Aurélien Robert

THE DIVERSITY OF HUMAN LANGUAGES AND CLIMATE THEORY. PHILOSOPHY AND MEDICINE IN MEDIEVAL COMMENTARIES ON ARISTOTLE'S DE SENSU ET SENSATO

From the thirteenth century onwards, some commentaries on Aristotle's De sensu et sensato ask whether a deaf person is necessarily mute. In the passage under comment (1, 437a16-17), Aristotle simply affirmed that sight and hearing are the most important of the five senses, and that sight is even more excellent than hearing. However, because hearing allows us to be educated through oral instruction, it contributes greatly to our knowledge. For this reason, he continues: «the blind are more intelligent than the deaf and mute (τῶν ἐνεῶν καὶ κωφῶν)». Ancient commentators wondered why Aristotle added here «mute», since he does not explain further the relationship between deafness and muteness. Alexander of Aphrodisias, for instance, simply states that «a consequence for those who are deaf from birth is that they are also dumb» 1 . But this «consequence» is problematic in many respects. Does this mean that the learning of a language necessarily involves oral instruction? How can we describe the origins and the beginnings of a particular language? Shall we infer from this that nothing is innate in our language skills? Is language purely conventional, or can we still describe it as a natural phenomenon? Let us imagine an individual whose organs function perfectlyhe is not deafbut who is in a situation in which he never heard any human language: will he nevertheless speak a particular existing language or invent a totally new one without any oral instruction? Among the many puzzles raised by this passage, 1. Alexander of Aphrodisias, On Aristotle On Sense Perception (On Perception and Perceptibles), trans. A. Towey, London 2000, 27. For some Medieval interpretations of this passage, see Kevin White's contribution in this issue. some commentators on the De sensu added the following quaestio: where does the diversity of languages come from (unde provenit diversitas idiomatum) 2 ? Some of these quaestiones about deafness and muteness have been studied in detail by Theodor W. Kohler 3 and more recently Sten Ebbesen 4 . As it appears from their analysis, the vast majority of commentators stick to the position of Alexander of Aphrodisias: the deaf from birth is necessarily dumb. Moreover, most of them affirm that the learning of languages necessarily involves orality and therefore hearing. Some deaf people may invent their own words, but they will not use a language, properly speaking, as they will be the only speakers of that language. They also predominantly reject the theory of Hebrew as the mother tongue of the isolated child who never heard any human language. Despite this apparent unanimity, which seems to point in the direction of a conventionalist view of communication languages, some commentators do attempt to retain some natural character to language and its diversity 5 . Quite surprisingly, to defend their point, they consider our linguistic practices as partly dependent on environmental or climatic conditions, understood as 2. The same quaestio apparently existed in commentaries on Aristotle's De animalibus, but we will focus here on the commentaries on the De sensu. See, for instance, Boethius Dacus, Modi significandi sive Quaestiones super Priscianum Maiorem, ed. J. Pinborg, H. Roos, et S. S. Jensen, in Boethii Daci Opera, IV, København 1969, 61-62: "Si autem tu queras unde est diversitas modorum loquendi apud diversos homines et distinctio ydiomatum cum naturaliter debeat esse idem apud omnes, hoc dictum est in quaestionibus nostris super librum De animalibus […]». For the broad context of these debates, see I. Metzler, "Speechless: speech and hearing impairments as problem of medieval normative textstheological, natural-philosophical, legal», in Social dimensions of medieval disease and disability, ed. S. Crawford and Ch. Lee, Oxford 2014, 59-69.

3. Th. W. Köhler, Homo animal nobilissimum. Konturen des spezifisch Menschlichen in der naturphilosophischen Aristoteleskommentierung des dreizehnten Jahrhunderts, 2 vols., Leiden-Boston 2008, passim.

4. S. Ebbesen, «Psammetichus's Experiment and the Scholastics: Is Language Innate?», in The Language of Thought in Late Medieval Philosophy. Essays in Honor of Claude Panaccio, ed. J. Pelletier, M. Roques, Cham 2017, 287-302. The relevant texts are edited in S. Ebbesen, «Does Language Acquisition Depend on Hearing a Language? A Text Corpus», Cahiers de l'Institut du Moyen Âge Grec et Latin, 86 (2017), 138-215.

5. The background of these debates is probably connected to the discussions about linguistic naturalism between some modistae and some masters of the Faculty of Arts in Paris at the same time. See I. Sekizawa, Le Naturalisme linguistique de Boèce de Dacie. Enjeux et discussions, thèse de doctorat sous la direction d'I. Rosier-Catach, Université de Paris Diderot (Paris VII) 2010.

geographical and astronomical determinations 6 . The present paper will focus on this aspect of the debate, i. e. the defence of a naturalistic account of the origin and diversity of human languages, which has not received full attention from specialists.

It must be recalled first that these discussions on climate and languages are quite rare among medieval commentators of Aristotle's De sensu. Only four commentaries studied and/or edited by Sten Ebbesen address the hypothesis of an influence of environment and climate on languages:

(A) Anonymous, Quaestiones super librum De sensu et sensato, q. 7, Vat. Lat. 3061, f. 146va-vb: Utrum surdus sit naturaliter mutus; and q. 8, ff. 146vb-147ra: Utrum si aliquis puer positus in nemore a principio suae nativitatis debeat loqui idioma determinatum. (ed. Ebbesen, 164-70) (B) Anonymous, Quaestiones super librum De sensu et sensato, q. 7, Vat. Lat. 2170, f. 120va-vb: Utrum surdus sit naturaliter mutus. (ed. Ebbesen, 170-74)

(C) John de Jandun, Quaestiones super librum De sensu et sensato, q. 7 Utrum omnis surdus a nativitate sit mutus (ed. Ebbesen, 178-83)

(D) Nicole Oresme (?) or Albert of Saxony (?), Quaestiones super librum De sensu et sensato, q. 3, Quartum dubium: unde processit diversitas ydiomatum ? Cum omnes homines sint eiusdem nature, quare non omnes loquuntur idem ydioma? 7 To these four witnesses, we may add an unedited anonymous commentary conserved in Rome:

(E) Anonymous, Quaestiones super librum De sensu et sensato, Biblioteca dell'Accademia Nazionale dei Lincei e Corsiniana, Fondo Rossi 415 (36.F.6), ff. 103r-132v. Q. 4, f. 107vb: Utrum omnis surdus sit mutus (…dubitatur primo unde processit diversitas ydiomatum) 8 . 6. For an overview of the uses of this notion, see M. J. Tooley, «Bodin and the Medieval Theory of Climate», Speculum, 28 (1953) 8. I would like to thank Roberto Zambiasi for bringing this commentary to my attention. On this text, see the Appendix in R. Zambiasi, «I commenti latini (A) and (B) date from the turn of the thirteenth and fourteenth centuries, and are most probably from Paris, as Sten Ebbesen observed, since (B) is similar in many respects with Radulphus Brito's commentary. (C) and (D) were also written in Paris in of the fourteenth century. The last commentary (E) seems to depend partly on John Buridan and partly on (D), and the quaestio on deafness is a copy almost verbatim of (D), so that it certainly belongs to the same Parisian tradition. Of course, the list of commentaries in which this issue is discussed may grow in the future, as new commentaries are still being discovered 9 . Here we will focus on these five texts, which are directly connected and respond to each other.

The aim of this paper is to shed light on the philosophical and medical foundations of this discussion on climate and linguistic diversity. Why these authors seek to explain the variety of oral languages by natural causes and not only by conventions and other social habits? Our impression is that it is a matter of opposing the theological explanation of the dispersion of languages after Babel (Genesis, 11, 1-9) 10 . Not all of them reject explicitly this narrative, but their analysis, which borrows from a very old tradition of med-ical origin, endeavours to bring language back among natural phe-nomena. Without denying the importance of free will in the inven-tion and renewal of particular tongues, they consider languagethe capacity to speak and form articulated words and sentencesas a natural phenomenon that always existed. After a brief survey of their arguments, we will look at the possible sources for such ideas, in Ancient and Medieval medicine and natural philosophy, in order to underline their rather exceptional character. This will lead us to some concluding remarks on what these discussions say about these commentaries, their authors and their intellectual context.

The Influence of Environment on Vocal Sounds and The Speakers' Mind

When the anonymous commentator (A) explains why the deaf is naturally mute, he affirms that while he conceives things (res), he cannot conceive oral words and their conventional meaning, which, he adds, is always ad placitum. He is therefore in the situation of someone who hear a foreign language he never heard before, except that he is in this situation in front of all possible languages. Moreover, the deaf person is in the same relationship with any given language and all the conventionally signifying vocal sounds as someone who has never heard French in relation to the French language […] but the person who has never heard French does not know how to express himself or herself in this language with certain knowledge and understanding; therefore the deaf person is naturally mute 11 . This argument suggests that in order to truly speak a language, one must have inner representations of vocal sounds in order to be able to manipulate them and form sentences with them. So, even though oral words have a conventional meaning, to use these words as a language requires something like a natural representation of these sounds in the mind 12 . The deaf person can therefore form certain concepts that another able-bodied person also forms through his empirical contact with external realities, but he cannot think with an oral language, and even less pronounce those words that he cannot conceive in himself. 4. The necessity of inwardly conceiving the words of conventional languages has been a much-discussed theme from Augustine and John Damascenus, who already mentioned the importance of imaginatio vocis, to the theories of mental language contemporary with the texts we read here. See C. Panaccio, Mental Language. From Plato to Ockham, New York 2017; and A. Robert, «Les deux langages de la pensée: à propos de quelques réflexions médiévales», in Le langage mental du Moyen Âge à l'âge classique, ed. J. Biard, Leuven 2009, 145-68.

