Tristam Shandy - Robin Small

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The British Society for the Philosophy of Science

Tristram Shandy's Last PageAuthor(s): Robin SmallSource: The British Journal for the Philosophy of Science, Vol. 37, No. 2 (Jun., 1986), pp. 213-216

Published by: Oxford University Press on behalf of The British Society for the Philosophy ofScienceStable URL: http://www.jstor.org/stable/686979

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Tristramhandy's astPage 2 I 3

TRISTRAM SHANDY'S LAST PAGE

This note criticisesan argumentused by W. L. Craigagainstan actual nfinityof past

events. He argues hat if Russell'suse of the story of TristramShandy,who took ayear to recounteach day of his life, is extended nto an infinite past, then Cantor'sprincipleof correspondenceeads o the absurd onclusion hatTristramShandyhasalreadywrittenhis last page. I show thatno such conclusioncan be drawn,andthata'past'version of the story whichdoes allow this principle o be applied eads to noparadox.

Argumentsover the infinityof the existence of the world in the past haveundergone an interesting revival in recent years. The most extensivetreatmentof this questionhas been providedby W. L. Craig I979]. Here Iwish to assess one argument which Craig uses to demonstrate theimpossibilityof an actual nfinityof pastevents.This argumenthas its originin an example provided by BertrandRussell. In an often quoted passage,Russell writes:

TristramShandy,as we know,tooktwo yearswriting he historyof the first wo daysof his life, and lamented hat, at this rate, materialwould accumulate aster han hecould deal with it, so that hecould nevercome to an end. Now I maintain hat, if hehad lived for ever, and not weariedof his task, then, even if his life had continuedaseventfully as it began, no part of his biographywould have remainedunwritten

([I903], p. 358).

Craig takes Russell to conclude that 'the entire book could be completed,since by the method of correspondence ach day would correspond o eachyear,andboth are nfinite' [ 979], p. 97). He points out, reasonably nough,that this is an untenableassertion.Some other writers nterpretingRussellin much the same way have made a similar objection. (See e.g. Whitrow[I978], p. 42.) However, we may query whether such a claim can beattributed o Russell, at leaston the basis of the passage ust cluoted.Russelldoes not say that the bookcould be completed, f this meansthat ts last page

couldbe written. In fact,there s nothing n the passage hat need be rejectedby anyonewho denies the possibility of an actual nfinite. Yet Russell doesrefer to his example as a 'paradox'.He does so because he uses the storyabout Tristram Shandy as an illustration of the Cantorianapproachtoinfinitesets. What makes the examplea paradox s not that it containsanycontradictionwithin itself,but that when used in this way it is inconsistentwith the familiarprinciple 'that the whole cannot be similar to the part'([I903], pp. 359-60). For it providesan instanceof the kind of one-to-onecorrespondencewhich,according o Cantor, hows that two infinitesets areequivalent.

One of Craig'smain aims in arguingagainstthe possibility of an actualinfinityof past events is to show that the Cantorian pproach s not valid forthe real world. He thereforeargues that the principle of correspondenceleads to absurditieswhen it is applied to collectionswhich are both actualand infinite. His own argument is based on a modificationof Russell'sexample.

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2I4 RobinSmall

But let us turnthe storyabout:supposeTristramShandyhas been writingfrometernitypastat therateof onedayperyear.Wouldhenowbe penninghis finalpage?Herewe discern he bankruptcy f the principleof correspondencen theworldof

the real.For according o thatprinciple,Russell'sconclusionwouldbe correct:aone-to-onecorrespondencebetween days and yearscould be establishedso thatgiven an actualinfinitenumberof years,the bookwill be conapleted.But such aconclusion s clearlyridiculous,for TristramShandycould not yet havewrittentoday'svents down. In realityhe could never finish, for every day of writinggeneratesanother year of work. But if the principle of correspondenceweredescriptive f therealworld,hewouldhave inished which s impossible [X979], .

98).

Craig s assumingherethatapastinfinitywouldbe anactual nfinity.If this

weredenied (as it is in anorthodoxAristotelianaccount) herewouldbe no

needto referto Cantor'suse of the methodof correspondence.But if it isaccepted, he objectioncontained n thispassagecanbe raised.Withinsuch

an actual nfinitywe couldestablisha one-to-onecorrespondence etween

daysandyears,which in turnwould indicatethatTristramShandycould

now be writinghis last page. Since that is impossible,however,we must

reJecthe hypothesisof an infinitepast.

