Abstract
As is well known, medieval logicians gave a lot of attention to the analysis of different sophisms in which there are propositions that include complex terms one of whose parts is a term in an oblique case. The propositions ‘cuiuslibet hominis asinus currit, ‘ab omni homine enuntiatum est verum / ab utroque istorum enuntiatum est verum’, ‘omnem hominem videns currit’, ‘omnis homo videt omnem hominem’, ‘utrumque oculum non habens potes videre‘, ‘omne caput habens est unum solum caput habens’, which receive attention in all kinds of treatises1 (Instantiae,2 Abstractiones,3 Distinctiones,4 Sophismata,5 Syncategoremata,6 Summulae,7 in the commentaries to the Analytica Priora 8 and to the Sophistici Elenchi,9 etc.), seem to be the most famous representatives of
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Notes
Concerning the history and characteristic features of different logical literary genres, see: H.A.G. Braakhuis, De 13de Eeuwse Tractaten over Syncategorematische Termen, 2 vols., Meppel: Krips Repro. 1979; N. Kretzmann, “Syncategoremata, exponibilia, sophismata”, in The Cambridge History of Later Medieval Philosophy, ed. N. Kretzmann, A. Kenny, J. Pinborg, Cambridge: Cambridge University Press 1982, pp. 211-45; A. de Libera, “La Litterature des ‘Abstractiones’ et la Tradition Logique d’Oxford”, in The Rise of British Logic, ed. P.O. Lewry, Papers in Mediaeval Studies 7, Toronto: Pontifical Institute of Mediaeval Studies 1985, pp. 63-114; L. M. De Rijk, Some Earlier Parisian Tracts on Distinctiones Sophismatum, Artistarium 7, Nijmegen: Ingenium 1988.
Y. Iwakuma, “Instantiae. A Study of Twelfth Century Technique of Argumentation with an Edition of Ms. Paris BN Lat. 6674 f. 1-5”, Cahiers de l’Institut du Moyen Age Grec et Latin 38, 1981, pp. 40–41.
See Alain de Libera, “Les ‘Abstractiones’ d’Hervé le Sophiste (Hervaeus Sophista)”, Archives d’Histoire Doctrinale et Litteraire du Moyen Age 52, 1985, pp. 163-230 (especially, pp.168, 176, 187 (sophism 26), 188 (sophism 29), 190 (sophism 44)).
De Rijk, Some Earlier Parisian Tracts, especially, pp. 61–68 and 197-202.
Albertus de Saxonia, Sophismata, Paris 1502, repr. Georg Olms Verlag, Hildesheim-New York, 1975, sophisms VI, VII, VIII and XLIII.
J. R. O’Donnell, “The Syncategoremata of William of Sherwood”, Mediaeval Studies III, 1941, pp. 46-93, especially pp. 51–3.
In chapters devoted to the “suppositio terminorum”, or to the “fallacia figurae dictionis”, the analysis of this kind of proposition is a commonplace. A. de Libera, “Les Summulae Dialectices de Roger Bacon. I-II De Termino, De Enuntiatione”, Archives d’Histoire Doctrinale et Litteraire du Moyen Age 53, 1986, pp. 171-289, especially, p. 267(434): De Suppositione; A. de Libera, “Les Summulae Dialectices de Roger Bacon. III De argumentatione”, Archives d’Histoire Doctrinale et Litteraire du Moyen Age 54, 1987, pp. 171-272, especially, pp. 256-7 (585 and ff.): De fallacia figura dictionis); Peter of Spain, Tractatus, called afterwards Summule Logicales, ed. L.M. De Rijk, Assen: Van Gorcum 1972, especially pp. 222-4; Logica (Summa Lamberti), ed. F. Alessio, Firenze: La Nuova Italia Editrice 1971, especially pp.172-3.