It is in the next question (Utrum si aliquis puer sit positus in nemore a principio suae nativitatis debeat loqui idioma determinatum) that the idea of environmental determinism appears. In the quod sic arguments, the author mentions the idea that the organs of speech (organa loquendi) are determined by place (locus), so that even the isolated child from birth will have some dispositions for such or such language according to the place where is was born. Another possibility examined in this dialectical part of the quaestio is that this child will naturally speak Hebrew. But both of these options conflict with the philosophical view attributed here to Aristotle according to which the deaf cannot conceive vocal sounds inwardly. For this capacity necessarily starts from an empirical knowledge of vocal sounds, that is through hearing.

In his own response, the author affirms that the isolated child will not speak a particular language per se. But he immediately adds two short dubia. The first is the following: if deaf people from birth do not naturally speak a particular language, what about those who have the use of their organs but never had contact with any speaker of a human language? The answer is not entirely clear: generally speaking, he says, we indeed speak a certain language, but it is not determined per se, which means that it depends on several factors. Therefore, an isolated child will probably emit sounds corresponding to a fictitious language (debet loqui sermones significativos fictos alicuius idiomatis), not to any previously existing language, since it has nothing to do with a common usage to communicate with other people (illud non habet ex usu nec communicat cum hominibus).

The second dubium is the following: where does the distinction and variety of languages come from? This is where climate comes into the picture. The author argues that if we consider the words in themselves, i.e. their acoustic materiality, languages depend directly on climatic variations insofar as the organs that enable us to speak are directly affected by the environment. For example, the dryness or humidity of the tongue have a direct impact on our phonetic skills. But, according to him, the influence of place extends beyond physical dispositions of the bodily organs and also affects the imagination and the desires of the speakers.

Secondly, where do the distinction and number of languages come from? […] To the second point, it is answered that several things are necessary to speak a particular language, namely a disposition of the body, the imagina-tion, a desire, and so by their diversity is caused the diversity of languages, because from one climate to another men have different imaginations and different desires to express vocal sounds. The disposition of the body is also different here and there, namely in the tongue, the palate and so on: some have a very dry tongue, others have a moist tongue, others have a large tongue, and from this comes the differences in the articulation of vocal sounds, and thus the languages are distinguished in different people 13 . The author does not say exactly how the climate affects our imagination and desire, but since they are faculties located in the body, they are most probably affected directly by variations in the com-plexion of the organs. Indeed, it was rather common in medieval medicine and philosophy to consider the variations in the complexio corporis as the effect of several internal and external factors, including the influence of place and climate 14 .

The Eternity of Languages

What is more surprising in this text is the attribution of a radical thesis to Aristotle: particular languages would be eternal, so that if they disappear from one region, they could reappear elsewhere at a different time. Aristotle's opinion was that there never was a first language, because, according to him, the world is eternal, as it appears in Book VIII of the Physics. Thus, since operations, desire, and imaginations fall to the lower things, languages are also eternal, so that if a certain language were destroyed in its climate, it will be generated again in another; so etc. 15 .

Aristotle never explicitly formulated such a strong claim. But in Book VIII of his Physics, when he deals with the eternity of motion as the principal argument for the eternity of the world, he raises the following objection: In the case of animate beings, it seems possible for an individual to be completely at rest before starting to move; so it seems possible for a movement to arise from total rest; therefore, motion may have an absolute start, so that we can imagine a starting point in the motion of the world as well. Aristotle's answer is that this argument applies only to local motion, but not to all kinds of motions and changes in animate beings. Many other motions arise in one's body as a result of the environment (περιέχον in Greek; a continente in Latin) 16 , and these motions in the body in turn set in motion the thought and desire of that individual. For this reason, these motions cannot be absolute starts. Our anonymous author probably had this passage in mind, since it might enable him to show that if languages depend upon imagination and desire, and more generally on thought, they are subject to the causality of the environment through the body.

What is curious is that he draws from this a radical conclusion about the eternity of languages. Aristotle's argument aims to show that motion is eternal, but our commentator affirms that this must also apply to languages, insofar as the motions responsible for the appearance of such and such language are themselves eternal. It looks as though he was supporting the idea that the environment itself is subject to these eternal motions. From this perspective, his position resembles that of Avicenna concerning spontaneous generation and the possibility of a rebirth of mankind after the universal flood: the world being eternal, the conditions favourable to the generation of mankind could be fulfilled again, so that if man came to disappear, he could nevertheless exist again 17 . In the same way, languages could spontaneously revive once the suitable environmental or climatic conditions are present.

The first consequence of this claim is that if languages are somehow eternal, or can be revived several times during the history of mankind, it is impossible to say whether one language appeared before the others. The diversity of languages would have always existed, at least potentially, waiting for the good natural conditions to occur. A second consequence is that climatic determinism cannot be too strict, since the same language could reappear elsewhere, at different times, in different regions. Climate is therefore conceived as changeable and not fixed, contrary to what is usually presented in medieval astronomical texts and cosmographies.

What is clear is that the author is trying to present language, i.e. both the locutio understood as the faculty of speech, and the idioma, which results from the exercise of this faculty, as one natural phenomenon among others, even though he otherwise continue to defend the idea that a language is always learned through oral teaching. He also maintains that words have a conventional meaning, but conventions are in turn influenced by imagination and desire, and thus indirectly by the environment. Doing this, he probably seeks to guarantee both the uniformity of the functioning of our linguistic practices (everywhere sounds must be conceived before they are uttered, and we are all determined to pronounce such and such sounds according to the climate in which we live) and the natural diversity of languages (no language is more natural than another, none is prior or superior to the others). This is crystal clear when the author responds to the mother tongue argument. As he puts it: Among languages there is no maternal and first language, because between them there is no essential order, but only an accidental order. And when it is said that Hebrew is the first and mother language, I reply that this is false, because there is no first language, since the world is eternal according to the Philosopher 18 .

The same theoretical background can be found in all the texts of our corpus: as soon as one accepts the eternity of the world and the role of natural philosophy in the explanation of language and its diversity, theological explanations, such as the dispersion of lan-guages after the construction of the Tower of Babel, are no longer operative. The diversity of languages is no longer thought of as a punishment, but as a fact of nature, in which the only active will is that of man. The barely disguised allusion to the Avicennian theory of the universal floodconsidered here as a natural counterpart of the Biblical floodshows the ambition to replace the biblical nar-rative with that of a natural history of languages.

The commentary (B) supports a similar position. It simply adds that celestial bodies must be counted among the environmental con-ditions which have an effect on languages. such a climate; and thus the diversity of languages is produced by natural principles. And this is said according to the Philosopher, whence, according to him, as the world is eternal, so are the languages 19 .

In his commentary on Book II of the De anima, Averroes does not address the issue of climate 20 . Aristotle's text simply stated that the voice is an animated sound, i.e. accompanied by imagination. Averroes only paraphrases this passage, adding that two powers are required: the desiring power and the imaginative power 21 . It is indeed our anonymous commentator who introduces this new dimension of the influence of the environment on the body and the sensitive soul. With the introduction of celestial bodies, this text also comes closer to the medieval notion of climates, which correspond to parts of the world defined by astronomical landmarks. But what is striking here is the assertion that the stars do not only have an effect on the organs of the voice, but also on the imagination and desire of human beings. For this reason, as the text says, the variety of human languages can be explained by and only by natural causes (fit diversitas idiomatum per naturalia principia).

These two anonymous commentators show a strong desire to explain linguistic diversity by natural causes and not by the traditional explanation provided by the biblical episode of Babel (which is explicitely mentioned in (D) and (E) only). According to them, there is no need to appeal to a transcendent principle, to divine will and to the notions of sin and punishment of humanity. Not only is the variety of languages natural, but it has no beginning. Like the world itself, human languagesin the pluralhave existed from all eternity, at least potentially. As the first of these anonymous commentators makes clear, it is not a question of saying that all languages have always existed, but only that their existence, though contingent, since it depends in part on environmental causes, can be actualized at different moments in time, provided that all the natural conditions are fulfilled. These two authors thus defend a form of radical naturalism that defies the explanation of theologians head-on.

John of Jandun on Climate and Human Linguistic Conventions

In his commentary on the De sensu, written ca. 1309 in Paris (C), John of Jandun follows the questioning of the two anonymous commentators, but places much more emphasis than they did on the importance of social life and conventions in the structuring of human languages. Like the others, he affirms that the deaf from birth is necessarily dumb, since «knowing the formation of a convention-ally signifying speech is not done otherwise than by habit and common life with other humans»22 . It is therefore not only a ques-tion of being able to form representations of words of different oral languages within oneself, but also of being able to interact with other human beings through oral communication. John of Jandun would not deny the need to internalize the languages of communi-cation in order to be fully proficient in them, but he emphasizes the social handicap caused by deafness. At first sight, therefore, he seems to opt for a more conventionalist view of meaning, but also of lan-guage. But when he asks why human beings do not all speak the same language, he also considers the hypothesis of environmental determinism suggested by others (aliqui):

On the second point, some argue that this diversity <of languages> does not arise from the specific nature of men, but from their individual nature, because men in one region have a natural aptitude for a different manner of speaking from those in another region, e.g. those who live in a cold region are accustomed to speak slowly and more low-pitchedly, those who live in a warm region are naturally disposed to speak more high-pitched and quickly; and so on for other differences. Furthermore, they say that this may be due to the celestial bodies, for the celestial bodies produce various influences in various regions and in various men who live in those regions, and from these various influences follow diversities in their actions […]23 . John of Jandun is clearly referring here to one of the anonymous texts presented above. But he introduces their theory from an interesting angle, by shifting the analysis to the individual determinations that incline towards this or that linguistic practice. At first sight, the expression «individual nature» does not seem appropriate, since the argument of climatic influence is more about human groups than individuals. But Jandun is using here a version of the traditional distinction between «universal nature» and «particular nature», originally taken from Avicenna24 . Universal nature is what guarantees the general laws for a natural species, whereas individual nature stands for what affects these general laws and makes individual variations possible 25 . According to these aliqui, each individual, depending on the region where he lives and the various factors that affect him, would thus have particular aptitudes for this or that particular lan-guage, due to the immediate environment and the action of celestial bodies. According to them, the influence of the environment would not only concern phonetics, but also and more generally human actions, including the act of speaking.

