History of Logic from Aristotle to Gödel by Raul Corazzon | e-mail: rc
"Abelard composed four works on logic:
1) Introductiones Parvulorum, which consists of short glosses on Porphyry Eisagoge and Aristotle Categories and De Interpretatione;
2) Logica Ingredientibus (so called because ingredientibus is the first word of its text), which consists of longer glosses on the texts covered by the previous work together with Boethius' De Differentiis Topicis and was probably written while Abelard was teaching in Paris before 1120;
3) Logica Nostrorum Petitioni (so called because nostrorum petitioni are the first words of its text), which consists of longer glosses on the Eisagoge and may date from the time of his teaching at the hermitage of the Paraclete;
4) Dialectica, which has the form of an independent work about the subjects covered by Boethius' logical writings and Victorinus' treatise De Definitionibus and seems to contain materials from different periods of Abelard's life but probably did not reach its final form until a late date, perhaps the time of his stay at Cluny shortly before his death. Of these the second and the fourth are the most valuable.
The Dialectica indeed, though based, like that of Garland, chiefly on the works of Boethius and written with the prolixity which was all too common among medieval authors, is an original composition of great importance for the development of logic. Abelard's mind was the keenest (though not in all respects the most admirable) that had been devoted to the subject for more than a thousand years, and he approached his task with the belief that it was still possible to make discoveries: 'Non enim tanta fuit antiquorum scriptorum perfectio ut non et nostro doctrina indigeat studio, nec tantum in nobis mortalibus scientia potest crescere ut non ultra possit augmentum recipere.' (1) The Dialectica survives in a single manuscript which lacks the opening sections. Excerpts from it were published by Victor Cousin in 1836 in his Ouvrages inédits d' Abelard. But unfortunately the text was not printed in full until 1956, and before that date it was therefore not possible to appreciate the magnitude of Abelard's contribution to the doctrines we regard as characteristically medieval. (...).
The text is divided into five tractatus which correspond to groups of Boethius' writings and are called respectively: I Liber Partium, II De Categoricis, III Topica, IV De Hypotheticis, and V De Divisionibus et Definitionibus. Of these the first is subdivided into three volumina dealing with the antepraedicamenta (or quinque voces of Porphyry), the praedicamenta (or categories of Aristotle), and the postpraedicamenta (or questions about meaning raised in the De Interpretatione). (2) But our sole surviving manuscript lacks the whole of the first volume and the opening of the second. This is unfortunate, since the missing part probably contained Abelard's last thoughts about universals. We can be reasonably sure also that it contained an account of the distinction between words of first and words of second imposition, since this was mentioned by Boethius in his commentary on the Categories and is taken for granted later by Abelard." (pp. 203-204, some notes omitted)
(1) Dialectica p. 535.
(2) In later times the name antepraedicamenta was used (more naturally) for the subjects treated by Aristotle in his Categories, 1-3 (i.e. equivocal and univocal naming, simple and complex expressions, etc.), and the name postpraedicamenta for the subjects treated by Aristotle in his Categories, 10-15 i.e. kinds of opposites, kinds of priority, etc.).
(3) Dialectica p. 122.
From: William & Marta Kneale, The Development of Logic, Oxford: Clarendon Press 1962.
See the page Editions and Translations of the Logical Works for the bibliographical details.
"Geyer's editions [...] gave the first decisive stimulus to the study of the Palatine Master's philosophical writings.
Up to 1919 (the year of Geyer's first edition) the known Abelardian writings were limited to those edited by Cousin (7): this French scholar attached the most importance to the comments on Porphyrius, the Categorie and the Topici of Boetius and the passages of the Dialectica. On the whole the material was fragmentary, uncritically sifted and confused with fragments of non-Abelardian comments, which Cousin nonetheless considered were his. De Rémusat's incomplete paraphrase in French of a comment on the Isagoge was then added to these texts.
In 1919 Geyer began publishing Ingredientibus (8): under this name he has edited a comment on the Isagoge, a second on the Categorie, and a third on De Interpretatione. A prologue (from the beginning of which Geyer took the name Ingredientibus) presents these comments as a unit which has a certain compactness; this is confirmed by other observations which are intrinsic to the work, such as the internal cross-references from comment to comment, the persistence of a similar attitude and of an identical -- terminologically as well -- solution when confronted by the problem of universals in all the comments (9), the 'dictum' theory present in the three comments. (10) From internal cross-references that Abelard makes to an essay De Hypotheticis (11), Geyer concludes that the work must have included other comments as well as these. From hints dropped by Abelard in De Interpretatione, it seems highly likely to me that a comment on De Categoricis also belonged to Ingredientibus. (12) Dal Pra has shown that the comment on De differentiis topicis, edited by him, is clearly distinct from the literal comments, and concluded that this is a comment that comes within the framework of Ingredientibus. (13) We thus have four of the seven comments on the usual 'septem codices' (14) that Abelard considered fundamental.
Also part of the Philosophische Schriften edited by Geyer is a comment on the Isagoge of which Rémusat had edited an incomplete paraphrase in French. In the prologue Geyer singled it out as part of an organic work, called Nostrorum (15) by him from the words at the beginning: here too Abelard proposed an entire treatment of the logical corpus usually used by him. Today we still have only the comment on the Porphyrian quinque voces.
In 1954 Geyer's edition was joined by the edition of the literal comments edited by M. Dal Pra. In this edition the comments are arranged in the order which Abelard himself indicates at the end of the logical treatise and to which he also holds in Dialectica. The comments on the Categorie and on De Interpretatione thus come after the comment on the Isagoge. The presence of a comment on the Boetian De Divisionibus indicates that Abelard used the 'seven codes' from the outset and leads one reasonably to suppose that he had worked on other comments of the same type as De Syllogismis categoricis, De Syllogismis Hypotheticis, and De Differentiis topicis which we do not have now. This seems to me to be confirmed by certain references of Dialectica, which are remade in the comments on De Differentiis topicis and De hypotheticis in the Introductiones parvulorum (16), identified by Geyer with the literal notes. We have already seen how the comment on De Differentiis topicis edited by Dal Pra in the Scritti Filosofici must be assimilated, on the contrary, to the corpus of notes in Ingredientibus.
