The Invention of Relations: Early Twelfth-Century Discussions of Aristotle's Account of Relatives¹

1 Work on this study was supported by an award from the Marsden Fund Council administered by the Royal Society of New Zealand.

Abstract

Aristotle's discussion of relatives in the Categories presented its eleventh- and twelfth-century readers with many puzzles. Their attempt to solve these puzzles and to develop a coherent account of the category led around the beginning of the twelfth century to the invention of relations as items which stand to relatives as qualities stand to qualified substances. In this paper, I first discuss the details of Aristotle's accounts of relatives and the related category of ‘situation’ and Boethius' commentary on them. I then examine some of the earliest mediaeval commentaries on the Categories showing how the notion of relation, and in particular of individual relations, was developed. I conclude by showing how Peter Abaelard's treatment of relations in his Dialectica was part of an ongoing and sophisticated debate over the nature of relations.

Keywords:

• Aristotle
• Boethius
• William of Champeaux
• Peter Abaelard
• Categories
• relatives
• relations
• ad aliquid
• individual accidents
• material essence realism

Notes

1 Work on this study was supported by an award from the Marsden Fund Council administered by the Royal Society of New Zealand.

² Pros ti and ad aliquid both translate as ‘to something’ – relatives are characterized by Aristotle as items which are referred to something. The Latin verb referre, to refer, or relate, translating anapherō, has relatus, referred or related, as its past participle and anaphora and relatio are the corresponding abstract nouns.

³As read by the mediaevals in Boethius' translation: ‘Ad aliquid uero talia dicuntur quaecumque hoc ipsum quod sunt aliorum dicuntur, uel quomodolibet aliter ad aliud'. (Categoriae, Boethius trans., 18.4–6).

⁴Aristotle's ‘antistrephōn’ is, however, translated by Boethius as ‘convertens’ and ‘correlativus’ is not used in twelfth-century discussions of relatives.

⁵‘Huiusmodi autem definitio Platonis esse creditur, quae ab Aristotele paulo posterius emendatur'. (Boethius, In Categorias, 217C). According to Simplicius (In Categorias, 159.12–22), Boethus the first-century BCE Peripatetic is responsible for this attribution. Simplicius disagrees and maintains that Plato, like Aristotle, characterized relatives in terms of mutual dependence of being rather than the forms of predication.

⁶Cum itaque Aristoteles tot inconuenientia sequi conspiceret ex ea definitione relatiuorum quam Plato nimis laxam dederat, ausus est errorem magistri corripuise et eius magister fieri cuius se fuisse discipulum recognoscebat. … Quae quidem ab alia in eo maxime diuersa creditur quod hanc Aristoteles secundum rerum naturam protulit, illam uero Plato secundum constructionem nominum dedit. (Abaelard, Dialectica, 86).

⁷Ergo nihil impedit easdem res ad aliud atque aliud uersas diuersae praedicationi substitui. Ipsum uero ad aliquid praeter ullum aliud praedicamentum intellegere non possumus, ut patrem et filium, dominum et seruum secundum substantiam consideramus. Nam et qui dominus et qui seruus est, substantia est. Duplum et triplum secundum quantitatem haec enim in quantitate consistunt, scientia<m> uero et inscitia<m> secundum qualitatem. Secundum enim has quales dicimur, scientes scilicet atque inscii. (Boethius, In Categorias, 221A–B).

⁸‘Ipse quoque habitus ad aliam praedicationem dictus fit iterum relatiuus: quod enim habitus habilis rei habitus est, ad aliquid est; et quod alicuius uirtus est, ad aliquid uirtus est, et quod alicuius uitium est, ad aliquid quoque ipsum est.’ (Boethius, In Categorias, 221A).

⁹For the development of the idea of a relation as something which functions with respect to relata as qualitas does with respect to quale by Simplicius and the brief discussion in his commentary on the Categories of the reality of relations as something ontologically distinct from their substrates and the other kinds of accidents see Luna, ‘La Relation Chez Simplicius’ and Harari, ‘Simplicius on the Reality of Relations’. Simplicius’s commentary was translated into Latin in 1256 by William of Moerbeke and widely used thereafter. See Chase, ‘The Medieval Posterity of Simplicius’ Commentary'.