John of Jandun does not really criticize this position and his own solution is rather evasive. His aim is nonetheless clear enough: the effect of climate must be limited. To show this, he reminds us that if we follow Aristotle's opinion in the second book of the Meteorologica, the habitable places on Earth may change over time, depending on the action of celestial figures 26 ; we must therefore add a temporal (illa tamen transmutatio est propter ordinem temporis), if not historical, dimension to climate theory, which is merely geographical and astronomical. John of Jandun therefore proposes a sort of thoughtexperiment:

I will say, therefore, that when one region first begins to be inhabited, while it was not inhabited before, it may happen that in that place various men came and instituted a language for the common concord, for the sake of civil communication, through which they would express their concepts; and so in another region others also did so, and according to the variety of their imaginations different languages were instituted, because those who were in one region called man by this vocal sound homo and others with this word anthropos, as it pleased them, and so on 27 .

In this casus, which could tell of something like a rapprochement of men after Babel, individuals of different countries, even though determined by their climate of origin, find themselves in the same place where no language was spoken before and they have to invent 26. Jandun refers here to Meteorologica II 5, 362a32-363a18, where the representation of habitable zones is discussed. In this text, Aristotle does not speak of the evolution in time of these zones, but indicates a link between these zones and the constellations, since the climates are defined by terrestrial and celestial coordinates.

27. Johannes de Janduno, In De sensu, ed. Ebbesen, 181: «Dicam igitur, cum aliqua regio primo coepit inhabitari cum prius non habitabatur, potuit contingere quod ibi provenerunt diversi homines et propter bonitatem communicationis civilis instituerunt ibi aliquod idioma secundum concordiam communem per quod exprimerent suos conceptus, et sic in alia regione fecerunt alii, et secundum diversitatem imaginationum istorum diversificabantur idiomata instituta, quia illi qui fuerunt in una regione vocaverunt hominem hac voce 'homo' et alii hac voce 'antropos', sicut placuit eis, et sic de aliis». a new common idiom, which has nothing to do with the place where they began to speak. And this is necessary in order to create a community based on what Jandun calls «common concord» and «civil communication».

It would seem, then, that for John of Jandun climate is not really the determining factor for the creation of a new language, although it can play a role in the structuring of a particular language, notably at the phonetic level. It is the conventional institution of the meaning of words that is truly paramount 28 . Even if our abilities to pronounce certain words were determined by the influence of the environment on the dispositions of the organs, linguistic diversity would still be primarily based on human conventions. Of course, according to Jandun, the diversity of these conventions depends on «the diversity of the imaginations». But contrary to the two anonymous commentators, John of Jandun seems reluctant to affirm that imagination is determined by the stars and more broadly by the environment, as it appears also in his other works 29 . As for the eternity of the world and the idea that languages could be reborn anywhere if they were to disappear, John of Jandun would probably not object to either of these ideas 30 .

28.

A rather similar position is found in Radulphus Brito's quaestio on the scientificity of music (F. Hentschel, Sinnlichkeit und Vernunft in der mittelalterlichen Musiktheorie, Stuttgart 2000, 293-94, quoted by Sekizawa, Le naturalisme linguistique de Boèce de Dacie, 330-31. One respondens argues that music is not scientific because it is not identical in all people (the Spanish do not sing like the French, the text says). Radulphus Brito replies that: «[…] nullus istas melodias facit nisi per doctrinam vel inventionem vel ex consuetudine quadam, et non facit hoc a natura».

29. Johannes de Janduno, Quaestiones super libros Aristotelis De coelo, I, q. 30. Regarding the actualisation of the possible intellect, Jandun considers that there is always a part of the world, a climate, where people think, so that the unique intellect is always actualised by human individuals. The same is certainly true of language. See J.-B. Brenet, Transferts du sujet. La noétique d'Averroès selon Jean de Jandun, Paris 2003, 406-32.

John of Jandun and Dante on Climate and Conventions

Similarities between the thought of John of Jandun and that of Dante, especially concerning their theories of the intellect and politics, have been noticed by several scholars 31 , not their common interest in the question of the origin of the diversity of languages. Indeed, in the De vulgari eloquentia, Dante interprets the Babel episode in a rather singular way: God would have made men forget the first language and would have given them in exchange the pos-sibility of repairing their sin thanks to their bene placitum, their good pleasure, which is at the origin of their numerous and variable lan-guages. But what is interesting about Dante's position is that according to him, the real reason for the existence of various languages is nothing but human nature. Indeed, «since all our language […]comes from our good pleasure […]and man is the most unstable and variable animal, no language can be durable and permanent, but must vary, like other things that belong to us, for example morals and habits, according to the distances in place and time» 32 .

As with John of Jandun, it is unclear whether the «distances» evoked in this text refers to the theory of climates, augmented by the historical dimension, or whether it simply alludes to the impossible community of people separated in time and space. As far as time is concerned, Dante clarifies what he means: we understand the language of our distant ancestors far less well than the language of our contemporaries. As he puts it: «On this account, therefore, I make so bold as to declare that if the ancient citizens of Pavia were to rise from the grave, they would speak a language distinct and different that of the Pavians today» 33 . From this point of view, he points out, the illusion of unity and immutability of the language of a city or even a country comes from the length of a man's life, which is too short to measure the evolution of his own language. As far as space is concerned, Dante contents himself with an a fortiori argument: if languages vary within the same community living in the same place, «the speech of people who live distant and apart from each other also varies in many ways, just as do their mores and customs which are not maintained either by nature or by a shared agreement (consortium), but arise from human preferences (humanis beneplacitis) and geographical proximity (localique congruitate)» 34 . For Dante, there is a language fixed by nature and given by Godthat of Adamand languages fixed by conventionthat is, by grammars, like Latinbut for the rest, that is, for the living vernaculars, they depend on the goodwill of the speakers and, albeit somewhat mysteriously, on place. Giorgio Stabile endeavoured to show the importance of what he calls the complexio locorum in Dante's theory of language, even though he does not mention Jandun and the other commentaries on the De sensu [START_REF] Stabile | La Torre di Babele: confusione dei linguaggi e impotenza tecnica[END_REF] . Indeed, in the Commedia (Paradiso XXVI, 127) Dante suggests that the bene placitum «follows the heaven» (seguendo il cielo), while he insists on the remaining freedom left to man in the construction of his languages. For Dante, heavens incline, but do not determine human beings, as it appears in Purgatorio XVI (67-81). Giacomo Gambale and Irene Rosier-Catach have described very precisely how some of the first medieval commentators of the Commedia understood the expression «seguendo il cielo» as a reference to the theory of climate [START_REF] Gambale | Confusio et variatio selon les anciens commentateurs de la Commedia[END_REF] . Although he may have changed his views on this issue, Dante may also have defended a position close to that of John of Jandun, according to which it is always the freedom of the speakers that takes precedence over the natural causes, such as the environment and the celestial bodies, even if these causes cannot be totally eliminated from an overall explanation of the diversity of languages. As a consequence, Dante would have no difficulty in asserting that language is both natural and conventional, since particular languages vary from place to place, and time to time, because of different natural and human factors 37 .

A few years later, the author of the commentary on the De sensu attributed to Nicole Oresme or Albert of Saxony was still wrestling with this question of multiple layers of causality in the origin and diversity of languages.

The Multiple Causes of Linguistic Diversity

The fourth commentary (D) attributed to Nicole Oresme pursues the reflections of the three commentators examined so far, while pointing out new limits to the hypothesis of a climatic influence on the diversity of languages. As a first approximation, the author affirms that the diversity of languages is usually described as coming from the stars and the variations in the natural complexion of human bodies 38 . But, he continues, «this is not true, because we see that men of the same climate and even neighbours speak different languages; and the influence of heaven does not produce such diversity, nor does natural complexion, because men with almost the same complexion speak different languages and others with different complexions speak the same language» 39 . The argument is not the same as that of John of Jandun, but it leads to the same conclusion: the diversity of languages cannot be based entirely and solely on the influence of the environment and the heavenly bodies on our complexion. The author does not give a final answer to this problem and 38. Nicolaus Oresme sive Albertus ed Saxonia, ed. Agrimi, 69: «Quartum dubium: unde processit diversitas ydiomatum? Cum omnes homines sint eiusdem nature, quare non omnes loquuntur idem ydioma? Dicendum quod duplex videtur esse causa: una remota, scilicet influentia celi, alia propinqua, scilicet complexio naturalis».

39. Nicolaus Oresme sive Albertus de Saxonia, ed. Agrimi, 71: «Sed illud non est verum, quia videmus homines eiusdem climatis ymmo vicinos loqui penitus diversa ydiomata; nec et sic influentia celi facit talem diversitatem, neque naturalis complexio, quia homines quasi omnino consimilis complexionis loqui diversa ydiomata videmus et alios valde diversarum complexionum simile ydioma loqui». suggests two possible solutions, one from the point of view of faith, the other from the point of view of philosophy.

According to faith, the diversity of languages has its origin in the Babel Tower episode. But this explanation can be understood in two different ways according to our author: either it was by simple divine decree, or it was due to the departure of men from the Babel Tower, so that the natural explanation could still hold.

According to faith, one would say that this diversity begins with the building of the Tower of Babel; but it seems to be questionable whether this tower was begun after the flood, and so, if we suppose that before the flood there were various languages, how far did this diversity remain, when men multiplied in a certain way, they moved away from each other, and so, owing to the diversity of place, and the influence of heaven and complexion, and habit, they began to deviate from the first language, and gradually there were different languages. Or one may say that this was the immediate effect of the divine will 40 .

Either God himself is the direct and immediate cause of a modification in our linguistic capacities, or he is only the cause of the division of human groups, which led to linguistic pluralism with the help of natural causes. This second option does not preclude the possibility that there was linguistic pluralism before Babel (which would be seen as a contradiction by medieval theologians).

