Sonderdrucke aus der Albert-Ludwigs-Universität Freiburg

KLAUS JACOBI Statements about events Modal and tense analysis in medieval logic Originalbeitrag erschienen in: Vivarium 21 (1983), S. 85 - 107

Vivarium XXI, 2 (1983)

Slalemenls about Events Modal and Tense Analysis in Medieual Logic*

KLAUS J ACOBl

In modern research into niodal logic, niodal ternis are usually scmantically interprt:ted in terms of the niodel of possible worlds:

ncccssary (N) = df true in all possible worlds itripossible ( -M) = df'false in all possible worlds kiossibl<: (M) = df true in at least one possible world contingent (K) = dl'irue in at least one possible world and

falsc in at Icast On<: possible world.

Now phi1osophc:rs havc thought about modal terrris, modal proposi- tions and modal syllogisms long before the notion of possible worlds was enteriained. The question what interpretative model they used is a relevant one today. Jaako Hintikka and the circle of pupils and col- lcagues connected with hirn, in particular Simo Knuuttila, have tried to answer this qiiestion. 'I'hcy advancc thc following thcsis': undcr- lying thc modal analysis proposed by Aristotle and the scholastic

* Thc liillowinn paper was first rcad at the Syinpvsium on the Flistory of 1,ogic whirh iook place in May 1981 undcr the direction of Professor Ignatio Angelelli i r i Pamplona. 1 should likc to thank thosc who took part in discussing thr paper, especid- ly Professor Marin Mipucci , for valuatile cornrnents which I have wherever possiblr includcd in this vcrsion. 1 am also most grateful to Pmfrssor Simo Kniiuttila, who very kindly sent rnr some comments on thc Iia1w:r at a latcr {latc; thcsc havc hclpcd rnc to clarify my views at various [wints. 1 shoiild also likr to tharik Dr. Ricca Edtnr)ndson- Wörner for her translation of the paper irito Eriglish. ' 'I'his thcsis was first advanced by .Jaako Hintikka in 1957, and then in ii seritrs of furthcr papcrs which werc collected in 1973 in thr voliimr 7'ime nnd Nec(o.\-.rity, Studk.~ in Aristo~le's 7Xeog~ of Modaliv (Oxiorcl). (In whac f'ollows I shall rckr in ihis volurne as 'Hintikka'). The samr line of interpretiition was followe<l ir i Arii-~otb on Modal+ nnd Uererminism in: Acta Philosophica Frnnica, 20, 1 (Arristrrclatri 1977) hy Jaako Hintikka, Unto Remes and Sirno Knuuttila. (This I shiill rekr to iis 'Hin- tikka-Rernrs-Kniliittila'). Iliritikka's ~>upil aiid collcagu<:, Kriuuttila, has in a work eclitrd in 1983 (R,$org~ng th Crtai Chain (!f &in,<, Dordrecht) tried to show that the scholastics ilritil thr rrid nT ilic 13th crntury alrnost all took this view of time and rrio<lality; vid. Tim nnd M o h l i Q iri Scholusticism, op. cit. 163-257 (referrrd to in thr hllowing as 'Kriuilttila').

writers there appears, at 1t:ast in central sources2, a rriodel r>fniodality in which the modal terms are semantically interpreted like this:

N = df always the casc (or: always truc) -M = df never the casc: (or: always falst:) M = df sometimes the case (or: sometimes ~ r u e ) K = df sometimes the casc and somctimcs not thc case (or:

sometirries true and sometimes false).

According to this, the modal terms arc intcrprctcd by rcfcrcnce to periods of time in ihr: history of this one real world. In contrast to the semantics of possible worlds, this interpretation woiild be reductionist. In thc rcfcrcnce to alternative worlds the modal term 'possiblc' rcap- pears; it Counts as an irreducible basic term, and the definitions only set out the relations of thc othcr modal terms to the notion of possibili- ty. Against this, when reference is made to time periods in this onc actual world lhc modal tcrms are removed frorn the dffinien.~. Thus in this thcory "modal notions are in the last analysis r(:duciblc to cxten- sional terrns7'%.

A reduclionist lhcnry of quantification over time periods is not, strictly speaking, a modal thcory at all. Anyonc systeniatically interested in rnodal logic and analysis (:ould thcrcforc, if Hintikka arid Knuuttila wer<: right, leave Aristotle and the scholastics iinrcad; according to therri these wrilers offcr only attcmpts to abaridon the problem of modalitics altogcther.

I disputc thc correctriess ol'ttie (hesis which Hintikka and Knuuttila advance. In my opinion wc can learn a great deal about the problcms of modality froni Aristotle, Roethius and in particular Pcter Abelard, William of Shyreswood and 'I'homas Aquinas. Thc scholastics' analyscs pcrtain to the question what is meant when, in both cvcrydüy and scicntific lariguage, we describe somcthing as in thc real sense possible, impossible, ncccssary or (:ontintycnt4. One 01' iheir main thernes is prccisc rcflcction on thc differerice between iniensional and

At variuiis poirits ihr ai~ihors rcmark that this was not the unly rriudrl prupoiindcd 1,y Aristotlc arid thc sch<ilastics; ci'. Hintikka-Kernes-Kniiuttilii 14; Kriuiiitila 165, 199, 203. 'l'hese remarks art: huwc:vvr ul' n rriarginal naturc, and thc central signilicancc of thc statistical paradigm is repeiitetlly erril>hasisc<l.

Knuuttila 235; cf. Vll-1X and pilssirii; Iliritikka 113 and passim; Hintikka- Rerries-Kniii~~tila 13 and passim.

Vid. triy articlc, M@iichkeil, in: Handbuch phiiorophirchcr C~rundhqqn//., cd. Hcrmaiin Krings, Hans-Michael Baurnpu-tner i lr i t l C:tiriatul)h Wild (Munich 1973), 930-947.

extensional language and on the relationship bctwccn these manriers of sp(:aking5.

Tn the lirst part of the following investigation T shall preserit the thcsis put forward by Hintikka and Knuuttila, and my objcctions to ith. In the second part I shall expand my criticisms by ofTering a counterinterpretation. I shall takc u p the topic on which the authors rrientioned above have worked-the relationship between tense and modal qualifiers in Statements about events-and shall put forward my own interpretation of the scholastic analyses. This I shall do in the forrri of a systematising reconstruction in which rriy concern will bc to indicatc basic features, not to diflerentiate the contributions and posi- tions of individual philosophers in a manner which is historically cxact at every point.

I. The "Statistical " Interpretation uf Modal Modal i'ernis-an Account nf the Thesis, und 0hjtc~ion.r lo it

1. Thc l'oint of ilcparturc: thc "Yrinciplc of Ylcnitiide"

Arthur Oncken Lovr.joy's 7'ht Crtat IJhnin oJ Btin,g7, appeared in 1936 and was reprintcd in 1950. According to Lovcjoy, thcrc is onc basic assumption at the rooi 01' the thinking of many of the philosophers in thc: Wr:stern traclition. This (:an t~ r : t(:rm(:d thc 'prinsi- ple of plenitude', according to which nothing which is possible iri this world can rcmain unrcalis(:dY In that part of his investigation which concerns the early history of' this thought, Lovejoy puts forward the view that the principle of plenitude was accepted by Plato, but not by Aristotlc. At this point Hintikka cmphatically contradicts him.

