Possible Worlds, Physics and Metaphysics

f 68

David Lew&' Theory of Passible Worlds

he develops his theory. Thus Lewis identifies &propertywith a set of particulars, existing in various possible worlds. (a has F-ness if and only if a belongs to the set identified with F-ness.) But no particular belongs to two worlds. So we may associate with any set of particulars the set of worlds to which those particulars belong. Hence, on ]Lewis' theory, with each property F-ness there is associated the set of worlds in which F-ness is instantiated. But far many properties we can show there is no set of possible worlds at which that properly is instantiated. Consider, for hiance, the property being m d i m n . Our 'above' world construction shows that, given a purported set of all worlds containing electrons, there is an 'above' world which also contains electronis but is not a member of that set.

Schoul of History, Politics and Philwophy, Macquarie University. &prtme~i of Traditional and Mudern Plhilos~phy, University of Sydney Received April 1983

REFERENCES B r d , C. D,f 1933)- Examimtion of McTaggurt's Phiimophy, Vol. 1, Cambridge University Bra. Lewirs, David t 19731, CounZerJ~cfuals,Blackwelt.

I

BRIAN S K Y R M S

I

POSSIBLE W O R L D S , PHYSICS A N D METAPHYSICS*

(Received 24 December, 1975)

The idea that many possible worlds may exist, not merely as abstract stmctures but in a concrete and robust a manner as our own, has long been familiar to fans of science fiction.' Recently, it has acquired proponants from two distinct areas. David Lewis, in his book, Counferfactuals,argues for just such a view: I believe that there are possibIe worlds other than the one we happen to inhabit ... I emphatically do not identify possible worlds with respectible linguistic entities; I take them to be respectible entities in their own right. When I profess realism about possibIe worlds, I mean to be taken literally. Possible worlds are what they zre, and not some other thing. i f asked what sort of thing they ate, I cannot give the sort of reply my questioner probably expects: that is, a proposal to reduce possible worlds to something else.

I can only ask him to admit that he knows what sort of thing actual worfd is, and then explain that other worlds are more things of that sort, differing not in kind but only in what goes on at them. Our actual world is only one world among others.'

But it is not only metaphysically-minded modd logicians who support a many-worlds view. Some physicists have argued that such a view is required for a correct interpretation of quantum mechanics. IkWitt and Graham, in their preface to The h n y - h r l d s Interpretation of m n m m Mechanics write:

...

Hugh Everett 111, propounded a new inttrprrtation of quantum mechanics that denies the existence of o *parate clasdcal nalm and asserts that it makes sense to talk about a state vector for the entire unive~e.The state vector n m r cohpws, and henst reafiW as a whole Is rigaously deterministic, This rtaiity, which t &scribed jointly by the dynamicol variables and the state vector is not the reailty we customaiiy think of, but a reality composad of rnarsy worlds. By virtue of the temporal developmnt of h tehe d~nrtrnicralvariabbs the sate vector decornpaseg natur4.b hrs orttacygonal vectors, reflecting a cantinun1 rglitting of the universe into a multitudc of mutual& ~ n ~ b w m a b k but equally rcd worlds

..."

In light of such suggestions, the! f~Uowingquestions of 'pldosogkcal sciencefiction' take an.a wider significance. PhiIosophicgI Studief 30 (2976)323 -332. AZZ Righa R m c ~ e d Copyright 43 1976 by D. Reidel fib2bhin.g Company, Dodrccht-fiiknd

P O S S I B L E W O R L D S , PHYSICS A N D M E T A P H Y S I C S

1.

11.

Is the contention that more than one possible world exists (in the sense our own) cr=7fisistenf? If it is Consistent, how do r;Ne fmd out the facts of the matter?