In the philosophers' solution, there also remains the question of why there is such a natural diversity of languages without any starting point like Babel. According to the author, two explanations are possible to avoid falling into arbitrariness or inexplicability. One can either invoke the beauty of the universe (propter pulchritudinem universi), variety being always more beautiful than uniqueness. But this is at the very least vague and weak as an argument. Or one should return once again to climate theory, via the influence of the stars and the complexion of the body. 40. Ibid.: «Secundum fidem diceretur, quod ista diversitas incepit in edificio turris Babilonie; sed dubitari videtur an illa turris fuit incepta post diluvium, et ideo supposito quod ante diluvium fuissent ydiomata diversa, quod illa diversitas processit quia, quando homines fuerunt aliqualiter multiplicati, elongaverunt se abinvicem, et tunc propter diversitatem loci, influentia celi et complexionis ac etiam consuetudinis inceperunt aliqualiter deviare a primo ydiomate, et sic continuando fuerunt ydiomata penitus diversa.Vel potest dici quod hoc fuit immediate a voluntate divina».

According to philosophy, one would say that from all eternity there have been various languages, so this diversity never began. It is said that this exists because of the beauty of the universe, insofar as it is more beautiful that there are several languages than just one; thus, in eternity it is sufficient to assign a final cause, since there is no efficient cause. Or else it is said that this diversity comes from the influence of heaven, through habit and complexions 41 .

In both cases, according to faith and according to philosophy, the alternative can be summarized as follows: either we explain diversity by some form of divine or natural finalism (the divine will or a mysterious aesthetic purpose of the universe), or by natural efficient causes such as the action of the environment on the complexion of the body and human habits. Alfonso Maierù 42 and Irène Rosier-Catach 43 consider this alternative as a radical choice between two possible narrativeseither the diversity of languages has a beginning or it is eternalwhereas Benoît Grévin 44 sees this as a mere con-tradiction. With the three previous commentaries in mind, it appears that he tries to reconcile the position of the two anonymous com-mentators with that of John of Jandun 45 . 41. Ibid.: «Secundum philosophiam diceretur quod ab eterno fuerunt diversa ydiomata, ideo numquam illa diversitas incepit. Sed illud non sufficit, quia dubium est quare fuerunt diversa, sive illa diversitas fuit ab eterno vel non. Dicitur, quod hoc fuit propter pulchritudinem universi, quia pulchrius videtur quod sint diversa ydiomata quam si unum esset; modo in eternis sufficit assignare causam finalem, cum non habeant efficientem. Vel potest dici quod illa diversitas provenit propter influentiam celi, propter consuetudinem et complexiones». Despite the limits set out at the beginning, the author does not really settle on the issue, merely indicating the difficulty of com-pletely abandoning both the climatic argument and the role of social habits (consuetudines) without falling into the arbitrariness of divine decree or into a rather weak teleological aesthetics. The benefit of the climatic hypothesis is that it provides an alternative solution to that of the theologians or to the defenders of an old version of the intelligent design thesis. The diversity of languages would be natural, without absolute beginning, and above all it would be contingent, since the determinations of the environment and the celestial bodies change at least as much as human intentions and conventions.

The last anonymous commentary (E) repeats almost verbatim (D), but adds a few more lines, in which he specifies the consequences of the philosophers' position to which he seems to subscribe more clearly. First, he insists on the importance of the temporal dimension in the evolution of languages and on the great diversity introduced by this historical factor 46 . Secondly, instead of considering, as in (A), that the same languages can be revived spontaneously if the necessary natural conditions are fulfilled, he prefers to consider this vari-ety as possibly infinite, which makes it possible to give full scope to the bene placitum of men.

[…] and therefore, in the course of time, <a language> may be so diversified that one who understands Latin well now would understand nothing <of the Latin of the past>. It follows from this that there may have been an infinity or at least many languages such that if a man spoke them today no one would understand him. From this it further follows that in all languages no vocal sound is imposed de novo in such a way that it did not mean already the same thing several times or an infinite number of times 47 . This addition clearly shows the will to break radically with the idea of an absolute beginning of languages and even with that of a fixed and limited number of languages in human history. As for the idea that words can change or lose their meaning over time, it is present in Dante's De vulgari eloquentia, but also earlier in scholastic texts [START_REF]Multa vocabula ceciderunt ab usu. Les mots, le cercle de vin, et le beneplacitum des locuteurs[END_REF] . Since words have a meaning ad placitum, they can lose their nature as signs at our discretion, as the history of languages sufficiently shows [START_REF] Rogerus | Compendium studii theologiae, §116, edition and English translation[END_REF] . But the commentators of the De sensu in the tradition of Nicole Oresme do not intend to reduce the variability of languages to the mere pleasure of their speakers and trypossibly as John of Jandun and Danteto keep all the variables as relevant in the explanation of this natural phenomenon.

It is worth noticing that the position defended by (D) and (E) is quite compatible with the conception of languages defended by Nicole Oresme in some of his other works. As a translator of Aristotle into French at the court of Charles V, he was particularly sensitive to the issue of linguistic diversity. In the excusacion that precedes his translation of Aristotle's Nicomachean Ethics, he does not hesitate to write that it is impossible to translate everything from Latin into French [START_REF] Oresme | Le Livre de Ethiques[END_REF] . He adds that this is necessary, however, since one takes more pleasure in reading the language of his own country than another language [START_REF] Oresme | Et comm edit Tulles en son livre Achademiques, les choses pesantes et de grant auctorité sont delectables et bien aggreables as genz ou langage de leur païs[END_REF] . Moreover, in his translation of Aristotle's Politics, he gives some rather long and detailed comments on the theory of climates, calling on numerous authorities (Pliny, Orosius, Priscian, Ptolemy, Vitruvius, Al-K¯ınd¯ı, Albert the Great, etc.) [START_REF] Oresme | Le Livre de Politiques d'Aristote[END_REF] . He does not mention the case of languages, but takes care to specify the causalities at work in the geographical variability of human mores.

In order to understand this variability, one must take into account the geographical particularities that act directly on the complexion, he says, but one must not neglect the divine will that put the world in order [START_REF] Oresme | [END_REF] . Between these two poles of causality, he adds the action of the planets and the constellations [START_REF] Oresme | Et donques convient il mettre autres causes des variations des seigneuries desus dictes. Et pour ce, l'en peut dire que la variation des constellations des autres planetes et des estoilles fichies entre elles et ou resgart du solail est cause de tele mutation de royalmes[END_REF] . If there is a necessary ordering cause (God), the action of second causes remains contingent, especially when it comes to human affairs. For Oresme, indeed, if man can be inclined to this or that action, he remains absolutely free. This is why, if astronomy might be able explain the origin of a kingdom or a city, political history shows that the places of cultural, economic and military domination were not always the same. He therefore insists on the extreme variability of morals in history beyond the framework defined by the theory of climates. Mores vary within the same climate (as defined by astronomy) and the most powerful kingdoms evolve over time, from Babylon to France, via Egypt, Persia, Greece and Rome 55 . It would therefore not be surprising if commentaries D and E were written by Nicole Oresme or one of his disciples. For the causal scheme used by Oresme for morals is very similar to the one used in these commentaries for languages.

Nicole Oresme quickly addresses the problem of languages in his various commentaries on Aristotle's Meteorologica. In the redactio prima, written in 1346, while he wonders about the changes that can occur in the habitability of the Earth, he is interested, in the wake of the Arabic astronomer Abu ¯ Ma'shar, in political changes, mainly in changes in cities and kingdoms [START_REF] Oresme | Questiones in Meteorologica[END_REF] . After explaining the natural causes that can render a place uninhabitable (infection, terrible storms, unforeseen droughts, etc.), he states that «if the world were eternal, no city would be eternal» 57 . The same is true of kingdoms, which all have a beginning and an end. Some kingdoms last longer than others, for a variety of reasons that are not only natural, but are related to population migrations, due to wars for example. Two of the manuscript witnesses add a corollary on languages:

[…] there are also changes in languages; therefore, perhaps, if the world had lasted for ten thousand years, we would probably not speak as we do now, etc. The sign of this is that some names and denominations lose their use and new ones appear and <this> also because of the intermingling of peoples with other peoples with different languages […] 58 .

As it seems, languages are not eternal, and if lost languages were to be revived, it would be due to human decisions.

While the series of questions to which this one belongs is concerned with the natural causes of changes that take place in the world, even those that lack regularity, as far as social institutions are concerned, be they political or linguistic, one gets the feeling that Nicole Oresme is uneasy, like John of Jandun, and wishes to preserve a major role for human factors, which escape in part from the determinism of the stars and, more generally, of the environment. Just as in John of Jandun, it is the mixing of individuals and populations that first leads to changes in languages.

This same hesitation can be found in the ultima redactio of his commentary on Aristotle's Meteorologica, when Nicole Oresme addresses a question that is surprising at first sight: do the same sité de Fribourg, sous la direction de T. Suarez-Nani, 2019, vol. 2, 248-52. On the natural history of kingdoms, cities and religions, and on the influence of Abu ¯ Ma'shar in the fourteenth century, see Ch. Grellard, «Une histoire naturelle des religions: Blaise de Parme, les astres et les sectes», in La philosophie de Blaise de Parme. Physique, psychologie, éthique, ed. J. Biard, A. Robert, Firenze opinions recur an infinite number of times? The context of this quaestio is close to the one we are interested in here, since the question is whether the eternal return of the same opinions is the effect of the eternity of the world. In the course of his argument as to why this phenomenon can be observed, he points out that:

There is not only variation in opinions relating to speculative matters, but also in practical matters, such as laws, mechanical arts, languages, ways of transmitting science and the like. This is why we see how much greater the variation is in the mechanical arts: indeed, clothes that were pleasing at one time are no longer pleasing now, or the reverse. Similarly, languages vary greatly over time in different regions. Similarly, there are often variations in the way science is transmitted. We see this because the ancients transmitted science in a different way than the moderns and had a different way of communicating than the moderns, as it appears in the books of the ancients 59 .