In 1956 De Rijk published an edition of Dialectica which enhances the picture of the Palatine Master's logical work. Dialectica is not a comment but an organic treatise based nonetheless on the 'septem codices'. The most serious gap, by extension and importance, is that which deprives us of the treatise on the Porphyrian quinque voces which was certainly included in the work, because Abelard hints at it. Two passages in this work show us Abelard's concept of it (17): the Palatine Master here presented himself as an auctor in line with Aristotle, Porphyrius and Boetius, whose works he would perfect, as he proudly declares.
In Abaelardiana inedita edited by Minio Paluello (18), two texts are edited, the first contained in a manuscript now in Berlin, and the second belonging to a manuscript in the monastery of Fleury, both from the 12th century. The existence of these two manuscripts was not unknown to us. (19) The text of the Berlin manuscript, a commentary on De Interpretatione, is three-quarters identical to the Ambrosian manuscript edited by Geyer as a section of Ingredientibus and the part that differs is without any doubt more coherent with the preceding part than the Ambrosian manuscript which contained a noteworthy break. The contribution of this new edition consists in a rigour and a greater accuracy in the reading of the Abelardian text: it does not, however, appear that in this last part of the commentary there are motives that complete or at least modify the weight and the general meaning of the commentary itself.
The text of the Fleury manuscript is more interesting, even if, with regard to the attribution, it is more uncertain. This concerns the analysis of a paralogism and of five sophisms that emerge from a nominalistic interpretation of the concept of totum." (pp. 2-4)
(7) Cousin, op. cit., and Petri Abaelardi opera hactenus seorsim edita ..., Paris 1859.
(8) Philosophische Schriften, Münster 1919, 1921, 1927. Abbreviated to G.G.
(9) See G.G., pp. 16, 127, 403, and G.L., p. 235; G.G., pp. 38, 246, 334-5, and [Scritti filosofici, Milan 1954, abbreviated] G.L., p. 221.
(10) See p. 79, note 39.
(11) G.G., pp. 291 (25) and 389 (7).
(12) G.G., p. 394 (10-26).
(12) Dal Pra, 'Introduzione', in G.L., pp. XXIX-XXXII.
(14) Dialectica, p. 146 (10-7).
(15) G.G., p. 505 (3-5).
(16) Dialectica, pp. 269 (1-3), 329 (4), 482 (4-6).
(17) Dialectica, pp. 146 (10-20), 496 (18-26).
(18) Abaelardiana inedita, Rome 1958.
(19) Id., pp. XIIff., XLI.
From: Maria Teresa Beonio-Brocchieri Fumagalli, The Logic of Abelard, Dordrecht: Reidel 1970.
"...of whose seven books everyone in this art with an education in Latin should be armed. Only two of Aristotle's books are still known to the use of the Latins, namely the Categories and the De Interpretatione. One book is Porphyry's: that is the one written about the five 'predicables' (genus, species, difference, property and accident) [the Isagoge]; this is an Introduction preparatory to the Categories. We usually treat Boethius as four books: that is the De Divisione, the De Topicis, the De Syllogismo Categorico and the De Syllogismo Hypothetico. The text of my Dialectica will include a very full summary of all of these, and it will see the light -- so that readers can use it -- provided the Creator of our life grants us a little time and Envy relaxes her grip on our works."
From: Petrus Abaelardus, Dialectica. First complete edition of the Parisian manuscript with an Introduction by L.M. de Rijk, Assen: Van Gorcum, 1970 (second edition), p. 146, lines 10-20 (cited from M. T. Clanchy, Abelard. A Medieval Life, Malden: Blackwell, 1997, p. 98).
"The Aristotelian texts available to Abaelard.
The Introductiones parvulorum contain short glosses on Porphyry's Isagoge; Aristotle's Categories and the Peri Heraineias; and Boethius' De topicis differentiis and the De divisionisbus et definitionibus. The Ingredientibus contains longer glosses on the texts of Porphry and Aristotle. The Nostrorum petitione sociorum elaborates on Prophyry alone. Additional texts available to Abaelard were Boethius's Introductio ad categoricos syllogismos, the De syllogismis categoricis, the De syllogismis hypotheticis and Cicero's Topics. Abelard was surely using the extended, newer Boethian translation of the Isagoge (secunda editio) rather than the older translation based on Marius Victorinus. The glosses of the Categories relied on a copy of the editio composita of Minio-Palüello (Aristóteles Latinus I) — probably the close redaction, Ms. Chartres 497. Both Minio-Paluello and de Rijk find similarities between Abaelard's and Thierry of Chartres' use of Ms. Chartres 297 , in part, a Boethian translation of the Peri Hermeneias.(1) With respect to the nova-texts available to Abaelard, it is certain that he had some acquaintance with both the Prior Analytics, cited in the Dialectica, and the De sophistici elenchi, cited in the Ingredientibus. As his acquaintance with the Prior Analytics is certainly not from indirect sources, he most likely used the recensio Carnutensis Boethian translation found in Ms. Chartres 497 which also contained the Categories. A translation of Aristotle's Topics is also found in the same codex. While the text is not quoted in any of Abelard's extant writings, it seems probable that he reviewed the text. The De sophistici elenchi is found in Ms. Chartres 498. While Abaelard states that he did not always have access to the work (Ingred. 400,33-4), it is evident that he knew the text-- probably from this manuscript. While there was an anonymous translation of the Posterior Analytics circulating in Abaelard's day, it is highly unlikely that he had ever seen the work. It is not quoted in any of the extant writings. He was certainly unacquainted with the nova translations of James of Venice which started to circulate sometime after 1130. Unfortunately, James' translations of the De anima and the Metaphysics first appeared a few years after Abaelard's death (and, in fact, they had few readers at the time). Aristotle's Ethics was not translated until early in the thirteenth century.