¹⁰The Latin translates Greek articular infinitives, ‘to anakeisthai', etc. Abaelard takes these to be equivalent to present participles: ‘ … SEDERE, id est persona sedens, quae scilicet sessione affecta est, NON est ipsa positio, sed DENOMINATIUE dicitur a positione, quia scilicet nomen habet hoc quod est sedens, denominatiuum a sessione'. (Abaelard, ‘Ingredientibus’, 203).

¹¹The claim that ‘iacere’ is denominated from ‘accubitus’ translates the claim in Greek that ‘anakeisthai’ is denominated from ‘anaklisis’. The verb should presumably be as Minio-Paluello suggests ‘anakeklisthai’(Categoriae, 19). Abaelard notices the problem here and suggests a different solution: ‘Et notandum, cum iacere ab accubitu denominatiue non dicatur apud nos, apud Graecos fortasse denominatio erat in illis <quae> pro istis accipiuntur. Poterit fortasse dici, quod denominatiuum large hoc loco accipit pro sumpto' (Abaelard, ‘Ingredientibus’, 203).

¹²Omnis autem denominatio non est id quod est ea res, de qua nominatur, ut grammaticus non enim idem est quod grammatica, de qua nominatus est. Quocirca, si sedere de sessione et stare de statione denominatiuum est, sessio uero et statio relatiua sunt; sedere et stare, quae a relatiuis denominatiua sunt, relatiuorum genere non tenentur. Et uniuersaliter quicquid ex quibuslibet positionibus denominatur, illud non ad relatiua sed ad praedicationem, quae situs dicitur, reduci potest. (Boethius, In Categorias, 220B–C).

¹³Ammonius, In Categorias, 69.1–21.

¹⁴Boethius, In Categorias, 221D–222B. Philoponus (In Categorias, 110.1–111.8) also had both ‘unequal’ and ‘equal’ in his text of the Categories and raises the same problem. Simplicius (In Categorias, 177.1–14) had a text which did not include ‘equal’ and he explains why more or less apply to unequal but not to equal. He goes on, however, to consider how the equal and unequal can admit of more and less since they apply only to quantity. His answer is just that given by Boethius – equal and unequal are qualities of quantities – equal is similarity of quantity and similarity is a quality.

¹⁵In particular the Vatican version of the text C8 to be discussed below.

¹⁶Prima namque praedicatio est ab ala. Dicimus enim alam auis, et hoc quaerimus ut ad alam praedicatio conuertatur. Ergo ab eo quod prius dicitur, illi ad quod conuertitur nomen fingendum est, ut ea quae prius dicitur ala, rei ad quam conuertitur sic ut conuenienter aptetur, fingendum est nomen alatum, quod ipsum ex ala denominatum est, atque hoc idem et in caeteris relatiuis licet intelligi. (Boethius, In Categorias, 225D–226A)

¹⁷Aristotle, Categories, 8b15–21. Aristotle's claim about heads here has rightly exercised commentators who point out that he notoriously maintains elsewhere that detached body parts are only homonymously referred to with the name of the attached part. See Aristotle, Categories, 101.

¹⁸‘ … sunt ad aliquid quibus hoc ipsum esse est ad aliquid quodam modo habere'. (Aristotle, Categoriae, 22.20–21). ‘Ad aliquid quodam modo habere’ or ‘se habere’ as Boethius gives the lemma translates Aristotle's ‘pros ti pōs echein’. On Aristotle's use of this phrase and its history see Sedley, ‘Aristotelian Relativities’.

¹⁹Videsne ut habitudine quadam et comparatione res aliud in natura retinentes, aliud tamen ad se inuicem sint? et hoc non ex propria sed ex inuicem natura mutuentur, nam quod est duplus numerus ex medio trahit, quod est medietas ex duplo, atque hoc iis quae sunt ad aliquid extra euenit, et ideo nihil patientibus neque permutatis ipsis quae ad aliquid referuntur, ipsa ad aliquid fiunt, nihil enim permutato de quaternario duplus ipse est, si ad binarium referatur, et nihil de binario permutato, medietas est binarius, si ad quaternarium dicitur. (Boethius, In Categorias, 236A–B).

²⁰Simplicius stands apart from this tradition in denying that such change is accidental. See Luna, ‘La Relation Chez Simplicius’, 140–5; Harari, ‘Simplicius on the Reality of Relations’, 261–9.

²¹Aristotle, Categories, 8a35–7. ‘hōrismenōs’ translated as ‘definite’ by Boethius.