Languages would be like clothes: their evolution follows a process comparable to that of fashion. Without denying the existence of natural factors, the permanent renewal of words is ultimately due to the bene placitum of men. What is particularly interesting in this quaestio, as in those that precede it in this commentary, is that Nicole Oresme, although opposed to astrology [START_REF] Caroti | La critica contro l'astrologia di Nicole Oresme e la sua influenza nel medioevo e nel rinascimento[END_REF] , concedes that these variations are in part the product of the movements of the celestial bodies. They act on the complexion of human bodies and incline them, without determining them purely and simply. As for the deep reason for this variation, i.e. its final cause, Nicole Oresme makes the same assumption as (D) and (E), namely that it is for the decor uni-versi, because multiplicity and variability make the universe more beautiful (pulchrius) 61 . He no longer opposes teleological explanation to natural efficient causes, since the latter are part of a well-ordered universe. Rather, he endeavours to give a complete and non-exclusive panorama of the causalities that act on our linguistic practices. The debate we reconstructed so far is quite exceptional in medieval philosophy of language. And, as we would like to show, the historical precedents are pretty rare.

Ancient Medical and Philosophical Sources

The first precise analysis of the influence of the environment on the body and health is to be found in the Hippocratic treatise Airs, Waters, and Places, where it is stated that in cities exposed to certain winds «the inhabitants are of better complexion and more blooming than elsewhere, unless some disease prevents this; they are clear-voiced, and with better temper and intelligence than those who are exposed to the north, just as all things growing there are better» 62 . As for those who are sheltered from the winds blowing from the East, «they are likely to have deep, hoarse voices, because of the atmosphere, since it is usually impure and unhealthy in such places» 63 .

If such considerations on the voice as a natural and variable phenomenon can be found in other ancient sources, such as Polybius or Pliny the Elder for example [START_REF] See | Traces on the Rhodian Shore. 65. On the Epicurean theory of language, see among the many existing studies: A. Verlinsky, «Epicurus and his predecessors on the origin of language[END_REF] , the stronger idea that the origin of languages is causally linked with climates is pretty rare. There is, however, one notable exception in Antiquity, namely Epicurus and his school 65 . Indeed, in his Letter to Herodotus Epicurus defends a form of linguistic naturalism, in which climate seems to play a deci-sive role:

Hence, names too did not originally come into being by convention, but by the very nature of men, which undergo particular affections (πάθη) and receive particular representations (φαντάσματα) according to the tribes (ἔθνη) they live in, expelled air in particular ways as determined by each of their affections and representations, in accordance too with the various local differences among their tribes (ὡς ἄν ποτε καὶ ἡ παρὰ τοὺς τόπους τῶν ἐτνῶν διαφορὰ εἴν). And later [the names] were established by a general convention in each tribe, in order that their meanings might be less ambiguous for each other and might be expressed more succinctly [START_REF] Epicurus | Letter to Herodotus[END_REF] .

Epicurus thus distinguishes two stages in the formation of human languages: one is purely natural and consists of associating sounds with the objects that affect us and for which we form natural representations (or imaginations: φαντάσματα), and this first process depends on natural factors, such as the environment; the other is conventional and is the result of culture and aims at a more sophisticated and efficient communication between human beings. There is no need to decide between these two aspects, since they are in a way superposed. Language is a natural phenomenon to which cultural and conventional layers are added in the history of the human species.

The Epicureans reject above all the idea of a first linguistic prescriber, a first impositor of names. Lucretius is very clear on this point, when he claims that «it was nature that compelled them to produce the various sounds of speech, and utility shaped the names of things, […]; thus, to imagine that someone at that time allocated names to things, and that this is how people learned their first words, is utterly absurd [START_REF] Lucretius | Lucretius: De natura rerum V[END_REF] .

The similarities between the Epicurean position and some of the arguments presented in the medieval commentaries on the De sensu studied above are striking. But even though the Epicurean theory of language was partly known in the Middle Ages, notably through Lactantius and Vitruvius, it is unlikely to have played a direct role in the advent of medieval discussions on the influence of climate on languages [START_REF]On the reception of Epicurus in the Middle Ages, see Ch. Kaiser, Epikur im lateinischen Mittelalter: mit einer kritischen Edition des X[END_REF] . Whatever the case for a possible Epicurean ancestry of these medieval theories, this way of dealing with the variety of language remained marginal in Antiquity, but also in the Middle Ages.

The Tower of Babel and Linguistic Conventions in the Middle Ages

The Etymologies of Isidore of Seville probably played a decisive role in the dissemination of a purely phonetic model of explanation of the diversity of languages. In Book IX, devoted to languages and peoples, Isidore first states that the diversity of peoples is consecutive to the constitution of languages. As he writes at the end of the chapter: «We have treated languages first, and then nations, because nations arose from languages, and not languages from nations» [START_REF] Of Seville | [END_REF] . While he readily uses the theory of climates to define the physical appearance and mores of peoples of different regions of the world 70 , he does not establish any causal relationship between climates and languages. On the contrary, he was radically opposed to any form of linguistic determinism that would limit the proficiency in a lan-guage to innate abilities linked to birth and climate. As he states very clearly, «every human is able to pick up any human languagewhether Greek, or Latin, or that of any other nationby hearing it, or to learn it by reading with a tutor» [START_REF] Of | [END_REF] . Therefore, if the history of languages parallels that of peoples, it is not because of natural causes, but because of social relationships based on oral transmission.

Like most authors up to the twelfth century, Isidore simply recalls that the diversity of languages comes from Babel 72 . Before that, there was only one language: Hebrew. Once the first peoples were separated, they forged different languages.

All the nations of the Eastlike the Hebrews and the Syrianscrunch together their speech and words in their throats. All the Mediterranean nationslike the Greeks and the people of Asia Minorstrike their speech on the palate. All the Western nationslike the Italians and Spaniardsgnash their words against their teeth. Syrian and Chaldean are close to Hebrew in speech, mostly agreeing in sound and in the pronunciation of their letters [START_REF] Of | [END_REF] .

In the Carolingian period, a new interest in writing systems, i.e. in letters and their history, emerged [START_REF] Treffort | De inventoribus litterarum: l'histoire de l'écriture vue par les savants carolingiens[END_REF] As in the case of spoken languages, the origin of the various forms of writing was usually related to the flood [START_REF] Fritz | Translatio studii et déluge. La légende des colonnes de marbre et de brique[END_REF] . For fear that the words would disappear, they had to be written. Despite this new element, letters from different languages were considered as derived from Hebrew 76 . Even in the most original treatises, such as Rhaban Maur's De inventione linguarum, which describes the spelling of several languages, there is no challenging explanation for this diversity [START_REF] Maurus | Melchior Goldast, Alamannicarum rerum scriptores aliquot vetusti[END_REF] .

With a few notable exceptions, such as the analysis proposed by Rodrigo Jimenez de Rada at the beginning of the thirteenth cen-tury, who insists more clearly than Isidore on the historical aspects of the diversification of languages [START_REF] Grondeux | For the Latin text, see Rodericus Ximenius de Rada[END_REF] , the most common view in the thirteenth and fourteenth was the myth of Babel [START_REF]See for instance Vincentius Bellovacensis, Speculum doctrinale, I, c. CXLIV[END_REF] .

Medical Discourse and the Emphasis on Phonetics

By contrast, the action of climate on human language is often discussed among medieval physicians, even though they limit their analysis to the particularities of pronunciation. It is not impossible that the Hippocratic Airs, Waters, and Places may have been at the origin of these reflections, since it was known very early in Latin, through a first translation made in the sixth century, then through a translation from Arabic in the twelfth century [START_REF] Kibre | Hippocrates latinus: Repertorium of Hippocratic Writings in the Latin Middle Ages[END_REF] . What is more, Galen's commentary on this treatise was also known in Latin and still copied in the fourteenth century [START_REF]See, for instance, ms. Città del Vaticano, Bibioteca Apostolica Vaticana[END_REF] . As a matter of fact, however, this text is rarely cited by physicians and philosophers of the late Middle Ages.

Reflections on language in the field of medicine mainly concern the physiology of the voice (vox) and its pathologies, and sometimes the related affections of the soul or more precisely of the organs of the sensitive soul, such as the brain or the heart [START_REF] Chandelier | the tone of voice is considered as a sign of the speaker's virtue or vice. See also the Quaestiones super Physiognomoniam of an anonymous author (perhaps Radulphus Brito) edited in I. Costa, «La voix humaine (vox) dans deux textes du début du XIV e siècle[END_REF] . Physicians are therefore interested in the individual variations of the voice, which can be due to the environment, not in general explanations about the origin and diversity of languages.

According to Jeffrey Wollock, except from Galenic works in which the organs of the voice are precisely described, such as On the usefulness of the parts of the body or On the affected parts, the most important sources used by physicians were the Aphorisms of Hippocrates and the Problemata attributed to Aristotle [START_REF] Wollock | The Noblest Animate Motion. Speech, Physiology and Medicine in Pre-Cartesian Linguistic Thought[END_REF] . Medieval commentaries on the Aphorisms do not often use climate theory and are limited to linking pronunciation problems to defects in the organs of speech or sometimes in the brain, as Taddeo Alderotti for example 84 . In the Problemata tradition, commentators wonder how some defects in the voice are related to excesses or defects in the qualities that make up the complexion of the body and its organs, or in the humours (several problems are devoted to the link between melancholy and defects in speech). Thus, they discuss problems about deaf-mutes, as in the commentaries on the De sensu, but also about other defects or disabilities, such as dysfluency, stammering, or alteration of the voice by excessive consumption of alcohol. But in the course of their analysis, they rarely say something general and philosophical about the very nature of language and its diversity.

