TO BURT ORE BEN im iend ad constuctive critic down the decades opyight C 192, 10 by the Prsidnt and Fellows of Havard olege All ights rv ed Pnted in the Uited Stats of Amia 10 9 8 7 6 5 4 3 2 1 ist Havard Uiversity Prss paerback ediion, 192 Libray of Congrtss Cataloging-in-wbliltion ata I. Quine, w. V. (Wllard Vn Omn) Pursit of tuth I W. V. Quine. - Rev. d. p. cm. Includes bibliograpical referencs nd index. ISBN -674-73951-5 (pbk. : lk. paer) Meaning (Plosophy) 2. Refernce (Phlosophy) 3. Knowledge, Thoy o. 4. Semnics (Plosophy) I. Title. B94 5·Q5 3P87 192 UI-dc20 92-506 CP Preface to the Revised Edition irst appeared, I was in th e g alan t ittle Republic of San Marino for a week-long international colloquium on my philoso phy. Six months later I was in medieval Girona, in Cata loia, giving the Josep Ferrater Mora Lecturs-ifteen hours of them and ive of discussion. Donald Davidson, Bur to n Dreben, Daginn F0Uesdal, and Roger Gibson were ll im por ted wit h me, to add depth and zest to the discussion. The busy months of p re pa ration and the stimu lating exch n ges on thse occasions sparked thoughts that would have made for a better book if the chronology had b een inverted. I am approimang such an invers io n as best I can by tis ear ly re vis ed edit io n Old §13 , "Ontological r ela ti vit y, has become more emphaically "Ontology defused," and incorporats bits from my responses in the projected San Maino volume. My treatment of domestic meaning n §22 is utterly In May 1990, a mere four months ater this book . " changed, and so also, thanks to Davidson's and F0Uesdal's a b et ting , are March 192 §§28-29 on propositional attitudes. W.V.Q. Preface to the First Edition In these pages c l a ri fy I have undertaken to upda te, sum up, and my variously interseng iews on cognitive mean ing, objective reference, and the grounds of kn owledge. S ome of the progress is expository and some substantive. The substnce has ben precipitating sporadicaly over the past ten years, and some of it has surfaced in lecturs, nfor mal d iscuss ions, and scattered paragraphs. In interrelating these thoughts I have occasionlly found a faulty joint and ha ve irmed it up to my satisfaction. I intend tis ittle book no less for my past readers than for my new ons, so I have curbed my exposiion of things already belabored n my other books. I do retrace fa miliar ground where 1 s e an impro ve ment in the idea or its pre sentation, and also where the new reader needs a ittle brieing to be kept abreast. The bits of the book that have pre viousl y appeared in pr in t add up to a scant nine pages, and are ident iied on a back page. Unpublished l ect u res were a richer source. My lecture "The Mentalistic Heritage" in Calcutta, 1983, is a source of §3 I, and "The Forked A im l" y ielded earlier parts of Chapter IV. That lecture was the third of four Immanuel Kant Lecures that I gave at Stanford in 1980. The tide of the seies offour was "Science and Sens ibilia , a ake of of John Austin 's takeof of J ane Austen. The four lecurs appeard as a little b ook in Ilian, a scienza e i dati " viii P REF A C E T O F IRS T E D I T I ON di senso, translated by Michele Leonelli ( Rome: Armando, 1987) . Instead of publishing them intact in English, I have used portions of them in subsequent publications, as here. Much of my lecture "Three Indeteminaies, " prsented at the Quine symposium at Washington University in April 1988, is woven into Chapter I, and bits into Chapter V. That lecture is to appear in the symposium volume, Barrett and Gibson, editors, Prpectives on Quine ( Oxford: Black well) . Another overlapping publication in the oing is "Tuth," witten at the request of the Institut International de Philosophie nd slated for Philosophical roblems Today ( The Hague: Njho) . I drew heavily on it for Chapter V , b y prior arrangement. I am blessed with bright and earnest readers . Leonelli wrote me from Pis a that my new blend of reiication with observation gave him una sona di crampo mentale. After two letters I began to feel the cramp mysel. Result: a substantial revision ofChapters I and II. A letter from Felix Mihlholzer n Munich prompted me to insert a couple of paragraphs recognzing the untidy side of scientiic method . A diiculty spotted by Lars Bergstrom of Stockholm is now noted and dealt with in the text, and my indebtedness to Donald D aidson, Daginn F011esdal, and Roger Gibson is noted at appropriate points. I am much indebted to Buton Drebn, who