of these bi l lions! Ca n you bel ieve tha t ther e areever any s tones whose essence is as re f ined an d tenuou s as th a t? A s e c o n d t h o u g h t ,

o n r h e s i d e o f l a ng u ag e , m i r r or s t h e f i r s t : C o n s id e r t h e s e n t e n c e , “ T h e r e is a s t o n e

b e f o r e m e n o w , ” a n d d i s c o u n t a ll p r o b l e m s o f v a gu e ne ss e x c e p t t h o s e m o s t d i re c t -

ly concer ned w i th ‘ stone’ . Wi th a p romis ing candida te fo r s toneho od before you ,

imagine per ipheral a tom s ex t rac ted in ‘ th e s ty le of ou r sori tes . We are to evaluate

t h e s e n t e n c e a f t e r e a c h n e t r e m o va l. W e s u p p o s e t h e s e n t e n c e a t f i r s t to express a

g e n u i n e s t a t e m e n t t h a t i s t r u e . B u t c a n a s ing le a t om ic removal a l t e r the p rope r

eva lua t ion? To s u p p o s e i t c a n r e q u ir e s u s to s u p p o s e a n e n o r m o u s s en s it iv it y o n t h e

par t o f ou r wo rd ‘ stone’ . Th is , I suggest , is q ui t e incredible .

7 . THE INCONSISTENCY OF ‘PERSON’

I t is n o w t i m e to e x t e n d t h e r e su lt s so f a r o b t a i n e d to th e key express ion ‘person’ .

I shal l argue t ha t chis term is a qual i ta t ive vague discr iminat ive ter m an d, as such, i t

is incons i s ten t . Accord ing ly , as no th ing then Sa ti sf ies the express ion , anym ore tha n

any thin g sat isf ies ‘perfectly squ are tr iangle’ , ther e are no peo ple . Lik e perfec t ly

squ are t r iangles , peop le are logical ly impossible ent i t ie s .

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W HY T H E R E A R E NO PEOPLE 203

Shou ld w e a r r ive a t such a nega tive resu lt fo r people , a paradoxica l s i tua t ion

wil l ar ise . Brief ly , if the re is no t an yb od y, then the re is n o on e to unders tand these

a lleged acco unts , a rguments , an d conc lus ions to t h a t e f f e c t. So, perhaps , these last

may themselves be negated or dismissed as “self-defeat ing.” But , i f our account is

o therwise unobjec t ionab le , we may then employ i t aga in , to com ple te a paradoxi-

cal c ircle and begin a ne w one. Now , in the sect ion direct ly KO fo l low th i s one , I

shal l a rgue tha t th is adm i t ted p aradox can not se r ious ly nu l l ify ou r n ih il i st i c account .

But , f i r s t , in th i s p resen t sec tion , I shal l a rgue tha t th e paradoxica l s i tua t ion cannot

be avoided. I shal l a rgue , tha t i s, th a t o ur ac cou nt o f vague express ions Cannot be

b r o u g h t to res t a t som e rela tively unp rob lemat ic s to pp ing p o in t .

T he expre ssion ‘person’ is a vague discriminat ive term and , as suc h, an incon-

s i s ten t express ion . T o Support th i s thou ght , su i tab le sor i t es a rguments sha ll be

sought . Now, as with ‘s tone’ , 1 have no very good idea how to specify adequately

those dimensions of difference with respect to which ‘person’ purpor t s to m a k e

discriminations. I t is n o t t h a t I have no th ing a t a ll to say on the mat te r : Perhaps ,

pow er o f thoug ht , o r in te ll igence, p rov ides on e such d ime ns ion ; perhaps Capaci ty

for var ied feelings and exp erience s provides one. B ut I should p re fe r t o regard th ese

proposals as primarily illustrative, and to cons t ruc t our Sor i tes a rguments on the

basis of ideas in which 1 have m ore conf idence . To war d th is en d , we reca ll ou r ex-

per ience w i th ‘ s tone’ , fo r we had success the re by adop t ing a p roced ure tha t re-

qu i red n o speci f ica tion of dimensions. So, l e t us look fo r a sor i t es o f decompos i -

t ion by minute removals that wil l work well for ‘person’ . We may best begin in a

modera te ly real is ti c ve in. Then we can m ove ro th e u t te r ly fan tas t ic , so t h a t t h e

conce p tua l na tu re o f th e a rgumenrs may b e mor e c lear ly perce ived .

I n o u r c o m m o n t h i n k i n g o n t h e m a t t e r , t h o u g h t h i s w a s n o t a l w ay s so, i t is

supposed tha t the re a re some people , i f no t a l l , who a re composed of many ce l l s ,

though of a f in i te number . W e dist inguish, of course, between a person and hisb o d y . B u t , t h e n , w hi le w e t h i n k t h e b o d y to be of a ce r ta in weigh t , and to b e c o m -

posed of such cel ls , we also th ink the person h imse l f t o b e . N o w , s o m e p e o p l e, I

s u p p o s e , d o n o t g o a l o n g w i th t hi s id e a a n d t h i n k t h a t , w h a t e v e r m i g h t b e t r u e o f

the bod y , th e person h imse l f never consi s ts o f any ce ll s, o r o f any o the r spat ia l ly

extended things. But even these people , I imagine, wil l agree that , in the case of

m a n y p e o p l e , e a c h o f w h o m h a s a b o d y , t h e r e is a cer tain close association, o r in-

t imate re la t ion , whatever i t s speci f ic charac te r , be tween each of these people and

his or her respec tive bod y . (T ha t in t imate re la t ion , fo r a ll I am say ing , might be

tha t o f iden t i ty . ) A nd , no d oub t , they wil l a l so agree tha t the re is a c lose re la t ion ,

perhaps ano ther one , be tw een each of these peop le an d those ce ll s se rv ing KO c o m -

pose his or h e r b o d y . So, all of us m ay agree th a t i f the re a re any peop le a t a l l,then som e of them , a t least, are in a c lose association with cer tain cel ls , or with

cer ta in g roups o r complexes o f ce ll s, and th a t each such su i tab le g roup , whi le con-

ta in ing mo re th an ten ce ll s, has on ly a f in i te num ber o f ce l ls in i t .

Now, I t h i n k t h a t a n o t h e r t h i n g w e a g re e o n is this : t ha t if ther e is a person in

a s i tua t ion , and tha t pe rson is in some such a foresa id c lose re la t ion wi th a ce r ta in

grou p of ce l l s, th en , if on ly one ce l l is r emoved f rom th e g roup , and th i s is d o n e i n a

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204 P E T E R UNGER

way most conducive to there being a person in such a close relat ion with the re-

main ing ce l ls , then there wil l b e a person in th e s i tua t ion a f te r the removal . In ce r -

ta in ins tances , o f co urse , th i s way will have to i n c lu d e t h e i m p o r t a t i o n i n t o t h e sit-

ua t ion of ce r ta in l i f e -suppor t appara tus , and of ce r ta in it ems fo r suppo r t ing con-

sc iousness . F or m at te r s w i th peo ple seem more com plex than wi th s tones , however

unreal a l l of these may eventual ly prove to be . We may say , then , tha t wha tevers u b s t an c e s o r p r o p e r t ie s a r e supported by som e ce l ls , so tha t a person i s the re in

close a ssociat io n, the y wil l a lso be suppo rted , and in suff ic ien t degree, with only

on e cel l less , providing, of cou rse, that t he lesser comp lex is so chosen , and so al-

l o w e d to f u n c t i o n , t h a t i t c a n d o a s g o o d a j o b a t su c h s u p p o r t i n g as is p os s ib le for

a g ro up ob ta ined by such a s l igh t removal. Of course , in th e cases to be cons idered ,

t h e i m p o r t e d m a t e r i a l d o e s not replace cel ls ; ra ther l ike a kidney machine, it j u s t

he lps ce l ls , and wh at the y se rve to c o n s t i t u t e , to f u n c t i o n .

These shared su ppos i t ion s y ie ld a sorites a r g u m e n t to t h e e f f e c t t h a t t h e r e a r e

n o peop le a t a ll . Fo r , if any person is c losely associated with a cer tain gro up of

cells, say, N i n n u m b e r , so will one be there wi th a g rou p of N -1 cells. I s u p p o s e

tha t , a s mat te r s p rogress, w e shal l ge t do wn to a brain, in a vat , then half a brain,

then a th i rd , and then a s ix teen th . In each case , we mus t say , the re i s a person in

t h e s i t u a t i o n , o n e w h o is in a special close association with the remaining cells.

Eventua l ly , the re a re bu t th ree l iving ce ll s in some so r t of c o m b i n a t i o n , a nd i t m u s t

be said th a t th e re i s a p e r s o n t h e r e. B u t w e h a ve a l s o a gr ee d t h a t , w i t h n o m o r e t h a n

ten ce ll s, the re wil l be n o such assoc ia ted person. Thu s , suppos ing there to be a per-

s o n a t r h e s t a r t , t h e r e b o t h is a n d i s n o t a p e r s o n in c l o se a s s o c ia t i on w it h o u r t h r e e

cells. Of cou rse, this argues th at the re never are any peop le in close association with

any groups of cel ls . So, f ina l ly , we ma y con c lude , the re real ly a re no t a ny people

a t a l l.