It is the case with Pietro d'Abano's commentary on the Problemata, which is one of the longest and most influential in the fourteenth century [START_REF] Siraisi | The Expositio Problematum Aristotelis of Peter of Abano[END_REF] , and was read and revised by John of Jandun 86 . Among the 62 problemata dedicated to voces the Italian physician mentions only in passing the role of place 87 . Only one problema deals with a more general question about language: how it is possible for a child to speak before the usual age, which the author says is 20 months [START_REF] De | Quare est quod aliqui antequam perveniant ad tempus naturaliter constitutum ad loquendum ut circa 20 menses loquuntur sermon articulato manifesto[END_REF] . After pointing out that there is nothing natural about this such a child is a monsterunless one means that he speaks a language that is unintelligible to the auditors, which would mean that he does not really speak. Either he is inhabited by some foreign spirit or he does not understand what he is saying and imitates what he has heard thanks to a particular disposition. The appearance of language and the mastery of a particular tongue are therefore not purely natural, since it is necessary that there be teaching, if only by imitation. At the very end of the text, Pietro d'Abano mentions the possibility that this is a disposition linked to the stars [START_REF]It would not be surprising if Pietro d'Abano advocated such ideas, but if he did not do so[END_REF] .

Actually, one of the most interesting medical texts to describe the climatic variations of languages comes from Urso of Salerno, an Italian physician who probably died at the beginning of the thirteenth century. He describes very carefully the phonetic differences between Hebrew, Arabic and Greek, but like Hippocrates, he limits the influence of geography and climate to the different sounds of the voces [START_REF] Salernitanus | Die medizinisch-naturphilosophischen Aphorismen und Kommentare[END_REF] . According to him, what makes our voice human is first and foremost its phonetic structure. The variations that can be observed among nations can therefore be explained partly by the effect of climate on pronunciation, partly as the effect of conventions or habits.

The situation is not much different in the Arabic world, both Muslim and Jewish, as it appears in Irene Zwiep's important works [START_REF] Zwiep | Mother of Reason and Revelation. A Short History of Medieval Jewish Linguistic Thought[END_REF] . In his Kita ¯b al-Huru ¯ f (Book of Letters), which has not been translated into Latin, al-Fa ¯ra ¯bī uses Galen to present a theory of the origin of languages based on the action of the environment and the stars. Maimonides in turn would have used this presentation by al-Fa ¯ra ¯bī, insisting however on the fact that climatic variations would only concern the phonetics, not the syntactic structure and even less the semantics of the different tongues [START_REF]Maimonides nonetheless affirms that Greek cannot be the best language because of the climatic situation of Greece, as Galen suggested, and tries to bring Hebrew and Arabic into the picture[END_REF] . The same is true of Ibn Ezra, who explicitly quotes Hippocrates' treatise and its commentary by Galen, with the same limitations to phonetics [START_REF] Zwiep | [END_REF] .

On the other hand, a theory similar to those discussed in the Latin commentaries on the De sensu was severely criticized by the Jewish grammarian Profiat Duran (c. 1350-c. 1415) 94 . According to this theory, the stars and climates would affect not only the physical conditions of men, but also, as a result, the faculties of the soul, and thus language as a whole. As Zwiep summarizes, according to the anonymous author referred to by Duran, «the temperaments and anatomy, in their turn, determined man's thinking and his language. Therefore, since our language ultimately depended on the heavenly bodies, it should be perforce be considered natural» 95 . For his part, Profiat Duran considers languages as strictly conventional and points out the inconsistency of the defenders of linguistic naturalism, who resemble much the Epicureans.

Phonetics, Linguistic Skills, and Climate Theory in Some Scholastic Latin Texts of the End of the thirteenth Century

Let us turn back to the Latin World. In the thirteenth century, Albert the Great seems to pursue Urso's naturalistic effort. After distinguishing the vox from a simple sound, defining vox as a «sound that is produced with the faculty of imagination, from the mouth of an animal in order to make evident some affect», he defines discourse (sermo), which is proper to man, as an «articulated and lettered voice, making known a person's mental conception» 96 . As for particular languages (idioma), it is a discourse that must be learned. For this reason, he continues «those who are mute from birth suffer this because they are deaf from birth. It is true that they have a voice, but they do not have distinct and ordered speech, because they cannot learn idioms from hearing them» 97 . As for the variability of particular tongues, this is partly explained by the variation of voces due to environmental differences: «Voice and idiomatic speech differ by regions and localities in heaviness and sharpness because the voice of the northerners is sharper and more feminine than the voice of the southerners, owing to the softness of the lungs and their windpipe and because of the windpipe's greater narrowness» 98 . If words vary from one region to another, their meaning depends on conventions and oral teaching. As he explicitly states: «This indicates that the meaning of a vocal sound is no more natural than speech (locutio). Rather, it follows the teaching of the speakers. Because voices are natural, the voices of humans are alike in species, but languages (locutiones) vary» 99 .

Roger Bacon defends a similar position. In the Opus maius, after having described the principles of dividing the world into regions in the manner of the astronomers, he explains that place (locus) is at the origin of many properties of bodies, but also of the soul. But, he adds, it is practically impossible to scientifically examine all these environmental factors, as each place receives a singular influence from the stars, not to mention all the other factors related to the air, altitude, rivers, etc.

But place is the beginning of our existence, just as a father, as Porphyry says. And we see that all things vary according to different localities of the world not only in nature, but also men in their customs; the Ethiopians have one set of customs, the Spaniards another, the Romans still another, and the Greeks yet another. For even the Picards, who are neighbours to the true Gauls, have such a difference in customs and language, that we cannot but wonder at such diversity in neighbouring localities 100 . Moral and linguistic differences between the nations can be explained in the first place by the influence of the place on the complexion of the body, and more precisely on its radical complexion (complexio radicalis), i.e. that which an individual possesses at birth. And when the child at birth is exposed to a new air, another world as it were, he then receives apexes of celestial pyramids as respects his separate members, and thus receives new impressions, which he never gives up, because what the new jug receives it tastes of when old. And then is formed the radical complexion, which remains to the end of life, although the current complexion may be changed for a whole day. And this radical complexion is followed by inclinations to morals and to sciences and languages, and to all the trades and occupations, and to all that diversity which we see in all things 101 . This thesis is repeated in the Opus tertium 102 , where he confesses that he simply observedoculata fidethis linguistic diversity. The only indication he gives, in the Opus maius, is that our linguistic inclinations would be mainly the effect of the fixed stars on the complexion of the body 103 .

We must nevertheless attribute to him a position close to that of Albert the Great. For in the Opus tertium, he clearly states that languages vary according to the pleasure of the speakers 104 . The stars 104. Rogerus Baco, Opus tertium, c. 28, ed. Brewer, 102: «Notitia linguarum est prima porta sapientiae, et maxime apud Latinos, qui non habent textum incline, but do not determine us. We remain free in the face of these external factors that influence the human body. It is also consistent with his philosophy of language, which constantly insists, especially in the De signis, on the theory of the imposition of names ad placitum.

Concluding Remarks

The defence of some form of linguistic naturalism on the basis of a theory of climates is pretty rare in the Antiquity and the Middle Ages. Apart from the Epicurean tradition, medical and philosophical theories tended to limit the action of the environment to the tonal variations of the voice considered as signs of potential It is only in the thirteenth century that the Western Latin world saw the emergence of an application of climate theory not only to phonetics, but also to language skills in general. The five commentaries on the De sensu et sensato examined in this paper are therefore quite exceptional. Indeed, (A) and (B) come very close to the Epicurean theory of language, even though their arguments are totally different from this materialist tradition. John of Jandun is less radical and tries, like Roger Bacon, to reconcile a naturalistic description of language with the freedom of the speakers to invent and change their languages. However, because of commentators like (A) and (B), and the increasingly traditional opposition in Paris between the points of view of philosophy and theology, Jandun was forced to discuss much stronger hypotheses about environmental determinism. The same is true of Nicole Oresme and his followers who, while insisting even more than John of Jandun on the importance of conventions and institutions in human practices, nonetheless acknowledge the existence of natural causalities at work behind linguistic abilities and practices.

What is most striking in these fourteenth century Parisian debates is the desire to go beyond the theological explanation of the Gene-sis, and to show that language must be included, at least partially, among the objects of natural philosophy. If we follow this path, it becomes possible to conceive of a natural history of languages that theologiae, nec philosophiae, nisi a linguis alienis; et ideo omnis homo deberet scire linguas, et indiget studio et doctrina harum, eo quod non potest ea cognoscere naturaliter, quia fiunt ad placitum hominis, et variantur secundum hominum voluntatem».

is not based on the myth of a common origin for all languages and that is not only thought of in terms of progress or decadence. By appealing to the thesis of the eternity of the world, (A) and (B) intended to change the scale so that linguistic changes would no longer be measured by our historical experience and knowledge. They try to conceive of a natural history of languages that is not necessarily linear. And if John of Jandun and Nicole Oresme are less insistent on this aspect, their questioning goes in the same direction, notably when they imagine at the same time the infinite changes in languages and the possible return of the same structures, due to natural causes which are just as structuring as human habits and conventions, which also vary under the effect of the free will of humans and the contingencies of history.

These commentaries on Aristotle's De sensu probably did not have much immediate impact on the debate about languages in the late Middle Ages. They are nevertheless indicative of changes in the way in which the geographical and historical variability of languages is approached, changes which will still be felt in the modern era and the Enlightenment, in Leibniz, Rousseau, Herder, Humboldt, etc. It would be necessary to write the history of these theories over a long period of time, but this is far beyond the scope and ambition of this paper.

«

  Micrologus. Nature, Sciences and Medieval Societies» XXXI* Special Issue (2023), pp. 153-90 (ISSN 1123-2560 • ISBN 978-88-9290-210-7 © SISMEL -Edizioni del Galluzzo 2023)

17.

  See R. Kruk, «A Frothy Bubble: Spontaneous Generation in the Medieval Islamic Tradition», Journal of Semitic Studies, 35 (1990), 265-82. For Avicenna in particular, see A. Bertolacci, «Averroes against Avicenna on Human Spontaneous Generation: The Starting-Point of a Lasting Debate», in Renaissance Averroism and Its Aftermath: Arabic Philosophy in Early Modern Europe, ed. A. Akasoy, G. Giglioni, Dordrecht 2013, 37-54.