In order to answer these questions, we must be clear about just what sorts of possible worlds are at stake. 1f a possible world need only be a mathematical structure which is a model for a dven language, then the co-existence of many possible worlds poses no conceptlid problem But it is clear that it is existence is at issue here. Neither not that sort of possible world physicist not science fiction writer is interested in such pale and abstract possibnities, and Lewis explicitly says that he isn't either; "I cannot believe ... that our o m world is a purely m a thematical entity. Since X do not believe that other worlds are different in a n d from ours, I do not believe that they are either."4 What I take kwh tobe saying, and what makes his claim really p ~ ~ ~ iworlds b l e are red as Afghanistan exciting, is the contention that A- Lewis, DeWitt and the typical science or the emter of the Sun or fiction story all claim that possible worlds exist in just as ~ ~ ~ c ra eMY t e as One possible! Our O I W . f Suggest that we take tm as implying &at more world is real in the following sense: A world is real if-and-only if every proposition true-in-that-world is m e . 5 T h i s seems a modest requirement, designed only to separate genuine physical or metaphysical c]-s from metaphoficafl~ presented rnode1 theory- But this innocent requirement imediateJy leads to difficulty. It is plausible t o adopt the following principle of individuation for possible worlds: A world w is identical t o a world w 2 if and only if exactly the same propositions are true-in-wl as are tme-in-w, ~~t n m if two possible worlds are disrinct then there is a proposition wlrich is tme-&-one and whose denid is tmt-betheother; and if two distinct worl& aarc: m d then there is s propositon such that both it and its denid arc? tme. me many-worlds hypothesis is prima JPcie inconsistent! T h e situation is reminiscent of ;i?az old metaphysical problem, the problem of rhge.' Change involves apdmf&ie contradiction - f i t Fa, then -Fa with the first a d second &uations being quite red. Some phifosophers have taken this d i f f i e d as ~ showing change; is impossible. Others have conduded that contradictions me possible. Neither of these views is now much favored,

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Rather, it is generally held that the appearance:of contradictionin the demiption of change arises from an incomplete specification of the statements involved. We do not have 'Fa' and '-Fa' both being true. Rather, we have a true the relational statements 'Fat,' and '-r;irtz3where 'tl' and 't3' refer to different times. 'Socrates is young at t t ' no more contradicts 'Socrates is old at t2' than 'Socrates loves Alcibiades' would contradict 'Socrates cares not for Democritus', This medicine is such a successful treatment for the paradox of change that it h hard to resist trying it out on the paradox of many real worlds. We will say that what we took to be 'Fa' is really 'E;izwlY a d what we took to be '-Fayisreally '-Fav,'. Thus 'Socrates is wise in wodd 1' no more contradicts 'Socrates ia silly in world 2' than Socrates is young at tl' contradicts 'Socrates is old at t2'.7 But now, we no longer have two distinct possible worlds in the sense laid down. What has happened is that what looked from an earlier perspective (the Fa; -Fa perspective) like distinct possible worlds, have from the later ( F w , , - F m z )perspective been incorporated into a single 'supr-world'. Thus, the answer to question 1 is: yes and no. It is strictly inconsistent to maintain that two distinct possible worlds are real. But is always B consistent to take what, from a certain perspective are distinct possible worlds; incorporate them as indicated into a single 'super-world'; and contend that that super-world is real. More precisely, we see that the notion of a possible world is languagerehtive. Relative to the language in which 'Fa' is a closed sentence we have two distinct worlds, but relative to the richer language in which ' F i i 3is a closed sentence they are but objects; a part of the substance of the world. A language, L , can always be replaced by a richer language, L', in this manner so that the worlds relative to L, are objects relatiye to L'. Consequently, tha claim that more than one po~ribleworld sxistJ must be taken ss s~sertingthat tome language, L, is not adequate to d e s r i h mality, but that a richer L' which requires many worlds-nlative-to-l m n g its objecb ir .&qua&.

kt us examine the reasons adduced by both mtaphysicim a d physicia, in support of hais claim. Lewis writes: If an argument is wanted, it is this. 10 is uneontrovody true that things nt@t ha= k e n oth~mimthan they am, I & W e , md xr 13o you, that thin@caW hare hem pellmits; the W e s n t in countlea ways. But what dues this arm?O r d h w many ways that things mdd haw hen, b e a s the sully t h y p m p w : these are. On tfre face of it, this sentenm is mi exkbntid q ~ ~ c s t i oftnsays . &at

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POSSIBLE WORLDS, PHYSICS A N D METAPHYSICS

there exist many entities of a certain description, to wit 'ways things could have been',

ary way of doing 'possible-world-semmtics'. One must admit, on this approach, that the real world is not a 'possible-world'. But to insist that it must be is perhaps to take a metaphor too literally. Lewis' robust realistic theory of possible worlds is not required by possible-world-semantics; it is rather an intellectual adventure su&gested by possible-world-semantics. Finally, it is not at aU clear why Lewis' truism, "things could have been otherwise" should not apply also to the enriched language which numbers among its 'things' the possible worlds relative t o the initial language; and thus gnerate a runaway ontology.'0 This metaphysical-semantical line of argument, then, fails both internally, and because it is an inappropriate kind of argument for deciding what is essentially a physical question. A compelling argument for a reality composed of many worlds would have take the form of a demonstration that the best physical theory available required such an expanded reality. (If, for example, a new physical theory required a 5-dimensional reality, we could regard it as a reality composed of many 4-dimensional worlds, with the appropriate topological and causal relations holding between them.) Such news from physicists would be important and exciting, but would not, I think, satisfy Lewis. For Lewis assumes that the initial language is the Ianguage of physics, whatever it is, and that his worlds are worlds relative to t h t Ianguage. He thus forecloses access to the only sort of evidence that could support his robust realism.