"Vid. my monograph, L)ie M o d a l h g n ~ j in d m lo~i.\-~.htn Schniftm da>- Wilhalm uon Shyra.ruiood und in anllnm Komhendim de.~ 12. und 13. ~Jahrhundarts. Filnktion~basfimmung und Gehruwh in der lu~isclrm Analyse (Sfudim und Zixfe zur C;eislcs~es~hi~hie des Miiielaltnv, <:CI. Alhcrt Zimmerman; vol. X111, Leiden-Colo,pc 1980), csp. scciinn X , 337-35.5. G On Hintikka's intcrprctation of Aristntlc's modal ihcory C I M . M . Mulhcrn, Arisioile on 1Jniuer.suli~ und Nece.v.\-iiy ', in: Logiquc ci Analyse, 12 (1969) 288-299; Mar- tha Kricalc's rcvicw 01' Time unrl NICI.\-sify, i r i : Piiilr>solihic:al Qiartrrly, 24 (1974) 367-370; .Jonathan Harnes's review of 'li'me und Necessip, in: Journal of Hcllcnic Siudics, 97 (1977) 185-186; Kichard Snrahji, Ncces-.city, C>uu\-e and Hlame, l'~~.rpectiur\- on Ari.cfofle's 'lireory (Ithaca, Ncw York 1980), vitl. intlcx nn Hintikka; R . T. McC:lcllari(l, i i w w und Modnli6y in Arislolie, Melaphysics IX .7-4, in: Archiv für C:cschichtc clcr I'hilosophic, 63, 2 (1981) 130-143.

A. 0. I.ovrjoy, Tha [:raut Chain ojBeinf; A Sfudy ojfhe IJisfory o jan Idca (Thr William James Lrcturrs drlivrrrd at Harvard Univrrsity 1Y33, 1936, 2nd rdn. 1950).

Cf. 1,ovrjoy (01' cit.) 52; vid. index on Plenifude, principle of; Hintikka 94-96; Knuuttila 163.

Hintikka's and Knuuttila's researrh into Aristotle's modal theory and thc scholastic work conncctcd with it starts from the claim that Aristotle himself consciously presupposes this principlcy.

It is indisputable that Aristotlc docs not define the modal lerms by referencc to a totality of possiblc worlds; for hirri, what is possible is possible in this real world. Given this, i t is the sc:(:ond sct of dcfinitions ol' the modal tcrms at the beginning of this papcr, to which Hintikka and Knuuttila rel'er as the 'statistical rriodel ol' niodality"", which exylicate thc "principle of plenitude". Morc cxactly, as Hintikka remarks", thc theses

'What is never the case is impossit~lc' 'What is always thc case is riecessary'

'What is possiblc is sorrietirnes the case' 'What is not nc(:cssary is sorrirtirrirs not the case'

an: based ori the "prin(:ipl(: of plcriitude"; whereas thc oppositc implications

'What is impossible is never the rast:' 'What is necessliry is always th(: casc' 'What is sometimt:~ thc case is possiblr' 'What is somctirries riol the casc is not nc:(:(:ssary'

are valid indepcndcntly of this principle.

(:an Hintikka and Kriuuttila provc t h a t Aristotlc arid the scholaslics until thc end 01' the 13th ccntiiry accept the "principle of plcnitu<l(:"? Hiritikka can show that Lovcjoy brinys no conclilsive proofto thc con- trary. Th<: sources cited by I..ovejoyi2 allow not only ol'the interpreta- tions 'Some possibilitics' or 'Every possibilily can remain for euer

unrealisecl ' , hut alsci-ancl rriore plausibly -'Somc possibilitics' or

Hirii ikka 95; Knuiittilii X . Cf'. tcio t h : iridict:~ on f'rinciple of f'lmifude. In Hintikka 103. Cf. in the index: Necerriv, rfutivtz~ril cnncepf ?/; - und omni im~ora l i~y; - unrl the principle of pleniiude; FJo.\-ovsibilify, nlwuy.\ rculucd in fhe l o n ~ run; - realization o/;- -- realized in iime; -. staiistical ccinccf~l ! I - and fhe pnnciple of pleniiude; (:onrin~cncy, anrl fhc prkciple of plmifude. Kniiuttila <lo<.s rioi spcak only of a statistical rnodel or para<ligrri, b u ~ also of thr stiitisticiil ttirory ~I'riiotlali~y: r.g. X, 235. 'I Hintikka 96f.; d: iliritikka-K<:tiics-Knuuttila 21.

Aristotlr, Mctnfih. ßcia 6. 1003a 2; I.arnbda 6, 1071 1) 13-14; CI'. Lovcjoy (op. cit.) 55.

'Every possibility can ~ornetzrnts remain ~nrca l i sed"~ . Thus inter- prctcd, the sources are cornpatible with the principlc of plcnitude. Howevcr, Hintikka's atterrlpt tn press ttiese scntcnces liirthcr, so that they confirrn the validity of the principle, 'Every shcer possihility (con- tingency) w i l l inJact bc realised at sorrie time'", is at least as forcible as Lovejoy's attempt to claim thern for the contrary thesis.

According to HintikkaI5 and Knuuttilaib, it is possible to clairn with regard to a passage in Metaph. Theta that

"'l'his passagc clcarly shows liow thc assurril>tion that earh gcnuinc possihiliiy is realizril ai some monit-rit of time was oric 01' the prrsiippiisitions of Aristotlc's thiriking"17.

The passagc runs:

"ouk c*ntlcchctai aletliis i:inai io eipeiri lioti dunaton nic:ii todi, ouk estiii di:. hostc ta aduriata cinai taute diiil>hciigcin''

"Ii is not po~sil>l<. ihai i t can tx triic to say, 'This is lic)ssiblc, hut will ncvcr be the rasc;' this wt>ill<l hc to rule oiit i r ~ i p ~ s s i b i l i t ~ " ' ~ .

I:' Ilititikka 97. '+ rhi(1. 'Win t ikka 1071'.; cf. thr othrr rc:li-rcnces in tlii. indcx. 'Wnuutt i la 166. l 7 Ibid.

Aristotle, Mctupli. 'l'heta 4, 1047 b 4-6. Ttitr English trarislation, on wtiii:h Hintikka and Kniiiittila basc their rrrriarks, runs: "11 cannot be triic to say that 'ttiis is possiblr but will not be', whicti would irnply thr disappcarancr ofirnpossihle things". R. T . McClelland (scc r i . 6) has receritly cxarninecl tliis passage, rclating it to Aristotle's discussions in Mefnph. Theta 3-4. He reactics thc concliision thai Aristotlr ilocs not accept ttic 'principle of p1i:nitudc' (146 , 147). He translatcs the passagc in question, like G.E.L. Owen and Martha Knealr t>trli>rc hirn, as Lillows: "It <:annot bc true to say that this is possible Iiut will not happen aiid to say this io such elli:ct that the ex- istence ol' tlii: impossible will cscape us in this way" (131 , 146). Mi:Clclland paraphrascs this in orck:r ro niake Aristotlc's arpmeritativc intentiori i:ltrarcr: "If 'ttic possible' ie as we tiave deecribed it-or, is derivablc linrn what wc havc said-. it is clrarly thc rase that it cannot be true to say of any givcn thing 'this is now capablt: of happening but it never will happen', iritiinding by such rncans to rriakr of 'the irripossi- ble' an trriipty Iocution of which therr iirc no inslances" (146) . Cf. Soratji (see n. 6) 136: "Kneale iind Owcn suggest that Aristotle is not objccting to a clcnial of the ~irinci- ple of I>lcniiudc, but oiily to a ccrtain rrioral rnispidedly drawn fmtn thc denial. Ttic rnistiiken rnoral is that whai. ncver hapkiens is in eu-y cusc possible. . ..As S. Mansiori points out ( L e , / u p e n t dJKxi.rfmce chez Anitufe, 2e Cd., 1.ouvain 1976, n. 13), if the Passage is inrcrpreted iri this way, it artiiatly gocs against. thc ascription to Aristotlr cif thc principle of plrriitudc. k'or in resisting ihe idea that all t h i n g wtiich fail to happen are possiblc, Aristotle will bc allowing that .som rhings wh~ch never happcn are nonc the lcss possible". Thc interpretatiori o l thc passagc cnncerned givcn by Thornas Aquinas, I n Metaph. T..IX, 1.111, n. 1807, very largt:ly agrees witti this.