has read earlier drafts with care and insight nd has made many helpful suggestions. W.V .Q. CONTENTS I . EV I D EN C E I I. Stimulation and prediction 1 2. Obsrvation sentences 2 ) . Theoy-ladn? 6 4· Observation categoricals 9 5. Test and reutation 12 6. Holism I) 7. Empiri4l content 1 6 8. Noms and aims 19 II . REF ER EN C E 23 9. Bodies 2) 10. V.lues of variables 25 11. Utility of reication 29 12. Indferce ofontology )1 I). Ontology deosed )) I I I . ME A N I N G 37 '4. Thefold linguist's ntering wedge )7 15. Stimulation again 40 16. To each his own 42 17. Translation resumed 44 18. Indeteminacy of translation 47 19· Syntax 49 x C O NTE NTS 20. Indeteminacy of refrence 50 21. hither meanings? 52 22. Domestic meaning 53 23. Lexicography 56 I V. I N TE N S I O N 61 24. Prcption and obsevation sentnces 25. Percption extended 63 26. Percption of things 64 27. Belief and prcption 65 28. ropositioal attitudes 67 29. Anomalous monism 71 30. Malities 7 3 31. A mentalistic heritage 74 V. TRUTH 77 32. Vehicles of tu th 77 33. Tuth as disquotation 79 34. Paradox 82 35. Tarski's constuction 84 36. Paradox skited 86 37. Interlocked hierarchies 88 38. Excluded middle 90 39. Tuth versus waranted belief 93 40. Tuth in mathematics 94 41. Equivalent theories 95 42. Iresoluble ivaly 98 43. Two indeteminacies 101 References 105 Credits 109 Index 111 61 PURSUIT OF TRUTH 'W'�.I Tl x.I6�Q. PLATO Save the surface and you save all. SHERWIN-WILLIAMS I EVIDE NCE 1. Stimulation ad p rediction From impacts on our sensory surfaces, we in our collective and cumulative creaivity down the generations have pro jected our systematic theory of the extenal world. Our system is proving successfl in predicting subsequent sen sory input. How have we done it? Neurology is opening strange new vistas into what goes on between stimulaion and erception. Psychology and more particlarly psycholinguisics may be loked to for something to say about the passage from percepion to ex pectaion, generlization, and systematization. Evolution ay genetics throws further light on the latter matters, ac countng for the standards of simlaity that nderlie our generalizations and hence our expectations. The heuristic of scientiic creativity is illuminated also, anecdotally, by the history of science. Within tis baling tangle of relations betwen our sen sory stimulation and our sientiic theory of the world, there is a segment that we can gratefully separate out and clarify without pursuing neurology, psychology, psycho linguistics, genetics, or istoy. It is the part where theory is tested by prediction. It is the relation of evidential support, 2 P U R S U I T OF T R U T H and its essentials can be schematized by means oflittle more thn logical analysis . Not that prediction is the main purpose of science . One major purpose is understanding . Another is control and modiication of the environment. Prediction can be a pur pose too , but my present point is that it is the test of a theory, whatever the purpose. It is common usage to say that the evidence for science is observaion, and that what we predict are observations . But the notion of observation is awkward to analyze. Clariica tion has ben sought by a shift to observable objects and events. But a gulf yawns between the m and our immediate input from the e xtenl world, which is rather the trigger ing of our sensory receptors. I have cut through ll this by settling for the triggering or stimulaion iself and hence speing, oddly perhaps, of the predicion of stimulation . By the stimulation undergone by a subj ect on a given occa sion I j ust mean the temorally ordered set ofa11 those of his exteroceptors that are triggered on that occasion. Observation then drops out as a technical notion. So does evidence, if that was observation . We can deal with the quesion of evidence for science without help of 'evidence ' s a tecnicl term . We can make do instead with the notion of observaion sentences . 