Abelard and Frege: the Semantics of Words and Propositions

Sonderdrucke aus der Albert-Ludwigs-Universität Freiburg

KLAUS JACOBI

Abelard and Frege: The semantics of words and propositions

Originalbeitrag erschienen in: Vito M. Abrusci (Hrsg.): Atti del Convegno Internazionale di Storia della Logica : San Gimignano, 4 - 8 dic. 1982. Bologna: Ed. CLUEB, 1983, S. [81] - 96 A 7TI dd Convr~noInlrrnazionulr di Boria drllo Lo~ic-U. Saii Giiriigiinno. 4-8 diicrnbrc 1982. (-'IIJFIt. tIoIog11a (llaly) C) 1983.

ABELARD AND FREGE: THE SEMANTlCS OF WORDS AND PROPOSITIONS Klaus Jacobi

Universiiic lluisburg, Ciesaniihochschulc. FB I - Fach Philosophic. Lotharstr. 65. 4100 Duibburg

Petcr iibrlard was born in the year 1079 and djcd in 1142. Gottlob Frcge lived from 1848 to 1925. Frcgc's Begriffsschrift was published in 1879, eight hundred years after Abelard's birth. Historians of uhilosophy say that cach man marks the beginning of an epoch in the history of logic, and beyond that, that each left a deep imprint on thc coursc of further developments. It is wcll-known that Preqe felt himself isolated and deprived of due recognjtion. Fcw of his colleaques, whether from thc-mathe- matics or the philosophy dcpartmcnt, bothered to study his works. Surcly none of his contemporaries adjudqed Frege's works to be epoch-makina. Nor did F'regc havc students who continucd his in- vestigations. His impact began with Russeii, Wittgenstein, and Carnap. Although the threc diffcr widely in the style of thcir thinking and in the questions they pose, all claim Freqe as their true intellectual fathcr. Abelard, on the other hand, found cnthusiastic listeners wherever he lcctured. He was a famous man, such that the mention of his namc cvokcd either sreat admiration or bitter enmity. Nonetheless, thc substance of his success as a teacher is not casy to grasp. Abelard was not dcstined to found a ncw nhilo- sophical tradition, as Peter Lombard and latcr Thomas Aquinas and John Duns Scotus were. Abelard was never an "authority" in thc scnsc in which thc scholdstics used the word. His influence is less to be attributed to a sct of theses which he developed than to his distinctive manner of approaching questions. The historical transmission of his thcological and loqical works was weak, but his philosophically probinq, discussinq, and analyzinq attitude toward knowledgc camc to be reaarded as exemplary. Frege was not familiar with Abelard or any of the other scholastics. Thcre is no hjstorical connection between the two philosophers, be it direct or indirect. When I speak on Rbelard and Fregc hcre, the theme is selected with different intentions from thosc for a papcr on say Freqe and Leibniz. I intend to conduct a comparison in systematic perspective. This comparison cannot bc bascd on thc dcmonstration of an influence of Abelard on Preqe undiscovered until now or upon somc aqreeing or dis- senting reference to Abelard in Freqe's works. Thus I vould likc to provide you witha brief explanation of what motivated me to the comparison. First, I wish to makc clcar that in selectinu this theme I do not intend to Open a debate nn Progress or reqrcssion in phi.10- sophy or the field of logic. I am not goinq to have the two philosophcrs compete with each other. I am not going t-o measure the one against the other. Thus no attempt will be madc here to demonstrate that Abelard "anticipated" later insights of Frege or that Freqe "rediscovered" carlier insiqhts which Abelard had reached. In my lectures and writings on scholastic loqic, I am con- fronted with thc problem of translatinq the medieval technical terms into a modern vocabulary. One has no choicc herc but to cmploy words whi.ch have become technical terms in modcrn loqic theory thanks to Freqe and his successors. Now we are often warned of the dangcrs inherent in a translation of scholastic d.iscussions into modern synibolic lanquagc. But whercas onc can forego such translations or devclop a more appropriate syrnbolisni in the field of loqical Syntax, in scmantics and philosophy of logic onc cannot avoid the dangcr of misinterpretation by simply renouncing all translation. One docsn'l: nct very far without such terms as 'sense', 'refcrcncc', 'designation', and 'dcnomination'. In ordinary languagc, these terms have hroad semantic fields. Thcy are used in various senses which oftcn ovcrlap. In scholarly usage the mcaninqs of such terms arc defined more precisely, at the very minimum by coordinatin~them wiLh or scttinq thcm in opposition to other terms within thc theory nt hnnd. When one makcs use of them to translate scholastic terms, it is necessary to state plainly which scnse is considered appropriatc ror thc new context. A rcturn to the everyday usagc can hardly be satisfactory, for the philnsophical or scientific theorics within which these words havc become technical tcrnis must also be taken into consideration. I am myself better versed in thc scholastic scientia sermo- --cinalis khan in modern theorics of loqic. Occasionally, in reading Fregc or one of his succcssors, I try out translations into the tcrminoloqy of thc scholastic controversics in ordcr to sharpen my conception of thc problem under discussinn. In- evitably, I ask myselF if any similaritics between the modern trains OE thought and ccrtain positions in the scholastic con- troversies can be found, This is of Course just as much a matter of clarifying thc differences as of holdinq on to TO- inciding elemcnts. Abclard stands at the outset of the scholastic development in loqic, Frege at the outset of modern developments. Neither finds a finished terminology for his philosoylhical investiqa- tions laid at his disposal. He must develop such a terminology himsclf. In questions of semantics, Abelard could find more Support in the preparatory work of his predccessors than Freqe. Abelard worked on questions which had been dealt with hy Boethius, Priscian, grammarians of the time, and Abelard's own logic teachers. Yet his lanquage often impresses us as being awkward and forccd in comparison with the crystalline clarity and elcqant brevity of tiiqh sctiolnst i.c aiithors. On thc othcr hand, Ahclard is free of ttie Set scheniata of qucstioninq and thinking wiiich bccamc charactc:ristic of later sctiolastics. He discussed lincjuistic [ihenomena such as impersonal. construct i.ons whi ch arc lat.cr ncgl.cctcd bc:causc they arc sim~lynot accessible to ttie analytic iristrunients of the thcory of the sup~iosj.tio.Ire furthcrmorc considcred alternative approaches to sucti problems as the theory of predication, whereas later other authors dis- cusscd a conspiciously narrowcr spcctrum oF lihcorics. - The samc can gcncrally be said of Frcqc in comparison with say Carnap, to takc onc cxamplc. Frcgc Corcihly wrcsLcd his tcrmino- loqical distinctions, such as that between 'Sinn' and 'Weutung' , froin ttie languacyc, whcreas Carriap simply laid down such distinctions by definition. Freqe strained to dcvelo? adequate formu- 1.ations 01 new questions and to discover new intergretational t.cchniqucs. IIis successors rnerely took ttiern over. - Thus it sccms Lhat a comparison 01 Abelard and Freqe recommends itself as a starting point whcn onc wishes to undcrt-akc a comparison 01 scholastic and rriodern loc~ic. Howevcr, a comparison will be mcaningful only if thcrc is a manifest Consensus on relevant points. This also tiolds wtien Lhc objcct of the comy?arison is to point out the differences in the rcspccLivc positions. Or coursc, d i.sti nctions arc of valiic only when it is possible to mark out preciselv to wtiat extent the basis upon which the disLincLions havc bccn drawn is a common one. Thus the question presents itself whcther this fundamental prcrcquisitc For a comyiarison is fulfilled in our case. Well, in the Course of rny studies of Abelard with an cyc to parallels to Preqc and of Frcgc wiLh an eye to Abclard, I have swayed back and rort-h on how to answer ttiis r:uestion. Sornetimes I find a surprising dcgrce OE similarity in the way each approaches semantic questions, despite their quitc diffcrcnL sLartinq points - for Abclard thc scicniia scrmoncinal is as a Loqical analysis of the language of argumcnLaiion and scholarly in- vcstj.ga(iion, Tor Freqe the demonstration ttiat ttie axiorns of arithmetic acc of a purely lociical nature. At ottier times, I sccm to have deceived niyself: the aqreemcnt secms to be no more ttiari verbal - cach man uscs cxnressions which sound prac- tically alike to discuss cornpletcly diFFcrcnti mattcrs. To work my wav out of this con"usion, I have carefully noted what it is T pay attention to in eacti case. 1 would li.kc t-o take you alonq for a part of my scarch. In the cxccl,lcnt prcscnLati.on of Ircqc's work givcn by Willia~nKneale, onc finds thc following: "In thc ordinary use 01 languaqe for maklncj statements, asking yuestions, qiving orders, &C., ii is to bc assumed that every dist-inquishable complctc sign has both sense and reference. The reference is an object of some kind, but not nccessarily a perceptible object. ... Thc sense, on the ottier hand, is sorncthing by which the object may bc singlcd out for attention. It is not an idca, if by that we mean an imaqe or sorncthing private to an individual thinkcr. For all comniunication dcpends on thc exnression of sense by one man to another, and in spccial circumstances siys may have a public sense cvcn though they lack all reference." 84 KIA IJS JA CORI