Hintikka and Knuuttila clearly read this sentence as a Statement about the inconsistency of a particular corribination of truth-values: 'The proposition, "Something is possible and will never be the case", can- not be true'; this can be formalised as ' -M(Mpc - %(F)-t))'. Read in this way, the sentence really does presuppose the principle of plcnitudc; it allows of tht: t:quivalcnt reformulation, "l'hi: proposition, "If sorriething is possible, it is sorrietirries the case", is necessarily true3-forrnalised as 'N(M~--B;(~-~)) ' . However, I suggest another intcrpretation. According to my rcading, thc scntencc quotcd hcrc has nothing to do with the contentious principle. Aristotlc is not iri the least concerncd with the qucstion whether the truth values ofproposi- tions rcprcscntablc by variables are compatihle with each other. Rather, he is disputing the reliability of ihe Sollowing prognostication: 'This is possible, but will never be the case'. Anyone who advances claims about particular cvcnts must bc prepared to justify thest: claims in argument. The prediction, 'This will never be the case', which covcrs the wholt: of futurt: timc, could bc justificd by, 'This is not possible'. And if anyone says about a particular event, 'This is possi- ble', he ought to be in a position to advance reasons For which ii mighi occur". I agree with Hintikka when he writes of this passage20, "Aristotle . .. warns us against assuniing that sorriething is possible but will never lie". But I disputt: tht: contcntion that this mmns thc samt: as, 'Aristotle tells us that whatever is possible will be the case'.

In other cases too ihe apparent corroborative force ol' the sources cited hy Hintikka and Knuuttila in support oi'their thesis disappears as soon as one investigates which question is actually being discussed in the tcxt conccrncd. In answcr to the question, 'What do we understand by "It is pcissiblc"?' the reply, 'It is sometimes the casc', is false. And none of the authors examined by Flintikka and Knuuttila does give this reply". Howevcr, in answer to the quiie diffcrent quesiion ' O n what is the claim based that this is possilile'? the reply 'Something of tht: sort is the case or has been the case, and it cannot be ruled out that it will occur again', is pcrfcctly appropriatc. Wc do not rcfcr to what is

' V o r il rriorc: rxat:t ilt:count of this reflrction, in which it is also shown that that which only cxceptioilaily occurs is noi a possible objeci of prcdiction, vid. rriy article, Kontin~:tntc Natur~cschehniss~, in: Stu~lia Mcdiewistyrne, I R , 2 (1977) 3-70; esp. 21, 32. 20 Hintikka 108. 21 Hintikka hirriscill'allows that Aristotlr riever drliries the modal terms with r e f rence to the principlc of p1,lt:riiludc (1021'.), but without [Irawing the c:onsetliitiric:tis o T this admission.

or has beeri the case in orrlcr to deline 'possibilily', but in ordcr to justil'y siihstantive claims about particular possihilities. Corresponding observations apply to tlie olher moclal lerms.

The conncction bctwceri modal and tense qualiliers is not a matter ol'definition but one of argumentation. If somcone says, 'This is possi- ble', he has siifficiently supported his claini if he can show that states of aflairs of the sanie t.ypc as that to which he is rcferririg somctirries do occur. If he says, 'This is not ncccssary ( = possibly not)' he has suffi- cicntly support(:d his claim if he can show that statcs OS affairs of the same type as that to which he is rcfcrring somctirries do not occur. Neithcr case prcsupposes irriplications such as 'If possiblc, then sometimes thc case' ('Only wtieri sornctirries ~ h c case, then possible'), or 'If possible that not the casc, then sometimcs not thc case' ('Only if sometimes not the casc, theri possiblc that not t.hc case'). l'hc argu- ment takcs placc, rather, ac:cording. io the schcma, 'Becausc somctirries thc c:ase, thereforc possible', or 'Becausr: sometimes not the casc, thereforc possible that not ihe case'. C:laims about the ncccssity or th(: irripossihility of somc state ot' affairs cannot bc supportcd by refcrcnce io cxperiences nor to interpolatioris and cxtrapolations gcneralising aboiit thcrri. The argumentative relationship betwecn statcrrients containing modal and time qualiliers is reversed hcrc. Jf soriieonc says, "l'his is always th(: c:asel, he is clairiiing that his statc- ment is valid for future tirne as well. He has adequately supported his <:laim if he (:an show that thc state of affairs conccrned bclongs to a type to which neccssity pertains. If he says, "This is nevcr the casc', hc has adcquately supported his claim if he can show that the statc: of' affairs conccrried bclongs to a type wliich is impossible in itself. Arguing in these ways, orie does not presuppse irriplications such as, 'If always the casc, then nt:c:cssary' ('Only if' neccssary, then always thc case'), or 'If never thc case, ttien impossible' ('Only il'impossible, then never thc case'). 7'hc argurnent runs, rather, according to the scherria 'Bccause neccssary, thereforc always ihc case', or 'Bccause irnpossiblc, therefort: ncver the <:asc'.

The thescs which Sollow from the "principle of pleriitudc'' do not occur in thc schemata I have given. Both refert:nccs to what is actually the case and timc rcferences arc coriipletcly out ofplacc when wc wish to cxplicatc what is rrieant by 'possihlc', 'coritingcnt', 'impossible' and 'necessary'. Thomas Aquinas expressly refuses to define, as well as to differentiate, the modal terms by rel'erencc to what will bc the case. Attemptcd definitions of this sort, he says, are "incompetent".

Modal terrns should not be defincd "a poslcriori" and "externally", but interisionally, by rcfcrcnce to that io which a thing "is dctcrmined by its Ir1 ordcr to cxplain why he attaches the term "a fiosteriori" to thc suggested delinitioris, 'That is impossible which will never bc thc casc', "l'hai is possible (in thc scnsc of "coniingeni") which will someiimes be the case and sornetirnes not', Thomas adds,

I' For sonirthing is not ncccssnry hc<-;iils<. i t will alw;iys he thr rase; it will always br the case becausc i i is ii<.cc*ssary; arid rlriirly thc same applics io ihc o1hi.r (att<:rriptc<i drfinitions)' "'.

Knuuttila has disciissed this passage2'. According to him, if Thomas had followed his thought through io the erid he would havc had to say-correspondingly to what h(: has said about thr conccpt of necessity-that somcthing is not contingent bccaust: it will sometimes be ihe case and somctimes not; ii will sorrietirncs bc thc casc and somctimes not hecause it is contingc:ni. And this would be to give possihiliiy as a sufficicnt rcason for soniething's bring thc case on oc:casion-thai is, it would )I(: to advance whai ihe "principle of plenitude" advances. Hut ii seerris t o rric that Knuiitiila is looking here in vain for corroboration for his owii iriterpretation. Thomas argucs as hllows against the atiempted defiriitions I havc siirnmarised: even $in all thcsc dcfiniiions both sides were <:quivalrnt; if, ihai is, ii were valid not only to say, 'If impossible, ihen ne\.er thc casc', but also 'If never thc casc, ihen impossible'; not only, 'If necessary, then always the case', but also 'Tf always the case, then nc:c:(:ssary'; not only to rnake thc con.jiinction of thr transposiiions t'or the lirst pair of irriplications, '11' not ncvcr ( = soineiimes) arid not always the case, then contingcnt', but also 'If conting(:nt, then sonietimes the case and sornctimes not'; even this would bc irrelevant to the delinition of the modal terms. This passagc will not do Sor testirig which irnplications l'homas recognises bctwccn modal and tense Statements. Thomas's argurrientativc: intention is preciscly to t:xpt:l references to what is actually the casc-whether always o r riever or somctimcs and somctimcs not-frorri definitions of modal terms. As he ollen does elsewhere, hcrc too 'I'honias makes all possiblc admissions to his opponents in ordcr to bring ihe controversy to its dccisivc point:

" Thomas Aquinas: In Pnih. T . . I , I.XtV, n . 183; cr. iiiy articlc rrirntionrd in n. 19 ativve, 25f. 29 Thvmas Aquinas, Icit:. c : i t . 24 Sirri<) Knuuttila, 7 7 ~ Stuiisiiml Infnpretafion of Modaliv in Aumnr~s and Thnmar Aguinar, in: Aiaiils, 37 (1978) 79-98; hcrc: 94.