2. Obsrvation sentences We were ndertaking to examine the evidential support of sience. That support, by whatever name, comes now to e seen as a relaion of stimlation to s cieniic theory. Theory consists of sentences, or is couched n them; and logic con nects sentences to sentencs. hat we need, then, as iitial EV I D EN C E 3 links in those conecng chains, are some sentences that a re direcdy and irly associated with our stimulations. Each should be assoiated airmaively with some range of one's stimulations and negatively with some range. The sentence should command the subject'S assent or dissent outright, on the occsion of a simulation in the appropiate range, with out further nvestigation and independendy of what he may have been engaged in at the ime. A urther requirement is intersubj ectivity: unlike a report of a feeling, the sentence must command the same verdict from al linguistically competent witnesses of the occasion. I cal them obsevation sentences. Exampls are 'It's rain ing' , ' It's getng cold', ' That's a rabbit' . Unlike ' Men are mortal' , they are occasion sentences: true on some occsions, false on others . Sometimes it is raining, sometimes not. Biely stated, then, an observation sentence is an occasion sentence on which speakers of the language can agree out right on witnessing the occasion. See further § I S. Observaionity is vague at the edges . There are grada ions in an individul 's readiness to assent. What had passed for an obser vation sentence, say 'That's a swan', may to the subject's own surpise leave him undecided when he en counters a black specimen. He may have to resort to con vention to settle his usage. We shal need now and again to remind ourselves thus of the untidiness of human behavior, but meanwhle we foster perspiuity by fancying bound aries. he range of simulations assoiated with an observation sentence, airmatively or negatively, I cal its airmative or negative stimulus meaning for the given speaker. Each of the stimulations, by my deinition, is global: it is the set of all the triggered exteroceptors, not just the ones that happened PURSUIT OF T R U T H to eliit behavior. Hence the stimulations encompased in a stimulus meaning wll difer wildly from one another in their inefective irings, but in their efective core they are ound to be similar to one another in some rspect, by the subj ect ' s lights; l similar, that is, in eliciting similar behav ior. His according them all the same obser vation sentence is itself a case of similar eicited behavior. An obse rvation sntence may consist of a single noun or adjetive, thought of as a sentence; thus ' Rain' , 'Cold', or 'Rabbit' , for ' It's raning ' , 'It's cold ' , ' It's a rabbit'. Obser vaion sentences also may e compounded to form further obervaion sentences, for example by simple conjunction: 'The sun is rising and birs are singing'. Another way of compounding them is predication: 'This pebble is blue', as a compound of 'lo, a pebble' and 'lo, blue'. An equivalent rendering is simply 'Blue pebble' ; they have the same stimulus mean g . But they are not equivalent to the mere conjuntion 'Lo , a pebble, and 10, blue'. Their c onnection is tighter. The conj unction is ulilled so long as the stimula ion shows each of the component obsevation sentences to e fullled somewhere in the scene-thus a white pebble here, a blue lower over there. On the other hand the pre cation fouses the two fulllm ents, requirng them to coin ide or a mply overlap . The blue must encompass the e ble. It may also extend beyond; the construction is not symmetic. What brought us to an examination of observation sen tences was our q uest of the nk between observation and theory. The obervation sntence is the means of verbaliz ing he prediction that checks a theory. The requirement 1 Hnce ercepally similar, not recepually. Ros pp. 1-18. of Rermce, EV ID EN C E s that it command a verdict outight is what makes it a fml checkpoint. The requirement of intersubjectivity is what makes science objetive. Observation sentences are thus the vehicle of scientiic evidence, we might say-though without venturing a dei nition of 'ev idence' itself. But also they are the entering wedge n the leaning of language. The infant's irst acqui sitions in cognitive language are rudimentary observation sentences, including 'Mama', 'Milk', and the ke s one word observation sentences. They become associated with stimulations by the conditioning of rsponses. Their direct association with concurrent stimulation is ssential if the child is to acquire them without prior language, and the requirement of intersubj ectivity is essential in order that he learn the expressions from other speakers on appropriately shared occasions. That observation sentences serve in both ways-as vehi cles of sientiic evidnce and as enterng wedge into lan guage-is no cause for wonder. Observation sentences are the link between language, scientiic or not, and the rl world that lanuage is all about. Observation sentences as I have deined