31.

  For instance, R. Imbach, Dante, la philosophie et les laïcs, Paris-Fribourg 1996 (in particular chapter VI). See also J.-B. Brenet, Je fantasme, Paris 2017 (in particular chapter 13). 32. Dante, De vulgari eloquentia, ed. P. V. Mengaldo, Padova 1968, I, IX, 5-6: «Cum igitur omnis nostra loquela […] sit a nostro beneplacito […] et homo sit instabilissimum atque variabilissimum animal, nec durabilis nec continua esse potest, sed sicut alia que nostra sunt, puta mores et habitus, per locorum temporumque distantias variari oportet». 33. Dante, De vulgari eloquentia, I, ix, trans. S. Botterill, Cambridge 1996, 21.

37.

  On these two aspects of language in Dante, see I. Rosier-Catach, «Dante et le langage: ni modiste ni cabaliste», in Dante et l'averroïsme, ed. A. de Libera, J.-B. Brenet, I. Rosier-Catach, Paris 2019, 79-115.

  , 64-83; C. J. Glacken, Traces on the Rhodian Shore: Nature and Culture in Western Thought from Ancient Times to the End of the Eighteenth Century, Berkeley and Los Angeles 1976. For its application to the description of ethnic groups, see The Origins of Racism in the West, ed. M. Eliav-Feldon, B. Isaac, J. Ziegler, Cambridge 2009. 7. Edited by Jole Agrimi, in Le "Questiones de sensu» attribuite a Oresme e Alberto di Sassonia, La nuova Italia editrice, Firenze 1983, 69-72.

al

  De sensu et sensato di Aristotele (XIII-XIV sec.). Status quaestionis e prospettive per un inventario», Aristotelica, I (2002), https://doi.org/10.17454/ARIST01.05 and Roberto Zambiasi's contribution in this issue. 1. For a preliminary list of question commentaries, see S. Ebbesen, C. Thomsen-Thörnqvist and V. Decaix, «Questions on De sensu et sensato, De memoria and De sono et vigilia. A Catalogue», Bulletin de philosophie médiévale, 57 (2016), 59-116. Roberto Zambiasi's forthcoming doctoral thesis already lists several commentaries not listed by Ebbesen, Thomsen-Thörnqvist and Decaix. 2. On the reception of the narrative of Babel as the origin of linguistic diversity, see A. Borst, Der Turnbaum von Babel. Geschichte der Meinungen über Ursprung und Vielfalt der Sprachen und Völker, 6 vol., Stuttgart 1957-1963.

3 .

 3 Anonymus, Quaestiones super librum De sensu et sensato, Vat. Lat. 3061, ed. Ebbesen, 166: «Item, ille qui est surdus se[d] habet ad omne idioma determinatum <et> ad omnes voces significativas ad placitum sicut aliquis qui num<quam> audi<vi>t gallicum (…); sed qui non audivit idioma gallicum nescit ipsum exprimere ex certa scientia et cognitione; ideo surdus naturaliter est mutus».

  19. Anonymus, Quaestiones super librum De sensu et sensato, ms. Vat. Lat. 2170, ed. Ebbesen, 173: «De tertio, sc. unde provenit distinctio idiomatum, dicendum ut dicit Commentator secundo De anima: provenit ex parte corporis et ex parte animae: <ex parte animae> ut imaginatio et appetitus, sc. quod anima imaginatur aliquid et appetit illud exprimere; a parte corporis ut pulmo, palatum, vocalis arteria, lingua. Ex hoc provenit distinctio. \A parte animae/ quia homines sub alio et alio climate existunt, sed in diversis climatibus sunt diversi motus corporum caelestium, et secundum hoc fiunt diversae imaginationes et appetitus; quare †etc. † a parte animae provenit distinctio. Iterum ex parte corporis, quia quidam habent linguam magis humidam, quidam magis grossam, et aliter et aliter dispositam secundum diversas dispositiones quas homines contrahunt a corporibus caelestibus quia sub alio et alio climate existunt, et sic fit diversitas idiomatum per naturalia principia. Et hoc dicatur secundum Philosophum, unde secundum ipsum, sicut mundus est aeternus, ita et idiomata» (italics mine). 20. On this issue, see Averroes, Commentarium magnum in Aristotelis De anima libros, comm. 89-91, ed. F.S. Crawford, Cambridge 1953, 266-69. 21. Ibid., 268: «[…] vox est sonus qui fit cum ymaginatione et voluntate. Et ideo dixit animatum et cum ymaginatione. Innuit enim quod ista actio completur duabus virtutibus anime, quarum una est concupiscibilis et altera ymaginativa».

  1, Venetiis 1551, f. 2va (quoted by E. Grant, Planets, Stars and Orbs. The Medieval Cosmos, 1200-1687, Cambridge 1994, 590): «[…] Corpora coelestia sunt causa omnium inferiorum exceptis actibus humanis […] corpora coelestia non habent virtutem ad causandum intellectum adintelligendum vel non intelligendum et ad necessitandum voluntatem ad eligendum vel noneligendum, vel volendum vel non volendum». See also, A. Vella, Voluntas aeterna. Causalità e infinito nelle Quaestiones in Aristotelis de caelo di Giovanni di Jandun, Roma 2013.

  Classical and Medieval Linguistics, ed. G. Lepschy, London 2014, 272-306 (see page 281). 43. I. Rosier-Catach, «Babel: le péché linguistique originel?», in Adam, la nature humaine avant et après: épistémologie de la Chute, ed. G. Briguglia, I. Rosier-Catach, Paris 2016, 63-86: 76. 44. B. Grévin, «De la rhétorique des nations à la théorie des races. L'influence des théories scientifiques sur la pensée des stéréotypes nationaux à partir du XIII e siècle», Preprint, available at the following adress http://gas.ehess.fr/ docannexe/fichier/107/grevin.pdf (consulted in March 2022). 45. It is not impossible that Nicole Oresme knew some of Dante's theses. See Ch. Grellard, «La monarchie universelle: une fiction poétique? La critique de Dante par Oresme», in Ut philosophia poesis. Questions philosophiques dans l'oeuvre de Dante, Pétrarque et Boccace, ed. J. Biard, F. Mariani Zini, Paris 2008, 53-73.

42. A. Maierù, «The Philosophy of Language», in History of Linguistics. Vol. II:

  46. Anonymus, Quaestiones super librum De sensu et sensato, Biblioteca dell'Accademia Nazionale dei Lincei e Corsiniana, Fondo Rossi 415 (36.F.6), f. 108rb: «[…] sicut videmus quod a multo tempore citra (?) sunt maxime diversitates in idiomate […]».47. Anonymus, Quaestiones super librum De sensu et sensato, Biblioteca dell'Accademia Nazionale dei Lincei e Corsiniana, Fondo Rossi 415 (36.F.6), f. 108rb: «[…] et ideo in processu temporis ante (pro tam?) potest diversificare quod ille qui nunc bene intelligit latinum tunc nichil intelligeret. Ex isto sequitur quod possibile infinita ydiomata fuisse vel saltem plura, quibus si homo nunc loqueretur a nullo posset intelligi. Ex isto ulterius sequitur quod nulla vox imponitur de novo ad significandum in omni ydiomate sic quin pluries vel infinities idem significavit».

  2019, 59-82. 57. Nicolaus Oresme, Questiones in Meteorologica (prima lectura), I, 33, ed. Panzica, 250: «[…] di mundus esset eternus, nulla civitas adhuc esset eterna». 58. Nicolaus Oresme, Questiones in Meteorologica (prima lectura), I, 33, ed. Panzica, 251: «[…] sunt enim permutationes linguarum unde forte si mundus adhuc duraret per decem milia annorum non loqueretur probabilius sicut nunc etc. cuius signum est quia quedam nomina et denominationes recedunt ab usu et alia noviter veniunt et etiam propter mixtionem gentium cum gente diversosum ydiomatum […]».

95 .

 95 Ibid. 96. Albertus Magnus, De animalibus, IV.ii.2, ed. H. Stadler, Münster i.W. 1916, 397-98 (trans. K.F. Kitchell, Albertus Magnus on Animals: A Medieval Summa Zoologica, Baltimore 1996: «Praedeterminare autem oportet, quod vox est diversa a sono, eo quod vox est sonus cum ymaginatione ab ore animalis ad aliquem affectum demonstrandum prolatus. Sonus autem est genus vocis quodlibet videlicet a sonante procedens, quod auditui infert passionem. Sermo autem est tertium diversitatem habens ad utrumque istorum. Est enim sermo vox articulata et literata, conceptum mentis hominis denuntians, et hic non competit nisi homini […]». 97. Ibid., 400-401 (trans., 481): «Illi vero homines qui ex generatione sunt muti, patiuntur hoc, quia sunt a generatione surdi, et illi habent quidem vocem, sed non habent sermonem distinctum et literatum, quia ydiomata discere per auditum non potuerunt».

98 .

 98 Ibid. (trans., 481): «Vox autem et sermo ydyomatum diversificantur secundum regiones et loca in gravitate et acumine quoniam vox septentrionalium est magis acuta et feminea quam vox meridionalium propter mollitiam suarum pulmonum et suae cannae et propter maiorem artitudinem ipsius». 99. Ibid. (trans., 481): «[…] et hoc significat quod significatio vocis non est naturalis sicut neque locutio, sed est secundum doctrinam loquentium. Voces autem, quia naturales sunt, ideo voces hominum sunt consimiles in specie, sed locutiones variantur». 100. Rogerus Baco, Opus maius, IV, v, ed. J. H. Bridges, 2 vol., London-Edinburgh-Oxford, Williams & Norgate, 1897-1900, vol. I, 138 (trans. R. B. Burke, Philadelphia 1928, 159): «Locus est principium generationis quemadmodum et pater, ut dicit Porphyrius. Et nos videmus quod omnia variantur secundum loca mundi diversa, non solum in naturalibus, sed homines in moribus; quoniam alios mores habent Aethiopes, alios Hispani, alios Romani, et alios Gallici. Nam et Picardi, qui sunt veris Gallicis vicini, habent tantam diversitatem in moribus et in lingua, ut non sine admiratione possit esse unde sit tanta diversitas locorum propinquorum».