Hintikka and Knuuttila quote, paraphrasc or nanie parts of texts, but only in cxceptional cases2' do they analyse whole Patterns of' argu- ment. More usually thcy omit to consider thc subject ol'clebate in cach of the contexts from which their exc:crpts are taken. 'l'hcrc are, though, relevant diffcrcnces between them. One oT the formulations in which Hintikka perceives the principle of plenitude runs as follows: 'Nothing eternal is contingent'". This scntence is, in fact, Aristotle'sw. Hut Hintikka appears to overlook the fact that Aristotlc only uses the word 'aidios'-'eterna1'-for events in thc heavenly sphere; the sentence quoted here has no application to the sublunary world. It cannot hc understood as a principlc: of tense or modal logic, but as a substantive principle of a specific scicnce, that of celcstial physics. The convcrsion of this sentence, 'Nothing contingent is etcrnal', can be taken as a valid rule in earthly physics insofar as its principles can basically only claim to apply to that which occurs as a r ~ l e ~ ~ .

T o surrimarise: there is no single lext namcd by I-Jintikka or Knuuttila in which Aristotle or Abelard or Thomas directly support the principlc of plenitude or expressly accept the "statistical" intcr- prctaticin of modal terms. Where the semantic intcrpretation of modal terms is in question, it is, rathcr, continually emphasised that thcsc terms are not reducible. In most of the texts quotcd by Hintikka and Knuuttila it is claimed only that in our substantive speech about particular possibilities wc remain bound to what can he cx- pericnccd-that is, to what is at sonie time thc case. This has nothing to do either with the principle ol' plenitudc or with a statistical inter- pretation of rriodal terms. In the rernaining rcfererices it might be investigated what is bcing discussed in thc surrounding contexts, so as to discover undcr which conditions a reductionist intcrpretation of modal terms might bc atlmissible.

2. 'I'hc Problclii: Logical Determinisrri

Hintikka"%nd KnuilttilaJ4 also advance as onc place in which the principle of pleriitude is applied the famous sentence from De Znt. c.9":

29 Therc arc two of thesi tixccptinns. Onc is Hintikka's inicrprctation of Arisii)ilc's Ut Int. C . 9; thc other is Kniiuttila's paraphrase of'niins Scnius's Ue Primo Principlr~ IV, 4, 3 . I'roof. Y" Hintikka 96.

Cf. Hintikka 104. Cf. Soraljji (scc n. 6) 60, 128-132; also iny article mentiorierl in n . 19.

33 Hintikka 151f.; Ijintikka - Kemes - Kriiiiittila 44. " Knuuttilii 166, 235; cf. 170f., 181, 183. Y5 Aristotle, De Int. 9, 19a 23-24. In-J. 1 . . Ackrill's translatiori (Arls totk' .~ Calq~orics und

i C to tnen nun einai to on hnfan Z, kui to mF on rne einai holan mt? C, ana,ckF"-"Necessarily, what is, is, when it is; and what is not, is not, wheri it is not". This sentence can be regarded as followirig liom thc principle in qiiestion only on condition that it is postulated that it is valid not only for types of cvent, but also ior individual o n e ~ . ' ~ I con- sider it quitc irnprohable that Aristotle a<:c:c:pts the principlc in this extreme H e would, if' he did so, have to admit that it applicd also ta events distinguished not by dating but by qualifiers of qiiality, placc or position.

I shall rriake clear latcr how I understand the contentious sentence; first I shall continue to examiric the steps takcn by Hintikka and Knuuttila. The sentence, as thcy understand it, is a deterministic one:

"Hcnce all statrnirnts a h u i cvcnts that artb individual in thr scrisr ol'heing tied to a partiriilar rrioriicrit of timr, will bi: cithcr nccrssarily truc or nccessarily fal~e"~".

According to thcsc authors, Aristotlf: bclicved, though, that he could render tliis dctcrrriinism harmlcss by emphasising thc dillerence hctween 'necessary that p at time to' and 'ncccssary that p'.

De Inlerprefationr, Oxford 196:3), ihc sentencr is rcndcrcd, 'What is, nccessarily is, when it is; anti what is riot. riccessarily is riol. when it is not'. Hintikka quotirs ihis iranslation, 1)iit. with slightly dtcrcd punctiiatiori: "What is nri.cssarily is, wheri i t is; and w b a ~ is not necrssar.ily is not, wtitrri i t is not" (156). In Hintikka - Rcmcs - Knuuttila tlic punctuatiori is as follows: "What is, necessarily is when it is; iintl what is not, nc:i:i:ssarily is not wticn it is not" (44).

A Lorinal proof, wliich Hintikka iintl Knuuttila do rici i prnvide but irisicad repliice witti li,rinulations siicti as 'seems to ii,llow' (Knuuttila 166), could be givirn as follows: Givcn: M p - X t (1)-I). This assumpiion cari, according to ttic laws of rnodal and predicatc logic, be trarisformed into tlic c:quivalent

V t (p-t) - N p. Application: M (P-ti) - (1.)-t,). By counterposition find transforrrialiori, valid iri riiodal logic, this yii:lds:

- (P-ti) - N - (P-ti). From this, t>y substituting p-ti / - (p-1;):

(p-ti) - N (p-ti). " Hintikka claims (160) tliat Aristotle rxpi-i:ssly presup1,osi:s ihc axiom 'l>ossibility cquals sorriiitiinc truth' iii ße Int. 9, antl as proof of this hc quoies the sentcnce, ' C hommrn gar ... hoti holos estiri cn iois me aei iirii:r.gousi to diinatori cinai kai mC" - "We sei: tliat ... in things that arc not alwilys actual there is ttit: possibility of h i n g and not bcing" (19 a 9-11). This argiimcnt is Siiulty. In 'What is riot always actual is con- tingerit' thc principle of' plenitude is, as Hintikka himself rcmarks elsewhcrc ('Jöf.), noi iinplied. ' - V I (p-t) - - N p' can bc ti.ansbrmed, ii<:cording to the laws of propositional anti modal lo@i. arid hy suhst i tut i r~~ p-I. / - (p-t),,into the equiva1i:rit ".&I t (11-1) - M P'; but c.>rily '3 t (p-t) - M p' is deperi<lcrii. on Hintikka's postulated principle. Y'' IIiritikka 151f.; CI.. 161, 174; Hintikka - Remes - Knuuuila 31-58 arid passim; Knuuttila 166; and piissirii.

"Aristotlr tries to avoid terition frorn statrrrients stiiterrierits'"'

deterrninistic conclusions by shifiing ~ h c focus of his at- of typr (3) ( = p ; ~ t timr t,,) 10 rc~iiporall~ utiqudtlicil

-riarriely thosc of thc type ' p simp1iciit.r' or 'p now'. 'l'he individual evcnt is not rcgardcd as individual, but sccn in relationship with similar occiirrences. Hut ii is not posiulaied 01' ihis class of'occurrences that thcy arc cithcr ncccssarily truc o r nccessarily false40.