The question ‘De syllogismis ex terminis obliquis’ is one of the places in which the analysis of this kind of proposition is ordinarily tackled. See R. Kilwardby (attributed to Aegidius Romanus), In Libros Priorum Analyticorum Expositio, Venetiis 1516, repr. Frankfurt: Minerva G.M.B.H. 1968, especially f. 46rb; Iohannis Buridani Tractatus De Consequentiis, ed. H. Hubien, Louvain-Paris: Publications Universitaires 1976, especially, pp. 98-104; Albertus de Saxonia, Perutilis Logica, Venetiis, 1522, repr. Hildesheim-New York: George Olms Verlag 1974, especially ff. 29vb-30rb.
The question ‘De fallacia figura dictionis’ is another of the places in which the analysis of this kind of proposition is usually tackled.
Other important parts of this Medieval Logic of Three-Term Propositions are those referring to propositions that have, as parts, disjunct or conjunct terms, or to reduplicative propositions.
Other important parts of this Medieval Logic of Relations are those referring to the terms of the category of relation, or to the relative pronoums.
Such questions, already quite clearly stated in the second half of the twelfth century, were the object of attention until at least the beginning of the sixteenth century, when, in my opinion, they attained their maximum development on the ocasion of the treatment of the suppositio mixta, on the part of the logicians of John Mair’s school. See E. J. Ashworth, “Multiple Quantification and the use of Special Quantifiers in Early Sixteenth Century Logic”, Notre Dame Journal of Formal Logic 19, 1978, pp. 599-613, repr. in idem, Studies in Post-Medieval Semantics, London: Variorum Reprints 1985. Discussions regarding such questions have at times gone beyond the limits of purely logical discourse and have attained considerable cultural significance. Thus, on the one hand, some of the theses defended in this regard were the object of the Oxford condemnations of 1277, and, on the other hand, humanists such as Thomas More and Vives found in these questions the occasion for their critique of scholastic logicians and philosophers. See, regarding these matters, V. Muñoz Delgado, “La Logica en las condenaciones de 1277”, Cuadernos Salmantinos de Filosofía 4, 1978, pp. 17-39; P.O. Lewry, “The Oxford Condemnations of 1277 in Grammar and Logic”, in English Logic and Semantics. From the End of the Twelfth Century to the Time of Ockham and Burleigh, ed. J. Pinborg, Artistarium, Supplementa I, Nijmegen: Ingenium 1981, pp. 235-78.
See nn. 18 and 20.
See n. 17.
“Si vero terminus obliquus praecedat terminum rectum, tunc nihil est subiectum, loquendo de subiecto quo ad logicum, nisi terminus obliquus, et totum residuum se tenet ex parte praedicati, ut patet in ista: ‘cuiuslibet hominis asinus currit’, et in consimilibus; hic nihil est subiectum nisi li ‘hominis’, et residuum se tenet ex parte praedicati.” W. Burley, De Puritate Artis Logicae. Tractatus Longior, p. 41. “Conclusio ergo quod sicut in sophismate solum ly ‘hominis’ distribuitur ita solum ly ‘hominis’ subiicitur et non hoc aggregatum ‘hominis asinus’. Sed diceres contra: in praedicta propositione ponitur ly ‘asinus’, ergo oportet quod sit pars praedicati, et hoc non quia precedit copulam, vel pars subiecti, et sic habetur intentum. Respondetur quod est pars predicati, et dico quod non est inconveniens partem predicatiali quando precedere copulam, immo aliquando totale predicatum precedit copulam, sicut in ista propositione: ‘homo animal est’; tunc dicendum est quod in predicta propositione solum ly ‘hominis’ sit subiectum.” Albert of Saxony, Sophismata, sophisma viii. In the Perutilis Logica, however, Albert seems to defend the opposite thesis: “4a suppositio. Cum syllogicamus ex obliquis, non oportet quod maior aut minor extremitas sit subiectum vel predicatum alicuius premisse, nec oportet quod medium syllogisticum sit subiectum vel predicatum in antecedente. Unde aliquando valet Syllogismus ex obliquis et medium syllogisticum nec est subiectum nec predicatum in maiore, nec pars subiecti nec pars predicati; similiter nec maior extremitas nec minor est subiectum vet predicatum in conclusione nec in premissis.” (f. 30ra). “Si vero terminus obliquus precedat terminum rectum, tunc nihil est subiectum secundum logicum nisi terminus obliquus, et totum residuum se tenet ex parte predicati.” Vincent Ferrer, Tractatus De Suppositionibus, Stuttgart — Bad Canstatt: Frommann-Holzboog 1977, p. 138.