Wi th an appropr ia te ly rea li st ic a rgum ent before us, t is n o w t i m e to reasonc o u n t e r f a c t u a l l y , so as to see the concep tua l bas i s of t h e i d e a t h a t t h e r e a r e n o

people . L e t us imagine a wor ld in which there a re en t i t i e s tha t we should cons ider

persons , and th a t cons ider themse lves as such . We sha l l suppo se tha t these pu ta t ive

people have a l anguage jus t l ike ours . They a re a b i t m or e in te l l igen t than we , bu t

the i r powers o f imagina t ion fa r exceed ou r own. The i r g rea tes t d i ffe rences f ro m us,

however , a re these : un l ike us, hese people have n o phys ica l ex i s tence ; they have n o

bodies nor a re they in any very c lose re la t ion wi th a ny phys ica l phenomena . Fur -

t h e r , a s a m a t t e r of imagined fa ct , they are nei ther divis ible , dimin ishable , nor even

suscep t ib le o f any m ajor change . Each of them has a lways ex is ted and a lways wil l

ex i s t , and a lways is a t o r n e a r r h e pe a k of his sensibi li t ies an d powers . So, these be-

ings are , I s u p p o s e , q u i t e as som e ph i losophers have supp osed ourse lves real ly to be.F i n a l ly , l e t u s s u p p o s e t h a t t h e r e a r e n o o t h e r s e n t i e n t b e in g s i n t h i s w o r ld .

Cons ider a c r i t ica l ph i losopher among them. H ow m ight he convince h imse lf

tha t his term ‘person’ , whic h is the same as our expression, is a logical ly inconsis-

t e n t t e r m ? N o w , h e h a s n o r e l ev a nt g r a d a ti o n s in r e a li ty to he lp h im base a sor i t es

a r g u m e n t . A n d , w e s u p p o s e , i t is not c lea r to h i m e i t h e r h o w to spec ify th e d imen-

s ions o f d i f fe rence wi th respec t to which ‘person’ purports to discr iminate . Now,

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W H Y T H E R E A R E N O PEOPLE 205

wha t th i s reasoner should d o is t ry to supply h imse l f wi th a sequence o f imagined

enti t ies that differed gradual ly with regards to a t leas t one such re levan t d imens ion .

Whi le by our poor s tandards it would take a g rea t fea t o f imagina t ion , how be t te r

f o r h i m to d o t hi s t h a n to imagine a world J u s t l ike ours is (supposed to be) in fac t?

In th i s w or ld , thus imagined by h im , whatever fea tu res were re levan t would b e sup-por ted by bra ins , each of which was compo sed of billions of cells.

Our phi losopher , in p ar t i cu la r , migh t imagine som eon e exac t ly l ike you your -

self ; l iving, kicking, breathing, and thinking, i f anyone ever does, in just such a

wor ld as you now f ind yourse l f to be. He would th in k to himsel f , we m ay suppose ,

f i rs t , that i f a n y o n e is a person , then th i s be ing l ike you would be a p e r s o n , f o r t h a t

is our same wo rd , ‘person’, th a t i s f igur ing in h is p remis ing . What more w ould th a t

f ree sp i r it endeavor t o th ink? Well , we might imagine , he cou ld say t o himse lf th a t ,

under the total c ircumstances imagined, i f there is indeed a person just l ike you,

then.so to o wil l the re by a perso n w hen a s ingle cel l is rem oved, mo st conducively

f o r t h e c o n t i n u e d s u p p o r t o f a p e r s o n , f r o m t h o s e t h a t m a y h av e s u p p o r t e d t h e

or ig ina l cand ida te . Far be t te r than we can d o , he cou ld imagine in de tai l the impo r -

ta t ion o f tho se l i f e sup por t an d consc io usness suppo r t sys tems invo lved in a mo s t

c o n d u c iv e w a y , so as to establ ish a su i table sequ ence of ent i t ies . Of course , he can

imagine th i s whi le s ta r t ing , no t on ly wi th an imagined counte rpa r t o f you , bu t wi th

t h a t of any of a g r e a t v a ri et y o f t h e p u t a ti v e p e o p l e w e s u p p o s e t o p o p u l a t e o u r

wor ld . For our wor ld , in genera l, he cou ld th en premise tha t a s ing le ce ll r emoved ,

in such a c i rcumstance and ma nner , wil l never mean th e d i f fe rence be tween a t leas t

one person be ing in th e S itua tion and there be ing none . For he cou ld reason tha t , in

such a w or ld , n o on e ce ll wil l mean a d i f fe rence , on t he d imens ions in ques t ion , to

which ‘person’ is sensit ive. F urth er , ou r thin ker could say tha t , in this world, wh en

there were n o mo re th an ten ce ll s in a re levan t g ro up or c o m p l e x , t h e n t h e r e would

b e n o person in the s i tua t ion . Fro m these p remises , by fami l ia r s tepwise reason ing,

our ph i l sopher wo uld now conc lude tha t i f a be ing l ike yourse lf w ould be a person ,

t h e n , w i t h t e n c ells s u p p o r t i n g a t t h e i r b e s t a n d u t m o s t , t h e r e both would be a p e r -

so n in close association and also would not b e . T h u s , h e s h o u l d c o n cl u d e t h a t t h e

being f i rs t imagined, the on e just l ike y ou yours elf , was never an y person in the

f irs t place. A nd , f inal ly , by his very f i rs t premise, he could no w reason tha t there

w e r e n o t , or are no t , any people a t a ll . Thus , w i thou t any real ity to h e l p h i m , o u r

imagined ph i losopher cou ld see fo r himse l f th a t the re co u ld never be any peop le ,

even while having n o clear idea how to speci fy wh at d imens ions o f d i f fe rence se rved

to de te rm ine t he impossib il i ty thus perce ived .

I have made my imagined ph i losopher a mos t p r i s t ine soul , a be ing whose“na ture in i t se l f” would seem immune to sor i tes a rguments . Moreover , if he ap pre-

c ia ted h is n a tu re , th a t awareness would d o no th ing to suggest our word ‘person’ .

B u t so long as this being does share o u r express ion , he m ay reason to expose i t s

incons is tency and , thus , i ts l ack o f app l ica t ion . To m a k e t h e s e p o i n ts , I m a d e m y

imagined phi lo sophe r as descr ibed.

There i s ano ther reason , too, for my giving this being such a logical ly unob-

jec t ionab le na ture . Fo r ph ilosophers have som et imes sugges ted th a t o u r o w n n a t u r e s

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206 P E T E R U N G E R

are much as I have s t ipulated his to be a nd , wha t is pe rhaps mo re in te res t ing here ,

even t ha t ou r term ‘person’ analyt ical ly requires such a natur e for i ts appl icat ion.

N o w , l e t us s u p p o s e t h a t a n y b e in g w i th s u c h a n a r u r e a s t h a t c a n n o t b e d i m e n s io n -

a lly co mpa red wi th , or re la ted to , an y o th er be ing . Wi th these suppos i t ions in fo rce ,

we may advance , fo r ‘person’ , a c o n d i t i o n o f incomparab i l i t y :

(3 p) I f an ent i ty sat isfies ‘person’ , then there is no dimens ion of d i f fe rence

such th a t wi th regard t o i t the re a re en t i t i e s which d i f fe r f rom t ha t pu-

tat ive sat isfier .

Accord ing to th i s condi t ion , the re wi ll b e n o en t i t i e s th a t th us d i f fe r minu te ly , o r

substant ia l ly , f rom a sat isf ier . So, one m ight well th ink th a t were such a condi t ion

to hold fo r ‘person’ , b u t perhaps no t f o r ‘ s tone’, then , un l ike ‘ s tone’ , ‘person’ migh t

be a perfect ly con sis te nt term af te r al l.19

But th i s suppos i t ion o f cons is tency fo r ‘person’ would b e much mis taken . F or

as our sor i t es a rguments ind ica te , ‘person’ is a vague discr iminative expre ssion and ,

whatever e l se may be t ru e o f i t , the te rm i s governed by (1 ) a n d (2), o u r d i m e n s io n -

a l condi t ions of vagueness and of discr iminat iveness . So l o n g a s th e s e c o n d i t i o n s d o

govern i t , which we have seen no good reason to den y , th e express ion wil l be incon-

s i s ten t . Whatever fu r th er co ndi t ions may govern i t as wel l canno t e rase the t wo f or

w h ic h w e h a ve a r g u e d o r , t h e n , t h e c o n t r a d ic t i o n s t h a t t h e y s er v e to genera te . Th is

incomparab i l i ty cond i t ion , i f the re be o ne govern ing ‘person’ , wil l no t m ake mat te r s

be t te r fo r the te rm. On the con t ra ry , i t wi l l se rve on ly to c o m p o u n d t h e t e r m ’ s

t r o u b le s . F o r t a k e n t o g e t h e r w i t h e i t he r o f o u r p r i o r two condi t io ns fo r ‘person’,

the incom parab i l i ty condi t ion , (3p ) , y ie lds a con t rad ic t ion f rom t he supp os i t ion

tha t any en t i ty sa t i s f ies the te rm. For, by e i ther of t h e p r i o r t w o , if t h e r e is a per-

s o n , t h e n t h e r e are e n t i t i e s t h a t d i f fe r dimensionally f rom any sa t i sf ier . And , b y our

new condi t ion , if th e re is a person , then there a re n o such ent i t ies . Henc e, if the re isa person , the n there bo th a re and a l so a re no t such d imens iona lly d i ffe ring en t it i e s ,

which i s absurd . Hence , by (1 ) a n d ( 3 ~ ) . nd a l so by ( 2 ) a n d ( 3 p ) , t h e r e a r e n o

people . Supp os ing an incomp arab i l i ty condi t ion f o r ‘person’ , we sh ould say , no t

t h a t i t is a c o n s i s te n t t e r m , b u t , on h e c o n t r a r y , t h a t “ p e r s o n ” is inconsis tent fr om

mult iple sources.