(The Development of Loqic, p. 496; cf. p. 578). The Passage could be taken word for word to characterize Abe- lard's semantics. Comparc: "Nomina ... et verba duplicem siqni- ficationem habent, unam cpidrm dc rcbus, altcram dc intcllccti- ,~us.Res enim significant constituendo intellectus ad eas per- tinentes, hoc est naturam aliquam earum vel proprietatem at- tendentes." (Super Peri crm., 307, 26-30; cf. 308, 19-22; 367, 9-10). 'Res' is the name Abelard gives to that which we refer to in speaking and comprehendinq, that which we reqard as qiven to our understanding. In his writings on the question of universals, hc emphasizes that the thinq (E) is in each case definite and singular, whercas generality is a characteristic of the sense of expressions in languagc. Don't thcsc cxplanations also fit well for what Fregc means with 'Gcgcnstand' as the 'Bedeutunq' of a sign? One also seems to be ablc to usc 'i~tcllcctus'in Abe- lard's sense for Frege's 'U'and vice versa. We do not ap- prehend the thina in its full concrete rcality. In speakinq and understanding, we attend to certain pcculiaritics of thc thing. Isn't the point of view from which the attention is concentrated and directed at a given object the Same as what Frcqe mcans when he explains his tcrm 'Sinn',namely the mode of presentation of the object and the way in which we conceive of it? Just as Frcgc distinguishes the Sinn, Abelard distinguishes the intellectus from ideas. An idea is a picture of an object; in this manner thc indivi.dua1 subject retains a mcmory of the object. By contrast, the sense which is understood is not private in this rc- spect; it is thc result of the dircction of thc attcntiveness of the distinguishing mind at a given object inasmuch as this object shows definite characteristics. But after more exact study, doubt arises as to whether Vrcqc's and Abelard's terms can really be used for each othcr in all contexts without disturbinq the cohcrence of the line of thought. Frcge's thesis that sentences stand either for the True or fnr the Falsc, from which follows that thc Truc and the False are objccts which we refer to in sentcnccs, will.not bc discussed here in detail. X.ct it suffice for thc moment to mention that. Abclard introduces the terms 'truc' and 'Talsc' quite different- ly. What these words mean could never be called a '='. Such an "expansion" of the use of the term 'E' as Frcgc undertook for 'Gegenstand' would have spoiled Abelard's contribution to khc question of univcrsals. The doubts which accumulate about the equi.valence of 'e' and 'intcllcctus' arc cvcn more insistcnt. 'Intellectus', neu- trally translated by "understanding". can often bc translated by 'concept'. Thus Abelard savs in Super Peri ermenias, "when thc mind attends to somc charactcristic of a thing, inasmuch as it is a thing or it exists or it is a substance or a body or white or Socrates, this is then called an understanding (G- tellectus) ." (Su~erPeri erm. 317, 12-13; cf. 313, 10-15). For Frcgc, however, the concept which an objcct fal-1sunder, and the mode in whj.ch an objcck prcscnts itsclf and is apprehendcd scem to have nothinq to do with each other at all. Frege makes a sharp distinction between predicative propositions and idcntity propositions. The distjnction bctwecn Sinn and Bedcu- AßEIARD AND 1;KEL'E 8) tung is infroduced to make CI-ear how identity propositions can be informative. An equatioh or identity proposition 'a = b' ex- prcsscs that one and the Same object has different modcs of presentation. 'a' and 'b' as desiqnations for thcsc different modes are "propcr names" for the object. Conccpt words must be strict- ly distinquished from propcr names. Freqe would have broken down the list of examples cited abovc for modes in which the mind can attend to Socrates into three complctcly different types of propositions. First, Socrates' name is 'Socratcs'. Second, Socratfs falls under the concept 'white', undcr the concept 'body' and under the conccpt 'substance'. Third, Socratcs is an instantia- tion of some concepts, through reference to which onc can show that thcsc concepts are not em~lty. Anyone trained on scholastic texts would wish to inquire more prcciscly here. Can the mode in which an objcct presents itself be so clearly scparated from the concepts which this objcct falls under? Preqe uses various dcscriptions of the samc objtct in tiis examples of informative idcntity propositions. In bhcse dcscriptions, for example 'morninq star' and 'evenin7 star' or 'the student of Plato and teacher of Alexander the Great who was born in Stagira', we find concept words, and ncccssarily so. 1s the sense of descriptions providcd not just by the concept words? Dy this point at thc latcst, I reach the state of perplcxity mentioned earlier. I feel like somcone who is trying to keep his balance with zach foot in a different boat and who suddenly rea- lizes to his consternation that thc hoats have bequn to drift in opposite directions. 'Ln ordcr to gct hold on soniethinq steady oncc morc, I ask wtiat kind of words it is that Abclard is talkinq about with his distinction betwecn siynificatio intellectus and signj.fj.catio reit and what kind of words it is Frcqe is talking about with his distinction betwccn cxprcsscd sense and designated referencc. Thc Eormulation uscd by W. Kneale seems to fit Abelard and Frcgc equally well. Kneale says "Every distinguishable complete sign has both scnsc and refcrence". Perhaps the aqreement is mcrcly verbal. Whisch speech sisns are "complete"? For Abelard we havc ttie information:' "Nomina '. . . et vcrba duplicem sicynif icationem habent". For Freqe the answer is thnt propcr names and - something wc havcn't mentioned yet - sentences are complcte expressions. In order to understand each man's answer, it is