326

I believe things could have. been different in countless ways; I believe permissible para* phrases of what I believe; taking the paraphrase at its face value, I therefore believe in the existence of entities that might be called 'ways things could have been'. I prefer to call them 'possible world^'.^

Taken at face value, this argument seems rather cavalier. Are there then 'ways in which things could not have been" (e.g. triangles having 4 sides) which are impossible worlds? Etc. But, Lewis redly has a more sophiticated argument in mind. Thus: I do not make it an inviolable principle to take seeming existential quantifications of ordinary language at their face value. But I do recognize a presumption in favor of taking sentences at their face value, unless (I) taking them at face value is known 5 0 lead to trouble and (2) taking them some other way is known not to ... 1 do not no any successful argument that my realism about possible worlds ieads to trouble ... All the alternatives I know, on the other hand, do lead to t r o ~ b l e . ~

M a t this argument comes to, I think, is the contention that the most viable sernanticd theory for our ordinary counterfactual and modal discourse is one which assumes the co-existence of many actual possible worlds, Even if this contention were correct, it would constitute a weak argument. If I were convinced that the smoothest sernantical theory that could make sense of o r d i n q talk about the Easter rabbit; goblins; angels; and Pegasus was one which assumed that such things really existed, I would not thereby be convinced of their existence. Rather, I would hold such ordinary talk suspect. I have no reason to believe that emantical theory for ordinary discourse is a reliable guide in these matters. What J require here are physical reasons (rabbit track, etc,). What about possible worlds? If possible worlds are supposed to be the wme sorts of things as our actual world; if they are supposed to e d s t in as concrete and robust a sense as our own ; if they are s u p p e d to-be as real as Afghanistan, or the center of the sun or Cygnus A, then they require the same sort of midence for their a&istence es other consti&mbs. ufphysicaI rmZity. What is required t o show &at thr: sort of possible wodds Lewis wants exist, is their presumption in the best phyrsiml theory. Furthemore, the contenticin that this sort of robust realistic theory of possible worlds provides f;he most viable foundation for re =mantical theory for rnodiils and counkditctuds seems t o me quite clearly false. T h e reason is that abstract mathematical structures (Lewis c& them "Ersatz possible worlds") w# do just as weZI as the 'pasible-worlds' in 'possible-worldw m n t i ~ for ' modal and counterfactud logic. f n fact, this is just the cwtom-

M a t news h e n , do we h m from physicha concerning the existence of many worlds? Quantum mechanics, under the Everett-Wheeler interpretation, has the initial appearance of being just n theory of many worlds. In fact, h w i t t md Graham have chwen to cntide their coflaction of afticlex of the EversttWheeler interpretation '?Re Many-Worldr Inferpretntion of QzLantum ~'cknics.' In languags reminescent of Lewis, DeWitt dtscribes the many worlds : Our univttxse mwt be viewed aai constantly splitting into a stupndous number of bnhches, all resulting from the m ~ u r t n r t ninterntion ~~ between its my&& of

*

COragponcn.ts, Because there exists neither a mchanism within the f-w~rk of foraamm nor, by definition, an entity outride of tfit universe that de-h whhh branch of the gmad superposition is the 'real' world, PU bmcfies must be remded as q w y

real.1=

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BRIAN S K Y R M S

...although S is in st definite state 9 '8,the subsystems S, and S, do not posses mything like defiite states independently of one another ... We can however for any choice of a state in one subsystem wigueiy assign a carresponding rektive state in the other subsystem ...

Why then, do we not observe such splits? Everett expliiins: In reply to a preprint of this article, some correspondents have raised the question of the rfrm$ition7 from possible to actual,' arguing that in 'reality' there is - as our exprience testifxes - no such splitting of observer states, so that only one branch can ever actually exist. Sincc this point may occur to other readers the following is offered in expbtion.