²²Sedley, ‘Aristotelian Relativities’, calls this the ‘principle of cognitive symmetry’.

²³The received text has Aristotle claiming in Ackrill's translation: ‘For whose this (tinos gar hautē) head is, or whose the hand, it is not necessary to know definitely'. Sedley points out that the problem raised by Aristotle concerns secondary substances and argues for an emendation which will allow us to read Aristotle as offering a solution to it. If we read ‘autē’ rather than ‘hautē’ we have Aristotle claiming that ‘it is not possible to know definitely to what it is that head or hand as such belongs’. Sedley (‘Aristotelian Relativities’, 331) argues that cognitive symmetry fails in the case of a head because a headed thing is not the kind of thing which can be known definitely. Like the Greek commentators, however, Boethius read ‘hautē’ and translated the claim as ‘cuius enim hoc caput uel cuius haec manus non est dicere definite’ – where Boethius has ‘dicere’ the received Greek text has ‘eidenai’.

²⁴Iwakuma, ‘Vocales Revisited’.

²⁵‘C8’ etc. are the numbers assigned to the texts in Marenbon, ‘Medieval Latin Commentaries and Glosses’.

²⁶Iwakuma, ‘Vocales Revisited’, 89–91.

²⁷Mutant alii hanc sententiam, et non dicunt idem esse positionem et situm esse generalissimum, sed dicunt positionem esse subalternum genus in qualitate et habere species accubitum, stationem, sessionem. … Situm esse quoddam est generalissimum tota essentia a qualitate diversum, habet ipsum quoque suas species quae eisdem nominibus appellantur, sed tamen tota essentia diversae sunt … (Q 36rb).

²⁸Positio est alicuius rei secundum locum collocatio, id est quaedam res secundum quam res dicuntur in aliquo loco sitae, ut sunt statio, sessio, accubitatio, etc, secundum quas substantiae quibus adiacent dicuntur esse sitae, id est sedentes, stantes, accubita[e]<ntes>. Et ita descriptum hoc generalissimum situm esse, id est positio, significat omnes eas res et eas tantum quae aliis rebus adiacent et secundum [eas] <quas> aliae res [quae] in aliquo loco dicuntur esse sitae, ut statio et cetera huiusmodi. (P 210va) [] = proposed deletion, <> = proposed addition or emendation.

²⁹Item dici potest quod <hoc> generalissimum, esse situm, vel positio, est nomen vocum positarum in suo praedicamento vel sumptarum a vocibus positis in suo praedicamento, sicut dictum est in aliis praedicamenti, ut nomen huius vocis ‘statio’ et nomen sui sumpti, scilicet ‘stans’. (P 210va).

³⁰Quod itaque quaelibet substantia iacens aut stans aut sedens dicitur, ex quibus<dam> adiacentibus positionibus uenit, a quibus haec denominatiua esse Aristoteles in tractatu Ad Aliquid docet, cum enim positionem quoque relationibus secundum platonicam definitionem adiungeret. … ex quibus quidem uerbis magna solet esse dubitatio. Cum enim iacere et stare positiones esse concedantur, a positionibus ipsa denominatiue non dicuntur. (Abaelard, Dialectica, 81).

³¹Unde quidam (quorum unus, memini, magister noster erat) ‘positionis’ nomen ad qualitates quasdam aequiuoce detorquent atque etiam ipsarum nomina specierum ‘statio’, ‘sessio’ etc., a quibus ipsos situs denominari dicunt tamquam a quibusdam proprietatibus suis, ita quidem ut sessio situs a sessione qualitate denominari dicatur. (Abaelard, Dialectica, 82).

³²‘Quod autem <statio> sit actio et species situm esse, habet auctoritas; sed quod qualitatis species accipiatur, nec auctoritas habet nec ratio cogit'. (Q 36rb on Categories, 7) ‘Volunt et alii sessionem sub qualitate accipere. Sed ut sub qualitate accipiatur, nec habet auctoritas nec cogit ratio'. (Q 48ra on Categories, 9).

³³The text of V is difficult to construe here and perhaps corrupt and it is not quite clear whether the theory that positio and situs are not identical which is described there is being advocated or attributed to others. P does not discuss the question.

³⁴See Tarlazzi, ‘“Iam Corpus” or “Non Corpus”’, # 1 Material Essence Realism, and the sources cited there for recent discussions of William's theory.