ncccssary to makc clear to oneself ttie purpose- - of the distinction in each answer. For Abclard, nomina et verba constitute the sum total of all words which are mcaningful in and of themselves. Since he qroups nouns and verbs together, wc can assume that he firimarily has qeneral terms in mind. The difference between gcneral terms and singular terms docs not come to bcar in this context. Pre- positions and conjunctions stand in contrast to nouns and verbs as mcrely "CO-significative" words, later called 'svncateqorema- -ta'. In Abelard's time there were two theories about such words. Tbc first thcory was maintained principally by grammarians and held that such wocds have mcrcly an indefinite and vague nieaninq Their mcaning becomes dcfinite only through their association in sptech with words which are meaningful in and of themselves. Accordi.ng to the second theory, maintained by loqicians for the most part, prepositions and conjunctions convey nothiny at all. One does not comprehend a conccptual content through them. What they do is to direct one to comprchcnd in a ccrtain way the concept.ua2 contcnt of thc cateqorematic words with which they are associated in speech, namely thaL thcy arc to bc undcrstood as relatinq to each othcr, as joined to each other, as disjojned, et cetera. When Abelard talks about the double dcsignatj.ve function of speech signs, hc is referrinq to cateqorematic words. In the first function, the siqnificatio intellectus, they convey something. What they convey can be explained in a paraphrasc or a definition, for cxamplc. The word is to be taken herc as it appears to us in a dictionary entry. The second functiion nornally stipulated of categorcmatic words, the siqnificatio rei, is that thcrc is something outside of thc mlnd for which these words stand. Ttie words scrvc to describe a ciiven thinq. What a word desiqnates in this second scnsc is cxplained by c~ivinqexarririles of its use. The word is aktributcd (impositio vocabulorum). For Abelard the siqnificatio i.ntcll.cctus is primary, the siqnificatio rei subordinate. Two of his arguments should be mentioncd here. Another two will occupy us later. First, the meaninq of a word to thc intellect remains constant, whercas iLs meaning in rcspcct to the thing changcs. A scnsible word retains its sense irrcspective of whether or not therc is at all times an existcnt thincj which it stands for. Second, one must always ask, particularly whcn joininq severnl cateqorematic words together, whctihcr the ttius formed "complex concept" (intellectus composiLus) means sornethinq or j.s a notion to which nothing corresponds. Each of its constitucnt parts may mean somethinq while at the Same time there is no thinq to whicli the complex as a whole can be applied. It should now have become clear that the catcgorematic words to which Abelard attributes sensc (siqnificatio intellect~:~) and refcrcncc (siqnificatio rei) arc predicative words. They arc the smallest unitis of spcech which are meaningful in and of themselvcs. When we direct our attcntion to Preqe, everlrthinq begins to look quitc different. Predicative cxpressions are concept words. Frege Sees conccpts as a special kind of function. It is characteristic of functional expressions that they include an empty place or a placc holder for an arnument sign. The functional expression is not a complete entity; the place holder ex- presses that a complction is necessary. What was said about the functional expression holds for thc function itself, too. The function must be made complctc by insertinq a particular arpu- ment for the place holder. The completc entity resultinq once the gap has been fillcd with a particular argument is called the value of the function for this argument. Dy fillinq in thc gap, the function reaches completion. But the completing clement, the argument, is also a complete entity. The function is an instruction to associate two entities with each othcr, namely argument and valuc. If concepts are functions of a particular kind, then cvcry- Lhinq specified about functions in gcncral must iilso apply t.o concepts. Ttie inhcrcnt: inconipleteness of conccpts can be expressed by usi-ng uredicative cxprcssions instead of conccpt:~ words such as 'man' or 'wise' and by marking thc subject position with a place holder. Thus, 'C is a man' and '5 is wise'. Proper namcs can be inserted as ar~umentsiqns. Each stands for a particular objcct. With each insertion, a tirue or false propositi-on is crcakcd. That is to say, t.hc predication allows only one of thc two trutk valucs for each arqumcnt. l'hus accordi.ng to Freqe a conccpti is a function with one cmpty place, ttie vrilue of which for every arquinent is onc or the other of thc twc~truth values. An objccL is sornething whicli is ncver predicable but rathcr that of which soniettiinq is predjcatcd. Ob- jccLs fall under concepts, not undcr othcr objects. Concepts stand in relations of subordination and suy>ernrdination to each othcr. The subordination of one conccpL Lo another must bc kcpt st-rictly scparatic from an object's fallinq undcr a coricept. From t.hi.s bricf review of !?rege's distinctions between function and argumcnt on thc onc hand and concent and objcct on the otlhcr, it is cvident which expressions Frcgc regards as cornplcte and which ho considers incorriplete. Exprcssions reqard- cd as complete are, first, propcr names for particular objccts and, second, sentenccs. frrcspcctive of their capacity to take thc subjecti position in sentences, proper names have to per- form soniethinq for which thcy are fully adequate, being to name ohjectis. Frege also regards definitc dcscriptions as proper names, for a definitc dcscription also serves to namc a particu- Lar object. Fropcr names and definitc dcscriptions arc for Frege ttie signs which are primarily said ko have sense and refcrence. Two propcr namcs or definite descriptions havc different referenccs if and only if they name different objects. They have the samc reference but differ in scnsc if and only if they charactcrizc the Same object in different ways. Wien Abelard distinguishes between the siclnificatio intellec- Lus and the siqnificatio rei, hc is talking about cateqoremakic words. His goal is to demonstratc that such words do not stand dircctly for things. Thcy stand for things only by means of tke intelligible contcnt which they desiqnate dircctly. When Frege distinguishes between Sinn and Iicdcutung, he is mainly talking about proocr namcs. He applies the samc distinction to sentenccs, too. His attempts to apply it to concept words do not lead to satisfactory results. Frege assumcs that names stand for objects. Now it happens ttiat the Same object sometimes has been aivcn various nanies. This occurs not just in ordinary