From: Daniel F. Blackwell, Non-Ontological Constructs Bern: Peter Lang, 1988, pp. 309-310.
"When the medievals dealt with dialectics, they meant logic as such, and dialectic in the historic Greek sense of the term that was at issue from the Sophists through Aristotle largely fell by the wayside. For the medievals, then, dialectics was logic at large, the science of demonstration through which rational inquiry sought veritatis seu falsitatis discretio.(16) And as such dialectic constituted a key part of the institutional trivium of grammar, rhetoric and dialectic (i.e., logic). Thus while the medieval treatment of "dialectic" forms an important chapter in the history of logic, it can be left aside in the context of the history of dialectic as traditionally understood in its relation to philosophical methodology.(17) However, insofar as dialectic is a feature of the actual practice of academic disputation, it continued to play an important role in higher education throughout the middle ages.(18)" (p. 137)
(16) Abelard, Dialectica, p. 435. For an English translation of a typical medieval treatise on dialectic see John Buridan, Summulae de dialectica tr. by Gyula Klima (New Haven, Conn: Yale University Press, 2001). A look at the elaborate table of its Contents shows that with regard to topics that the treatise remains well within the boundaries of Aristotle's logical organon. Not until the Renaissance did Petrus Remus reconstitute the idea of dialectic as the art of disputation (doctrina dispusandi. See his Dialecticae Constitutiones (1543).
(17) Over and above the standard histories of logic, the following treatments of medieval dialectic are highly instructive: T. J. Holopainen, Dialectic and Theology in the Eleventh Century (London: Brill, 1996); J. A. Endres, "Die Dialektik and ihre Gegner im 11. Jahrhundcrt," Philosophisches Jahrbuch, vol. 19 (1906), pp. 20-33; N. J. Green-Pedersen, The Tradition of the Topics in the Middle Ages (Munich, Philosophia Verlag, I984); and above all, Eleanore Stump, Dialectic and its Place in the Development of Medieval Logic (Ithaca, NY: Cornell University Press, 1989).
(18) On medieval academic disputation see A. G. Little and F. Pelster, Word Theology and Theologians (Oxford: Clarendon Press, 1934), pp. 29-56. A vivid account of scholastic disputation is given in Thomas Gilby, O. P., Barbara, Celarent. A Description of Scholastic Dialectics (London, New York: Longmans, Green, 1949), see especially Chapter XXXII on "Found Dialectic," pp. 282-93; and see also Bromley Smith, "Extracurricular Disputation: 1400-1650," Quarterly Journal of Speech, vol. 34 (1948), pp. 473-96. On medieval and renaissance discussions of Platonic dialectic see Raymond Klibansky, "Plato's Parmenhks in the Middle Ages and the Renaissance" in Medieval and Renaissance Studies, vol. I (1941/43), pp. 288ff.
From: Nicholas Rescher, Studies in Idealism (Collected Papers, volume III), Frankfurt: Ontos Verlag, 2005.
"3. The linguistic theory of Abelard is centred around the correlaion or correspondence between the "word" and the "thing" or the signifiant and the signifié as we would have them today. According to Abelard, if a word or a sound signifies, it is because something is added to its physical being, essentia; this something is the significative function,officium significandi. The sound, just like the thing that it represents in a give language, remains the same from one community of speakers to another, it belongs to the sphere of things, which is natural; the significance, on the other hand, changes due to the diversity of languages, it depends upon institution, upon a human convention, positio hominum, voluntas hominum.(1) We have already the distinction between the sphere of significance and the sphere of things. The sound or the physically pronounced utterance is of the order of nature while significance is created when "something" is added to its being, and, this "something" is due to human intervention in a human, social institution. For Abelard, words give birth to or "generate" intellection which then correspond to things. Thus, argues Abelard, threre is a double series of correspondence between words and intellections, and between intellections and things, and consequently, between words and things. These are three distinct but related spheres.(2)
In Peri Hermeneias, Abelard insists that first of all the words signify "intellections" and only by implication and consequently, the things, otherwise there would be no logic. At the level of utterance, we deal with ideas which are "abstracted" from things but which are not found in any one thing. The reference to things is always indirect, intellective.(3)
Words are imposed upon things by human convention and they do not carry the same significance from one language to another, hence they are "arbitrary", but as they signify "intellection" of a given thing, they operate within the sphere of logic. Words constitute intellections, or what are called "analyses" in the eighteenth century by Condillac and his followers, they represent logical propositions on the object under study. They do not correspond to the physical, empirical reality of the thing (object) but to its intellective reality. Hence, the move from one word (utterance) to another is in fact a move from one intellection to another. This is why, for Abelard, to say that a word signifies is to say that it manifests an intellection of the one who pronounces it, and that it generates a similar intellection for the one who hears it. To signify is to constitute intellection but the act of communication requires a speaker and a hearer where there must be a similarity of intellection.(4) Abelard continues the argument in Super Peri [Hermeneias] and explains that linguistic communication is an affair between two thinking beings. (5)
Language thus is not only a matter of forming logical propositions on the perceived reality of things, it is an institution where two thinking beings, beings who reflect upon the nature of things, exchange their intellections or analyses. But the so-called perfect exchange can take place if the same intellection is generated between two persons.
There are three degrees of knowledge, argues Abelard in Peri Hermeneias: sensation, sensus, imagination, imaginatio, intellection, intellectus. One can feel without imagination, imagine without thinking but imagination presupposes sensation and, there can be no intellection without image.
Our words turn our attention towards the resemblance of a thing so that it may be applied, not to this resemblance, but to the thing that it represents. This is the role of the image. One may compare it with a statue of Socrates. We apprehend it not as a thing but as a resemblance. Our intellection is not concerned with it, it only represents Socrates. When our sensation perceives it, it orients it towards the real Socrates. Image is thus situated within the mental operation which leads to knowledge. It serves as a substitute for the thing that is absent. An image alone can also be the object of thought, but in that case, it is not really an image, it has to be considered as an object in itself without another image serving as an intermediate. In any case, we see that feeling or sensation, in itself or across an image, serves as the basis of our intellection. But neither sensation nor image is sufficient for our knowledge; in the first case, we remain at the surface, manifest level, in the second, there is confusion. It is through the application of our esprit that we pass on to intellection. It leads us to the knowledge of the nature and the properties of things which are imperceptible to senses or to imagination.