them far exceed the pimitive ones that are the chld's entering wedge. Many of them are leaned not by simple condiioning or imitaion, but by subsequent construction from sophis ticated vocablary. The requirement of direct correspon dence to ranges of stimulation can e met either way. Which ones are leaned directly by conditioning, and which ones indiretly through higher language, will vary from person to erson. But the two requirements, ntersubjectiv ity and corresondence to simulation. assure us that any observation sentence could e leaned n the direct way. We 6 P U R S U I T OF T R U T H hear our fellow speakes aiming and denying the sentence on just the occasions when we are simulated in the charac teistic ways, and we join in. J. Theoy-laden? My deiition of observation sentence is of my devising, but the term is not. Philosophers have long treated in their several ways of what they called observation terms or ob servation sentences. But it has now ecome fashionable to question the notions, and to claim that the purportedly o servable is theory laden in varying degrees. It is ponted out - that when scientists marshal and check their own data or one another's, they press no fa ther than is needed to assure agreement among witnesses conversant with the subject ; for they are reasonable men. 'The mixture is at 180°C' and 'Hydrogen slide is escaping are observational enough for ' any of them, and more recondite reports are obse vatio nal enough for some. I agre that the pracical notion of obser vaion is thus relaive to one or another limited community, rather than to the whole speech community. An obseva tion sentence for a commnity is an occasion sentence on which members of the community can agree outright on itssing the occasion. For philosophical purposs we can probe deeper how , ever, and reach a single standard for the whole seech com munity. Obsevable in this sense is whatever would be at tested to on the spot by any witnss n command of the language and is ive senses. If scientists were perversely to persist in demanding further evidence beyond what suiced for agreement, their observables would reduce for the most part to those of the whole speech community. Just a few, EV I D EN C E 7 such as the indescibable smell of some uncommon gas, would resist reduction. But w hat has all this to do with a sentence's being theoy la den or theory-free? My deiiion dstinguishes obser vation sentences from others, whether relative to speial communiies or to the general one, without reference to theory-freedom. There is a sense, as we shal now see, in which they are al theory-laden, even the most primitive ons, and there is a sense in which none are, even the most p rofessional ones. Think irst of primitive ones, the enteng wedge in lan guage leaning. They are associated as wholes to appropri ate ranges of stimulation, by conditioning. Component words are there merely as component sylables, theory free. But these words recur in thoretical contexts n the fullness of time. It is precisely this s haring of words, by observaion sentences and theoretical sentencs, that pr vides logical conections between the two kinds of sen tences and makes observaion relevant to scientiic theory. Retrospectively those once innocent observation sentences are theory-laden indeed. An observation sentence contain ing no word more technical than 'water' will join forces with theoreical sentences containing terms as technical as 'H20' . Seen holop hrastically, as conditioned to stimulatory situations, the sentence is thoy-free; seen analyticaly, word by word, it is theory-laden. Insofar as observation sentences bear on science at all, afording evidence and tsts, there has to be this retrospective theory -lading along with the prisine holophrastic freedom from theoy. To impugn their observaionality thus retrospecively is to commit what Firth (p. 10) called the fallacy of conceptual retrojec tion. 8 P U R SU IT OF TRU TH More sophisticated observation sentences, inc lud ng those of specia li zed sientiic communities , are sim larly tw -faced, even tho ugh learned by composition rather than direct condiio ng. What qu aliies them as obse rvation sentences is still her holophras ic associ ation with fIXed ranges of sensory stimul ation, however that association be acq uired. Holophrastical ly they function sti ll as theory free, like C. I. Lewis's "expressive" sentences (p. 1 79), tho ugh when taken retrospectively word by word the self same senten ces