For any choice of basis in S, , {gi) it is always possible to r e p ~ m the t statc of S as a single superposition of pairs of states each consisting of a stab from fie bwb { t i ) in S, and its relative state in S, .I3

The whole issue of the transition from 'possible' to 'actual' is taken care of in the theory in a very simple way-there is no such transition, nor is such a transition necemry for the theory to be in accord with our experience. From the viewpoint of the theory a& elements of a superposition (all 'branches') are 'actual', none any more 'red' than the rest. It is m e e e s w to suppose that aU but one are somehow destroyed, since an the separate elements of a superposition individually obey the wave equation with complete indiffercnae to the prepence or absence ('actuality' or not) of any other elements. This total lack of effect of one branch on another also implies that no observer wig ever be a w m of any 'spjlitting' prmm.lZ

Given an ideal measuring interaction between a measured 'object' subsystem and a measuring 'apparatus7subsystem, for each state of the apparatw sysbm its relative state is the corresponding eigenstate of the apparatus system. For the composite system there is then;

...

a representation in terms of a superposition, each element of whkh contains a &finit% observer state and a corresponding system state. Thus,with each s u c o b ~ d iobservation i (or interaction) the observer state 'bmchw' into a number of different Jhtcr. f i c h b m c h represents a different outcome of the measurement avrd tho c o r r e ~ n d h g~ k n state for the object system state. bmches exist simultaneously in the superposition after m y given sequence of obs@;rvations.'*

But if the Everett theory is only one interpretaiiun of quantum mechanics; if other interpretations require only one world; and if the Everett interpretation is observationally indistinguishable from other interpreations ; shouldn't the Everett interpretation simply be eliminated by Ockham's Razor? The matter is not quite so straightforward. In a standard formulation of quantum mechanics, the state function, J, may change either (1) continuously, according to the Schrodinger wave equation or (2) discontinuously, as a result of a measurement, according to the projection postulate. In the Everett theory, only proms 1 is allowed; the projection postulate is denied. The entire universe may be treated quantum mechanically in the Everett theory, but not on t h e standard theory. Thus it is strictly incorrect to speak here of two different interprsalions of the same theory. What we redly have are two distinct, incompatible theories. The Everett theory cannot then, simply be dismissed as quantum mechanics plus metaphysical puffery. It must be rationally evaluated a s a genuine alternative theory. I do not want to pursue that evaluation here, but only to ask what sort of 'many-world$ pictun the Everett theory docs give us. Everett propats to regard wave mechanics as a complete theory, Thus, measurement must be reg;lr&d ;ts an interaction between two subsystems of a composite system, whicfi must itrdf be regarded from the standpoint of wave mechanics. Thus:

I"?& k s Eht conqaaeaa tjuit if the sets {tf$1 1 and sets

fT@S2 ) ~ - ~ m ~ l~e t f@ i o ~ of states fos $, ruid S, respectively, then the g3~nera.lstate of S can b~ written as P

superporzitim:

$8 = xfjy hS. nisz

329

o

~

For purposes of illustration, consider the Schrodinger Cat paradox. The catgeigercounter subsystem measures the radioactive source subsystem. Tney are coorelated 30 that the relative state of 'cat dead' is 'radioactire decay ~ ~ ~ u r r and e d ' the relative stale of 'cat alive' is 'radioactive &my didn't occur'. The state of the composite system is a superposition containing these pairs of states. Thus we are led to talk of a reality containing one world with radioactive decay and dead cat, and another with no radioactive decay and five cat, Here then, are the many worlds of the 'many-wotids interpntation of quantum mechanics'. What kind of worlds me t h q ? An unauphis.kicated reader might jump, from the example of Schrodinger7sc ~ tt,o fhc ~ o o c ~ w i ~ ~ ~ that they an classical worlds. But, of course, the uncertainty principk hmediately show that this cannot be so. A world cannot haw g g l . ~~ d t f e ~ for both a position md a momentum of a partide at a tim.Each world it quite th~mughlyquantum mechanical, md may be thought of a ~ ~ f t ~ ' ' in Hnbrt rpaos. Ks uni~m of mpny wad& m y llwr be %o@t of s?r a vwttw in Hilbsrk space. Now then, do the worlds and fhefr nlttiw constitute a larger reality? AU we can wy in the u n h r e ~of wad& h mch that it erm be r ~ p e m t E das a m p p m of the compi&mf. w* with m f i mf~ m a n . One may wonder at this point whether this b a theory of r n&ty composd of many ~oddnin tbe sew s t forth at the bcgi.dagofW prpr.