³⁵Omnibus paene videtur quod ‘numerus’ istud nomen significet quandam rem generalem in essentia quae substantialibus formis affecta redigatur in species, … quemadmodum animal illa res generalis per substantiales formas efficitur homo, homo item per accidentia efficitur Socrates, quae res una et eadem numero in actu rerum reperitur (V 51rb-va). V here apparently wishes only to reject the application of material essence realism to number while accepting the theory applied to substance. For the theory of individuation by accidents as a characteristic component of material essence realism, see Tweedale, Abailard on Universals, 107–9; Tarlazzi. ‘“Iam Corpus” or “Non Corpus”’, 6. The theory of individuation by accidents is rejected by Abaelard.

³⁶Eph. 3, 15.

³⁷‘Paternitas enim praecedit filiolitatem … ’ (Eriugena, Periphyseon II, 102, l. 2486 (600B)).

³⁸ … hae duae voces ‘ad aliquid’ et ‘relativum’ idem prorsus significant. Et accipiuntur diversis modis. Cum enim proprie sint adiectiva nomina, videlicet sumpta a relatione, ponuntur tamen interdum ut subiecta, et significant idem quod ‘relatio’. Nam quemadmodum ‘relatio’ est nomen ipsius generalissimi et omnium rerum sub eo contentarum, ita et illa nominant omnes relationes in essentia. Quemadmodum etiam ‘relatio’ accipitur nomen vocum relationes in essentia significantium, ut huius vocis quae est ‘paternitas’ et similium, ita illa duo. (V 56va-b).

³⁹Vel sic describitur: AD ALIQUID SUNT ILLA QUIBUS EST HOC IPSUM ESSE AD ALIUD SE HABERE … . In qua definitioni ideo non includitur generalissimum, quia ipsum in sua simplicitate ad aliud se non habet, sed per suas species potest ei convenire, quemadmodum nec individuis potest convenire nisi per suas species. In se enim considerata individua relationis non habent se ad aliud, ut quibusdam videtur … (V 56vb).

⁴⁰See the text quoted above in n. 34.

⁴¹Et nota hoc nomen ‘ad aliquid’ secundum hoc impositum <est> relativis quod ipsa quidem cum per se nihil sint, relativa tamen ad aliud constant, hoc est quibus ad aliud se habere ita est esse ut sine hoc esse non possint, sicut nec <homo> sine rationalitate. (V 56vb).

⁴² V 59va. In Categories 10 Aristotle characterises relatives as opposed to one another in a modified version of the predicative description: ‘What are opposed as relatives are said as that which they are of their opposites or in some other way relative to them'. (Aristotle, Categories, 11a24–25).

⁴³Generalissimo tamen in sua simplicitate accepto convenire non potest ut referatur ad aliud, quia neque ad rem sui praedicamenti neque ad <rem> alterius praedicamenti. Quod ad rem sui praedicamenti non referatur, hoc modo probatur: Quia neque ad paternitatem neque ad aliud. Ad paternitatem non refertur, quia paternitas iam poneretur ad positionem relationis et paternitas destructa destrueret relationem … Et de aliis similiter probare poteris. (A 31va).

⁴⁴Et <quamvis> habere se ad aliud non sit substantiale relationibus. Per se enim considerat<ur> est purum accidens, tamen in eo intelliguntur formae substantiales speciei relationis, velut habere se ad paternitatem quod est substantiale filiationi, et habere se ad filiationem quod est substantiale paternitati, non tamen paternitas est substantiale filiationi vel filiatio paternitati. (V 59va).

⁴⁵Both V and QA phrase the argument in terms of individual denominated relatives but since these can be related only if the corresponding individual relations are related and V poses the question in terms of both relatives and relations I have formulated it in terms of the latter.

⁴⁶Sed nec diversa individua patris possunt ibi referri, ad diversa individua <filii.>. Si enim diversa individua patris possunt ibi referuntur, tunc sunt in eodem; et si diversa individua patris sunt in eodem, tunc unus pater est plures patres, et ista est multi homines; et ita unus homo est plures homines, quod esse non potest. (V 59vb).

⁴⁷<sed> videtur incongrua propter <hoc> quod notat <?possessionem?> non relationem, et etiam propter sensum quod nullus est. (V 60ra).