languaqe but also in scholarly language. Seeinq that the difference is not simply a matter of thc phonetic or written forrns of the si.qns, the real basis of the differcncc must bc sought in the dimension OE that which thcsc signs designate. Thus Freqe reaches the following thesis: "A proper name (word, sign, sign cornbination, expression) -ex- presses its sense, stands for or designates its reference." (uber Sinn und Bedeutung, S. 3 1 ) . Abclard and Frege, we realize at this staqe of our investiga- tion, use similar analytic terms to deal with very different 88 KLA lJ.S,]ACOßI questions. Thus the deqree of commonality necessary for contro- versy, not to mention aqreemcnt, is lacking. For it would only makc scnsc to speak of different views when the viewpoints con- cerned the Same themes and questions. Let us imaginc an cx- change of thoughts betwecn Abelard and Fregc on the basis of what has bccn said up to now. It seems that this exchanqe could hardly turn out to be morc than expressions of incomnrehension. In any case, each author could reproach the other with the ob- servation that his semantic tlieory has unity thanks only to the circunistance that hc has failed to draw certain critical distinctions. Abelard could point out to Fregc the differencc bctwcen mere proper names and definite descriptions. IIe would surcly arguc that the idea of "scnse" is applicable only to dcscriptions, and this thanks to the conceptual clements in them. He would furthcrmore express reservations about the talk of "truth values", which is based On an unconfirmed "expansion" of the word 'function' to include whole propositions. Freqe's thcory of concepts seems to depend on whcthcr this expansion is ad- missible. Frege, for his part, would objcct that Abclard's theory of concepts is based on assuniptions which are not introduced in the framework of the thcory. IIe wvuld say that Abelard simply calls one's attcntion to the fact that cateqorematic words scrve to convey intelligible contents from speaker to listcncr. Abc- lard fails to provide criteria with which one can decide when words are diffcrent in respect to their intelligible meaning and whcn in respect to thcir referencc. Such criteria could only be provided if one were to dctermine the objcct mcaninq completely, that is to say, only in such a way that onc would speak of the proper name for a particular object. The criticnl distinction which Abelard Eailed to make was that between identity propositions with the form 'a = b' on the nnc sidc and predications with the form 'IJJ (a)' On the other. Finally, one must distinguish both from propositions about the marks of a concept. Are we thus forccd to relinquish our hope of findinq a point of accord betwccn Abelard and Frege? I believc not. For there is indeed a more deeply lyins and far-reaching cnnforrni- ty in the way both philosophcrs apwronch semantic questions. One discovcrs this conformity once onc has ceased tryinq to match the individual theses and terms directly. I call this point of accord the propositional approach of both loqicians. As previously mentioned, two of Abelard's arquments remain to be presented in which he intcnds to demonstrate why logical analysis must takc intelliqible mcaninq (significatio intellectuum) as its starting point. According to Abelard, thc logician occupies himself with the scmantics of nouns and verbs because he is striving toward a theory of the proposition. A proposition consists minimally of a noun and a verb. What consituLcs thc differencc between these two parts of the proposition? This diffcrence, argues Abelard, "cannot be discovcrcd throuqh thc consideration of the manifold charactcr of thinqs. For nouns and verbs dcsignate the samc things. Thus the verb 'runs (curi-it)'and the noun 'runninq (cursus)' desiqnate thc Same thiny." The differcncc between thcm lies in the intelliqiblc contcnt. In the noun 'runniriq ' , tl-ic thiricr designaied is undcr- sLood as an cntity and "without any temporal distinction". In the verb 'runs', it is understood as being üttributcd to a subjcct and as indi-catinq a particular time. (Super eri erm., 300, 19-33). A full portrayal of Abclard's search Eor reliable criteria to disiinguisti nouns Kram verbs cannot be qiven hcre. I will summarizc his results hriefly: 1) lL is not possiblc to niake a caicgorial distjnction betwecn nouns and verbs on the basis of fundamentally dcsignated conterit. Verbs are not universally words for actions. 2) According to Aristotlc, verbs, as distinguished Erom nouns, dcsiqnate in additi-on Lo ttieir [)rimary sense a particular time. This suggested distinction should not be misinterpreted as an advice for grammaiically determining a kind of word. Correctly undcrstood, it is a maLter of a logical distinct-ion. Every intelliqiblc content can bc cxpressed in both a nominal and a verbal. formulation, just as well without consiqnificatio tcmpo- --ris as with ii. Where no verb is to be found in thc languaqe Tor a ccrLain content, a noun can be qiven tcmporal co-siqnification by supplementinq it with a hclpinq verb. 3) The inflected vcrb should be conceivcd of as a sinqlc unit of speech, not as, say, a bastard compound consisting of a nominal element and a temporal element. Evcn when 'G','fuit', or 'G'is substituted for t-he tcnse indicat-or of thc inflect- cd form, the helping verb and the word it belongs to makc up a single unil of spcech. 4) Wc transform a noun inta a verb when and only when we mean to usc j.C in the predicate positi.on. Temporal CO-signif ication is explained by the prcdicative function. 5) The mosi suitable analysis of propositions is not t-hat which rcsolvcs ttie proposition into two terms bound toqethcr by the copula but ratlicr that which resolves the proposition into a subjcct and a predicate. For a succint formulation of these results, the form of no- tation introduced by Frege (or one similar to it) prcscnts itself quite naturally. Herc prcdicative expressions and proper namcs arc portraycd by various syinbols. The 1cC-C-ersof the Greek alphabct, which Fregc used for predicativc cxpressions, must simply be given a temporal indcx. Abclard's work on the conversion of temporally definite propositions brings hin1 in- dccd to insights which are surprisinqly close to those of modern quantificati-on theory. Yor if the subject and predicate of affirrriative particular propositions and negative universal propositions are interchangcablc, this shows that predication is at thc basis of ttie subject expression, too. Only proper names are really subject cxprcssions: all other nouns arc ab- breviated predications. Using symbolic lanquage, we could cx- press thc form of propositions as follows: 'All / some whl.ch Lnotl ili-t ('now' or 'bcfore' or 'after') [riotl