Knuuttila clairns to discover the sarne attcrript to solvc this problcm in the work of Roethius41, A b ~ l a r d * ~ , T,atiil>ert of A ~ x e r r e * ' ~ arid Thorrias A q ~ i n a s ~ ~ . H e crriphasisc:~ that it is mcrcly an apparent soluiiori:

' I Thc g<:n<:ralizaiiori wiih r~sp<:<:t t o t i t i ~ t . I<:av<:s li~lly i~ritoi~chrd the drtrrrninistic irnplica~ions of Aris~otlc's assunipiioiis conccriiiiig ictiiporally d<:tcr.tiiinc:d c.vi:rits aiitl s c n i t ~ i ( ~ t : s " ~ ~ .

Kniiutiila presents l luns Scotiis's new rriodal thcory as "Duns Scotus' Criticisni of t.hc Statistical Intcrprctaiion of M ~ d a l i t y " ~ ~ . Here I agree with Knuuttila's account at irnportant points. Duns Scotus dcvclops ihe basic traiis of a theory of possible worlds, and indeed does so iri thc coursc of critical commt:nts on the claims of his predecessors. But I tio not h(:lic:vc thai ihis argumeni proceeds exactly as Knuuttila dcscrihcs. I i seems io me [hat ii is not his preseritation of' Duris Scoius's positiori which is rriistakcn, t ~ u t rathcr his vicw of that from which Scoius disiances hiniself'. I cannot set out here thc points which I do Lclicvc n u n s S(:otiis to attack-1 shall make sorne remarks on ihis a t the crid of this papcr. At prcscnt I shall contcnt mysclf with drawing attcntion to ihe Sollowing. Duns Scotus quotcs the Aristotcliari seritericc frorri De Znterpretalinne. 'l'his scntcn(:<:, 'Omnt. quod es1 quando t..rl, 63-t n6~-essarium', is susccptiLlc of two intcrprctations. Tak<:n secundum diuisinnem, it appcars as a conditional scnience, whose sense Kniiiitiila corrcctly construcs as "Whc:n<:v<:r somcthing is, i t then necessarily is". T a k m ihiis, the senicnce is Ialse. Interpreted secundum cnmpnsi- tionem, it is a rritcgorical scnience, construed rorrectly by Knutittila,

"!' Hiiitikka 161 in t-ciriri<.<:ticiri with 1.51; (4'. IfiO; 1 lintikkki - Rernrs - Kiiuuuila 44f; Knuuiiila 167, 235.

Hintikka 1701: 4 ' Knuuttila 171. +' Knuuttila 181, 184. +.' Knuuttila 1!32.

Knuuttila 210f. Kniiuttila 167; rf. 221, 235f.; Hintikka - Kcnics - Kriuuitila 45, 46.

4"~~iiiitti l;i 21 7-234; C I 2361'.

when hc puts it, "Ncccssarily everyihing is whcri it is". lntcrprctcd thus, the scntcnce is t r ~ e ' ~ . Thcrc is, therefore, an intcrpretation of this disputcd, purportedly dcterniinistic sentcncc, accordirig to which the sentencc has no cleterministic implications and is perl'ectly iruc. And nor is this interprctation connected with the theory of possiblc worlds. How shoiild it bcl' ISthe generalisation to what can takc: place at other timcs in this world supplics no real avoidancc of logical detcr- rninism, thcn neither does thc generalisaiion to what can happen at

thc same tirne in diffcrcnt worlds. Now Duns Scotus does not succeed in givirig this scntcnce a triie sense, frcc of determinism, by virtue 0l.a new scmantic theory; he does so by means of a simple syritactic distinction. This, thc distinction bctwcen readings .recundum composi- tionem and secundum diutstonem, sterris ti-om Aristotlc4", and is an instni- ment farniliar io Hocthius ancl the s c h o l a ~ t i c s ~ ~ . Might it not bc plausi- ble to claim that Aristotle himsclf' and his interprctcrs before Duns Scotus also intended this scntence to bear thc construction according to which it is true? And cqually plausible to claim that it nwcr was deduced frorri any such postulated presupposition as tlie "principlc of plenitudc"?

11. On the Logic o j Y'ense und Modul Qualifiers in Scholastic Wrilings.: A Jj~ternatisin~e R~onstruction

1. The thescs advanced by Hintikka and Knuuttila refer to 'occa.rion ~entenc-es'~~. In what f'ollows, I sliall explain how I understand thc scholastic analyses rclcvant to this typc of sentence. I shall rwur only occasionally to oihcr typcs of sentencc and scliolasiic accounts of them; when I do mcntion these, it will be with the interition of marking thc distinction between thcm and the typc of sentencr. ccntral to the discussion. In scholasti(: works, the standard example for staternents about particular events is thc sentence, '.S'ocrates sed&'-'Socratcs is sitting'. Here 'Socratcs' does not refcr to the historical Socrates, but to any arbitrarily s(:l(:cted individiial, thought of as cxisting at the prcscnt tirne. For thc sake ol'simplicity I shall use the samc standard examplc.

2. Sentences about particular cvcnts are analyscd in terms of propositional and of assertoric clcrncrits. The thought cxpressed in thc

47 Knuuttila 229. Cf. Hintikka - Rcrrics - Knuuttila 48-50; Kriiiuttila 168. Cf. Knuutti1;i l641:, 176, 179f., 188f.. 191-195, 214, 221.

5U Cf. Hintikka 64, 150 n. 6.

sentence 'Socrates is sitting', its propositaonal content (dictum propositionis), is 'that Socrates is sitting' ('Socratem sedere'), or, substan- - -

tively, 'the sitting of Socrates'. Its comprehensible content is the sarne for thc statcmcnt (propositio) 'Socratcs is sitting' as for thc incomplctc expression 'sitting Socratcs', for thc qucstion '1s Socratcs sitting?' and Sor corresponding orders or requcsts. 'l'he question what a statement is, in contrast to incomplcte expressions, questions, ordcrs and so on,

can be answered by becoming clear about what is added to the corri- prehensiblc contcnt, in itsclf only a dcscription of a possiblc proposi- tion (enuntiabile). This added element does not comprise a new, categorematic content bui is the proposition's statemental or assertoric content. In the propositio a truth-valuc is assigncd to thc propositional content. 'Socrates is sitting' is explicatcd as, 'It is the case that Socrates is sitting', or 'It is true tliat Socratcs is sitting'. 'Socrates is not sitting' is explicated as ' I t is not the case (is Salse) that Socratcs is ~ i t t i n g ' ~ ' . The distinction stresscd hcrc could also suitably be for- mulated as that bctwecn possible and actual states OS af'fairs.

3. When statements such as 'Socrates is sitting' are rnade in a speech situation, they count as staterrients about what is thc casc nt the time qf utterance. This refcrcncc to thc timc of iitterance is usually implicit; it can be explicatcd by cxpanding the "token reflexive" Ln0W'.52- . L Socrates is sitting now', or, even rriore plainly, 'It is now, as

1 am saying this, thc casc (truc) that Socrates is sitiing'. When such staterrients are discuss<:d-as thcy are by logi-

cians-particular attention is paid to somcthing which is prcsupposed, automatically and thcrcforci tacitly, in a speech siiuation: that the reference to tlie situation in which a staterricnt is rnadc is part of the statement. 'Socrates is sitting', said at different tirnes, may somctimes be true and sometimcs falsc. Thc truth-valuc of statements like this is dependent on their time OS utterance; it is, so to spcak, unstablc.

It is our habit to makc Statements more precise by dating theni. Instead of indicating thc situation of uiierancr, we choose fixed times of ihe clock and calsndar as reference p ~ i n t s ~ ~ . The truth-values of statcmcnts datcd in this way are, of Course, stable. Riit the fact that

5 ' rior this part of my presentation shiill provide only a few selected references and make general reference to my investigation mentioned in n. 5. Exemplary for thc distinction between dictum propositionis and propositio: I'eter Abrlard: Lu~icu 'In~rt~lzcn- trhus', G1o.r.r~~ super t ' m ' m i a i , ed. B . Geyer (BWh'liuUA 21), 326, 37-327, 41. 52 C:L: Hintikka 64-66, 85, 150. 55 Cf. Hintikka 87, 151.