are theory- laden , like his "ob jecive" ones. When epistemology rounded the linguistic um, talk of observable objects ga ve way to tal k of observation terms. It was a g od mo ve, but not good enough. Observation sen ten cs w ere distinguished from theoret ical ones only deivati vely, as containing observation terms to the exclu sion of theory-laden or theoreical terms. Consequently Rei chenbach and others felt a need for "bridg e p rincip les " to re late the two kin s of sentences. No bridge is wanted, we now see, and bridging is the w rong igure. Start in g with sentences as we have done rather than with terms, we see no bar to a sharing of voc ab ulary by the two kinds of sentences ; and it is the shared vocabulary that links them. Starting with sentences has conferred the further bon of freeing the deinition of observation sentence from any de endence on the dist nction between the theory -free and the theo ry-laden. Yet a third adv antage of this move is th at we can then study the acquisition and use of observ ation sen tences without p rejudging what objects, if any , the compo nent word s are meant to refer to. We thus a re freed to spec late on the nat ure of reiication and its utility for scientiic theory -a topic for Chap ter II. Taking terms as starting point wou ld h ave me ant inssing reiication and EVI D ENC E 9 con ceding objetive reference out of hand, without consid e ing what it is for or what goes into it. 4. Observation categoricals The suppot of a theory by obsevation stands forth most expl icitly in expeiment, so let us look i nto that. The sci en t ist has a backlog of accepted theory, and is considering a hypothesis for possible in corporation into it. The theo ry tell s him that if the hypothesis under consideration is t rue, then, whenev er a certain obser vable situation is set up, a cert ain efect should be observed. So he set s up the situation in qu estion. If the p redi ct ed efect fail s to appear, he aban don s hi s hypothesis. If the efet doe s appear, hi s hypothesis may b e t rue and so can be tentatively added to hi s ba cklog of theory. Th us suppose a team of i eld minerlogist s have tu ned up an unfam liar rystaline minerl of a distinc ively p in k ish cast. They speak of it provisionally as litholite, for want of a better name. One of them conjeures its ch emical co mposition. Tis is the hypothesis, of whi ch I shall spare m yself the detail s. From his ba cklog of ch emi cal lore he reason s t hat if this chemical hypoth esis is true , then any pie ce oflitholite should em it h ydrogen sulide when he ated above 180°C. Th es e last p rovi sion s a re the observables ; for o ur min eralogist and hi s coleagues know litholite when they see it and hydrogen sul ide when they smel it, and t hey can read a the rmometer. The t st of a hypothesis thu s hin gs on a lo gical rel ation of i mpli caion. On one side, the theoretical, we h ave the backl og of accepted theory plus the h ypothesis. This com bination does the implying. On the other side, the observa- 10 P U R SU I T OF T R U TH tional, we ave an implied gneraity that the experimenter can directly test, directly challenge-in ths case by heating some of the pink suf and siing. A generality that is compounded of observables in this way-'Whenever this, hat'-is what I call an obsevation ategoial. It is compounded of observation sentences. The 'Whenever' is not intended to reify times and quantify over them. What is intended is an irreducible generality prior to any objective reference. It is a generality to the efect that the cirumstances described in the one observation sen tence are invaiably accompanied by hose dscibed in the other.2 Though compounded of two occasion sentences, the ob sevation categorical is iself a standing sentence, and hence fair game for implication by scientiic thory. It thus solves the problem of inking theory logically to observation, as wel as epitomizing the experimental situaion. That situaion is where a hypothesis is being tested by an experiment. An opposite situation is equally familiar: a chance observation may prompt us to conjecure a new obsevation categorical, and we may nvent a theoretical hyothsis to explain it. For example, we might notice wil lows leaing over a stream. This suggests the observation categorical: (I) When a willow grows at the water's edge, it leans over the water. 