Those who scc in Frege's loqic a stronq contrast to traditional Logic commonly regard the three-part anal.ysis of the proposition, resolvinq it into two terms bound togcther by the 90 KLA 1.I.S JACORI copula, as typical for traditional loqic. And I do in fact find that Abclard alone of traditional logicians weighs and qives his prefcrcnce to thc two-part analysis. That this analysis was at all thinkable and could be formulatcd within thc framework of traditional logic sufficcs t-o unsettle many an all too auda- cious and all too slick concel~tionof thc Course of thc history of loyic. I would like to qo back to Abelard's distinction bct-wccn signif icaLio in~cll.cG~us and signif icatio rei once again in order to throw light on anothcr point. Here, t:oo, the ttieme is explanation why-logical analysis must takc intelligible meanin~ as its startinq point. Abclard argues as Iollows: On thc level of siqns, a propos.i..t.ion consists mininially oT a noun and a vcrb. A proposition is understood by joining toqcther the undcrsCand- ings of i,ts parts (Intcllectus propositionis iungitur ex-- intel- lectihus parLiiim). But onc carinot carry the parallel rurther and say t-hat "the thinq of thc proposition" "is made up of" Lhc things desiqnatcd by thc units of spccch. Por "the propnsitinn," says ~belard,"is not bascd on a thing" (Xautcm propositio~, cum nullam tiabeat propositi.0 rcm subiectam, ex rebus vi,cahuloriim non consistit) . Thus, only thc inticll igible mcani ngs of ttie neun and the verb hclonq to thc constitution of a proposition. (Super Pcri erni., 308, 34-40). At this point, somcone well-vcrscd in Fregc would surely Cry out the following t-ranslation of Abelard's argument: On thc level of signs, a sentencc consists of a proper narnc and a pre- dicator. To the extent that ttic "qucstion (is) only, of thc sense oF ttie scntence, thc thought, it woiild be unneccsssry to bothcr with thc reference of a part 01 a sentencc; only the sense, not the rcIcrence, of the part is relevant to thc scnsc of the wtiolc scntence." (iiber Sinn und ncdeutunq, S. 33) . In t-his suggcsted translation lies a challenqe to Ahclard not to stop with the siqnjficatio intellectuum. As soon asa judgmcnt niust bc made as to the trutih or falsity of ttie ttiought expressed in a scntence, one must asccrtain, says Yrcge, that "cvcry proper nüme ... (tias) not only a sense, but also a rcfererice" (ibd.). In the remarks to follow, I will go on the assu:nption that the suggcsted translation is rcliable, and so I will now addrcss myself to the challcngc posed in it. What is Ahclard's theory on the si~nificatumpropositions? Wlint does hc mcan in saying that the proposition has no rtt:; s~~biccti?Oncc again I must limit rnysclf to providinq you wit.h a sununary of ttie results oT Abelard's invcstiqations: 1) A word strinq such as 'S~atcssedens', a sentence nomi- nalization such as 'Socratcm scdere' ( ' Lhat Socrates is sittinq ') , a "completc sentence" such as 'Socrates sedrt:' or even corrcs- ponding imgerativc, interrogatory, or wish sentenccs are not different in respect to their understandahle contents. The proposition 'Socrates sedet' has no new iinderstandablc content over 'Socrates sendens'. In the word striny 'Socratcs sendens', the two clements 'Socrates' and 'sederc' are rerjardcd as already being joined toqcLhcr. Thev arc not joined for the first time in a proposition of corresponding character. It is clear that this thcory came as a resulL of tlie debate Abclard conducted ABELAKLI A NLI IXLGK 91 with logicians who wished to base the theory of the proposition upon a thcory of thc copula. 2) Although we understand the Same contcnts in all three word strinqs, we don't undcrstand them in the Same way. We under- st-and thc proposition 'Socratcs sedet' as an assertion. Thc listener does not expcct rurthcr information. His question is wlietlier the claim to truth which lies in the asscrtion will sLand whcn put t.o LcsL. (Note: 'Socrates. seds' will not hc understood as a complete sentence in every contcxt in which it appears. As the antecedent in a conditional scntcncc, for example, it would not be asserted itself. The conditional sentence would be asserted as a wliole.) When one hears an cx- pression sucli as 'Socratem sedere', one expects it to he completed with an cvaiuation. The possible completions which inter- cst loyicians are tlie modes 'is true' , 'is possi hle' , 'is ne- cessüry', and thcir neqations. When one hears a word stri-ng such as 'Socratcs scdcnz' onc cxpccts it to be completed by a predicatc. Of coursc the atLribution (of 'sedens') is thc rc- sulL oT a prior act oT prcdication the Crut-h of which is pos- tulated to be known and accepted in the context. 3) The proposition does not dcsiqnate only a complex conccpli (intellectus compositus). In a propositions Chc truth of a complex, undcrstood content is asserted. '... is true' means 'such is thc casc with thc thing (jta cst in re)'. 4) The object meaninq of the proposition cannot be rcduccd to the object meaninqs of the elements of the proposition. Thc truth oT propositions is not in principle depcndcnt upon the subjcct ierm's mcaning an cxisking Lhinq. (Abclard shows this hy an analysis of jrnplicational propositions, negations, and tautoloqies.) 'Such is the case with the thinq' is not syno- nymous wit-h 'l'here is a thing which is so'. 5) '... is triic' and '... is false' secm to be predicates grammatically. Appcaranccs arc dcccptivc hcrc. Predicatcs are used "personally": 'Something $-t, naniely a'. The attempt to construc 'truc' and 'fa1,se' in a simi-lar way as predicates (on sentence noniinalizations as subjects), as in 'something i.s true, namely p', leads one astray. l'he use of '... is true' and '... is false' is "impersonal". 'True' and 'falsc' arc not qeneral terms which may bc applied to specific cases. What is said in propositions is not a bearer of truth or falsity in the samc way thai things are bcarers of properties. No one can fail to See that Abelard's expositions have an essentially negative character. I emphasize: essentially negative. All thc invcstiqations which Abclard madc in logic, all distinctions which he drew, all discussions which he con- ductcd, were quided by his conccntration on thc proposition. We have scen that Abclard rcjccts all attcmpts to differen- tiate nouns and verbs on the basis of their contents. They arc to bc difrcrentiated accordinq to thc function Chcy have in the proposition. Thc proposition is the point of depar- ture for the thcory. Its various aspects arc analyzed; but it is not broken down into separate elements. All of Abelard's discussions on the scmantics of the proposition are warninqs against reductional attempts. The various aspects differen- tiated from cach obher in thc Course of the analysis - the 92 K1.A 11.7 JA CORI thouqht, the way things rclatc to cach nthcr (cerum modus habcn- di se, W., 160, 35), the assertion - cannot be understood alonc. They can be understood only in the context of the proposition. The theories of the proposition with which Abelard contended bcgin with thc false assuumption that some or a1.L of thc various aspects of the proposition are independent and in themselves understandable elcmcnts which should thus servc as thc basis for a semantics of the proposition. Lct us turn once again to Frege in closing. His notaiiion of- fers itself here, too, for the symbolic expression of the difference between the assertivc aspcct of thc proposition and what can be evaluated. It is not my purpose here to elucidate the difference betwecn Frcge's introduction early on of the content and judgmcnt strokes and their later reinterpretation, nor to elucidate what is needcd in ordcr to asscrt a proposition of event on the one hand and a matheniatical proposition on the other (compare Der Gedanke, C. 64). Thcsc arc susidiary qucs- tions which would play a part in an extended comparison. For the present I wish mcrcly to mark the point of comparibility. It sccms to me worthy of noticc that Freqe introduces his distinction analytically. The content strokc dcsignates what remains when the judgment stroke is "omitted" (~e~riffsschrift, 6". 2). Frcgc formulates the propositional approach of his semantic theory in the second methodological principle of the Grundla- gen, which states that "onc must ask for the meaninq of words in the contcxt of a proposition and not in their isolation" (Grundlaqen der Ari.thmetik, S. XXII). Seeing that conccpts are nothing other than predicates, the semantics oF thc proposition cannot be built upon a semantics of words which pretends to bc prior to and independcnt of it. (Compare Frecje ' s Briefwechsel,