Our reason leads our esprit to intellection, without it we remain in the domain of confusion which is the characteristic of imagination.
To think is not to subject a given thing (object) to our intellection, but a nature or a property of that thing.
In its simplest form, an image presents only a resemblance of a thing perceived, it is confused, and like sensation, it does not allow us to distinguish the various properties of the thing. It is only a material to work on, to apply our intellection. Moreoever, the validity or invalidity of an intellection has nothing to do with the specific characteristics of an image. These images serve only as signs. Two persons may think of a non-sensible object, like rationality, across two different images, and both of them may formulate valid propositions. What matters is what is aimed at across these images, attentio rerum per imagines, and not the arrangement or the aspects of these images, dispositio imaginum vel forma.
Intellections may be simple or complex. A simple intellection corresponds to a noun (name), its object is composed of matter and form but it is apprehended in one unique perception, it is thus without any parts. A complex intellection corresponds to oratio as animal, rational, mortal; it groups several intellectual acts. The second division refers to an intellection of related or divided things, intellectio conjunctorum vel divisorum, on the one hand, and on the other, the intellection that relates or divides, intellectus conjungens vel dividens. The former refers to a reunion or a separation already made within the language. It is thus a simple idea, it corresponds to a definite or an indefinite noun as the things are related or divided. The intellection that relates or divides is, on the other hand, a composed or complex intellection; to a term already thought (analysed), it relates another. Such an intellection corresponds to animal + rational + mortal. Furthermore, there is the intellection that divides and the other that abstracts. The former separates one characteristics from the other but considers both in conjunction or disjunction. The latter considers only one term at a time, neglecting the other.
As the primary interest of Abelard is the interpretation of old sacred texts, he argues that as the ancient texts represent specific intellections of the authors, their true understanding would lead us to the understanding of the texts or the intellections, which are different from those of ours, but they would not shed light on the real nature of things, of the objects they refer to, of the mysteries of the Church. Before Abelard, Isidore had taught in the seventh century that once you know the etymology of a word, you know the "reality" of the thing. For Abelard, etymology informs us only of the intellection of the previous author. That intellection is no more related to the reality of the thing than our intellections are today. The etymological analysis gives only a "partial" view of what is really the thing. The etymology, says Abelard, sheds light more on the composition of the word than on the substance of the thing.(6) No wonder, he was excommunicated. For the logician Abelard, there is absolutely no confusion. For him, the science of logic is concerned only with the enunciative propositions and hence finds its precise object at the level of language, and not, at the level of the impression of things. The sphere of ideas is clearly distinct from the sphere of things.(7) It is interesting to note that following this reasoning, Abelard comments upon the ten categories of Aristotle and states that they are due to "human initiative", and hence due to the nature of language, otherwise such a homogeneity between the categories of language and that of the things of the world could not be envisaged.(8) Eight hundred years later, in a now celebrated article, Emile Benveniste makes the same point with the help of the modem Saussurian linguistics.(9) Abelard insists that the formation of words must be understood as a resultant of a certain mental activity and not as a perfectly adequate translation of the nature of things.(10) Furthermore, as the logical proposition is not a transposition of the natural rapports between things, we cannot talk simply of the differentiation between language and logic. Language regulated by simple grammar at the complex but spontaneous level of the construction of words does neither correspond to the logical structures, nor to the nature of things.(11) This three-way interrelation becomes even more complex when we realise that at times, the reference to a thing may be composed of several intellections and as such the utterance that describes this grouping may have a multiple signification. This multiplicity of reference is the crux of the problem of signification, not sufficiently emphasized in modem semiotics.
A proposition is both simple and multiple. It should therefore lead us, across several terms, to something that is unique, that is numerically one. It expresses something with the help of several words, but this something is not a thing. A proposition is materially composed of a noun and a verb; similarly, the corresponding intellection is constituted with the relations of the intellections of its parts. But what corresponds, in reality, with a proposition, not having any thing as its basis, is not composed of what corresponds, in reality, with the words, res autem propositionis, cum nullam habeat rem subjectam, ex rebus vocabulorum non constat. (12) In the sphere of intellection (analysis) of a thing, Abelard insists that it is "nothing", nil omnino, "absolutely nothing", nullam omnino rem, it is not an existing thing.(13) But what does not exist intellectively is the corporality of the thing. Intellection deals with what is called, the state of things, something like the sachverhalt [state of affairs] of phenomenology which corresponds well with the proposition of Abelard: quidam rerum modus habendi se.(16)
All experimentation in modem art in the sphere of the correspondence,between form and content point to what Abelard emphasized that there is no such thing as absolute reality, every thing, every object, is under some impact, physical or psychological, whether it is the impact of light for the impressionists or the impact of psychic turbulations for the cubists or surrealists, or economic or social impact for the Marxists. Abelard had realised in the early years of the twelfth century that the object of study is not already given, it has to be defined, it has to be constituted within a specific universe of discourse, and, all intellection and comprehension of this object has to be in the sphere of ideas, in the sphere of the logical propositions of reality. This is what he tried to do with Holy Trinity and he got into trouble with the Church. For Abelard, at the level of things, Father, Son and the Holy Spirit are three different things because there is no such thing as a universal thing. It is only at the level of intellection, at the abstractive level where a certain unity is envisaged in terms of certain definitions of a perceived characteristics that the Trinity becomes metaphorically one. It is only in the enunciative field of the Christian discourse that the metonymic sequence of Father and Son is obliterated. The move from individuality to universality is a move in the realm of intellection and not in the realm of empirical realism which the Church wanted to impose purely on the basis of Faith. For Abelard it is a problem of language, which is a problem of intellection par excellence. In fact, it is only in the realm of semiotics that the Unity of the Holy Trinity could be established as indeed did Abelard, but unfortunately he was too advanced for his times.