T h e i n c o n s is t e n c y o f ‘ p er so n ’ m e a n s t h a t n o p e o p l e e x i s t ; t h e y c a n e x i s t n o

mo re than can per fec t ly squ are t ri ang les . Do I e x i s t , t h e n , b u t a m no person a f te r

a l l? Things would seem o therwise : If I ex is t , then there i s a t leas t one person . So,

as there a re none , the re i s no me. Th is resu l t , pa radoxica l to say the leas t , can be

obta ined as well by sor i tes a rgum ents where there i s a purpo r ted d i rec t re fe rence to

m y s e l f , b y m e a n s , f o r e x a m p l e , o f s u c h t e r m s a s ‘I1, ‘Peter Unger’, and so o n . T h emost imaginat ive of our c o u n t e rf a c t u al s o r i t e s a r g u m e n t s m i g h t b e o u t o f p l ac e

wi th these te rms , o r a t leas t migh t have a ra ther d i f fe ren t bearing o n the i s sues . O ur

mo re real is t ic versions, how ever , will have obviously close paral le l argumen ts . Tak e

away o ne per iphera l cel l f rom P e te r Unger, wi th su i tab le l i f es up po r t sys tems in

p l a c e , a n d t h a t w ill n o t m e a n t h e d i f fe r e n c e b e t w e e n U n g er a n d n o U n ge r . B u t ,

with ten cel ls ther e is n o Unger . So, the re never was tha t Unger.

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W H Y T H E R E A R E NO PEOPLE 207

The ana lys i s o f , or the accou nt o f , even th e m os t rea li s ti c a rguments wi th

such s ingu lar t e rms wil l r equ i re , o f course , th e p resen ta t ion o f cond i t ions tha t logi -

cal ly govern th e key s ingu la r express ions . No do ub t , these condi t ions wil l be impor -

t a n d y a n a l o g o u s to those given here fo r qual i ta t ive vague ter ms ; perhaps o ur sug-

gest ions fo r such terms as ‘doo r’ wil l be of some help. Bu t these analyt ical qu est ions

t a k e us b e y o n d our top ic .

M o r e to the p resen t po in t , ‘pe rson’ is hardly the only qual i ta t ive vague ex-

press ion whose incons is tency mean s much d i f f icu l ty fo r us here. For examp le , the

express ion ‘en t i ty wi th a capac i ty fo r thought ’ m eans s imi la r t roub les fo r us, h o w -

ever th a t express ion may re la te to ‘ pe rs on ’. F o r t h e a r g u m e n t s t h a t p o i n t u p t h e i n-

consis tency in ‘person’ wil l d o as mu ch f or this longer expression. Moreover , as this

express ion i s o f th e pure ly qua li t at ive so r t , even th e suppor t ing accoun t o f the a rgu-

ments wil l b e a long th e sam e fami lia r l ines . Thus , fo r qu i te fami l ia r reasons , i t m a y

b e c o n c l u d e d t h a t t h e r e a r e n o e n t i t ie s w i th a c a p a c i t y f o r t h o u g h t . As w i t h t h o u g h t ,

n o capaci ty fo r exper ience cou ld be ours, nor fo r fee ling , nor fo r any th ing of im-

por tance . As regards each of these negat ive ma tters , we have, paradoxically eno ugh ,n o t o n l y a d e q u a t e a r g u m e n t s , b u t a c c o u n t s o f h o w t h o s e a r g u m e n t s w o r k a d e q u a t e-

ly . F or th e k ey expressions involved are , in each case, vague discr iminative terms of

the purely qual i tat ive sor t .

8. THE INABILITY OF PARADOX TO NULLIFY THIS ACCOUNT

Paradox , a l ready ind ica ted , can easi ly be m ade m ani fes t : i f the re a re no be ings wi th

a n y c a p a c i t y f o r t h o u g h t , t h e n n o a r g u m e n t o r s t a t e m e n t c a n b e u n d e r s t o o d , or ac-

cep ted a t a l l , and so n o n e to t h e e f f e ct t h a t t h e r e a r e n o s u c h b e in gs . So i t s e e m s

that we are dr iven back logical ly to the asser t ion o f o ur ex i s tence , o f th e ex is tence

of be ings th a t can th in k . Thus , the re is nex t the impl ica t ion th a t o ur express ions‘person’ and ‘ think ing be ing’ d o indeed app ly . And so, f ina l ly , we have th e impl ica -

t ion t ha t these te rms a re logica lly cons i s ten t ones. B ut th ings do no t rea lly s top

here , e i the r . Fo r , a long l ines tha t a re by now fami l ia r , we may in tu rn reduce these

asserrions to absurd i ty . Th us , the i r nega t ions ob ta in , inc luding th e p ropos i t ion tha t

there a re n o be ings wi th an y capac i ty fo r thought . T he reason ing goes a roun d and

around . What a re we to ma ke o f this para doxic al s i tuat io n? Sho uld w e ho ld OnKO

common sense robus t ly and say tha t the on ly genuine e r ro rs a re in our a c c o u n t o f

vagueness and in i t s connec t ing sor i tes a rguments? Fo l lowing th i s course , we m i g h t

be t te r t ry to be comfor tab le . Fo r then though ts of absurd i ty wil l be harder to keep

in mind . But perhaps , “so to uy to say ,” paradox does l i t t l e t o null i fy the basic

p o i n t a n d v a lu e o f o u r radica l accoun t and a rgum ents .

In avai lable terms, fo r Want of an y bet ter , I h a ve a rg u ed t h a t m a n y o f o u r

co mm on expressions are logically incons is tent terms, includin g such ke y expres-

s ions as ‘person’ and ‘ent i ty with a Capaci ty for thoug ht’ . Much of m y a r g u m e n t

began wi th th e inv enti on o f a ter m , ‘nacknick’, fo r wh ich inCOnSiStent inStrUCtiOnS

were given in i ts very intro duc t ion . The n, as ou r sor i tes argum ents progressively in-

dica ted, there appea red n o logical ly relevant differen ce betw een ‘nacknick’ and

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208 P E T E R U N G E R

such co mm on ex pressio ns as ‘s tone’ and even ‘person’. To b e s u r e , t h e l a t te r t e r m s

are n o t l ea rned f rom any exp lic it ins t ruc t ions a t a ll . But the re is still a parity of in-

cons i s tency , o r a t l eas t a very s t rong sugges tion of i t , th a t suppor t s my a ccoun t of

th e o rdinary ter ms as logical ly inconsis tent . D espi te wha tever parado xes our ac-

co un t may engender , the n , how can th i s apparen t par i ty be ra t iona lly den ied?

To deny th e shared incons i s tency , one c annot ra tional ly rely on p o in t ing to

p a r a d o x . For, l e t us cons ider t he impl ica t ions o f o ur l essons wi th ‘nacknick’ . Now ,

as th i s t e rm c oncerns on ly the shape of ob jec t s , i t is idle to s u p p o s e t h a t i t m i g h t

y ie ld the sorr of para dox th at an expression l ike ‘ thinking being’ was recent ly o b-

served to do . W hat is less idle, however, is to imagine th a t incons i s ten t ins t ruc t ions

w e r e , a t a s u i t a b l e p o i n t, imposed upon th e lea rn ing o f such te rms as ‘person’ and

‘thinking being’ . Let us imagine, then, a society much l ike ours , with this excep-

t i o n : After normal early learning bad occurred, expl ic i t incons i s ten t ins t ruc t ions

were given to the modera te ly young . Thus , ch i ld ren would hear words l ike th i se :

“Typical vague w ords t ha t yo u have learn ed, l ike ‘s tone’ an d ‘person’ , wil l now be

more clear ly revealed to y o u . To begin w i th , each of you should k now t ha t each ofthese word s se rves to disc r imina te , o r d i s t ingu ish , d i f fe ren t so r t s o f th ings . So, t h e

word ‘ s tone’ d i st ingu ishes be tween t he s ton es and e very th ing e lse , which d i f fe r so

f r o m s t o n e s t h a t t h e y d o n o t f i t t h e m e a n i n g o f t h e w o r d . O f c o u r s e , t hi s w o rd i s a

v a gu e o n e , a n d y o u s h o u l d k n o w t hi s a b o u t it too: i f someth ing is a s tone , and so

f i t s the word ‘ s tone’ p roper ly , then any th ing tha t d i ffe rs f ro m i t only a l i t t le bi t will

a l so f i t the w ord , th a t i s , wil l a l so be a s tone . To be sure , the re i s no def in i te l imi t as

to h o w m u c h s o m e t h in g m a y d i f f er f r o m a s t o n e a n d f o r i t y e t to be a s tone . Al l o f

t h i s , y o u a r e to unders tand , i s pa r t o f wha t i t is f o r t h e w o r d ‘ st o ne ’ to be a vague

word while s t i l l a l lowing us to ma ke usefu l d i sc r imina t ions wi th i t . An d , o f course ,

these points apply just as well to o t h e r t y p i ca l v a g ue w o r d s , f o r e x a m p l e , to such

w ord s as ‘house’, ‘person’, ‘red’, ‘soft’, ‘tall’, ‘runn ing’, ‘thinking’, an d so o n . N o w ,non e of th i s should com e as a surpri se to a n y o f y o u ; in f a c t , i n a w a y , y o u h a v e

k n o w n i t a l ready . But i t i s jus t as well f o r us to be exp l ic i t ab ou t these th ings , fo r us

to h a ve t h e m o u t in t h e o p en . ”

What resul ts would such instruct ions have i f they were of ten involved in

teach ing rou t ines? As th e people in th i s soc ie ty a re to be mu ch l ike ourse lves, i t

m u s t b e s u p p o s e d t h a t t h e y w ill m a s t e r w h a t t h e y a r e t h u s t a u g h t , s h o u l d m u c h

t ra in ing be im posed . L a te r in l i fe , even , should som eon e manage to c la im som e such

w o r d to b e prec i se , t he people wil l appea l to th e teach ings , which th ey co u ld rec i te

wi th l i t t l e d i s to r t ion . Thu s , i f some one sa id t ha t a s ton e cou ld no t be less than on e

i nc h in d i a m e t er , b u t t h a t i t c o u l d b e less t h a n o n e a n d o n e m i l l i o n th s i nc h es , h e

would be accused o f v io la t ing t he m eaning of ‘ s tone’ us t as we should accuse h im.