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POSSIBLE WORLDS, PHYSICS A N D METAPHYSICS

I think that it is not. The argument that I will ofler is an old one, and in no way orignal; but I think that for the concerns of this paper it should be underlined once more. It is evident, that if a universe of worlds U1contains at least one world, W,which is not contained in a univeme Ll; ,then U1 and U2are distinct. For instance, if we tried taking numbers as worlds, and the 'universe' containing several 'worlds' as just their sum, it would not wash for then the Zlniverse" containhg just 2 and 3 would be identical to the one containing just 1 and 4. The same point applies generally to taking vectors as 'worlds'and their vector sum, or a superposition of them with various coefficients as 'universe'. Now in quantum mechanics, the decomposition of the state vector is likewise not unique. The state vector might be written in terms of position eigenvectors or momentum eigenvectors (or in t e r n of some other basis). The idea of Everett-Wheeler is to disambiguate by using eigenvectors of the measurement actually performed, The performance of a perfectly sharp position measurement then splits one world into non-interfe~gbranches, each of which regsten a sharp position. What is important for us here, however, is that a perfectly sharp position measurement is an idealization - it never really happens. What we have instead are imperfect approximations to this model, where the world docs not split c l e d y into non-interfering branches. But now, there is no ma9011 not to decarnpose in terns of momentum mther than position, and by our previous argument, we have one quantum mechanical world rather &an many (just as we did before the imperfect measurement). From this standpoint, d l the 'garden of the forking paths' talk is an appealing metaphor which provides some insight into the theory of measurement, rather than an accurate description of the reality posited by the theory. I am not suggesting that the physic&@who are propanan& of the Everett-Wkedcr interpretation are deceived They know this all very well.' But we would be deceived if we took the reladve4tate formuIotion of q w t u m . mchmicrr to be a theory of m a y polasible wonlds Iln Pht mnse at issue in thb paper. In smw, &ens lis a sense jn which the con ten ti or^ &at many pmibte teat. MebphysicaI md moammntid a m c n e fd to &d& the 43taXiCXi. b t is required to %Upp~t*% the =y-wsfi& con&ntion is n demonstnrtion h t the b e ~ physical t theory requires a richer reality, w&& from the starsdgmkt of our cumnt penpctcti~e,is a =&ey af many worlds. I t k quite pcssible &at them might be such a physid theory. But Everett's "bEa&cf State' fum~latjolzof qmtu~lrmme~hmicdi& not meh

a theory. To the best of our present knowledge, the hypothesis that more than one possible world is actual fails.

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of Illi~~is at Chicago Circle NOTES

* This paper grew out of a talk entitled 'Parakl Worlds and the Principle of Planitatatas" given at Various times at University of Wisconsin; University of Chicago; fhlgblry University; U.C.L.A. and U.C. Berkeley, in which I presented, md then criticized a position much Like that of David Lewis. That paper, more than thls, exhibited my ambivlrlsma to a many-worlds view of reality which 1 find aesthetically attractive but, in final analysis, philosophically indefensible. Thank?;for hefpful comments am due t6 the audiences at each of these talks and also to Jim de Jong; Terry Patsons; Bas van F m n ; David Kapfan; David Lewis; Arthur Fine; Neal Grossman; Abner Shimony; Paul Teller; Ernest Adams; Phil Quinn; Gail Stein; Nancy CarWright and ladie Tharp (none of whom are to be taken as ensorsing the following). This paper is not an attack on modal logic. This paper is not an attack on the Everett-Wheeler interpretation of q w m m mechanics, T h e m l v e s , various episodes of DY. W h ,BBCRecent examples: Asimov, The TV. David Lewis,Counrerfactuals (Harvatd University Press: Cambridge, 1973), pp. 84-85. Bryce I)eWitt and Neill Graham (eda.), l%t! Many-Worilds inteqmtarion of Quantum Mechanics (Princeton University Press: Princeton, 13731, p. v. Lewis, Countmfacnurb, p. 84. "ibis definition, and the following argument are due to a suggestion of Terry M s o ~ . stated, the clefitions and the argument depend on a rather platonisticvkw of propasitions. Otherwise, there wouldn't be enough of them to fully characterize a world. Those who feel more comfortable with sentences might modify the argument as follows: ffa world is real then every sentence true-in-hit-world is true. Two worlds are d i r m f b l y distinct if and only if there is a sntence true&-one but not the other. A theow of m31Iy discernibly d i s h c t worlds then falls into the same difficulties; while a theory of ma~Iy distinct but indiscernible worlds is not too interesting. The Bnalogy between possible worlds and moments of time has Men pointed out by Prior, Montague, Kaplan, and Lewis, among others. NO@ that we cannot yet out of thcr general difficulties n h d with Just some buaincu about sountsrparrt. Consider the cuc where ' ( 3 ~hr' ) is trusinu, and its denirl is trus f "z* David hw&, Cosurt~~~facmbr, p. 84. David b w h , Cb~lntrtfocttdaik,p, 90. We slw that in order to wnsistcrntly rnrintnln that many paajibfrr worlds rrc we musf incoq3~rat.athem into a sfnOQ xwfity; a sir@@ hprworbl'. M& q e now mppaar at the lava1 of surparworw. Lewis blicvhs that o w md£tyk a stppemrld hccapgorat;ing many g d b h world. A mom convcntianrrl vbw hoMs h t OBK d t y incogorates only one pmdbla? worM. Ff, as I how w e d ,this iai ultj'saak& a &f3-ath@nt pk~siePlquastion, we would want to s y that it is p-bb that b w i is ~ Mt and W that h~ is wrong. That Fs t o my, in polpplik-world-a, that thcn k mem thsn A consistent d t must then hold tAat m y supe,~ar&are real, sad h m Q ~ m t tthem into an even richer reality, a augm-super w0tI.d. ft L c h that thir PFoccor ~ G Y W Tstop. NO naattt:rhow rick lp W g y thc rdkt portktkter, ( m a ifba