C.-- 1641.~ For both Abelard and Frege it is cxtremely difficult to kccp a firm grasp on thc propositional approach. Abclard follows the synthetic tradition of Peri Hermcncias in struc- turing his writings: the theory of the proposition follows the theory of individual words. Aqain and acrain Abelard must makc himsclf conscious of his own point of vicw, that of the logician. And Freqe tends again and aqain to succumb to thc tcmp- tation to impose a synthetic structurc on his seniantic theory. For example he speaks first of functions and then of an "expansion" of the conccpt of the function to include function equations and truth functions. Onc must bear in mind, however, that he can introduce the concept of thc valuc of a function only by alrcady making use of cquations which are true (Funk- tion und Begriff, S. 8). An element of Prege's teachings held by him to be central but dcstined to drive all students of Freqc to wrack their brains is the thesis that thc reference of evcry scntence is either the Truc or the Palse and that all true sentences (and likewise all false sentences) are thus identical in cach casc in "BedeuM" and different only in "Sinn".If Abelard had been prcsented with this thesis, he would surely have rejected it as a furthcr attempt at rcduction. The scmantics of the pro position is reduced here to thc paradigm of naminq. Abelard AREIARD ANU FREGE 93 would counter that naming is also based upon thc act of prcdication, at least to ttie extent ttiat the name has an undcr- standable sense and not merely a reference function.