Unl ike us , however , the people in th is o th er soc ie ty , to s u p p o r t t h e c h a r g e t h a t s u ch

a claim of precision is in way of be ing an a rb i t ra ry s t ipu la t ion , would appea l to t h e

expl ic i t , r epea ted teach ing rou t ines . They would appear to be in a qu i te obv ious ly

g o o d p o s i ti o n , t h e n , to c la im tha t the re is indeed a s t ipu la t ion here and , moreover ,

o n e w h i c h c o n f l i c ts w i t h t h e l e a r n e d, a c c ep t e d m e a n i n g o f t h e w o r d .

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W H Y T H E R E A R E NO PEOPLE 209

N o w , l e t us suppose tha t , jus t as I a m d o in g f o r our own words, a ph i losopher

in this society put s forw ard t he idea t ha t typical vague terms are inconsis tent . This

is hardly an arbi t rary su pposi t io n now , given wh at we have already imagined. F or i f

I have supposed as muc h w i th n o such exp l ic i t t each ing to suggest th e thoug ht to

me , h ow muc h easie r i t will be fo r a th inker w ho i s amid s t so m u c h a p p a r e n t i n c o n -

s i s tency . Focus ing on th e teach ing , h e w ould po in t o u t the incons is tency in the in -s t ruc t ions . Now , in tha t soc ie ty , s ince th e people a re assumed to be much l ike us,

the re w ould be th inkers o f a ra ther conserva tive ben t , who would wish to cleave to

th e accep ted th ink ing of the ir cu l tu re . H ow sho uld these conserva tives defend tha t

th ink ing ; how should they ra tional ly rep ly to th e nihi l ist ic cr i t ic?

Whatever repl ies may be open to t h e m , i t s e e m s to m e t h a t among rhe least

effective of these w ould be an appeal to comprehens ive paradox . True enough , i f

such expressions as their ‘person’ and ‘ thinkin g being’ are logical ly incons is tent , as

the exp l ic i t ins t ruc t ions fo r them ind ica te , then they would have to c o n c l u d e t h a t

n o o n e - c o u l d a c c e p t, or even unders tand , th e c r it ic ’ s arguments . But i f t he mat te r

were al lowed to rest there , or even if th e burden o f a rgument were thoug ht to b e

substant ia l ly shif ted, those conservative thinke rs w ould display terr ibly l i t t le phi lo-

sophica l sense , and v i rtual ly n o dep th o f tho ugh t or understanding. General ly , we

may no te t ha t any thorou ghgoing rad ica l c r it ique of a language, or a sys tem of

t h o u g h t , c o n d u c t e d i n t h e t e r m s or conce p ts o f wh a t is c ri t ic ized , mus t , o f course ,

have thi s paradoxica l q ua l i ty . But th i s doe s no t mea n th a t such a cr it ic i sm ca nno t

b e , so to t ry to say , appropr ia te to i t s ob jec t . In the soc ie ty now un der cons idera -

t ion , wha tever mos t o f i t s members may th ink on the m at te r , such a c ri ti c ism will

b e q u i t e a p p r o p ri a t e i n d e ed .

Now , i t seem s c lea r to m e t h a t t h e s it u a ti o n is no t re levan t ly d i f fe ren t in our

own case . I t i s, o f c o u r s e, t r u e t h a t t h i n g s a r e n o t e x a c t l y t h e s a m e w it h us, f o r w e

have had n o exp l ici t ins t ruc t ions fo r ou r typ ica l vague te rms , much less have we an yth a t a re incons i s ten t . But , a s ou r a rgum ents have ind ica ted , wha t o ur imagined SO-

ciety’s members will have learned explicitly we seem to have learned implici t ly . T he

logic of our expressions is no t a t va r iance wi th the ir s . So, i t is mos t un l ike ly , 1 sub-

mi t , tha t po in t ing to paradox wil l be fut i le against their radical cr i t ic but ra t ional

against a critic in ou r less explicit socie ty. As i t will not be rat ional there , so i t is

no t ra t iona l here . Po in t ing to paradox , then , does l i t t l e or noth ing to null i fy the se

presen t e f fo r t s .

The po in t tha t pa radox cannot nu l l i fy our account wi l l s tand jus t as wel l

should we agree tha t , in add i t ion to th e paradoxica l s i tua t ion a l ready n o ted , va r ious

o the r , pe rhaps deeper , pa radoxes a re con sequences o f o u r a c c o u n t . F o r e x a m p l e , i t

migh t be he ld tha t i f the re a re no en t i ti e s wi th any capac i ty to t h i n k , or to use lan-guage, then there will be n o sen tences , o r any o the r expressions. And , it m i g h t b e

he ld t ha t i f the re a re none of these la t t e r , then there a re n o s ta teme nts or propos i -

t i o n s, n o a r g u m e n t s or a c c o u n ts o f a n y s o r t , a n d n o t j u s t n o n e t h a t a r e e v er un d e r -

s t o o d or accep ted . If th i s may be m ain ta ined , then fu l ler , or mo re d i rec t , pa radoxes

c a n b e a d d e d to o u r account’s conse quen ces. B ut , as o ur discussion has already in-

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210 PETER UNGER

dica ted amply , th i s wi ll d o l i t tl e to worsen mat te r s fo r us. F o r , whatever paradoxes

ou r acco unt sh ould eng ender will a ll be rat ionally t reat ed al ike. They all wil l best be

t a k e n , it seems clear , as showing the comprehensiveness of our radical account ,

ra ther tha n i t s fu t i l i ty .

9.A REEXAMINATION O F OUR ARGUMENT FROMINVENTED EXPRESSIONS

O ur acc oun t of vague expressions has been provided. I t has g iven suppo r t to o u r A r -

gum ent f rom Inven ted Expressions, sup por t which will n o t be nu l li f ied by any

charges of paradox . I f we are to main ta in co mm on sense s t il l , and ho ld th a t the re

rea l ly a re people , we mu s t ob jec t to o n e o f t h e p r e m is e s o f t h a t A r g u m e n t , t h o u g h

few courses fo r such a n o b jec t ion appear s ti ll to be available. To take last things

f i r s t , the re is l i t t le to be said against the Argument’s f inal premise:

(111) If the expre ssion ‘person’ is logical ly inc onsis te nt , then ther e are no

people .

Fo r a den ia l o f i t , a s I have argued in Sec t ion 1, wil l res t on ly up on a confus ion . So,

objec t ions m us t com e aga inst i t s f i r s t tw o premises, fo r th e Argum ent ’ s fo rm is no t

f a u l ty . A t t h e o u t s e t of o u r re e x a m i n a ti o n o f t h e m , w e n o t e t h a t a t th i s p o i n t t h e se

premises look wel l suppo r ted . So, now, 1 sugges t , the burd en of a rgum ent is on an y

a t tem pted ob jec t ion . Can thi s burden be shouldered e f fec t ive ly?

L e t us r e e x a m i ne o u r s e c o nd p r em i se , in a n a t t e m p t to review m at te r s back to

ou r beg inn ing :

(11) T h e expre ssion ‘person’ is logical ly on a p ar w ith ‘nacknick’; i f the la t-

t e r i s incons i s ten t , then so is t h e f o r m e r .

So far as we have been a ble to discern, f rom our ear ly exper im ents onw ard , the re i s in -

deed th i s logical pa r i ty . I f th e mat te r i s jus t a n empi r ica l , o r con t ing en t , or causal one ,

to be decide d pr imari ly by exp erim ent and observation, then p ar i ty seem s surely r ight .

F o r o n ly t h e m o s t to r t u o u s a n d f o r c e d i n t e r p r e t a t io n o f o u r r e c e n t e xp e r i m e n ts a n d

observa t ions would have th ings be o therwise . For an ob jec t ion to (11) to b e a t a ll

p laus ible , the n , i t m us t be m ain ta ined th a t i t is fo r som e concep tua l o r log ical rea -

sons tha t the re i s a d i spar i ty be tween our inven ted express ion and ou r o rd inary one .

N ow , we have a l ready a rgued tha t , wh a tever e lse may be true of i t , ‘person ’ is a qual-

i ta t ive vague discr iminat ive term. As s u c h , i t is logical ly on a par with such oth er , less

c e n t ra l c o m m o n e x p r e s si o n s as ‘stone’, ‘tall ma n,’ and ‘cubical object’. So, in e f fec t ,

wh a t th e ob je c t ion m us t c la im is th a t the re is a logica l ba r r ie r to a parallel between‘nacknick’ and ‘cub ica l ob jec t ’ , and even ‘ob jec t wh ose shape i s qu i te s imila r to t h a t

o f a cube’ . Bu t how migh t the c laim of suc h a logical barrier be ra t iona l ly suppor ted?