This is at leastagenuineparadox. tsconclusion s thatwhereasTristram

Shandy must be assumed to have completed the task of writing his

autobiography,he factthatevery dayof writirlggeneratesanotheryearof

workrulesoutany suchcompletion.Craig aysthat'TristramShandycouldnot yet havewrittentoday'seventsdown'.This is not a good example,for

presumably omeof today'seventscannothavebeen writtendownsimply

becausethey have not yet takenplace. More to the point is the fact that

TristramShandycouldnot yethavewrittenyesterday'sventsdown,since t

wouldtakehimthenextyearto do so. Andthis doesof course mplythathe

cannothave completedthe last page of his autobiography, he one that

bringsthe accountup to the presentday.This sideof the paradoxs validwithoutquestion.It is theothersidethat

has notbeenproven.Its basislies in the claimthatwithinan infinitepast'aone-to-onecorrespondencebetweendaysandyearscould be established'.

In theoriginalcaseinvolving uture imethere s no problem nestablishing

this correspondence:he firstdayof TristramShandy's ife correspondso

thefirstyearofhiswriting, hesecondday to thesecondyear,andsoon. But

in thecaseinvolvingpast time,whatdaycorrespondso the latestcomplete

year of writing?Clearlythe most recentday whose eventscan havebeen

writtendownduringthis yearis a daywhichtookplaceat least a yearago.

But themostrecentdaywhoseeventscanhavebeenwrittendown ntheyear

preceding hisone is a daywhichtookplaceat leasttwoyearsago.Thereforethe mostrecentdaywhoseeventscanhavebeenwrittendownin the latest

completeyearis the dayafterone whichtookplaceat leasttwo yearsago.

Andthis argumentcanbe repeatedagainand again.We findthen thatwe

cannot ocatethedaywhichcorrespondso the latestyearof writing,or for

thatmatterto anyotheryearof writing.It is thereforenot the casethat'a

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TristramShandy'sLast Page 2I 5

one-to-one correspondencebetweendays and yearscould be established'.Accordingly t cannotbe inferred hat TristramShandywould havewrittenhis lastpage.

The failureof thisargument s due to the factthatRussell'sstoryhasnotbeen fully 'turnedabout'.Although it is now a storyaboutthe pastratherthan the future, one feature remainsthe same: it is still assumed thatTristram Shandy is writingabouteventswhich have already akenplace.This assumption mposes a limitationon the possible waysof establishinganyone-to-onecorrespondence etweendaysandyears,because t requiresthateach daymustprecedetheyear thatcorresponds o it. The outcome sthat no such correspondence anbe establishedwith respect to an infinitepast. A genuine counterparto the TristramShandysituationdescribedby

Russell would be this: supposethat TristramShandy plans the eventsofeachday of his life in advance,andthat it takeshim ayearto do thisforeachday.Could hehavecompleted hetaskup to thepresentday?If hehadbeencarrying it out through an infinite past, the answer seems to be in theaffirmative.For if today'seventswereplanned n acertainyear,yesterday'seventswereplanned n thepreviousyear,and soon. Here wecanestablishaone-to-onecorrespondencen much the sameway as in Russell'sexample.However, no paradoxof the kinddescribedby Craig s involved.

Ofcourse it is truethatTristramShandywill not be ableto continuehis

planningaftera certainday. But it is also truefor the originalversionthatTristramShandy'swork on his autobiographymusthavehad a beginning.Let us assume hatwe cangive justoneinstanceof correspondence etweenayearof his writingand a day of his life. Suppose we knowwhichday he iswritingabout n thecurrentyear. If weknowwhat daythis is,wemustknowthat it tookplace N yearsago. If TristramShandyhas been writing for atleastthat long, then on that dayhe must havebeen writingaboutthe daywhichoccurredN daysearlier,since these arejust the N days thathe hasbeenwritingaboutduringthe last N years.Now we can askwhichdayhe

waswritingabout on the daywhich occurredN daysearlier hanthe oneheis now writingabout. This proceduregives rise to a sequencewhich has adefinite imit, and it thusenablesus to determine he earliest imeatwhichTristramShandycouldhavebegunwritinghisautobiography.Allof this isanotherwayof showingthatRussell'sexamplecannotsimply be extended. . .

nto an lnfinlte past.

Craig'sargumenthas been criticisedby severalwriters in relatedbutslightlydifferentways.RichardSorabji, n his book [I983], notesthatevenifweassume hatTristramShandyhasalreadybeenwriting or aninfinityof

years, t doesnot follow thathe hasalready ecorded heevents of everydayof the past ([I983], p. 222). In a recentarticle [I984], David A. Conwaypoints out that although on this assumptionTristrarnShandy must havewrittenaninfinitenumberof pagesat anygiventime, it doesnotfollowthatanyparticularpage suchas his lastpage must be amongst hosealreadywritten [I984], p. I62). Whatthese argumentsshow is that we need not

p

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