4. In his Logica, Abelard discusses the intellection of the universals and individuals.(15) When intellection acquires a universal term, argues Abelard, we have a common and confused image formed from several realities. On the other hand, when there is an individual term, we have before us a form of one and unique being, a form that has a rapport with only one individual; when we hear the word, man, a certain representation emerges whose rapport with each of the men is such that it is common to all but specific to none. When we hear the word, Socrates, a certain form emerges which expresses a similitude with a given being. This vocable, Socrates, gives birth to a form of a being who is unique, it is a real thing which is certified and determined. For the vocable, man, on the contrary, the implied community leads us to confusion and we do not know which man is in question. In fact, the word, man, signifies neither Socrates nor any other man, it does not refer to any man even though it denominates all.
A real thing abstracted by intellection may signify either a veritable substance of a thing, when for example intellection is based on a sensible perception, or a mental conception of form corresponding a given thing, which, in the absence of such a thing, may correspond to a common or a specific form. By common form is meant a form which has the common similitude of a multiplicity of beings, but which, in itself, is considered as a unique thing.
As for the mental or conceptual forms, Abelard makes a distinction between the divine forms and human forms. He compares God with artisan who conceive mentally the form of the work that they are going to realise later in a specific body. But there is a difference, says Abelard, it is God who creates man, soul or stone, while man creates a house, a statue or a sword. Neither statue nor sword are natural works, the names which designate them are not based on substance but on accidents, they do not correspond to genres or species. Thus one can say that the Divine thought conceives by abstraction, the natural realities of universal character, while men know things only through senses. Abelard thus rules out the innate faculty of man in the realm of conceptualisation as proposed later by Descartes and further developed in the Port Royal School.(16) In this respect he is the precursor of the empirical school of Condillac in the eighteenth century(17), and consequently, of the basic hypothesis of modem social sciences where all creation is due to bricolage or due to establishing new relationships within the material culture which is already present. Apart from the works of Claude Levi-Strauss, we see this most clearly in the writings of A.G. Haudricourt where he demonstrates a relationship between the methods of plantation and cosmological conceptualisation in New Caledonia.(18)
Our intellection is based on two distinct operations: attraction and synthesis. Form and matter, argues Abelard, do not exist in isolation from each other but our "esprit" has the faculty to consider one or the other at a time or even together in a certain relationship. We abstract a certain element of a synthesis and examine it in its proper nature. When we re-establish a certain specific relation, we operate a synthesis. For example, we may consider the substance of a man, it may be body, animal, man, rationality etc. When we pay attention to any one of these in its material essence excluding all other forms, this operation is abstractive. Inversely, if we pay attention to only the corporality which we relate with the substance, the operation is synthetic.
These abstractive operations could be considered false, for here we perceive things not as they exist in reality; no abstracted element can exist in isolation. However, it is not so, for it is a question of intellection, of paying attention at a time to a specific element. The isolation of an element, substance or form is only intellective and not in its subsistence. It is a matter of considering a certain quality or characteristics separately and not as separated. For example, if we have a statue made of half gold and half silver, we can consider separately either gold or silver even though within this statue they do not have separate existence. The same is true of all complex realities whose comprehension is possible only if at times, we consider their constituents in their abstracted forms, and at others, by operating certain specific syntheses.
The same principle operates in the prevision of the artisan who conceives forms in advance of their realisation. This prevision is of the order of senses as it is based on establishing intellective relationships within the elements of things already present. These so-called pre-conceived forms of the artist are thus not based on nothing. It is simply an affair of the mental application of the operations of abstraction and synthesis. The creative process or the prevision of the artist involves the establishment of metaphoric relations, the relations which bypass the sequential relations of time and space in a metonymic, sequential or syntactic realisation within a given enunciative field." (pp. 4-12)
This study in Abelardian Semiotics was conducted during my stay at the Maison des Sciences de l'Homme, Paris as a Visiting Professor of Semiotics in 1987.
(1) Glossae super Peri Hermenias, 320, 12,27, ed. B. Geyer, Munster i.w. 1919-23.
(2) Glossae super Prophyrium III, 524, 3-10, ed. B. Geyer, Munster, i.w. 1919-23.
(3) Peri Hermeneias, 309, 1-13, V. Cousin, Ouvrages inedits d'Abélard, Paris, 1836.
(4) Glossae super Peri Hermenias, 307, 31 ed. B. Geyer, Munster, i.w. 1923.
(5) ibid; 374, 21.
(6) Dialectica, 128, 29-32, ed. L.M. De Rijk, Assen, 1956.
(7) Sup. Per. 3674, 21.
(8) Sup. Porph. 11, 24.
(9) E. Benveniste: Problèmes de linguistique générale I, Gallimard, Paris, 1966, pp. 63-74. [the essay is: "Catégories de pensée et catégories de langue", first published in Les Etudes Philosophiques, 13: 1958 pp. 419-429 and translated in: E. Benveniste, Problems in General Linguistics, Coral Gables: University of Miami Press, 1971]
(10) Sup. Per, 72-74.
(11) Sup. Porph. 11, 54, 34.
(12) Sup. Per. 308, 36.
(13) Dial. 157, 15
(14) Dial, 160, 35.
(15) Oeuvers choisies d'Abélard, M. De Gandillac, Paris, 1945, pp. 110-26.
(16) A. Arnauld and P. Nicole: La logique, 1644 edition, reprinted by Vrin, Paris, 1981.
(17) Condillac: Traité de 1'art de penser, 1796 edition, reprinted by Vrin, Paris, 1981.
(18) Nature et culture dans la civilisation de l'Islam, L'Homme, 4, 1964: 93-104.
From: Harjeet Singh Gill, The Abelardian Semiotics. In Abelardian Semiotics and Other Essays. New Dehli: Bahri Publications 1989. pp. 1-29.
"For Abelard there are primarily six modes of signification.