T h e s u p p o r t r e q u i r e d w o u l d h a v e to com e in th e fo rm of ‘ logica l’ t ru ths ,

which would logical ly y ie ld th e s ta tem ent of n o log ica l pa r i ty . Bu t any th ing tha t

migh t b e even p laus ibly cons idered a log ica l t ru th appears qu i t e inadeq ua te to pro-

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WHY THERE A R E NO PEOPLE 21

vide the needed deduc t ion . Here is an example o f the p rob lem, wi th a cand ida te fo r

relevant logical t ru th t ha t is mu ch be t ter th an m ost I h a ve e x a m i n e d : O n e m u s t

unders tand an inven ted express ion , if one u nders tan ds i t a t a l l, in t e rms of a se t o f

expressions (each of which is no t invente d and ) each of which is consis tent . While i t

m i g h t l a t e r b e d o u b t e d , l e t us now grant that , in a re levant sense, this is indeed a

logical t ruth. But , even so , of what use wil l i t be in deriving logical disparity be-

twee n inven ted and ordina ry vague expressions?

We have already enc oun tere d an invented expression which, if any ord inary

term sat isf ies this offered condit ion, qui te nicely meets the al leged requirement .

T ha t expression is ‘ t inkergrid’ , which 1 introduced and discussed in Sect ion 4.Dis-

count ing any minor l apse , I showed there tha t , un l ike bo th o rd inary vague te rms

and also the invented ‘nacknick’ , the invented ‘ t inkergrid’ , while i t was indeed in-

consis tent , had inconsis tency which was relevant ly grounded. What seemed to hold

only be tween ‘nacknick’ and the o rd inary te rms , none of which appear to satisfy

o u r o f f e r ed r e q u i re m e n t , w a s t h e fur ther parallel of having groundless incons i s ten-

c y . So, even i f we gra n t th e o f fe red requ i rem ent , the mo s t i t cou ld log ica lly yie ld ,i t should be clear , is tha t o rdinary vague expressions will dif fer f rom ‘nack nick’ as

regards the source o r na ture o f wha tever incons i stency they m ight have. T he par i ty

we a re concerned wi th , however , concerns wheth er , l ike bo th ‘nacknick’ and a l so

‘ t inkergrid’ , typical vague expressions are , in any way, and from whatever source,

logical ly inconsistent . As regards th e required dispar i ty , then , the offered require-

m en t, even if logically tr ue , is powerless to yield any result.

While ou r reconsideration of ‘ t inkergrid’ has sho wn th e offered requir em ent

to be irrelevant, it suggests as well great d ou bt as to i ts t ruth . I t seems incred ib le to

suppose th a t we might have inven ted a t e rm l ike ‘ t inkergr id ’ to parallel our ord inary

vague term s b ut fa i led with ‘nacknick’. Fo r of the tw o useful , incon sis tent inven-

t ions , i t i s the la t t e r tha t seems to provide t he closer paralle l here . So, o u r p r ob l em sc o m p o u n d : to have a ( logical) t ruth presen ted in th e f i rs t place, we are constraine d

to weaken o u r a lleged requ i rement . Perhaps the fo llowing has a decen t cha nce fo r

t ru th : One mu s t unders tand an inven ted express ion , if a t al l, in t e rms of a se t o f ex-

press ions (each of which i s no t inve n ted and ) a t l east some of which a re cons i s ten t

terms. But , now, we have avai lable to yield con t ra d ic t ion , in add i t ion to th e clashes

betw een co nsis tent ideas tha t ‘ t inkergrid’ display ed, th e inconsistency in var ious

vague expressions (which a re no t invented).

The exper ience we have jus t su f fe red is typical of what I have encou nte red in

m y e x a m i n a t i o n o f o b j e c t i o n s t o ( I I ) , t h e s e c o n d p re m is e o f o u r A r g u m e n t . T h e

more an o f fe red p ropos i t ion looks l ike i t migh t be a log ica l t ru th , and so su i tab le

for a counte ra rgument in tha t respec t , the less it looks relevant to yielding th e re-

qu i red ded uc t ion of d i spari ty . N o candida te , then , o f w hich I am aware , looks very

promis ing, and n o su i tab le co unte ra rg ume nt appears fo r thcoming . Whi le these mat -

te r s m us t , pe rhap s , a lways be so mew hat inconc lus ive , it t h u s s e e m s to m e t h a t t h er e

is n o good ob jec t ion to th e appa ren t log ical pa r ity be tween th e inven ted and ord i -

nary expressions.

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212 PETER UNGER

There is only one place lef t f or an objection to be effective against our Argu-

me nt, namely, in the place of ou r first premise:

(I) Th e invented expression ‘ nack nick’ is logically incons isten t.

This question brings us back to th e beginning of ou r essay. Could we have misinter-

preted our little learning experiments, so that the apparently obvious and rationalinterpretation was really out of place all along? As with ( I I ) , if the m att er is essen-

tially an empirical, or contingent one, there would be little chance indeed that we

have been misinterpreting things, and that some ingenious complicated hypothesis

mu st be preferred. Thus , the objection mu st be tha t there is some logical barrier to

the t ru th of our first premise. But ho w m ight it be argued .that we have been labor-

ing und er such an intellectual illusion?

The occurrence of a definite description at the head of our premise, “t he in-

vented expression ‘nacknick’,” may trigger the response that there may in fact

never have been any such invented expression. If so, then this premise will fail of

truth, whatever o th er status should then be accorded it. Now, it is clearly no good

to deny the thou ght that if there is any expression ‘nacknick’, then it is an invented

term. But i t will also d o no good to challenge the premise on th e ground t ha t there

is n o expression ‘nacknick’ at all. For anyth ing which will serve to argue that much ,

it appears, will undermine as well the idea tha t there are o rdinary vague expressions,

including ‘cubical object’ and ‘person’. Th e paradoxical cons equ ence s of ou r own

account, for example, can be used to this effect against the premise; but they will

undermine as well any typical vague expression, including ‘person’. So, this is no

good way to challenge our premise, as it gets rid of the baby along with the bath

water. Similar maneuvers will prove to no better critical effect. For example, i t is

n o g oo d to find ‘nacknick’ an expression bu t a meaningless one , fo r how should

‘cubical object’ and ‘person’ then prove m eaningful? The only plausible mann er ofobjection, then, will allow ‘nacknick’ as an expression that either is consistent or

else inconsistent.

I t remains to objec t, of course, th at this invented expression ca nnot possibly

be, in any sense that it might have, an inconsistent expression. I t appears th a t the

teacher, a t least , has an understanding of such an inconsistent term, b ut this appear-

ance, the objection continues, must be an intellectual illusion. How might this be

cogently maintained? I suspect that an idea which might motivate this objection is

the by now old one that meaning is use, or is a function of use, though perh aps in

one of that idea’s newer guises or forms. But, in whatever form, this idea looks

quite unrealistic. Even when we con sider terms th at a re no t vague, and which may

be allowed as consistent, there seems little value in this appro ach. Consider a sur-face. W ith certain purp oses in min d, som eone may say “This is flat,” his idea being

that the surface is suitable for those purposes. Weeks later, he may return with

other purposes, and say of the sam e surface “This is no t f la t ,” and then turning to

anoth er s urface may say of it “ Th at on e is flat.” But, we may suppose, th e original

surface did not become any less flat, and even may have been somewhat improved

in that respect. Weeks later still, with a third set of purposes, the same individual

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WHY THERE ARE NO PEOPLE 21 3

may declare the second surface to be not flat, now declaring a third surface to be a

flat one. And, so it may go, half a dozen times or more. How is this most plausibly

to be accounted? Surely, the meaning of the words did not relevantly change. And,

just as surely, the meaning of ‘flat’ does no t concern anyone’s purposes. The real-

istic explanation, I suggest, involves supposing that n o n e of the surfaces here ever

are f la t , and that while actually speaking falsely, the man is informally implying in

each case something like this: The currently indicated surface is sufficiently close

to being (absolutely) flat so as to be suitable for the purposes the speaker and

hearer now have in mind.”

If even apparently consistent terms are best accounted by thus distinguishing

meaning and semantic application from the uses to which th e words are put, a t least

as much should be expected where the terms appear to be inconsistent expressions.

I think we may do well now to consider once again our invented term ‘tinkergrid’.

This is a term that is to apply only t o certain abstract, mathematical objects. To say

of a wooden structure tha t it is a tinkergrid is, just for this reason, a plain failure to

speak the truth. If use is to match with truth and meaning here, it will have to comefrom quarters much further removed from directly observable behaviors and stimuli.

Perhaps we might ask various people to try to imagine tinkergrids. Various people,

perhaps unaware of any inconsistency, will frequently allege success. They are using

the term to describe what they imagine. But, 1 think we may agree that they can be

imagining no such thing, and that a literally accurate description of what they

imagine can be given only in some other terms. To go o n multiplying examples and

considerations would be inappropriate for us now. To be sure, it is most unlikely

tha t anything can be said on these matters tha t will prove absolutely conclusive.

But, lacking such certainty, perhaps we may still agree that I have invented some

inconsistent expressions, even if those terms are well suited fo r our use.

At this point, a subtler, and somewhat more plausible, objection may be at-tempted. The idea here is to grant that ‘nacknick’ is an inconsistent expression, but

to deny it much of a place in our experimental learning situations. I t is no t obvious,

however, precisely how this will serve to challenge our Argument. So, let us discuss

the matter.

