quine intensitons revisited

7/28/2019 Quine INtensitons Revisited

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MIDWES T STU DIES IN PHILOS OPHY, I1 (1977)

INTENSIONS REVISITED

W. V. QUINE

FORhe necessity predicate, as distinct from the necessity functor TI’, I shall write

‘Nec’. I affirm it of a senten ce , to mean that the sen tenc e is a necessary truth, or, if one

like, analytic. Whatever its shortcomings in respect of clear criteria, the predicate is

more comfortable than th e se nte nce functor, for it occasions n o de part ure from exten-

sional logic. Henc e the re would be comfort in bei ng able to regard ‘0’s mer e short-

hand for ‘Nec’ and a pair of quotatio n marks-thus ‘O(9 is odd)’ for ‘ Nec ‘9 is odd’ ’.

But it will not do. In modal logic one wants to quantify into necessity contexts, an d we

cannot quantify into quotations.

We can adjust matters by giving ‘Nec’ multigrade status:’ letting it figure as an

n-place predica te for each n.As a two-place predicate it amounts to the words ‘is neces-

sarily true of‘; thus Nec(‘odd’, 9). As a three-place predicate it amounts to those same

words said of a two-place predicate and two objects; thus Nec(‘<’, 5,9) .And so on up. In

terms now of multigrade ‘Nec’ we can explain the use of ‘0’n open sentence s. We

can explain ‘O(x is odd)’, ‘O(x < v)’, etc. as short for ‘NecJ‘odd’, x)’, ‘Nec (‘<’, x, v ) ’ ,etc. There is no longer an obstacle to quantifying into ‘O(x is odd)’, ‘O(x < y)’ , etc.,

since the definientia d o not quot e th e variables.This multigrade u se of ‘Nec’ is much like my multigrade tre atm en t in 1956 of the

verbs ofpropositional attitude.z Critics o ftha t paper reveal that I have to explain-what

I thought wen t without saying-that the adoption of a multigrade predicate involves no

logical anomaly nor any infinite lexicon. It can be viewed as a one-place predicate

whose arguments are sequ ence s. As for the use of quotation, it of course is red ucib le by

inductive definition to t he concatenation functor and names of signs.

Perhaps also a caution is in order regarding two ways o f taking ‘necessarily true’.

‘9 is odd’ is a necessary truth; still, that t he form of words ‘9 is odd’ means what it does,

and is t h u s true at all, is only a con tingent fact of social usage. Of course I intend ‘Nec’

in the former way. Similarly for its polyadic use, applied to predicates.

5



6 MIDWEST STUDIES IN PHILOSOPHY

Commonly the predicate wanted as argument of ‘Nec’ will not be available in the

language as a separate word or consecutive phrase. A t that point the ‘such that’ functor

serves. For example, the definiens of ‘O((x+ y ) (x - y) = xz - y’)’ is:

Nec(‘zw 3 ( z + w) ( z - w ) = z z-w2)’,2, y) .

The ‘such that’ functor, ‘zw 3’ n this example, connotes no abstraction of classes or

relations or attributes. It is only a device for forming complex predicates, tantamount to

relat ive c l a ~ s e s . ~

When predication in the mode ofnecessity is directed upon avariable, the necessity is

de re: the predicate is meant to be true of the vaIue of the variable by whatever name,

there being indeed no name at hand. ‘Nec(‘odd’,x)’ says of the unspecified object x that

oddity is of its essence. Thus it is true not only that Nec(‘odd, 9), but equally that

Nec(‘odd’, number of planets), since this very object 9, essence and all, happens to be

the number of the planets. The ‘Nec’ notation accommodates de dicto necessity too,

but differently: the term concerned de d ic to is within the quoted sentence or predicate.

Thus ‘Nec ‘9 is odd’ ’, unlike ‘Nec(‘odd’, 9)’, is de & t o , an d ‘Nec (‘number of planets

is odd’)’, unlike ‘Nec(‘odd’,number of planets)’, is false.

De re and de dicto can be distinguished also in terms o f ‘U’, but along other lines.

When the term concerned is a variable, there is nothing to distinguish; de re is de

rigueur. When it is not a variable, we keep it in the scope of ‘0’or de dicto:

O(number of planets is odd) (false)

and bring it out thus for de re:

(1)

In the system of definitions of ‘0’n terms of ‘Nec’ we observe a radical twist:

‘O(Xs odd)’ and ‘O(numberof planets is odd)’ look alike in form, as do ‘Nec(‘odd’,x) ’

and ‘Nec(‘odd’, number of planets)’, but the translations do not run true to form.