It is in the discussion of the nature of universals that we follow the development of Abelardian theory of signification. The problematic revolves around the relation between the signifier and the signified, the word and the thing, and its numerous implications for the general theory of semiotics (9). To signify or to designate is the function of words, to be signified is that of the things. A universal is that which by nature can serve as a predicate of several subjects, a singular, which cannot. It seems that both words and things can be considered as universals, one has to see how the definition of universal can be applied to things. Abelard states that some thinkers attribute universality to things by arguing that there is essentially the same substance in things which are different on in form. If we take away the forms, there would be no difference in things. The difference lies in form or accidents and not in essence. There is the same substance of man which becomes here Plato, there, Socrates, due to their respective accidents.
Abelard argues that this theory does not stand the test of "physics". Suppose that there is in fact a being essentially the same, even though it appears in different forms, exists in different subjects. It must follow that the thing that is within this form be the same in another form. For example, an animal inhabited by rationality be also the animal inhabited by irrationality, thus the rational animal is at the same time, the irrational animal; is such the two contraries exist in the same subject. Moreover, they will not really be contrary as they would co-exist in the same absolutely identical essence. In fact, the contraries cannot be together in the same subject, even under different rapports, as it is the case with relational and other attributes.
These contraries are presented by some thinkers under different perspective by stating that one should not formulate the proposition as "rational animal is irrational animal". A being can be rational from a certain point of view and irrational from another, the forms which correspond to he same subject are no more opposing forms. And, one does criticize propositions such as "rational and mortal animal" or "white animal and animal that walks", for man is not mortal inasmuch as he is rational or he is white inasmuch as he walks. The one and the same animal can have two properties under different rapports.
Then we come to the Aristotelian theory of ten essences or ten most general genres, for in each case we find the same essence diversified only due to different forms. Thus substances are absolutely the same beings, he same is true of all qualities and all quantities. The realities signified by Socrates and Plato are absolutely the same for essentially they are no more different than the substances to which they are attached as the quality of Socrates and the quality of Plato, for both are qualities. They do not differ from each other in the nature of their qualities or the nature of their substances as the essence of their substance is the same.
Abelard refutes this theory. First of all, why should one restrict only to ten essences. There can be more or less. And, how can we perceive a numerical multiplicity in substances if only the forms are different? We do not consider Socrates as numerically multiple just because he may have multiple forms. Another affirmation that does not stand the test of verity is he statement that the individuals are made by their proper accidents. If the individuals derive their being from their accidents, the accidents should precede them. If man differs from other species because of the difference n form, the individual named, Socrates, is distinguished by his accidents. Socrates thus cannot exist without his accidents nor man without his differences. Socrates is not the substratum of his accidents. If the accidents are not in the individual substances, they are not in the universal substances also. The theory that states that an absolutely identical essence is found simultaneously in different beings is illogical, asserts Abelard.
There are others who have a slightly better theory of universality when they state that the individuals do not differ from each other only due to their forms, they are also individually distinct in their very essence. Matter and form are both different in every individual. Even if the forms are suppressed, their individual distinctions stay because of the diversity of essences. But there is an impasse, for the theory of universality is not abandoned in this case. It is argued that the distinct beings are the same thing, not by essence but by non-difference. Thus the individual men are distinct from each other but they have the same being in man. They do not differ in the nature of humanity. This universality is due to this non-difference.
Abelard continues to present the divergent views within this doctrine of non-difference. There are some thinkers, he says, who perceive this universal element in the collection constituted of several elements. For them, Socrates and Plato by themselves do not represent a species, but all men taken together constitute the species, man, and all animals together form a genre. A certain unity is attributed to this collectivity, for without this one cannot have a predicate of several individuals. A universal thing will not have multiple subjects and the universals will not be as numerous as the singulars. As such, Socrates inasmuch as he is a man is dissociated from himself as Socrates. He cannot be his own genre or his own species if he is not in one way or the other different from himself, for the relative terms must oppose each other.
Abelard thus refutes this theory of collection. How can a collection of men taken together as one species be a predicate of several subjects and thus be universal while taken in its totality we do not attribute it to subjects taken one by one. If we accept that there is a predicate of different subjects according to its parts, it has nothing to do with the community of the universals, which according to Boethius, should entirely be in each subject. It is this that distinguishes it from the common base, which following its parts, is like a field whose different parts belong to different masters. We could then attribute the predicate, Socrates, to several subjects which would be his different parts, and he would himself be universal. Moreover, we will have to consider a universal any plurality of men put together. Similarly, we will make a unique universal substance from any collection of bodies and souls, and in that case the entire collection of substances will be one of the most general genres. In fact, argues Abelard, if one of the substances is subtracted, the remaining collection is not the most general genre while it is a universal substance. It must be a species of the genre of substance and should have a species which corresponds to it under the 1 same genre. A part is not identical with the whole but the species is always identical with the genre. How can then the entire collection of men be equivalent to an ensemble of animals?
Finally, Abelard presents the theory of those who consider individuals as universals inasmuch as they correspond with others, and accept that they are predicates of several subjects not because they are essentially multiple but because these multiple subjects correspond with them. But argues Abelard, if to be predicated of multiple subjects is equivalent to corresponding with these multiple, how can we say that the predicate individual is accorded to another that is isolated? How the fact of being predicate of several subjects distinguishes the universal from the singular? For, man, inasmuch as he is a man, corresponds with several subjects, but neither man, inasmuch as he is Socrates, nor Socrates inasmuch as he is Socrates, corresponds with others.
Man in Socrates and Socrates himself do not differ from each other. Nothing can be different from itself. This is why Socrates as white and Socrates as grammarian, even though with two different characteristics, is not different from himself, for he is not a grammarian in a way that he is not himself, nor when he is considered white. When they say that Socrates and Plato correspond with each other in "man", how can we believe this, for it is certain that all men are different from each other in matter and in form.