The attempted objection may take any of several forms, bu t they are all more

or less equivalent to this: our ‘nacknick’ is a term with two (or more?) meanings. In

one sense, which i t does seem forced to deny it , the term is indeed an inconsistent

one. In this sense, however, the objection continues, the term is not a useful expres-

sion. The sense in which the term is useful is another sense, in which the term is

consistent. And, what has happened in the learning situation? The teacher has in-

tended by his instructions, to inculcate in his hearers (or readers) the expression

‘nacknick’ in its inconsistent sense. But what his instructions actually have done is

to suggest to the hearers another sense for the term, a consistent useful one. The

hearers then learn ‘nacknick’ only in this lat ter sense; the former never gets further

than the teacher’s sounds or marks.2’

This objection, we may see, attempts to force an equivocation upon our Ar-

gument. Interestingly, the term upon which th e equivocation focuses is no t a com-

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214 P E T E R U N G E R

mo n, accepted one, bu t is our invented ‘nacknick’ itself. For the Argument to seem

to work, ‘nacknick’ must have one meaning in the first premise, on which the term

is inconsistent, and another meaning in the second premise, on which the term is

consistent. As the Argum ent thus eqhivocates, it is no t a cogen t piece of reasoning.

This objection has some plausibility, but it will not bear scrutiny. For i t towork, we must suppose that the only way for ‘nacknick’ to be logically on a par

with ordinary vague terms, in particular, with ‘person’, is fo r the new expression to

be taken in a consistent sense. But, might no t rhere be a deep parallel he re between

the two, so that ‘person’ as well as ‘nacknick’ has an inco nsistent meaning? If SO,

then our Argument will not equivocate, but wil l concern both terms, as regards

their inconsistent meanings. As such, it will be a cogent piece of reasoning, though

perhaps a bit lim ited in its scope.

My suggestion of this deep parallel implies that the inconsistent sense for

‘nacknick’ did get further than my marks or sounds , th at it was inculcated in you.

What might su pp ort this suggestion? We remem ber o ur instructive society, where in-

consistent instructions fo r learned ordinary te rn s became a m atter of widespread,repeated scholastic drill. Now, we n eed only exten d our experim ents with ‘nack-

nick’ to match their drills with ‘stone’, ‘cubical object’, and ‘person’. So, let us

imagine that after I taught you ‘nacknick’, we went over the instructions so much

th at you had the m d own p at. In such a case, there is no plausibility a t all in suppos-

ing t he inconsistent sense got no further than m y marks or soun ds, and never enter-

ed your learning. For, now, you would be confident that the aforesaid instructions

governed your ‘nacknick’, which you had learned from me. Indeed, after you per-

ceive the inconsistency in your term, you will be able to say of other expressions,

which are n o t thus inconsistent , that they are thus different from the expression

you just learned. Thus, you will say that ‘perfect cube’ is logically quite different

from the term yo u learned from me. B ut, of course, you will be ready to use ‘nack-

nick‘ for many objects anyway and to withhold i t of many o thers. I t appears quite

easy to te l l how our extended experiments will turn out, and what those results

show. For what occurs there explicitly also occurs, implicitly, in our original ex-

periments.

Now, none of this is to deny that my instructions may have inculcated in

you, in addition to ‘nacknick’ in the inconsistent sense, a consistent sense for the

expression. And, it is not to deny that this consistent sense may have been impor-

tant, even essential, for th e term’s being a useful o ne f or you. I think these last pos-

sibilities to be, in fact, quite unlikely. But there is still some plausibility in the idea

of them. What is impor tant f or us t o notice now is, first, ho w m uch less plausibleit is to think that with ‘nacknick’, as well as with ‘person’, no inco nsistent sense

ever got to you at a l l , no matter what else may have gotten to you, and, second,

t h a t it is this much less plausible idea th at is required fo r th e charge of equivocation

to work against o ur Argument.

To appreciate fully the failure of this charge, we should understand that

whatever we may say of ‘nacknick’ in thes e regards, we may say with just as much

reason, or just as little, in regards to ‘stone’ and ‘person’. Thus, even if it concerns

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WHY T H E RE ARE NO PEOPLE 215

terms only in one, conscious meaning, our Argument will have a second premise

suitable to match its first. For example, we may grant that there is an unconscious,

consistent sense for ‘nacknick’ which, in our experiments, you learned and then em-

ployed. Then we might say, of course, tha t you also used the term in its inconsis-

tent sense, perhaps doing so in (the process of) using it in its consistent one. But

then we might just as well say the same for ‘person’, or ‘stone’: We learn two senses

and, when we use ‘stone’ in its inconsistent sense, we d o so in (the process of) us-

ing it in its unconscious, consistent sense. For another example, we might say tha t

the consciously learned sense is never useful, and that there appears to be a use for

‘nacknick’ only in this inconsistent sense. But, then, of course, we might just as well

say that ‘stone’ is perfectly idle in its conscious, inconsistent sense, and is used only

in that unconscious sense in which it is a consistent expression. Whatever we may

say for ‘nacknick’, we should understand, we may just as well say for ‘stone’ and

for ‘person’. So, to repeat, our Argument does not rely upon equivocation, bu t is an

adequate piece of reasoning.

This final objection has failed. But i t suggests some ideas, recently consider-ed, that, while they do not constitute an objection to our Argument, may serve to

place limits on its application. For, if there may be two senses of ‘nacknick’, and

thus of ‘person’ also, it might be said th at our Argument concerns these expressions

in only one of those senses, the inconsistent one. Thus, for all that piece of reason-

ing says, there may be a consistent sense for ‘person’, as well as for ‘nacknick’, and,

in that sense, there may well be plenty of people. If our Argument is thus limited,

then the interest of our conclusion, it might be said, will be equally limited, though

perhaps still of some significance. What are we to make of this?

In the first place, we should remind ourselves that the postulation of these

additional meanings appears ro be quite gratuitous and, if i t actually is so, then

nothing further need be said. Indeed, can’t we leave i t at that? For these allegedmeanings are not only wholly unconscious ones, but we are to have no clue as to

how anyone might ever become aware of them. Of course, someone might take a

stab at articulating his putative unconscious meaning of ‘person’, bu t how should

he ever judge his success, let alone the propriety of extending his suggestion to my

own putative unconscious meaning for the term? To my mind, the postulation of

these alleged meanings looks t o be a desperate pretense.

But suppose we grant that there really are such shared consistent unconscious

meanings. So far as I can tell, we still cannot say anything much as to what they

are. Unlike the conscious inconsistent meanings, for which we can give at least such

conditions as in (1)and (2), these postulated entities are utterly obscure and mysten-

ous. But if we do not have any idea as to these obscure meanings, then we have none

either as to what it is for an entity to be a person, o r even to be a nacknick. Thus,

with respect to any entity whatever, even an alleged shoelace, we have no idea either

as to whether i t is a person or a nacknick, or both, or neither. In this sense of per-

son-and how masy others like it-perhaps there may be ever so many people. But

now the matter has become utterly mysterious and obscure. If this is all there is to our

Argument’s being limited, tha t reasoning seems not to have any serious limitations.

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216 PETER UNGER

10. SOME OUTSTANDING PROBLEMS POSED BY THIS ACCOUNTAN D ITS RELATION TO THEM

Largely by providing and em ploying an acc oun t of typical vague expressions as logi-

cally inconsistent, I have argued t ha t there are no people. We have discussed th e

chief o bjections to th e acco unt, including the charge of paradox, and we have sup-ported th e account by answering or disarming them. T hus, paradoxically enough, I

suggest tha t a t this point m y acco unt is to be ac cepted, at least as a working h ypo -

thesis fo r certain problems. I should no w like briefly t o discuss three of these.

A . The Problem of Explanat ion

If ‘person’ is an inconsistent term , t hen bow are a n y entities able, so to say, to use

it as successfully as it appears gets done q uite regularly? Indeed, how does this hap-

pen with any inconsistent expression? If such an expression is tied to consistent

terms, so tha t i t functions in place of them , then the m atter is no t very problemat-

ic. We saw this before, in Sectio n 1,where we discussed a working agreement to use‘perfectly square triangle’ in place of ‘to ma to which is both yellow and sweet’, sup-

posing t he l atte r expression to be consistent. But, without any such supposition as

that, which is o u r present problem situation, there is considerable explanatory

difficulty.

If o u r account is right, then any explanation given in available terms must

eventually, like the terms themselves, prove logically incoherent. So, we should no t

expe ct to o much here in the way of valuable results. Nevertheless, it is unhelpful t o

say no thing more than that there is nothing for us to do. F or, even if th ey are inco-

herent, the questions that introdu ced this problem for us appear to point up some

puzzling phenomena. So, I shall stick my neck ou t now an d offer the beginnings of

an ex plana tory suggestion.Perhaps we might understand the role of putative paradigms on the model of

an animal’s learning to respond to a stimulus. A r at can be taugh t to press a nearby

bar just when a certain s or t of stim ulus is present, fo r examp le, a triangular object.

Afte r learning w ith this stimulus, wha t ha ppen s with rats when, on the next trial, a

some what different st imulus is for th e first t ime presented, perhaps a more or less

rounded triangular object? We may plot measures of response against difference

from the original shape, those measures being frequency of any response, quickness

of response when one is made, strength of response, such as pressure on the bar,

and so on. With such suitable measures, a gradient, or curve, will be established for

a rat population and, by extrapolation, for a typical rat member. Fo r almost any

rat, the peak of the gradient will center quite precisely on the original shape, the

slope away from that varying somewhat from rat to rat. We might say, then, that

each ra t has his own idea of a triangular object, though there is important common-

ality to their ideas.