‘O(x is odd)’ and ‘O(numberof planets is odd)’ stand rather for the dissimilar formulas

‘Nec(‘odd’, x ) ’ and ‘Nec ‘number of planets is odd”, whereas what stands for

‘Nec(‘odd’, number of planets)’ is (1).

Definitional expansion of ‘0’h u s goes awry under substitution of constants for

variables. This is legitimate; unique eliminability is the only formal demand on

definition. What the irregularity does portend is a drastic difference in form between the

modal logic of ‘0 ’ and such laws as govern its defining predicate ‘Nec’. Drastic

difference there is indeed. In particular the distinction between de re and de d ic to is

drawn with a simpler uniformity in terms of ‘Nec’ than in terms of ‘0 ’ .

Some simplification of theory can b e gained b y dispensing with singular terms other

than variables in familiar fashion: primitive names can be dropped in favor of uniquelyfulfilled predicates and then restored as singular descriptions, which finally can be

defined away in essentially Russell’s way. That done, we can explain ‘0’ully in terms

of ‘Nec’ and vice versa by this schematic biconditional:

( 3 x ) ( x = number of planets . O ( X s odd)). (true)

O F x , x 2 . . . xn = Nec(‘F’,xI,x2, . . . , x , ) .

Here n may be 0. A certain liberty has been taken in quoting a schematic letter.

It may be noted in passing that ‘0 ’ on the left of ( 2 ) could alternatively be viewed

not as a sentence functor but as a predicate functor, governing just the ‘F’and forming

a modal predicate ‘ D F . 4

Th e reconstruction of ‘0’n terms of ‘Nec’ has lent some clarity to the foundations



W. V. QUINE 7

of modal logic by embe dd in g it in extensional logic, quotation, an d a special predica te.

Incidentally the contrast between d e re and de d i c to has thereby been heightened.

But the special predicate takes some swallowing. In its monadic use it is at best the

controversial sem ant ic predic ate of analyticity, and in its polyadic use it imposes an

essentialist metaphysics. Let m e be read, then , as expound ing rather than propounding.I am in the position of a Jewish chef prepar ing ham for a gentile clientele. Analyticity,

essence, and modality are not my meat.

If these somber reflections make on e wonder whe the r ‘Nec ’ may be more than we

nee d for ‘0,negative ans wer is visible in ( 2 ) : hey are interdefinable.

A project that I shall no t unde rtake is that of codifying laws of ‘Nec’ from which those

of modal logic can be der ive d through the definitions. Th e laws of ‘Nec’ would involve

continual interplay bet wee n quotations a nd their contents. Obviously w e woul d want:

Nec ‘. . . .’ 3 . . .,

where the dots stand for any closed sentence. Also, where ‘-’ and ‘. . . .’ stand

for any closed sentences, we would want ‘Nec ‘-= . . . . to assure the inter-changeability of ‘-’ with ‘. . . .’ inside any quotation prec eded b y ‘Nec’. This is

needed for the substitutivity of ‘El(-=. . . .) ’ in the modal logic. Also we would

need corresponding laws governing the polyadic use of ‘Nec’ in application to

predicates; and here complexities moun t. No dou bt modal logic is bet ter codified in its

own terms; such is the very utility of defining ‘0’nstead of staying with ‘Nec’. Th e

latter is merely of conceptual int ere st in distilling the net i mpo rt of modal logic over and

above extensional logic.

Necessity de dic to is notoriously resistant to the substitutivity ofiden tity. When only

variables are concern ed, the quest ion does no t arise; for they figure only d e r e , or, as I

have often put it, only in referential position. Moreover, we have de cid ed that only

variables are concerned, definitions aside. Still, let us consider how singular termsfare when restored definitionally as descriptions. Expanded b y those definitions, an

identity joining t w o descr iptio ns or a description and a variable obviously implies the

corresponding universally quantified biconditional. We may be sur e therefore that even

in de d i c t o positions, whe re substitutivity of simple ident ity fails, we can d ep end on

substitutivity of necessary identity, ro(< q)’; his is as sur ed by the substitutivity of

‘O(-= . . . .) ’ noted above.

The substitutivity of rO(<= 7)’ s gospel in modal logic. Still, some readers are

perhaps brought up short by my appeal to ‘O(< q)’, as if I did not know that

, ,

(3 )

The point is that I am not free to put < and 77 for ‘x ’ and ‘y’ in (3). Instantiation of

quantifications by singular terms is under the same wraps as the substitutivity of

identity.