Aristotlc arid the scholasiics pro<:<:cd differeritly does noi detract frnm the worth of'their analyscs, wtiich deal with thc: morc: complex type OS case. Sincc thc transitiori I'r.otii the morc cnmplcx to tlie sirnpler is always easicr than thc other way round, thcir analyscs are also instrur- tive for thosc who are interestcd in a logic ol' dated statements.

'I'hc "tokeri rellexive", 'now, at the tirrie I ani saying this', is not iniplicit only in statcmcnts in the present tensc, but also iri staterrients whose prctlicatcs are in the past or thc future. The past is what happcned belore now; thc futurc is what will happen aftcr now.

4. How should wc analysc statcrrients aboiit the past or about the futurc? Should the tense qualificr bc counted as ( 1 ) part of thc asser- toric aspect or (2) part of thc propositional content of a statcment? In the tirst casc, 'is the case (triie)' can bc made rnore precise by a tensc operator:

'1i was-earlier thiin riciw-ihi: c:asc (iruc) thai Socrates is sitting' $11 is-now-thr <:;ist. (trilc) ihai Socraics is sitiing'. '11 will bc-later thari riuw-tht: casc (truc) that Socrates is sitting'

In the second casc onc would assign a "time ~ignif ica t ion"~~ to the verb in the dzctum proposztionis: 'Socmttm .rtdoro9 would have ariother mcaning than 'Sucratem se/iis.tc' or 'Socratem sedentemfure'. 'I'hc modcl of analysis would be:

'11 is the riisr (triii.) itiai S<i<.i.atcs was siiting-eürlier thari now' '11 is thr ras< (truc) thai Socraics 1s siiting-now 'It is the casr (triic) ihai Socraics will be sitting-latrr ttian iiow'

Closcr cxamination shows that the question which rriodel of analy& to follow has not. yet bccn quitt. correctly put. 1i is in fact tci bc rccorri- mendcd that orie shoiild follow both. For a statenient of type (1)-'There was a pciint in tirrie at wliich it was true to say, "S is P" ', does indecd havc the sarne truth-value as thc type (2) Statement, 'It is riow true to say, "S was P" '; but these two statemcnts arc not saying exactly thc sanie thing. To put it evcn morc carefully and niore preciscly: thcy are accentuating the samc thing in dil'i'erent ways. In the first case thc spcakcr situates hirnselt; so to spcak, in another period in time, ficirri which he makes a statcmcnt in the present tense; in tloing so he draws attenticin to thc iristability oi' such Statements about particular cvcnts. In thc sccond case, however, the truth-valuc sccms relatively stable: if i t is now thc case that 'S' was 'P', then it will

Arisioile: 1)e Inl. c.3, 16 b 6.

bc thc case at cvery future rnotricrit that 'S' was 'P'. I Want to try to clarify this distinction by showing wiih what instruirirnts thc mcdicval logicians analysed tcnscd statcmcnts.

(1) In statcmcnts ahoiit the past, wc should bcar in mind the distinction bctwt:cn talking aboiit sorrieorie who cxistcd in thc past and onc of his actions or statrs, antl talkirig about an carlicr astion or statt. of sorrieone who still cxists now. In the I'or1rit.r case thc sub-jcct tcrm stands (as well, at any rate) for somcthing in the past; ttic tcnsc quafificr brings aboui aii extendetl rangt. oT refercncc (ampliatiu supposi- tlonlJ-). The tensc Operator (1ctcrrnint:s thc stateiiient as a wholc (sensu composi~o); acijusting the graniniar to erriphasisc thc: scnse, this gives, 'This was thc casc: Sorrates exists and he is sitting'. In the latter case, thc sub.jct:t tcrm stands for sorriething in thc present; the tense opcrator dctcrmincs, .ccnsu diuisv, orily thc v(:rt) of action or state: 'It is tiow the case that Soc:rat(:s cxists and was earlier the case that hc: is sitting"? -'Ibis distinction is derr~andcd by thc analysis of' tensrd statetnents I gavc first, at.(:ording to which thr tirne reSercn(:(: is extractcd l'rorri tlie fitum proposifioni.~ and coiiiited as part of thc stat(:m(:ntal aspect. 'I'he dictum is split up into various parts; for each part ofthe staietrir.nt's contcnt it has to bt: decided whether to assign it. a truth-valuc Sor thc prcscnt moment of tinie or for sorrie carlicr onc.

(2) Statcmcnts in tlie prrsrrit tcrise express what is or is not the case at thc rriorricnt of uttcring thcni. Statrnirnts in the past tcnsc, though, do not apply only at the triorricrits of tirnc: at which they are made. Both thc stateinent, 'Socratcs was sitting', and the Statement, 'Socrates was staridirig, so hc: was not sitting', can indeed bc truc ' L now7', if thc: prrson inakiny thrrri is refcrring to statcs of afrairs whic:h havt: oc:c:urrt:d at different tinies ir i thc past But if the state- inent, 'Socrates is sitting', has cvcr at any time been triie, the state- mc:nt, 'Soc:ratc:s was sitting' ( = 'It is thc casc that at some moment of iitrie earlier than this onc Soc:rates was siiiing') is valid for all sut>S(:- quent rriotrients oftirric. Statc:m(:nts in the past tense are, theri, valid Sor the wholc pcriod of time tollowing the rrionierit in which th(: cor- responding present statcmcnt is true, I'he dill'erence between thc "short-livcdW5~ qilality of Statements in thc present tense and thc

'V(:i'. Williarri of Shyreswood, Jntrorfuctionar in J,o%~icarn, ed. Mar~in (;rabrriari, iri: SB Hayi:rist:tir Akademie der Wisscrisctiaf'ten, Philosophisch-Historische At~teiiuns. .Jg. 1937, I i . 10 (Munich l937), 84, 12-30; 85, 16-31. 56 'lhis rrietaphor is coinctl hy G . Niichelmans in ihtorza.- C!/- Proposition; fincienl und Marfia~nl Cnncrplions oj'lhe Heurm ( I / Trufh nnd Palsip, Anisicrdarii 1973, 162; t:f. Knuiit- tila 180.

"long-lived" quality oS those in the past tense is easier to pcrccivc in that analysis OS tensed statements which distinguishes propositional contcnts iri tcrms of thcir tcnscs than in thc account I presented first. The scholastics recognise the distinction when they say that statements ahout thc: past arc, if thcy arc truc, ncccssary Per accidens. In order to makc clcar thc cxact sense of this cxpr(:ssion it is necessary at least briefly to look at the function of modal qualifiers in general. Before I do so, I should like to makc one more remark. It is logically quite un- pmblematic to transier the accounts we have now achieved for statements about the past to statements about the future and to say something like, 'Once the statement, "Socrates is sitting", is at some moment of time true, the statement, "Socrates will be sitting", is valid for all preceding morrients of But it is qucstionahle whether such a transfcrencc would bc sensible. The medieval thinkers hold that long-term prognoscs about particular events are possible if at all only in as t rono~r iy~~ , so in this type of analysis, wherc spcaking about the Suture is concerned, the hiddenness OS the future is usually <:mphasised. The transference I have rnentioncd bccom(:s a scrious subjcct of discussion, however, with regard to thc qucstion of God's preknowledge.

5. For mcdieval logicians, modal logic is not a spccial arca of thc: discipline. For them, rather, i t is an essential part ol' deterniining the sense o f any sentence at all to give its rnodalily, whether or not modal tcrms ovcrtly occur in it. Modal tcrrris serve to dctcrminc tht: way in which subject and predicate are linked in a statement. In giving the rnodality one makes clear in what way the statement should be counted as true or Salse.