I suggest that our conception of a triangular object, and of a nacknick, is sim-

ilarly based. Much as a rat can be trained to respond to an alleged paradigm nack-

nick, so I can more qu ickly learn to respond m ore flexibly with regard to such puta-

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WHY THERE ARE NO PEOPLE 2 1 7

tive objects, and with respect to my invented term for them. And, of course, so can

you. While our centers will not differ much, though with different people and differ-

ent individual paradigms some difference is to be expected, our slopes may be ex-

pected to differ significantly, especially for cases far away from center. Thus, various

behavioral borderline cases will arise where you and 1 are inclined toward disparate

judgments. Now, suppose my interior decorator tells me to use a nacknick in a cer-

tain place, though any shaped nacknick will be suitable. In a store, I come upon a

“borderline case” while shopping in your company. I am inclined to judge i t a nack-

nick, you t o judge it not one. Who is right? I t would be silly fo r us, even if we thought

there were some nacknicks, to force the issue and to declare tha t there must be a fact

of the matter. Behaving typically, we would not do that. Rather, I suggest, we should

treat the matter as a social problem, with each person having a chance to influence

the other. Now, to move you to my side, to apply, I will rely on the vagueness condi-

tion: Look, this is so like those others, in shape, which you agree are nacknicks; so

why should we stop just there, and not here? To move me, n ot to apply, you will rely

on the discriminative condition: But, see here, we have to stop somewhere, or justany old thing will do; so why not stop there, which is a perfectly good place to do

so? In the logic of the situation itself, there is nothing to settle matters. So, things

get settled by further considerations. For example, if you are an architect, and I have

no strong interest in conventional shape description, I may well yield to you, expect-

inglike treatment from you in areas where my classificatory interests are the strong-

er. Of course, if you are a king and I am a peasant, then I may expect to do a good

deal more yielding on matters generally. The discriminative vagueness of ‘nacknick’,

as established in our conditions, allows these accommodations to take place with n o

one getting the idea that he is giving up any truth , or being hypocritical.

Even in one’s own case, th e matter is similar. If my decorator told me to use a

nacknick, and I happen to have a putative borderline case free to hand, while most

nacknicks would be quite expensive for me, 1 might rely on the vagueness condition

to allow me to judge it a nacknick, even should I otherwise no t be much inclined to

do so. I want to follow my decorator’s advice, and I also want to use what is free if

possible, so as to keep my expenses down. By appealing to the vagueness condition,

I can happily satisfy both of my desires.

Now, I do n o t mean to place much stock in this bare explanatory suggestion.

I t points up a virtue, though, in our account, and a corresponding problem with

other ways of thinking about vague expressions. For people do differ as to how to

handle many such behavioral borderline cases, and a given person often differs from

himself over time. These do no t appear to be mat ten of losing truth, where thoughts

of self-deception should enter, or thoughts of losing one’s faculties owing to social

pressure. On the idea that ‘nacknick’ is consistent, and that i t actually applies to a

whole bunch of things, which are exactly the nacknicks, these bizarre thoughts

move to take over. For, as we saw in Section 3 , in every case, ‘nacknick’ either ap-

plies or else it does not, so that there are no logical borderline cases. Thus, on this

more usual idea, in accommodating, someone will often give up truth (for falsity).

But on our account, there are no such strange losses t o be further accounted.

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218 P E T ER UNG E R

In a way, though , the main point for us now is to see how we have succeeded

in avoiding the complex problem of explanation. We have done so by introducing

‘nacknick’, and by th en form ulating our Argum ent from Invented Expressions. For,

just as with ordinary vague terms, with ‘nacknick’ also we have no good detailed

explanation of h o w it might be useful to us even while it is inconsistent. But, wemay accep t the idea tha t ‘nacknick’ is both useful and inco nsistent, and also that it

is relevantly similar to ‘cubical object’ and to other typical vague expressions. So,

even in the absence of a worked out explanation for them, we may accept the idea

tha t our common vague expressions are useful even while they are inconsistent.

Of course, were I able to offer a good explanation of how they were useful,

that would offer more support for our account of common vague discriminative

terms. Similarly, were 1 able to offer a detailed explanation for ‘nacknick’, that

would further my s upport for my thoug hts about i t . In each case, th e better t he ex-

planation, the more the support we add. But, then, all of this is in the area of add-

ing support to an account which, by other means, is already supported. On the

other hand, should no good explanation be forthcoming for any of these terms,

tha t would no t , I suggest, detract much from th e credibility of my account. For the

problem of explanation might just be too difficult for anybody .

B. The Problem of Scope an d Comparison

On my account , our language is inconsistent in a certain respect: it is inconsistent

in (the fact that it has) its qualitative vague discriminative expressions, including

‘being with a capacity for using language’.22 Already we have found a fair number

and variety of expressions to be of this sort. Our uccess suggests tha t we in quire as

to which oth er ter ms can also be thus categorized. This is an inquiry into th e prob-

lem of th e s c o p e of our account.One of the first things we shall wish to examine, as regards the scope of our

account, are those expressions that are the negatives of expressions we have already

accou nted. Thu s, we look a t such expressions as ‘no t a nacknick’ and ‘ no t a person’.

While syntax thus often suffices to sp ot such term s, we may semantically define a

negative of an expression e quite simply: n is a negative of e just in case, with re-

spect to any ent i ty , n applies to the entity if and only if e does not apply to it .

Thus, ‘person’ is a negative of ‘no t a person’ just as th e latter is a negative of the

former. We should inquire, then, wh ether a negative of a qualitative vague discrim-

inative expression is also an expression of th at sort. T he issues here are, I think, ex-

ceptionally difficult and complex. Partly fo r this reason, I have no t broached them

in our previous discussions. For now, I think it will be enough to say this: If our

negatives are also terms of o u r key category, th at will mean a fur ther source of con-

tradictions a nd paradoxes.

For consider ‘not a srone’ and suppose i t applies t o a certain group of twenty

a toms, or to somethin g th ey constitute. N ow, if o ur first condition governs this ex-

pression, we may keep adding suitable atoms, one at a time, and it will apply to the

result in each case. But, if our second condition also governs it, we must reach an

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W H Y T H E R E A R E NO PEOPLE 219

entity that does not satisfy ‘not a stone’, if not by that additive process then by

some such procedure. But, then, as ‘not a stone’ does nor apply to this enti ty, any

ncgative of it will apply t o it, including ‘stone’. Thus, this entity , which by our

vagueness condition is not a stone, also is a stone. Thus, ‘not a stone’ does no t ap-

ply to our original complex of twenty atoms. So, any negative of ‘not a stone’ ap-

plies to tha t complex. Thus, as ‘stone’ is such a negative, those twenty atoms con-

stitute a stone! But, then, our familiar arguments show, as well, that those few

atoms do not compose a stone.23

What we say about our negative expressions, then, will determine whether or

not such new sources of paradox and contradiction are upon us. But, even if we

eventually say that these negatives are indeed of our typical vague variety, and so

have these paradoxes upon us, that will do nothing to discredit seriously our ac-

count of them, or of any other terms. For the points we made about paradox be-

fore, in Section 8, apply in full generality. Thus, in particular, they will fully cover

these present matters.

On a slightly more positive note, another thing we shall want to examine, in

connection with the scope of our account, is the logic of vague discriminative terms

tha t are not purely qualitative. For powerful sorites arguments are available KO e-

fute the existence of those entities th at putatively satisfy ‘bachelor’, ‘door’, and

many other terms, including arguments of a relevantly counterfactual form. To ex-

plain these arguments, we want to exhibit conditions that govern the key terms, ac-

cording to which those terms are inconsistent. I believe that many proper names

will find their logic exposed in this manner, as will various expressions that have

been supposed interestingly similar to names. In Section 2, I made some brief sug-

gestions for extending our account to cover discriminative expressions generally.

But, we want t o go far deeper into the matter.

While there is no real line separating them, we may conveniently move fromdiscussing this problem of scope to examining the related problem of comparison.

What we want to do here is show that the sort of source of inconsistency so far dis-

cussed, which has much to do with vagueness, is not an isolated phenomenon of our

language, but is only one of several linguistic sources of inconsistency. As a possible

example of another type of source, we may consider the putative expression ‘ex-

pression that does not apply to itself‘. I t seems that there really cannot be any such

expression, for if there is one, then it applies to itself if and only if i t does not,

which is absurd. This might be just a surprising case of reason cutting through illus-

ory appearance. But, it may not stop there. For if this alleged expression is really

not anything genuine, then, i t seems, there will not really be any expression ‘expres-

sion that applies to itself‘. But, if no t that, then no t either ‘expression tha t applies

to something other than itself‘ nor, then, ‘expression that applies to something’.

But, if not this last, then i t seems there is no real expression ‘expression’. And, with

this last gone, it seems we must conclude, in fact, that there are no expressions, and

SO no languages, at all. SO, comparative matters merit further examination.%

Now, we should notice that the putative expression ‘expression that does not

apply to itself‘, supposing i t does exist, might well be a vague discriminative expres-

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220 PETER U N G E R

sion. If so, then i t will yield inconsistency from a t least two sorts of source. And, if

that is so, then so much the better fo r our present account.

C. The Problem o f Replacement

What I regard as the most difficult problem posed by my account, but also the most

important, is that of devising consistent expressions to replace the inconsistent ones

that have been prevalent to date. Part of the problem is that it is unclear even in

what sense or way the new terms will replace the old. But the most dizzying part is

that the devising seems to require an indefinite number of choices for US o make,

and while these choices look like extremely important ones, they must be entirely

arbitrary. While these two parts may not exhaust this problem, it will be enough for

us now, in an attempt to understand the problem’s difficulty, to focus our discus-

sion upon them exclusively.