Le t instantiation th en b e ou r next topic. From the true universal quantification:

( x ) ( x is a number .>.O(5 < x ) v O ( 5 2 x ) )

we cannot, one hope s, infer the falsehood:

O(5 < number of planets) v O(5 2 number of planets).

From th e truth:

5 < numb er of planets . - 0 ( 5 < number of planets),




again, we cannot, one hopes, infer t he falsehood:

( 3x ) (5< x . 0 ( 5 < x)).

When can w e trust the instantial laws of quantification? Th e answer is implicit in the

substitutivity of = 7)’.or, instantiation is unquestioned when the instantial termis a mere variable ‘x’; and we can supplant ‘x’here by any desired term 7,hanks to the

substitutivity of ‘O(x q)l, if we can establish ‘(3x)O(x 7 ) ’ .This last, then, is the

condition that qualifies a term 7 or the instant ial role in steps of universal instantiation

and existential generalization in modal contexts. A term thus qualified is what F$llesdal

called a genuine name5 and Kripke has called a rigid designator.‘j It is a term such that

( 3 ) O ( x= a) , that is, something is necessarily a, where ‘a’ stands for the term.

Such a term enjoys de re privileges even in a de dicto setting. Besides acquitting

themselves in instantiation, such terms lend themselves in pairs to the substitutivity

of simple identity. For, where [and 7) are rigid designators, we are free to put them for ‘x ’

and ‘y ’ in (3) nd thus derive necessary identity.

A rigid designator differs from others in that it picks out its object by essential traits.

It designates the object in all possible worlds in which it exists. Talk of possible

worlds is a graphic way ofwaging the essentialist philosophy, but it is only that; it is not

an explication. Essence is needed to identify an object from one possible world to

a n ~ t h e r . ~

Le t us turn now to the propositional attitudes. As remarked above, my treatment ofthem in 1956r esem bled my present use of ‘Nec’. At that time I provisionally invoked

attributes and propositions, however reluctantly, for the roles here played by mere

predicates and sentences. Switching now to the latter style, I would write:

(4 ) Tom believes ‘Cicero denounced Catiline’,

( 5 ) Tom believes ‘x 3 (x denounced Catiline)’ of Cicero,

(6) Tom believes ‘x 3 (Cicero denounced x)’ of Catiline,

(7 ) Tom believes ‘xy 3 x denounced y)’ of Cicero, Catiline,

depend ing on which terms I want in referential position-that is, with respect to which

terms I want the belief to be de re. T he mul tigrade predicate ‘believes’ in these

examples is dyadic, triadic, triadic, and tetradic.

Whatever the obscurities of the notion of belief, the underlying logic thus far is

extensional-as in the case of ‘Nec’. But we can immediately convert the whole to an

intensional logic of belief, analogous to that of ‘ 0 ’ .Where ‘B!’ is a sentence functor

ascribing belief to Tom, th e analogue of the sketchy translation schema (2) is this:

BtFx,x2 . . . xn=. Tom believes ‘F’ of x l , x l , . . .,I,,

Parallel to (1)we get:

( 3 x ) ( x= Cicero . B,(x denounced Catiline)),

( 3 x ) ( x= Catiline . B,(Cicero denounced x)),

( 3 ) ( 3 y ) ( x = Cicero . y = Catiline .Bt(x denounced y) )

as our transcriptions of the de re constructions (5)-(7).In the 1956paper I dwelt on the practical difference between thede dicto statement:



W . V. Q U I N E 9

( 8 ) Ralph believes ‘ ( 3 x ) ( x s a spy)’

and the de re statement ‘The re is someone whom Ralph he lieves to b e a spy’, that is:

(9) (3y)( Ralp h believes ‘spy’ of y) .

I noted also the more narrowly logical difference between the de d i c t o statement:

(10)

and the de re statement:

(11) Ralph beli eves ‘spy’ of Ortcutt,

and conjectured that the st ep of ‘exportation’ eading from (10) to (11)is generally valid.

However, if we transcribe (10) and (11) into terms of ‘Br’ according to th e foregoing

patterns, we get:

(12) B,(Ortcutt is a spy ),

(13) ( 3 x ) ( x= Ortcutt . B,(x is a spy)),

and h ere t he existential force of (13)would seem to beli e the validity of the exportation.