Note : I havc presentcd this paper as a report on current and on- going work. It is intended to be a stimulus to discussion. It did not sccm appropriate to rework it into a formal essay after the fact. I have thus dispensed with the usual scholarly apparatus and providc sirnply a bibliography of thc works con- sultcd in the coursc of my rcscarch. Pctrus Abaelardus: Dialectica. Ed. L.M. de Rijk. Assen 1956

Petri Abaelardi Clossae super Peri erinenias. Ed. B. Gcycr (Peter Abaelards Philosophische Schriften, I. Die Logica 'Ingredientibus' ) . BGPhTtiMA 21,3. Münster 1927

Petri Abaelard Glossae super Periernienias B, carip. XI1 - XIV. Ed. L. Minio-Paluello (TwelEth Century Loqic. Texts and Studies 11: Abaclardiana Inedita) . Roma 1958

W.L. Combocz: Abaelards Bedeutunqsleiire als Schlüssel zum IJni- versalienproblem. In: Pctrus Abaelardus (1079-1142). Person, Wcrk und Wirkung. Hrsg. V. R. Thomas (Trierer ~heol.Studien, Bd. 38). Trier 1980, C. 153-164

Klaus Jacobi: Dic Semantik sprachlicher Ausdrücke, Ausdrucks- folgen und Aussagen in Abailards Komrncntar zu Peri IIermeneias. Erscheint in: Mcdioevo