Whenever logical Operators arc: part of a statement, it is necessary to detcrminc their rangc of' applicatiori, by syntactic analysis of' their logical structure. The distinction between sensu composito and sensu diuiso is an aid to doing this. When several syncategorernata occur together, i t must also be determined which OS them is the "inclusive" and which the "included", that is, the one which falls inside the range of application of the inclusive one.

6. The basic distinction in niedieval logic is that between statements which are either nccessarily truc or neccssarily false, on the

57 Cf. Aristotle, L)e Ini. c.9, 18 h 9-11; 18 h 33-19 a 1 . 58 EXceptions arc statcrricnts aboiit ttic Antit.lirist, whosr futurr apprarancr is takrn to have been guarantccd by thc authoriiy ol',jcsus; cl'. Lo,~ica '1Jt Tlicit', rd. T.. M. dr Rijk, in: Lq~ica Modmorum 11-2, Asscn 1967, 390.18-31.

onc hand, and contingcnt statements on the other. Hcre I sliall explain the thcory of necessarily truc and necessarily false ( = impossible) statcmcnts ony as far as is essential for purposes of distinction. Statements arc necessarily true if their prcdicate terms are contained in their siihject tcrms; they are necessarily false if their predicate terms are incompatiblc with their subject terms. 'l'hc theory of' necessity statemcnts and that of impossibility statements are systematically link- cd with each other by thc following equivalences: if 'P7 is part of the concept of 'S', theri 'not-P' is incompatible with 'S', and vice vcrsa. lf 'not-P' is Part of the con(:c:pt of 'S', then 'P' is incompatible with 'S', and vice vcrsa. Necessity and impossibility statements can be sum- marised as statcmcnts whose truth-valucs arc fixed by the intensions of the concepts used in therri, in short as semantically delermined statements. Semantically detcrmined statements arc univcrsally valid. For inten- sionally truc statements it can bc: said that all possible instantiations of thcir subject terms are also instantiations of their predicatc ternis. Tt can be said of intcnsionally false statemcnts that no possible instantia- tions of thcir subject terms will bc instantiatioris OS their prcdicate tcrms. Note that here it is rcquired only that the terms should be able to bc instantiated, not that thcy should have actual denotations in the prescnt.. Thc statement 'Homo est animal', ur 'Omnts homo iosl animal', is interpreted as 'Si es[ homo, est anirnal'.

Contingcnt statenients arc .remantically undetsrniined; their truth- values are not detcrmint:d by intensional c:onsici(:ratioris. Intensional examination of thc tcrrris used in them allows us to say only that in contingent statements prcdicate terms are compatiblc with subject terms, in thc cxact sense that the ncgation of the predicate term is also compatible with the subject tcrrri. Accordingly, the notion of con- tingency is dcfincd by a conjunction of dctcrrriiriarits, as I'ollows:

'K p ift' - N 1) c - - M p'; or, c:quivaleritly, 'K p iff ' M p M - p'.

Frorri this delinition it follows that if 'p' is a rontingent staterrient, then ' - p' is a contingcnt statcrrient too-and vicc vcrsa. If a contingcnt statcmcnt is asserted to be iruc, thc nianner of its bcing so will be giveri by the conjiinr:tion 'true, but not n(:r:r:ssarily true', or, equivalcntly, 'p s~ M - p'. I f a contingcnt statement is assr:rtcd to be falsc, thc rnodal qualification will bc, correspondingly, 'falsc, but not necessarily falsc', or ' - p aM p'.

7. Thc statcmcnts about particular cvcnts with which I am con- ccrncd here are all semantically undetermined, whether they deal with events in the pasl, prescnt or futurc.

It is riecessary to distinguish between the concepl of'semantic deler- niination and that of determinacy of truth-valuc. 'l'hcrc art: scman- tically iindetermin(rd stat(:mt:nts which havc dctcrminatt: truth-valucs. One type OS such stateinents has been mcntioned already. As soon as a Statement about a particular cvcnt has oncc bccomc truc, it is truc for all subsccpent points in tirrie that the statement has orice been true. Whcn such statements are termed ptr accidens necessary it is not being disputcd-on thc contrary, it is beirig af'firmed-that they are perse not ncccssary, but contingent. The delinilion of 'Per accidens necessary' is a specilication of the con~iunction 'true and possiblc that not truc:'. Roth parts of this conjunction are specilied as to time, and qualilied modally in opposite ways: somelhing is per accidens necessary if i t cannot be false in the prcscnt and futurc, but could have been false in thc p a s ~ Take thc statcmcnt, ' i t is the case that Socrates was sitting at sorrie point in time earlier than this'; tht: furthcr statenient, 'It is thc case that Socrates was, at somc point in time earlicr than this, not sitting' is rclated to the firsl as ils subconlrary, not its c ~ n t r a d i c t o r ~ . lfone bcars this in mind it is easy to sec that one can without coritradiction assert ptr accidens necessity both of 'Socrates was sitiing', and 'Socrates was noi siiting'. 'l'he problcm of logical dctcrminism docs not arise. The thcory of the Per accidens necessary rellects 1he law of the Sactual at the root of all particular facts: what is donc cannot be u n d ~ n e ~ ~ .

8. Statements in tht: prt.rtnl tcnse about particular evcnts also havc determinate truth-values; the proposilional contents corresponding to stich statcmcnts, though, do not. 'l'hat Socratcs is sitting can at various different times be true, false, and true again; but 'It is now the case that Socrates is sitting' is, at every randomly choscn momcnt at. which the statrnirnt is made, either "in a deterniinate sense (dtter- rninale) true" or "in a deterrninate sense t'alse"".

'I'he s(:holastics iisc the notion of necessity in order to recognist: deterniinacy of truth-values in the case OS statenienis in the present tense too. Here they take all possible care to avoid any confusion bctwccn thc: "teniporal ni:ci:ssity" meant in this context with

"' In scholastir works it is disputvd wtiettiec. ttiis law stioiilrl coiint as a logical principlc nr as a principle of nature. The question is usudly discussed in <:oricrete f'orrri: is it pnssihle for God to restorr lost virgiriity?

Cf. 'lnomas Aquinas, In Perih. [ , .I 1 .XITI, r i . 169.

"nc(:cssity as such". The tool thcy use to makc the distinction is not the transference from sentences "dctcrminate as to timc" to sentences "indctertriinate as to time"", which is only apparcntly applicahlc; in- stead they usc exact syntactic analysis. A sentence such as, 'Necess-e est Socratenl sedere dum sedet', is capable of various constructions, according to whether the range 01' appli(:ation ol'the timc con.junction 'as long as' and ofthe modal operator are fixed; the consistency of thesc construc- tions has thcri to he test(:(i. The sentcnce can be understood (1) in such a way that thc rircrssity opcrator, uninflucnccd by the time rcference, determincs the wholc: scntence: ' l t is necessary that what tlie Sollowing states is the (:ase: "Socratcs is sitting, while he is sitting" '. Understood in this way, thc scntencr is,/al.se; it is not necessary that thcrc should bc a tirrie at which the possihility of Socrates's sitting should be instantiated. (Formalised, this riins as Sollows: ' - Ngt (p-t)'.) ?'hc scritence can also be undt:rst.ood (2) as a temporal con- ncction in which thc latter part of the sentence is distinguished from the I'ormer only by an addcd tnoclal opcrator: 'As long as it. is the case that Socrates is sitting, it is the case that it is neccssary ttiat Socratcs should sit'. In this interpretation too, the scntcncc niust be re.jt:ctcd as Jalse. Its latter part is falsr I'or any randorrily selectcd rnotnent of tirnc; evcn supposing Socrates to be sitting now, the possibility that hc should not h(: doing so is a present one. 'l'ht: con,junction 'p & M - p', which characterises truc contingent statcrrients, is also valid wlien thc proposition variable is qualifit:d by 't;', which indicates some par- ticular point. in tinie; 'p-t; ~k M - (p-ti)' is dcfcndcd as consistcnt by thc scholastics. 'l'hc scntcnce can also (3) be interprctcd in such a way that thc modal opcrator itsclf is temporally qualilied: 'Socrates is sitting, and during the timt: in which ht: reniains seated it is not possi- blc that he should not be sitting'. Understood thus, tht- sentence is true. The dillerenc(: bctween this and thr rejectcd intcrpretation (2) can be clarifi(:d by li~rmalisation:

(2) 'V t; (p-ti - N (p-t))' is false: (3) 'N V t; (I)-[; - P-ti)' is iriic:"'.