Sleigh, moreover, has chall enged this st ep on other grounds.8 Surely, he observes

(nearly enough ),Ralph beli eves t here a re spies. If he believes further, as h e reasonably

may, that

(14) N o two spies are of exactly the same height,

then he will b elie ve that the shortest spy is a spy. I f exportation were valid, it would

follow that

Ralph beli eves ‘Ortcutt is a spy’

Ralph believes ’spy’ of the shortest spy ,

and this, having th e term ‘the shortest spy’ out in referential position, implies (9).Thus

the portentous belief (9) would follow from trivial ones, (8) and belief of (14).

Le t us consult incidentally t he analogues of (10) and (1 ) in modal logic. Looking to

the transcriptions (12) and (13),we s ee that the analogous modal structures are ‘ma’

and ‘ ( 3 x ) ( x= a . W x ) ’ .Does th e one imply th e other? Again th e existential force of th e

latter would suggest not. And again we can dispute th e implication also apart from that

existential consideration, as follows [abbreviating (14) as ‘14’1:

(15) O(14 >. the shortest spy is a spy),

(16) ( 3 x ) ( x = the shortest sp y. O(14 3. is a spy)).

Surely (15) s true. On t he other hand, granted (14),presumably (16) s false; for it would

require someone to be a spy de re, or in essence.

Evid entl y we must find against exportation. Kaplan’s judg ment , which he credits to

Montgomery Furth, is that the step is soun d only in the case of what h e calls a uiu id

designator, which is the analogue, in the logic ofbelief, of a rigid d e ~i g na to r. ~nd what

might this analogue be? We saw that in modal logic a term is a rigid designator if

( 3 ) O ( x u ) , where ‘a’ stands for the term; so the parallel condition for the logic ofbelief is that (3 ) B t ( x= a), if Tom is our man. Thus a term is a vivid designator, for Tom,

when ther e is a specific thin g that he believes it designates. Vivid designators,

analogues of th e rigid designators in modal logic, are the terms th at can be freely used to




instantiate quantifications in belief contexts, and that are subject to the substitutivity

of identity-and, now, to exportation.

Hintikka’s criterion for this superior type o fter m was that Tom know who or what the

person or thing is; whom or wha t the term designates.’OThe difference is accountable to

the fact that Hintikka’s was a logic of both belief and knowledge.Th e notion of knowing or believing who or what someone or something is, is utterly

dependent on context, Sometimes, when w e ask who someone is, we see the face and

want the name; sometimes the reverse. Sometimes we want to know his role in the

community.” Of itself the notion is empty.

It and t he notion of essence are on a par. Both make sense in context. Relative to a

particular inquiry, some predicates may play a more basic role than others, or may apply

more fixedly; and these may be treated as essential. Th e respective derivative notions,

then, of vivid designator an d rigid designator, are similarly dependent on context an d

empty otherwise. Th e same is true of the whole quantified modal logic of necessity; for

it collapses if essence is withdrawn. For that matter, the very notion of necessity makes

sense to me only relative to context. Typically it is applied to what is assumed in an

inquiry, as against what has yet to transpire.

In thus writing off modal logic I find little to regret. Regarding the propositional

attitudes, however, I cannot be so cavalier. Where does the passing of the vivid

designator leave us with respect to belief? It leaves us with no distinction between

admissible and inadmissib le cases of the exportation that leads from (10) to ( l l ) ,xcept

that those cases remain inadmissible in which the exported term fails to name anything.

It leaves us defenseless against Sleigh’s deduc tion of the strong (9)from (8)and belief

of (14). Thus it virtually annuls the seemingly vital contrast between (8) and (9):

between merely believing there are spies and suspecting a specific person. At first this

seems intolerable, but it grows on one. I now think the distinction is every bit as empty,

apart from context, as that of vivid designator: that of knowing or believing who

someone is. In context it can still be important. In one case we can b e of service bypointing out the suspect; in another, by naming him; in others, by giving his address or

specifying his ostensible employment.

Renunciation does not stop here. Th e condition for being a vivid designator is that

( 3 ) B t ( x= a) , or, in the other notation, that

(%)(Tom believes ‘y 3 y = a)’ of x )

Surely this makes every bi t as good sense as the idiom ‘believes of‘; there can be no

trouble over ‘y 3 y = u)’. So our renunciation must extend to all de re belief, and

similarly, no doubt, for th e other propositional attitudes. We end up rejecting de re or

quantified propositional attitudes generally, on a par with de re or quantified modal

logic. Rejecting, that is, except as idioms relat ivized to the context or situation at hand.

We remain less cavalier toward propositional atti tudes than toward modal logic only in

the unquantified or de dicto case, where the attitudes are taken as dyadic relations

between people or other animals and closed sentences.