In what sense or way is a newly devised term to replace an existing ordinary

one, for example, to replace ‘stone’? Normally, we should think of replacing one

term by another where we think of two consistent terms involved. Thus, an old ex-pression may apply to certain cases tha t we want t o capture as well with a new term,

bu t it may include other cases that we want newly to exclude. So, the new term will

be defined accordingly. If we then give up the old term, and no other available ex-

pression comes near to applying and excluding along these lines, we shall naturally

think of having replaced the old term by the new. But, in the present case, each old

term is inconsistent, applying to no cases at all. So, what does any do that a new

term may d o with a difference?

A “pragmatic” answer seems the only one relevant. While o u r inconsistent

terms are all logically on a par, different ones serve us differently. Roughly, this

difference in service is due to different response repertoires associated with the

different terms. Each term has, for any speaker at any time, associated with it a

certain pattern of responses t o different possible situations. While there is some

variation here, there will be, even across many speakers over a substantial period

of time, a considerable amount of agreement in response for a term. So, for each

inconsistent term, we might devise a consistent one that is to have a rather similar

response repertoire. Still, as conflicting responses each has no claim to be (more)

in accord with the old term itself, a ruling in favor of some, and against others,

will have no basis in the meaning of the common term. But someone’s repertoire

will suffer should any decision be made. Thus, it is not easy to tell what can pos-

sibly count as a successful outcome for such a project.

Letus

pretend that, for many vague expressions, this difficulty has been re-

solved. We are now to replace our term ‘person’. For this particular task, we should

reflect back on situations we have imaginatively encountered already. For example,

when we remove peripheral neurons, one at a time, from an alleged person, there

really seems nothing to choose, despite our generous reference to a “way most con-

ducive to there still being a person.” Thus, at (virtually) any point , th e removal of

(almost) any particular neuron does not leave an entity that is, in any acceptable

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WHY T H E R E A R E NO P E O P L E 2 2 1

sense, any less ofa p er s o n than would be le f t instead wi th t he removal o f (a lm os t )

any o ther . W i th no th ing fo r a gu ide , how are “we” to choose an expression tha t ,

unlike ‘person’, will select certain removals as preferable to others .

To highl igh t the p rob lem, cons ider tw o ra ther d i f fe ren t sequences o f removal ,

each d i spos ing of th e same nu mbe r o f neurons , mi ll ions o f the m, where the ne t re -

sul t , in terms of eventual ly sup port ed capaci t ies , is qui te dissimilar . Now, in cer tain

cases of this so r t , ou r associated response re pertoire m ay indica te on e resul t ing en-

t i t y to be pre fe r red as a person over the o ther . F or examp le , the capac it ies suppor t -

ed a t the e nd of o ne sequence may be mu ch grea te r as regards fee lings , while th e

main adva ntage resul ting fr om ano ther sequ ence may l ie in th e less personal area of

physica l dex te r i ty . But , in m any o the r such cases , whi le th e ne t resu lt s f rom th e se -

quences a re ap paren t ly d i f fe ren t in impo r tan t w ays , the re seems no th ing to choose

be tween them as fa r as be ing a person is concerned : suppo se one en t i t y is more in -

te l l igent and is bet ter able to exper ience p leasure, whi le th e o th er is m o r e s y m p a -

thet ic and is more sensi t ive to variet ies of pain. Now, wh at w e are to do, in devising

a new te rm, i s to m ake a cho ice anyw ay for even such a rb i t ra ry cases , which cho icewil l the n be ref lected in ho w th e term i tself “decides things.”

These d izzy ing mat te r s ge t fa r more d i f f icu l t when th e under ly ing c ircle of

our thoug ht is exposed and apprec ia ted . For , we want ou r key te rms , l ike ‘person’ ,

to ref lect c er ta in interests , which wil l favor those ent i t ie s included u nder th e term

over those no t so inc luded . But whose in te res ts wi ll thes e be? Th ey canno t be th e

in te rest s o f a ny people , s ince there a re no t a ny such th ings. But , even suppos ing any

of our descr ip t ions to be cohere n t , shou ld th e in te res t s o f en t i t i e s less b r il l ian t than

Einstein b e accorded in devising a m ost sui tab le replac eme nt fo r ‘person’? Shou ld

any weight be given to having eyes whose color l ies within a cer tain precise range

(of b r igh t b lue)? Shou ld , en t it i es wi th a very low d egree o f mus ica l ap t i tud e be ex-

c luded a l toge ther? We have f i rm ideas and s t rong feel ings on these mat te r s , bu t whoa r e w e to have feel ings and ideas tha t m at te r? There appe ars to be a n imposs ible

b o o t s t r a p o p e r a t i o n r e q ui re d o f a n y a t t e m p t a t r e p l ac e m e n t to achieve any pr ior i ty

or even significance. Indeed, I canno t see how there cou ld be , in any a rea o f in tel -

lectua l endeavor , a harder p rob lem than th i s one .”

N o t e s

1. In formulating these cond itions, I have been helped b y correspondence with Joh n Tien-

son.

2. I use the plural term ‘Expressions’ in naming this Argument because. while I , in fact,

chose to begin with ‘nacknick’. and with certain matters of shape, I could have begun as well

with other matters and invented expressions.3 . My discussion of this matter emerged from conversation with Samuel Wheeler.

4. I am indebted to several people for help in form ulating these com plex statements, espe-

cially to Terence Leichri. But there have been so many problems w ith previous versions that I

despair that some must srill remain. I trust, however, that the reader will no t judge m y philoso-

phy primarily in terms o f formulational details.

5 . For an extended discussion of the semantics of ‘flat’, and o f other such absolute terms,

see chapter I 1 of m y b o ok Ignorunce (Oxford, 1975).

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222 P E TE R U N G E R

6. For an alternative interpretation of why sorites arguments are sound, see two papers by

Samuel Wheeler: “Reference and Vagueness,” Synthese, Vol. 30. No. 3/4 (April/May. 1975)

and “OnThat Which Is Not,” Syntbese (forthcoming).

7. In the case of (almost) all the sorites arguments presented in this paper, in regards to

matters of formulation, I am indebted to Terence Leichti.

8. On he need for such a ”providing” clause, I am indebted to Ja mes Van Cleve.

9. In John Tienson. “Can Things of Different Natural Kinds Be Exactly Alike?”. Analys i s

10. This is suggested by the main point of Tienson’s paper, “Can Things of Different Natu-

ral Kinds Be Exactly Alike?”

11. Perhaps the most prominent recent exponent of this idea of incompleteness. or of an

idea much like it. is Michael Dummetr in his unfor tunate ly named “Wang’s Paradox,” Syn-

these 3 0 (1975). especially as on pages 309-12.

12. As I hope is indicated by the language, this general proposition is not intended to con-

cern future situations. As regards t he future, I think there are genuine problems, as made fa-

mous by Aristotle and his argument of the sea battle.

13. Various remarks in the section just ended are in response to conversations with Terence

Leichti and with David Lewis.

14. This argument, adapte d, shows that there is no genuine dyadic relation of similan’ty. For

we can now show that if there is such a relation. then i t must be transitive. But. also, qui te clearly,

if there is such a relation, then it is not transitive. Thus, despite intellectual appearances to the

contrary, there is no real similarity relation. (Th e question of r e s p e c t s , and of degrees . of simi-

larity changes nothing here.) This point first emerged for me in discussion with Vincent Tomas.

15. This objection, or on e much like it, was offered to me in conversation by Terence Leichti

and also by David Lewis. What I go on o say about t he matter is indebted to these helpful con-

versations.

16. For impressing upon me the importance of counterfactual reasoning in relation to sorites

arguments, I a m ndeb ted t o discussion with David Lewis.

17. See three recent papers of mine: “ I Do Not Exist,’’ in Epis tem ology in Perspec t ive , ed.

Graham Macdonald (London. forthcoming), which is the festschrift for Professor Sir A. J. Ayer;

“There Are No Ordinary Things,” Syntbese, forthcoming: “Skepticism and Nihilism,” N o u s ,

forthcoming.

3 7 (1977): 190-97.

18. See the three papers cited in the just previous note.

19. For discussion regarding an incomparability condition for ‘person’, I am indebted to

James Van Cleve.

20 . The points just mad e were suggested to me by an unpublished paper of John Tienson’s,

“An Argument Concerning Quantification and Propositional Attitudes.’’ I make some related

points in Ignorance.

21. This objection, or one much like it . was offered in conversation by David Lewis.

22. Saying that a language is inconsistent is admit ted ly somewhat unnatural. But if one speci-

fies appropriate respects in which it might be inconsistent. that unnaturalness will be harmless.

23. If ‘no t a sto ne’ is indeed a vague discriminative expression, the foregoing argument will

go against a good deal of what I said in Section 4 of “There Are No Ordinary Things.” But most

of what I said there is directed against cena in arguments from common sense and. as such, still

will stand.24. The paradox just sketched derives from the Grelling, which in turn derives from the

Liar. The Liar is attributed by scholars to the great Megarim thinker Eubulides. who is also

credited with inventing the sorites, as well as other important arguments. For some recent re-

search on Eubulides, see Jon Moline. “Aristotle, Eubulides and the Sorites.” Mind 78 (1969):

343-407. TO my mind, i t is puzzling how much th is great philosopher has been neglected.

25. In writing this paper. I have been fortunate in having been helped by many people, too

many to thank each individually. However, I should like to express thanks now to three who

were especially helpful: Terence Leichti, David Lewis, and Samuel Wheeler.