  101. Ibid.: «Et unc confirmatur complexio radicalis, quae semper manet usque ad finem vitae, licet complexio currens mutetur tota die. Et ad hanc radicalem complexionem sequuntur inclinationes ad mores et ad scientias et ad linguas, et ad quaecumque artificia et negotia, et ad omnem diversitatem quam videmus in omnibus». 102. Rogerus Baco, Opus tertium, c. 27, in Opera hactenus inedita, ed. J. S. Brewer, London 1859, vol. I, 120: «Secundum enim diversitatem locorum in complexione diversificantur res in complexionibus, et homines in artibus, et scientiis, et linguis, et negotiis, et moribus, ut videmus oculata fide, secundum diversitatem regionum». 103. Rogerus Baco, Opus maius, ed. Bridges, 380 (trans., 395): «Per coelum ergo complexiones omnium rerum habentur, et non solum regiones diversificantur per coelum, sed res eiusdem regionis et partes eiusdem rei […]. Et huius causa est duplex. Una est causa universalis, scilicet solis distantia vel propinquitas secundum quos superius in locis mundi est memoratum. Alia est causa particularis, scilciet diversitas stellarum fixarum super capita habitantium. Nam specialiter per has variantur res naturales in diversis regionibus, et homines, non solum in naturalibus, sed in moribus, in scientiis, in artibus, in linguis, et in omnibus».

As to the third point, namely, what is the origin of the distinction of languages, it is stated, as the Commentator says, in the second book of the De anima, that it originates partly from the body and partly from the soul: on the side of the soul, namely in the imagination and appetite, since the soul imagines something and wishes to express it; on the side of the body, namely the lungs, the palate, the trachea and the tongue. From this comes the distinction of languages. From the soul, because men exist in such and such a climate, and in these various climates there are different movements of the heavenly bodies, and from this various imaginations and desires are produced; therefore the distinction comes from the soul. And also from the body, because some have a wetter tongue, others a thicker tongue, and is disposed in such and such a manner according to the various dispositions which men acquire from the celestial bodies because they live in such and 18. Anonymus, Quaestiones super librum De sensu et sensato, ms. Vat. Lat. 3061, ed. Ebbesen, 170: «Ad aliam dico quod licet communiter dicant quod loquetur idioma maternum et primum, dico quod inter idiomata nullum est maternum et primum, quia inter ea non est ordo essentialis sed magis accidentalis. Et cum dicitur quod hebraicum e<s>t idioma maternum et primum, dico quod falsum est, quia nullum est idioma primum, cum mundus sit aeternus secundum Philosophum. Et ideo etc.».

Johannes de Janduno, In De sensu, ed. Ebbesen, 179: «[…] scire sermonis significativi ad placitum formationem non est nisi per consuetudinem et convictum cum hominibus; sed surdus a nativitate non potest assuefieri in expressione sermonis significativi, quia hoc requirit quod audiatur huiusmodi sermo si in eius expressione debet aliquis assuefieri; et hoc est manifestum».

Johannes de Janduno, In De sensu, ed. Ebbesen, 180: «Ad secundum dicunt aliqui quod illa diversitas non provenit ex natura specifica sed ex natura individuali, quia homines unius regionis habent aptitudinem naturalem ad alium modum loquendi quam alterius regionis, sicut illi qui habitant in regione frigida habent aptitudinem quod loquantur magis tarde et gravius, qui vero in calida levius et velocius sunt nati loqui; et sic de aliis diversitatibus. Item dicunt quod hoc potest provenire ex corporibus caelestibus, nam corpora caelestia diversas influentias faciunt in diversis regionibus et hominibus ibi existentibus, et de talibus diversis influentiis sequuntur diversitates in operibus ipsorum, et haec diversitas est in principio remoto, sicut nos videmus quod in una regione animal aliquod generatur et vivit etiam prolixius, et in alia non».

Avicenna, The Physics of the Healing, I, 1, trans. J. McGinnis, Provo (Utah) 2009, 5-6.

For other medieval uses of this distinction, see for instance C. Trifogli, "Avicenna's Physics in Roger Bacon's Communia naturalium», in The Arabic, Hebrew, and Latin Reception of Avicenna's Physics and Cosmology, ed. D.N. Hasse, A. Bertolacci, Boston-Berlin 2018, 433-57.


domain: math stat

text:
Véronique Maume-Deschamps

Oskar Laverny

Didier Esterina Masiello

published or not. The documents may come     Estimation of multivariate generalized gamma convolutions, application to dependence structure modelling in insurance.

A major topic is the evaluation and modeling of the dependency between those risks. Indeed, the properties of this dependency has a huge impact on the behavior of the total loss, and therefore on the capital management of the company.

Risks can be heavy-tailed, skewed, and are usually dependant with each other, including in the extremes.

The infinite divisibility may be a wanted property.

Why infinite divisibility ?

Definition (ID r.v. X)

1 X is n-divisible if and only if there exists X 1 , ...X n i.i.d. such that X = X 1 + ... + X n 2 X is ID iff this can be done for all n. 3 X i is called a piece of X .
Dependencies are largely unobservables in reinsurance;

Experts are providing information as divisibility parameters: "20% of this is driven by the same risk factors as 10% of that.." this means comonotonic pieces accross marginals.

Company's Solvency

Risk factors modelisation

In the internal modeling point of view, the distributions of several losses X 1 , . . . , X d are supposed to be known, but the dependence structure between them must still be evaluated and taken into account to assess the variability and behavior of the total loss:

d i=1 X i .
It might be achieved by a risk factors decomposition:

X i = k j=1 X i,j ,
where X i,j , X ,j are either independent or comonotonic. Divisibility allows to interpret the X i,j as pieces of X i . =⇒ multivariate generalized Gamma convolutions give an answer to that question.

Plan

Introduction / motivation

Multivariate generalized Gamma convolutions

Simulations

Motivation: interpretability of G d,n models X ∈ G d,n has an additive risk-factor structure: there exists gamma random variables G 1 , ...G n such that:

   X 1 ... X d    =    s 1,1 ... ... s 1,n ... ... ... ... s d,1 ... ... s d,n    •    G 1 ... G n    1 For all i ∈ 1, ..., n, G i ∼ G 1,1 (α i , 1)
2 G 1 , ..., G n are independent.

Goal: Estimate ν from observations of the random vector X. Pb: It is a deconvolution problem, which is numerically hard (can also be interpreted as a solution-less moment problem for the Thorin measure, see MFK 2 ).

The orthonormal Laguerre basis of L 2 (R d + )

Consider the following orthonormal basis of

L 2 (R d + ) called Laguerre basis 3 : let p ∈ N d , φ p (x) = d i=1 φ p i (x i ), with φ p (x ) = √ 2 p k=0 p k (-2x ) k
k! e -x . Any square integrable distribution density f can be expended as :

f (x) = p∈N d a p φ p (x) where a p = φ p (x)f (x)∂x Estimation Consider a random sample X 1 , . . . , X N of X ∈ G d (α, s). Let a p = 1 N N i=1 φ p (X i ).
Consider the integrated square error loss:

L(α, s) = k≤m ( a k -a k (α, s)) 2 and
( α, s) = argmin (α,s) L(α, s).

Remark that the theoretical Laguerre coefficients may be computed using the formula:

a k = φ k , f = E (φ k (X)) = √ 2 d k≤p p k (-2) |k| k! E X k e -|X| .
Multivariate log-Normal

  Capital): regulatory capital calculated using a risk measure that the re-insurer must have to absorb potential losses. For example, in the Solvency II directive of the European Union, it is the VaR(99.5%) of the P&L distribution.

Figure :

 : Figure: MLN case: n = 10

[START_REF] Miles | Risk Aggregation: A General Approach via the Class of Generalized Gamma Convolutions[END_REF]. In: Variance

[START_REF] Dussap | Anisotropic multivariate deconvolution using projection on the Laguerre basis[END_REF]. In: Journal of Statistical Planning and Inference

Oskar Laverny (2022). In: arXiv preprint arXiv:2203.13741

x, t ∈ R d , Recall: Cumulant generating function:

Example

All gammas, log-Normals, Paretos, α-stables, and sums and/or products of these are in G 1 .

No estimation procedures were available before our work. 1 Lennart Bondesson (Nov. 2009). en. In: Journal of Statistical Planning and Inference

Consistency

We have the following consistency result 4 under the thechnical well-behaved asumption (which holds for univariate Gamma convolutions, independent multivariate Gamma convolution and invertible linear transformations of them e.g.).

Dimensionality issues

The loss L(α, s) is too costly to work with when d gets large. Indeed, the number of coefficents to compute is given by

which is exponentially increasing in d and therefore unusable in high dimension (ok until d = 4 or 5.

Improvement of the method by Oskar Laverny 5 by using an approximation of an integrated loss function and random projections (tested for d = 1000).

Plan

Introduction / motivation

Multivariate generalized Gamma convolutions

Simulations

Conclusions

The univariate Thorin class is wide: LN, Pareto, α-stable, (some) Weibull, ...

The Multivariate analogue provides an asymmetrical dependence structure which include tail dependency, and can take a lot of different shapes.

Deconvolution is a hard inverse problem, and estimation of these distributions is complicated.

The final additive risk-factor model gives easy interpretation of parameters and easy aggregation schemes. Should be shortly used by SCOR in some parts of their internal model.

Improvement to go to high dimension in Oskar' work 6 and the open-source Julia package 7 provides the implementation.

6 Oskar Laverny (2022). In: arXiv preprint arXiv:2203.13741 7 Oskar Laverny (Mar. 2021). Version v0.1

Thank you

Thanks for your attention.