Even these relations present difficulties in respect of criterion. Belief is not to be

recognized simply by assent, for this leaves no place for insincerity or sanctimonious

self-deception. Belief can be nicely tested and even measured by the betting odds that

the subject will accept, allowance being made for the positive or negative value for him

ofrisk as such. Thi s allowance can be measured by testing him on even chances. How-ever, bets work only for sentences for which there is a verification or falsification

procedure acceptable to both parties as settling the bet. I see the verb ‘believe’ even in

its de dicto use as varying in meaningfulness from sentence to sentence.



W. V . Q U I N E 11

Ascribed t o t he d u m b an d i l l it e r a te an imal , be l i e f de d i c t o seems a contradic t to in

ad jec to . The be t t i ng t e s t i s never ava i l ab l e . I have sugges t ed e l sew here tha t some

proposi t ional a t t i tudes-des i re , fear -might be const rue d as a re la t ion of th e animal to

a se t of se t s of his sensory receptors ; bu t th i s works only for what I ca l l ed egocen t r ic

de s i re and fear. I2I se e no w ay of extend ing this to bel ief . Cer ta inly the ascr ipt ion of aspec if i c s im ple be l i e f t o a d um b an imal o f ten can be s upp or t ed by c i t i ng hi s obse rvab l ebehavior ; but a general def ini t ion to the purpose is r iot evide nt .

Raymond N e l son has a sc r ibed be l i e fs to m ach ines . I3 He has do ne so i n suppor t of a

mechan i s t ph i losophy , an d I share his a t t i tude. T h e objects of bel ief wi th wh ich h e

dea l s a r e d i sc re t e , obse rvab l e a l te rna t i ves , and t he mach ine ’s be l i e f o r expec t a ti on

wi th respect to the m le nd s i t se l f to a s t ra ightforward def ini tion. But th i s is of no ev ide nthe lp i n t he k ind o f p ro b l em tha t is exe rc is ing me he re . F or my prob l em I S not one of

r econc il ing m ind an d mat t e r , bu t only a q u e s t f o r general cr i ter ia sui table for unpre-

fabr icated cases .

F O O T N O T E S

I The word was first used by Goodman, at my suggestion.

* “Quantifiers and Propositional Attitudes,”]ournal o f P h i l o s o p h y 53(1956):177- 187, reprinted

in my Ways of Paradox an d Other Essays (New York, 196G) a n d enlarged edition (Cambridge,

Mass., 1976).

See my paper “Th e Variable,” in Logic Colloquium: Lecture N o t e s in Mathernutics -153, ed.

R. Parikh (New York, 1915), pp . 155- 168, reprinted in FVays of Paradox, enlargecl edition, pp .

272 -282.

For a study ofthe tnth theory ofa predicate functor to just this effect see Christopher Peacocke,

“An Appendix to David Wiggin’s ‘Note,’ ” n Truth and Meaning, eds. G. Evans and J. McDowell

(Oxford, 1976), pp. 313-324.

.

Dagfinn Fdllesdal, “Knowledge, Identity, and Existence,” Theoria 33 (1967): 1-27.

Saul Kripke, “Identity and Necessity,” in Zdentity and lnd iui dttuti on,ed. M. Munitz (New York,

1971). pp. 135-164.

‘See m y “Worlds Away,”Journal of Philosophy 73 (1976): 859-863.

’R. C. Sleigh, “On a Proposed System of Epistemic Logic,”Nol i s 2 (1968): 391-398, esp. 39711.

David Kaplan, “Quant ifying In ,” Synthese 19 (1968-69): 178-214, esp. pp. 193, 199-203,

reprinted in Words and Objections, eds . D. Davidson an d J. Hintikka (Dordrecht, 1969). pp.

206-242, esp. pp. 221, 227-231.-1 now discover, too late, a major anticipation of the present

paper in his footnote 3.

lo Jaakko Hintikka, Knowledge and BeZief (Ithaca, 1962).

Such variation is recognized b y Hintikka, p. 149n. For a study of it in depth see Steven E.

“Propositional Objects,” Critica 2 , no. 5 (1968): 3-22, reprinted in my Ontological Relatiuity

Boer and William G. Lycan, “Knowing Who,” Philosophical Studies 28 (1975): 299-344.

an d Other Essays (New York, 1969), pp. 139-160.

l 3 R. J. Nelson, “On Machine Expectation,” Synthese 31 (1975): 129-139.

quine intensitons revisited

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