Klaus Jacobi: Peter Abelard's Invcstigations into the Meaning and Funciions of the Sr~eectiSign 'e'.Erscheint in: J. Hintikka and S. Knuuttila (eds.): Studies in the Logic of Being

A. Maicru: l'crminologia loqica della tarda scolastica. Koma 1972

C. Nuchelmans: Theories of thc Proposition. Ancient and medieval conceptions oi the bearers of truth and falsity. Amstcrdam 1973

C. Nuchelmans: Thc Scmantics of Propositions. In: Thc Cam- bridge IIistory of Later Medieval Philosophy. Ed. N. Kret-zmann, A. Kenny, J. Pinbory. Canibridgc 1982, pp. 197-210

I,.M. de Rijk: fntroduction to the edition of Abailard's Dialec- tica. Asscn 1956

L.M. de Rijk: La signification de la proposiiion (dictum propositionis) chez ~bhlard.In: Picrrc Abhlard - Pierre le Vcnhrable. Actcs du collonue international, Cluny, 2-9 juillet 1972. Ed. R. Louis, J. Jolivct, J. Chatillon. Paris 1975, pp. 547-555

L.M. de Rijk: Die Wirkung der neuplatonischcn Semantik auf das mittelalterliche Denken iiher das Sein. In: Sprache und Erkennt- nis im Mittelalter. Akten des VI. Internat. Kongr. für mittel- alterl. Philos. der S.I.E.P.M., 29. Auq. - 3. Scpt. 1977 in Bonn (flliscellanea Mediacvalin, Bd. 13/1). Bcrlin - New York 1981, pp. 19-35

L.M. de Rijk: Abailard's Semantic Views in the Light of Later Developmcnts. In: English Logic and Scmantics. Acts of the 4th European Symposium on Mediaeval Logic and Semantics, Leiden - Nijmegen, 23-27 april 1979. Ed. by H.A.G. Braakhuis, C.H. Kneepkens, L.M. de Rijk (Artistarium Supplemcnta I), ~ijmegen 1981, pp. 1-58 M.M. Tweedalc: Abail-ard on Universals. Amsterdam - New York - Oxford 1976 M.M. Tweedale: Abelard and the Culmination of thc Old Logic. In: The Cambridge Ilistory of Later Mcdieval Philosophy. Ed. N. Kretzmann, A. Kenny, J. Pinbory. Cambridge 1982, pp. 143-1 57

G. Fregc: Begriffsschrift und nndcrc Aufsatze. Mit E. Ilusscrls und H. Scholz' Anmerkungen hrsq. V. I. Anqellelli. Darmstadt 21 964 G. Frcgc: Die Grundlaqen der Arithmetik. Kjnc loqisch-mathe- matischc Untersuchung über den Begriff der Zahl (Nachdruck dcs Neudrucks von 1934). Darmstadt 1961

G. Pregc: Funktion, Begriff, Bedeutung. Fünf logische Studicn. IIrsg. U. einqel. V. C. Patziq. Göttingen 21966

G. Prcge: 3oqischc Untersuchungen. Hrsg. U. cingel. V. G. Patzig GGttinycn 1976

G. Freqe: Wisscnschaftlichcr Briefwechscl, Hrsq. V. G. Gabriel, H. Hcrmes, F. Kamhartel, Ch. Thicl, A. Veraart. Hamburg 1976

C. Freye: Translations from the Philosophical Writings. Ed. by P. Gcach and M. Black. Oxford 1960 I. Angelelli: Studics on Gottlob Frege and Traditional Philo- sophy. Dordrecht 1976 I. Angelelli: Frcges Ort in der Beyriffsgcschichte. In: Chr. Thiel (rirsg.) : Freye und die moderne Grundlaqenforschung. Symposium, gchalten in Bad Homburg im Dez. 1973. Meiscnheim 1975, S. 9-22

D. Bell: Frcge's Theory of Judgment. Oxford 1979 V.H. Dudman: Fregc's Judyment-Stroke. In: The Philosophical Qunrterly, Vol. 20 (1970), pp. 150-161

M. Dummctt: Frege, Gottlob. In: The Encyclopedia of Philo- sophy. Ed. P. Edwards. Vol.111, pp.225-237 R. Grossmann: Reflections of Frege's Philosophy. Evanston 1969

E.D. Klemke (E.): Essays on Frcge. Urbana, Chicaqo, I.ondon 1968

W. Kneaic and M. Knealc: The Development of Logic. Oxford 1962 G. Patzig: Gottlob Freye (1848-1925). In: Klassiker der Philo- sophie 11. Hrsq. v..O. HöfFe. München 1981, S. 251-273; 487-489

R.H. Stoothoff: Dudman on Frege's Judqment-Stroke. In: The Philosophical Quarterly, Vol. 21 (1971) , pp. 166-167 Ch. Thicl: Sinn und Bedcutunq in der Loqik Gottlob Frcqes. (Monoqraphicn zur Philos. Forschun(j, Bd. 34). Meiscnhcim 1965 Ch. Thiel: Gottlob Frcge: Die Abstraktion. In: Crundlirobleme dcr großen Philosophen. Hrsq. V. J. Spcck. Philosophie der Gegenwart I. Göttiingen 1972, S. 9-44

J.D.B. Walker: A Study of Frcgc. Oxford 1965