" Kniiuttila says iliis (171f.) witti rcgard to Rwthiiis; 161 and 183f. with rcgarci to Abelard; 21 1-213 with resar~l io Tlioiiias Aquiniis. " 'C:. Peter Atr:lard, .Yupn Periermeni/l.i, cd. L. Miriio-Palucllo, in: Tu~elfth Cmfury Lqpic: 7>x1.1- nnrlStudles, 11: AhnplarrIinnn Inrdifa, Komr 1958, nn. öl-63, p11. 36.22-38,5; nn. 76-77, pp. 41,215-42,211; DI/I~CC~IL~/I, cd. L. M. CI(. Kijk, Assen 1956, 206,7-210,19.

advance. One can only talk ahout anomalies and exceptions to what nornially and naturally occurs hy distinguishing what riornially happens Ii-om what necessarily happcns. As soon as the contents of possible anomalii:~ arr: dcscribed, they are already being treat(:d as instances of somc rulc or lawb'.

10. Anyone who talks about particular cvcnts rnust ref'er to natural caiiscs and specific explanations; recourse to God's creation or to his ahility to work miracles is not admissible in the scicncc of nature:". Thomas Aquinas cmphasises that possibility and impossihility, con- tingcncy and necessity must be spoken aboiit in such a way that the standards of imputing thcm arc their relationships to their "pruximate" and "proper" causcs. It may well be the case, though, that somc cuncur- s u ~ causarum is not explicablc in tcrms of particular proximate causes and so has an accidcntal rclationship to themi, but that an explanation can aftcr all bc found for it if' it is traced back to some morc gcncral caiise. I,astly, it is not possiblc to imputc any okstacle to ths uniucrsal, Godly cause of all that is. Nonetheless, ncithcr from God's ornnipotence nor Srom his prcscicncc, to which everything that ever happcns is givcn in a timeless present, cari it be inlkrred that nur cstimation of events as contingcnt is simply an cxpression of our finite standpoint, seen kom which deterministic rclationships carinot be properly traced. 'l'he conccpt of contingency is not merely epistemic, it is an ontological one. Thomas solves thc thcological problcm of' determinism in the following way:

"l'he will of God rriusi bc undcrstood as outside thr ordrr 01' tiiririg, as a i:ausc underlying thr whole oF what is and ail its diversities. Riit <listin<:tions in what thrre is arc 'possiblc' and 'necessary'. And therefore ri<r<:essity and contingency in things, arid thc disiinctions hctwccn thern, made ir i terrris ol'ihc: liinciions of their proxirriatc causcs, havc thcir sourcr in thr will of Goi1 itsiilf. For tci ihosc efTci:ts which he wished to be necessary lie gavc neccssary causes; and to those effects whi<:h hc wishcd to be contingent he gavr <:ilusi:s whicli opcratc con- tirigcriily, tliat is, causes which may be drfi<:irrit. Ai-corcling 11) thc ways in whirh such causcs arc dctcrinincd their effects are terrned citht:r 'nc:ctisuary' cir 'con- ting-rrit', although aal1 depend on thr will of Go11 ns th<:ir- principal causc, which iransccnds t he ordcr of nccrssity im<l i:ontirigcncy "GG.

Duns Scotus's new modal theory does not arise from any discovery of internal difficultir:~ in the views 01' earlier scholastics and cspecially

" Cf. Aristotle, Melaph. Epsilori 2, 1027 a 21-26; on tliis, vid. thc coniinciitary by Thorrias Aquinas, L.VI 1.11. 65 Cf. Gcorg Wieland, Albnl der Crosse und die Ent i~ ick lun~ der mitlrolaltarlichm lihilu~uphle, in: Zt:itsctiril'i für philosophische Forschung, 34 (1980), 590-607; hrrr 592 witti refcrcnces to Abelard and Albert. <:f. 594 n. 21. " Thomas Aquinas, In Perih., I . . I l .XIV, ri. 197.

ol' 'l'horrias. For thcological reasons Scotus att.acks ttie principlc ttiat wc <:an judgc: of the necessity or contingency of the things or events in this world by lookitig at thcir proper causcs. For him, thc furictioning of the first causc alone can cit:tcrrriine whcthcr there should be only riecessary cvents or whcthcr there should also be cvcrits whirh may happcn and may not.: "Every secondary cause causes insofar as it is rrioved by thc first causc". If i t were assurricd that. thcrc were a first cause which caused evcrything else ncccssarily, its ncccssity woulti be transferred to cvrry secondary cause and thus to every causcd event. That therc are contingently caiisecl events-those which, when they happen, could also not have happened-can only be explaincd il' the first caiise causes contingcntly. Rut since obstacles to or other deticicn- cies in the working of the first c:ause are unthinkable here, a con- tingently causirig tirst caust: can only bc irriagined as a will-so that the causc itself detcrrriines whethcr or not i t shoulti take effcc:tb7.

Avicenna had thought of Cod as that bciny, which includcs its own being in its csserice. He had opposed io this being, neccssary in itself, thc totality of all tht: rest OS being, which can without inconsistcncy be thougtit of'both as existing and as not existing. What is in itsclf only possiblc cxists, when it docs cxist, throilgh some othcr cause, indeed through that bcing which is neccssary in itself, God. As an ctTcct of ttir first causc it is, according to Avicenna, necessaryo8. Duns Scotus adopts ttie whole mctaphysics ot'esscnccs from Aviccnna, biit without accepting his vicw that everything brought about by God nc:ccssarily happcns as it does happcn. What takcs place bccause ol' God is not broiight about neccssarily by him; i i is frcely willed by hirn.

It would bc ari interesting task to investigatc how Sar, in Lcibniz and- in modcrri authors, thc sernantics of possible worlds is expressly or implicitly bound up with a metaphysics of csscnces.

1)-5000 Köln 41 Thorrras Institut

h' Cf: Iliins Scotus, Tractotur I h Prim Principio-Ahhandlun~ über da\- i?~,rlc Prinzip, etl., transl. and wirh i a <:omrrirrit.ary by Wolfgang Kluxcn, L)armsta<lt 1974, ch. TV, scnicnce 4, r i . 56; <:1: Knuuttila 218-221 anrl-for ü detailt:d intcrpretation in thc crin- text t r f Lhns S<:otiis's rriciaphysics-Etienni: C;ilson,,johatinrs Duns Scoius. Einfuhrring in rIG (;'rundcedankm scinn Lehre, trünsl. by Wcrncr Dettlofi. Diisscldorf 1959, ch. 4, 11, esp. 326.328; 111, 3311'., 335-342; [V, 3471'. " CS. Guy ,Jalbcr~, NLccssiii ei Cnntinprr chet Saint Thorrrm d7Aquin ct chcz ses i'ridtcesseurv, C)t.t.awa 1961, ch. 11; E~icnne Gilsori (scc n . W ) , 338f.; cf: also the passages to I r found in the inclrx on 'Existenz', '1.ogik dcs Nichtriotwcndigcn', 'Mög!ichtis', 'Nczcssitarisrnus', 'Nich~notwendig(es)'. 'Nichtnotwendigkcii', 'Not- wcndig(es)', 'Noiwcndigkeit'.