⁴⁸Nam cum omne accidens in se consideratum sit universale, participatione vero individuae rei fiat individuale, paternitas adveniens Socrati individuatur, et manente Socrate in eodem, id est non mutato in eodem, paternitas individuari nequit. Nulla quippe posset notari differentia inter haec duo <in>dividua paternitatis, cum subiectum idem esset … . (V 60ra).

⁴⁹See n. 34 above.

⁵⁰But it does include interesting digressions, for example on the nature of comparison and whether comparative terms are relative leading to a discussion of the proper exposition of the comparison of items over time. J. Brower (‘Abelard's Theory of Relations’) claims that Abaelard develops a new theory of relations in the Ingredientibus but he unfortunately relies on a faulty transcription of the relevant text by Geyer. Where Geyer and following him Brower read ‘supponunt’ the manuscript has ‘supponit’. Once the reading is corrected and Geyer's unnecessary emendations ignored, it is clear that Abaelard is not claiming as Brower has him something about ‘underlying being’ but rather simply quoting Aristotle here: ‘sunt RES illae quibus est hoc ipsum esse quod supponit [Geyer mistranscribes as “supponunt”], scilicet “habere se ad aliud” (ms. Milan, Ambrosia M 63, 29r).

⁵¹Glossing the codependency description Abaelard uses ‘essentia’ to indicate ontological commitment: … id est quorum essentiae ita ad inuicem sese habent, ut non solum in subiectis suis simul naturaliter consistant, uerum circa ea ad se inuicem referuntur ac secundum se subiecta ipsa ad inuicem faciunt respicere, ut sunt paternitas et filiatio … (Abaelard, Dialectica, 83). Non dico quidem quin substantia patris absque substantia filii uel essentia filii absque essentia patris subsistere queat in suae proprietate personae uel in natura substantiae … sed in proprietate relationis, easque se<paratim> posse esse denego, ut nulla uidelicet substantia in proprietate patris esse queat, nisi aliqua sit in proprietate filii, et si qua filiationis formam susceperit, simul et aliquam formam paternitatis necesse est indui … . (Abaelard, Dialectica, 84).

⁵²Est enim, ut Aristoteles docuit, esse relatiuorum habere se ad aliud, id est ipsa proprietas secundum quam ipsum subiectum ad alterum respicit, ipsa est relatio, ut paternitas, quae hanc substantiam cui adiacet, ad illam cui filiatio inest, respicere facit, secundum id scilicet quod hic est illius pater. (Dialectica, 86).

⁵³Dicamus itaque omni ac soli relationi eius definitionem conuenire, ipsique relationi generalissimo, circa ipsa quoque eius indiuidua idque quod est omni ei conuenire. Si enim indiuiduis aptari non posset, nec utique speciebus essentiae. Neque enim substantia specierum diuersa est ab essentia indiuiduorum, … , nec res ita sicut uocabula diuersas esse contingit. (Dialectica, 89).

⁵⁴Et cum quaelibet substantia multis aliis secundum aequalitatem conferatur, quot in aliis erunt aequalitates, tot in ipsa eadem quae ad eas respicit, oportet intelligi. Similiter et de paternitate et de aliis relationibus, ut uidelicet cum idem sit pater diuersorum, quot sunt in diuersis filiationes, tot erunt in ipso paternitates. (Dialectica, 89).

⁵⁵‘ … etsi enim genitiuo non possit fieri, alio tamen modo potest assignari, ut uidelicet dicamus hic pater ad hunc filium hic pater uel quolibet alio modo dum hanc paternitatem gratia illius filiationis existere monstramus’ (Dialectica, 89). Likewise, Abaelard holds that unlike the denominated relatives the substantive names of relations do not satisfy the predicative requirement formulated using the genitive. We can, however, he tells us, indicate their connection in a different way: ‘Et nos quidem fortasse idoneam de substantiuis quoque nominibus relationem possumus componere, sed <non> iuncta per genitiuum, ut dicamus: “paternitas filiationis paternitas”, sed ita potius: “paternitatis essentia ex filiatione pendet” et “subsistentia filiationis ex paternitate” uel quolibet alio modo’ (Dialectica, 91).

⁵⁶The anonymous reviewers of this article both pointed out that an article on the subject has just been published though it was not available to me when I wrote and revised the paper. See now Erismann, ‘Paternité multiples’.