2 he obsevaion categorical is not to e confud with the obseva ion colitioz, a less fruitful notion that I ventured in 1975. he observa tion conitional is formd from two stnding sentences each of which has enbuilt upon an observation sentence with help of theory. al hings, pp. 6-,7. ee heoies EVI D E N C E II Tis suggests, n um, a theoretical hyothsis : 'A willow root nourishes maly its own side of the tree' . Taken t geth er with prior bits o f theory , such a s that roots get more nourishment from wetter ground, nd that nourishment p ro m ote s the growth of branches , the hypothesis is found to imply the obser vation categorical. Other ob se vation cate go icals will be imp lied too, and the continud testin g of th e hyothesis would proceed b y t estng various of them , a long with further testing of the one that happened to sugge st the hypothesis. The o bservation categoricl (1) exceeds my deinition n a sub tle way : it is not compounded of two self-su icient o b serv ation sentences. It cannot be read 'When a w llow grow s at the water 's edge, a willow leans o ver the water'. The component o bse rvation sentences ha ve to bear not ju st on the same scene, thi s time, but on the same part of the scene, the same w il low. Such was the force of'it' in (1). We h ave what may be called afocal observation categorical , as distinct from a ree one. In §2 we saw a contra st between conjunction and predica tion. Now the free o bservation c atego ri cal genera lizes merely on a conjunction, and claims that every occasion p re sent ng the one feature w ll p resen t the other somewhere about. The focal observation categorical generalizes ra ther on a pre dica tiona l observation sentence. (1) gener aizes o n the predicaion 'This riverine willow leans over the w ater' t o say that they all do. A more sucnct p red icati onal observation sentence is 'This ra v en i s blac k', o r 'Black raven'. It g enerali z es to the focal observation categ ori c a l 'When ever there is a raven , it is bla c k or, succinctly, 'All ravens are b la ck . ', ' P URS U IT OF TRU TH 5. Test ad reotation An observation categorical is tested by pairs of observa ions. It is not conclusively veriied by obsevations that are conformable to it, but it is refuted by a pair of observaions, one airmative and one negative-thus observation of lithoite at I80Ge but absence of hydrogen sulide, or obser vation of riveine wilows leang away from the water. he fre observation categoical 'When the sun comes up the birds sing' is refuted by observing sunrise among silent birds. The obsevational test of scientiic hypotheses, in turn, and nded of sentences generally, consists in testing obser vation categoicals that they imply. Here again, as in the cae of the observation categoical itself, there is no conclu sive veriiation, but only reutation. Reute an obsevaion categorical, by an airmative and a negaive observation, and you have refuted whatever implied it. Traditional epistemology sought grounds in sensoy ex peince capable of implying our theoies about the world, or at least of endowing those theories with some increment of probability. Sir Karl Popper has long stressed, to the contrary, that observation serves oly to refute theory and not to supot it. We have now been seeing in a schematic way why this is so. But again we mst bear in mind, as in §2, that we are schematizng: positing shap boundaries where none can e drawn. The pair of observations in purported refutaion of an observaion categorical may be indecisive ecause of un foreseen indeision over the stimulus meaning of one of the pair of observation sentences, as n the case of the black swan or an albino raven. A theory that implied the observa tion categorical 'All swans are white', or 'All ravens are EV ID E N C E 13 black', might or might not e refuted by the discovery of the odd specimen, depending on our own decision regard ing the vague simulus meang of the word. In both exam ples the verbal usages actually adopted, which do admit black swans and blond ravens, are the ones that make for the s moother terminology in the overall theory. It is clearly true, moreover, that one contnually reasons not only in refutation of hy pothess but in support of them. This, however, is a matter of argung logically or probabl isticaly from other beliefs aready held. It is where the tech nology of probability and mathematical statisics is brought to bear. Some of those supportng beliefs may be observa tional, but they contibute support only in company with others that are thoretical . Pure observation lends oly negative evidence, by refuting an observation categoical that a proposed theory implies. 