It is obvious that the things, whether they are taken one be one or together, cannot be considered universals, i.e., predicates of several subjects. Thus we must attribute this universality, argues Abelard, to words alone. The grammarians consider some nouns as "appelative", others, "proper". Similarly, for the dialecticians, some simple terms are "universals", others, "particulars", or "singulars". The universal is a vocable that is instituted to serve as a predicate of several subjects taken separately, as the noun, man, that one can join with specific men due to the nature of the real subjects to whom it is attributed. The singular is that which can be a predicate of any one subject, like Socrates." (pp. 38-41)
"Abelard's theory of signification is further crystallized in Logica Nostrorum where he makes a distinction between vox and sermo. The universals are neither things nor sounds, votes, they are due to sermones which may be singular or universal. A noun or a term is due to human institution but a thing or a sound is due to nature. The signifying act is thus a human fact, a cultural fact, as opposed to the physical aspect of the word that is purely natural. Abelard compares this phenomenon with the creative act. A stone and a statue are one and the same "thing" but they are derived from different sources. The stone is the work of God (nature) while the statue is the work of man (culture). The sermones are universal because they are created by man, they are predicates of several subjects. The sounds and things are not at all universal even if in physical reality votes and sermones are not different. Abelard's theory of signification is presented in an important article by L. M. De Rijk (**) where he distinguishes between Abelard's views on the signification of words and propositions. To signify, significare, with words, dictiones, is to generate an intellection in the soul of the hearer. The same is applicable to the denotation of external things, and in this case, the verb is synonymous with appellare, nominare, demonstare, designare. To signify with complete sentences, propositiones, is to generate an intellection which is constituted with the liaison of the intellections with its parts, dictiones. For Abelard the words first signify intellections, then the things which correspond them. The words generate intellections and with these we arrive at the knowledge of things. Intellections thus play an intermediary role. We have now to enquire about the exact status of things. For Abelard, the race, cursus, and he runs, currit, refer to the same things as it is considered in essentia, the race, and in adiacentia, he runs. Jean Jolivet believes that this linguistic approach is more concerned with the mental activity than with the exact nature of things. This is true if we think only of the external aspect of things. In this case, Abelardian theory is different from that of Aristotle. Aristotle's emphasis is on the external things and Abelard is primarily interested in the domain of the spirit or the domain of intellections. As such, we can say that the things signified by words are things as thought of or as produced by intellection. This difference with Aristotle is manifest most clearly in Abelardian theory of the proposition, propositio. Even though for Abelard the signification of a proposition is definite, its signified, significatum, is not a thing, it is a sort of a half-thing, quasi-res. It depends upon three aspects of the proposition. One may consider it as a verbal phrase, as an intellection expressed by words, or as a thing that is the object of the verbal phrase or the intellection. Abelard states that our expressions have a consignificatum rather than a signification so-called, and the task of the proposition is to present a mode of conception, modus concipiendi. It does not have a specific content, in istis nulla imagine nititur intellectus, but it is derived from it.
The signification of a proposition is further explained by means of the logic of implication, si rosa est, flos est. The logic of this necessity lies in the fact that what is stated by the antecedent, rosa est, cannot be stated without what is stated by the consequent, flos est. If the antecedent is taken either as a grammatical construct or as an act of intellection, it can be without the consequent which can be taken separately as a grammatical or an intellective construct. On the contrary, the antecedent taken as a fact of logic implies the logical existence of the consequent. This necessity is purely relational, quidam rerum modus habendi se and it does not concern the relation between the external aspect of things, nor between intellections taken as psychological or rational acts. It is a relation between the contents of intellections. In other words, these relations are purely logical or formal. The dictum of Abelard is neither an external thing, res, nor a mental act as such, but the objectivated content of this act, which being neither a thing nor an act, is called half-thing, quasi-res." (pp. 43-44)
(*) CF. Petrus Abaelardus, Dialectica, ed. L. M. de Rijk.
(**) L. M. de Rijk, "La signification de la proposition (dictum propositionis) chez Abélard", in: Jean Jolivet, Louis René (eds.), Pierre Abélard - Pierre le Vénérable. Les courants philosophiques, littéraires et artistiques en Occident au milieu du XII siècle, Paris: Editions du Centre national de la recherche scientifique 1975, pp. 547-555.
From: Harjeet Singh Gill, "The Abelardian Tradition of Semiotics", in: Harjeet Singh Gill and Giovanni Manetti (eds.), Signs and Signification. Vol. I, New Delhi: Bahri Publications 1999, pp. 35-67.
"Although Abelard draws the material for his studies on logic from such traditional sources as Boethius in the field of dialectic and Priscian in the field of grammar, many of his reflections are so fresh and original that in the history of the problems concerning the bearers of truth and falsity he belongs among the few pioneers who really broke new ground and contributed insights which were a lasting source of inspiration for later generations. The following survey is based upon his glosses on Porphyry's Introduction to the Categories and Aristotle's Categories and De interpretatione, which are found in the so-called Logica ingredientibus (1) , and upon his systematic treatise Dialectica (2).
Abelard defines a word (dictio) as a sound significant by convention none of whose parts is significant in separation (D 147, 21). Some words, namely nouns and verbs, have a definite signification by themselves; other words, namely conjunctions and prepositions, have an indefinite signification by themselves (D 117, 26). The definite signification of nouns and verbs, which for certain purposes include also pronouns, adverbs, conventional interjections, and participles (D 121, 8, 18; G 334, 23), is twofold: they signify thoughts (intellectus) and they signify things (res). Thoughts are the affections of the soul or the noemata of which Aristotle speaks in the first chapter of De interpretatione; Abelard interprets an intellectus as an act of attending to the nature or a property of a thing which is either present to the senses or put before the mind by means of a mental image (G 20, 30; G 312, 36; G 328, 18). In connection with a thought the verb significare either has the same meaning as exprimere ormanifestare intellectum -- the speaker or the word he uses expresses the speaker's act of thinking -- or, more often, it has the same meaning as constituere3 or generare intellectum: the speaker or the word he uses produces a certain act of thinking in the hearer's mind (G 307, 30). For this meaning of significare I shall commonly use the phrase 'to produce a thought'. Further, nouns and verbs signify things; for this kind of signifying Abelard uses, apart from significare, such verbs as appellare, demon-ware, denotare, designare, and nominare. For this meaning of significare I shall employ the phrase 'to denote a thing'. Although for several reasons Abelard regards the signification of thoughts as more important, in the context of his reflections on De interpretatione, than the signification of things (G 308, 19), there is some difference between his conception of the signification of nouns and verbs and Aristotle's. For the latter nouns and verbs primarily signify thoughts; they can only be said to signify things because of the fact that the thoughts which they signify are the likenesses of things. In Abelard, on the other hand, this difference between the directness of the signification of thoughts and the indirect character of the signification of things is less prominent; both significations are treated, so to speak, on the same level.