'

'

'

' "

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BRIAN S K Y R M S

goes to the trouble of postulating supenvorlds of transfinite order), we can always ask the modal question "Is it possible that reality is different from that postulated by the realist". And given that the reasonable answer is 'yes', the realist must postulate an even richer reaEty. The point is, that this regress is embarrassing to a realist in a way that it is not to a theorist who views possible worlds simply as mathematical structures. The latter needs only to be able to find appropriate mathematical structures given any reasonable modal language. The former must have a reality rich enough to accomodate all modal h g ~ ~ g eBut s . by the foregoing argument, whatever reality the realist postulates cannot be r i c h enouah. One might remark that the ontological situation here is no worse than that for set theory. Indeed! But it is one thing to take a conceptualistic attitude towards sets, and another to trike such an attitude towards physical reality. For proof that no language rich enough to contain arithmetic can express its own Concept of necesdty, sea Montague, LSyntacticalTreatments of Modality, with Corollories on Reflection Principles and Finite Axiornatizability', in ftoceedings of a CoZZoquium 0" and Many- Valued Logics: Aero Filosofiur Fennieo (Helsinki, August 19621, pp. 153-167. i i Bryce DeWitt, The Many-Universes Interpretation of Quantum Mechanics', in DeWitt and Graham,p. 178. " Hugh ~ v e r e t III t ' "Relative State" Formulation of Quantum Mechanics', Reviews of Modem Physics 29,454-462, reprinted in DeWitt and Graham,pp. 146-147. Is Everett, ' "Relative State" Formulation of Quantum Mechanics', p. 143. l4 Everett, ' "Relative State" Fo~rnulationof Quantum Mechanics', p. 146. I S ?dore correctly, the vector represents the state of the world at a time, but this does not affect the armmenf ------18 See DeWitt's discussion of imperfect measurements in T h e Many-Universes Interpretation of Quantum Mechanics', in DeWitt and Graham, pp. 210-215. w-

Propositional Objects

A declarative sentence is muany true or false. But your typical declarative sentence is not &edly true or false. It is true on one occasio~land false on another, because of the tenses of its verbs and the varying references of its pronouns or demonstrative adverbs or other indicator words. By incorporating additional information into the sentence, such as dates and the names of persom and places, we can obtain an eternal sentence: one that is fixedly true or fake. has an eternal sentence need not be a law of mathematics or of nature; it can also be a report of a passing event, Now a p~posftionis the meaning of a sentence. Mom precisely, since pmpu~itionsare supposed to be true or false ofice and for all, a proposition is the meaning of an eternal sentence. I 4 . o ~precisely tt is the cognitive m e d n g of an etemd sentence; &at is, just so much of the m e h g es affects the b t h value of sentence and not its poetic q d t y its

sm,

E t f f ' y ~tofie, ~:

Not that thZp & precise The word l i n e d g " d v - in my ~~pfmafiOrZ1 and it men a m d ~ u d e of sM.Whc;n I g:qb