6. Holism Let us recall that the hypothesis regarding the chemicl composition of itholite did not im p ly its observation categoical single-handed. It implied it with the help of a backlog of accepted sientiic theory. In order to deduce an obsevation categoical from a given hy pothesis, we may have to enlist the aid of other theoretical sentencs and of many common-sense platitudes that go without saying, and perhaps the aid even of aithmeic and other parts of mathem atics. In that situation, the falsity of the observation categorical does not conclusively refute the hy pothesis. What it refutes is the conjunction of sentences that was neded to imply the observation categoical. In order to retract that conjuncion 14 P URS U IT OF TRU T H we do not ha ve to retract the hypothesis in qusion; we could retract some other sentence of the conj unction in stead. This is the important nsight called holism. Pierre Duhem made muc h of it early in this century , but not too m uch. The sientist thinks of his experiment as a tst spe iically of his new hypothesis , but o ly because t his was the sen tence he was wonde ng about and is prepared to re ject. Moreo ver, there are also the situations where he has no preconcei ved hyothesis, but just happens upon an anoma lo us phenomenon . It is a case of his happening upon a co unter-instance of n observation categoical which, ac cording to his c urrent theory s a whole, ought to have been true. So he loo ks to his theory with a c ritical eye. Over-Iogii zing, we may pict ure the accommodation of a failed observation catego rical as follows. We ha ve before us some set S of pu rported truths that was fo und jointly to imply the flse categori cl. Implication may be taken here simply as deducibility by the logic of t uth nctio ns, quniicaion, and identity. (We can always pro vide for more substan ial conseq uences by incorporating appropri ate premisses explicitly into S.) Now some one or more of the sentences in S are going to have to be rescinded. We ex empt some membe rs of S from t is thre at on determining that the fateful implication still holds witho ut their help . Any p urely logical tuth is thus exempted, since it adds nothing to what S wo uld logically imply anyway ; and sun d ry irrele vant sentences in S will be exempted as well . Of the remaining mem ers of S, we rsind one that seems most suspect, or least c ucial to our o veral theory. We heed a maim of mi nimum m utilation. If the remaiing mem bers of S s ill conspire to imply the fa se categoricl, we try EVI DENCE 15 res inding another and restoring the irst. If the false categorical is still implied, we try rescindi ng both. We con tinue thus until the implication is defused. But this is only the begining. We must also track down sets of s entences elsewhere, in our overal th eo y, that im pl y th ese newly rescinded beliefs ; for thos e must be defused too. We continue thus untl co sistency sems to be re s tored. Such is th e mutilation that the ma im of min imum muti lation is meant to minim ze. In p articular the maxim constrains us, n our choice of what sentences of S to resind, to safeguard any purely mathematicl t uth ; for mathemat ics in ltrates all branches of our system of the world, and its disruption would r e verb erate intolerably. If sked why he spare s mahematics, the scientist wil perhaps say that its laws are necessaril y tue; but I think w e have here an explanation, rather, of mathem atical necessity itself. It resides in our unstated pol i ey of shield ng mathematics by exercising our freedom to re ject other beliefs instead. So the choice of wich of th e b eiefs to r ject is i ndifer ent only so far as the failed observation categorical is con cened, and not on other counts. It is well, we saw, not to rock the boat more than need be. Simplic ity of the resulting theory is another guiding consideration, however, and if the scien tist sees his way to a big g ain in simplicity he is even prepared to rock the boat very considerably for the sake of it. But th e ltimat e objective is so to choos e the r evision a s to m aimi ze future success i n pr ediction: future coverage of tue observation categoricals. There is no recipe for this, but m aximization of simplicity and minimi zation of muti lation are maxims by which science strives for v indication n future predi ions.
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