That conjunctions and prepositions have an indefinite signification is the view defended by Abelard in his Dialectica (118-120). When, for instance, the preposition de and the conjunction et are uttered in isolation, they have a signification which is vague and undetermined: the hearer's mind is kept in suspense about that to which they are to be attached. Only when the open places by which they are accompanied have been filled is their imperfect and indefinite signification rendered precise and definite. In the me of homo et lapis, for example, the general signification of et, namely that things are conjoined, has been made specific by the meanings of the two nouns: we now know that we are dealing with the conjunction of a man and a stone. In the glosses on De interpretatione, however, Abelard objects that this view makes it impossible to draw a clear distinction between, on the one hand, conjunctions and prepositions and, on the other hand, nouns and verbs; for the latter, too, can be said to have a signification which is not precise until they are combined with other words(G 337, 41). He therefore prefers to say that conjunctions and prepositions when uttered by themselves have no signification at all; they signify only in combination with other words (consignificant), but in that case they contribute a clearly distinguishable part to the meaning of the whole. It is necessary to hold that they have a signification of their own when they are used in combination with other words, since otherwise they cannot be differentiated from letters and syllables.
Whichever of the two views one adopts, there is a problem about the intellectus and the res which are produced and denoted by conjunctions and prepositions. If those words have a signification, either in isolation or only in combination with other words, they must produce some thought; and they can produce a thought only if there is a thing or a mental image of a thing to which the thought is directed (G 338, 41). According to Abelard some authors held that words with an indefinite signification produce a thought but do not denote a thing, in the same way as propositiones (D 119, 3). But it is hard to see how they could produce a thought if there is nothing to which the thought is related. Some grammarians tried to solve this difficulty by suggesting that prepositions denote the thing which is denoted by the noun to which the preposition is attached; but in that case the denotation of the noun would be superfluous. Abelard's own view is that conjunctions and prepositions denote a certain characteristic (proprietas) with regard to the thing that is denoted by the adjoining nouns or verbs. In the combination in domo, for instance, the preposition in denotes the characteristic of the house that consists in its containing something; and the conjunction ergo, placed between statements, denotes the characteristic that consists in the circumstance that the premisses prove the conclusion and the conclusion is proved by the pre-misses. Abelard finds it difficult, however, to state clearly the thought which belongs to each preposition and conjunction; it is as hard, he says, as stating explicitly the thought that belongs to utterances that are not used for the purpose of making a statement, such as 'Come to me' (D 118, 29).
The copulas est and non est get a separate treatment. They neither produce a thought nor denote anything, but they contribute to the affirmative or negative import of a propositio (ad vim affirmationis or ad vim negationis proficit) by causing the mind to combine or separate the things thought of (the intellecta or intellectae res; cf. D 154, 25-27). In understanding a propositio the mind performs three acts: it thinks of each of the two parts, the subject and the predicate, and it combines or separates the things thought of. Although the act of combining or separating the things thought of is not itself an intellectus, it nevertheless is part of the thought produced by the wholepropositio (G 339, 20). Similarly, the conjunctions si and non si have no signification, but they unite or separate significant sounds by inclining the mind to a certain mode of conceiving (animum inclinant ad quendam concipiendi modum; cf. also G 329, 29).
The same expression modus concipiendi is used in connection with the difference between a finite verb such as currit and a noun such as cursus. The verb and the noun denote the same thing, running, but the different mode of conceiving it causes a difference in the thought produced (diversus modus concipiendi variat intellectum). The distinction between parts of speech pertains to a difference in thought produced rather than to a difference of denotation (G 308, 25).
In D 124, 11, a distinction is made between the principal signification of a noun and its accidental significations, which have to do with the modes of signifying. The difference between singular and plural is said to be a difference of accidental signification. Differences in case and gender, on the other hand, are not related to any difference in signification, but only to the position which nouns can occupy in constructions (Cf. G 364, 2). Similarly, such pairs as comedere/vesci ('to eat') and carere/non habere ('to lack') have the same signification but they play different roles in constructions (D 125, .33; G 369, 27). The same is true of such forms as curro, curris, currit, curritur. They all have the same signification but the ways in which they are completed into a full propositio by the addition of such pronouns as ego, tu, tile, a me, a te, ab illo are different. In other words, differences in person are not connected with any difference in signification, whereas differences in number, tense, and mood are differences in (accidental) signification (G 138, 31)." (pp. 139-142)
(1) Edited by B. Geyer, Peter Abaelards philosophische Schriften, Beitrage zur Geschichte der Philosophie and Theologie des Mittelalters XXI, 1-3, Münster, 1919-1927; I shall refer to this work by means of the letter G, followed by page and line.
(2) Edited by L.M. De Rijk, Assen, 1956 (revised edition 1970); I shall refer to this work by means of the letter D, followed by page and line.
I Abelard D 112, 6; G 308, 11; G 357, 29) and others connect the phrase continuere intellectum with Aristotle, De int. 16 b 21:histesi -- ten dianoian had been translated by Boethius as constituit intellectum. They apparently took intellectum as referring to the hearer's thought.
From: Gabriel Nuchelmans, Theories of Proposition. Ancient and Medieval Conceptions of the Bearers of Truth and Falsity, Amsterdam: North-Holland 1973.