“Dubitatur hic primo an de obliquis syllogizari possit vel non. Videtur enim quod non: eadem enim est materia propositionis et enunciationis, quia ipse eadem sunt in subiecto, sed enunciationis principia materialia sunt scilicet nomen et verbum, quare propositionis similiter; sed nomen solum rectum est et verbum similiter, quare ex obliquis non fiet propositio syllogistica sicut nec enunciatio.” R. Kilwardby — attributed to Aegidius Romanus, In Libros Priorum Analyticorum Expositio, f. 46rb.
“Ad aliud dicendum quod si propositio et enuntiatio sint idem in substantia, differunt tarnen in essentiis sive ratione. Quod partes enuntiationis sunt nomen et verbum finiti modi exigit quod nomen ei supponens sit in rectitudine, hoc autem est subiectum; unde in enuntiatione semper subiicitur rectus. Aliter autem est de propositione, quia verbum non est pars ipsius propositionis, quia quicquid est pars ipsius propositionis est primum vel medium vel postremum in sillogismo. Subiectum ergo et predicatum sunt partes propositionis, sed subiectum et predicatum sunt nomen et verbum, et verbum predicatur lam in rectitudine quam in obliquitate et tarn <nomen> rectum quam nomen obliquum potest subici in propositione, in enuntiatione autem non.” Sophismata Parisius Determinata, ff. 14va-b, quoted in L.M. De Rijk, “Each man’s ass is not everybody’s ass. On an important item in 13th-century semantics”, Historiographia Linguistica, 7 1/2, 1980, p. 227. “Alii solvunt aliter, et dicunt quod prima est duplex ex eo quod potest iudicari penes subiectum propositionis vel penes subiectum enuntiationis. Subiectum vero propositionis appellant subiectum illud <sub> quo sicut sub medio potest aliquid sumi […] Subiectum vero enuntiationis nomen rectum appellatur (ex solo enim verbofinito et nomine recto componitur enuntiatio, sicut dicit Aristotiles).” Tractatus Florianus de solutionibus sophismatum, f. 42va. “Et respondendum ad primum quod enunciationis secundum quod huius(?) et propositionis secundum quod propositio non est necesse eadem esse principia materialia. Propositio enim in ratione propositionis potest habere pro subiecto quod enunciatio secundum quod huius(?) habet pro determinatione subiecti […] Si considerentur principia eius secundum quod propositio est et secundum quod enunciatio est potest enim proposition habere subiectum secundum obliquum et secundum rectos, sed enunciatio solum secundum rectum, et hoc est quod solet dici, et bene, quod duplex est subiectum, scilicet, propositionis et enunciationis.” R. Kilwardby, In Libros Priorum Analyticorum Expositio, f. 46rb.
These questions were already clearly formulated in the Ars Meliduna: “Dehinc queritur de quantitate earum quarum subiecti ex obliquo constant et recto.” (f. 227rb) “Notandum iterum quod non semper definiendum de quo fiat sermo indefinita propositione vel particulari per id totum quod ponitur in subiecto.” (f. 237va), quoted in L.M. De Rijk, Logica Modernorum, vol. II, part I, Assen: Van Gorcum 1967, p. 327 and p. 368.
“Sciendum tarnen quod in talibus solebat distingui duplex subiectum, scilicet, subiectum propositionis et subiectum locutionis. Subiectum propositionis est illud quod est subiectum quo ad logicum, et est illud sub quo debet fieri sumptio in syllogismo perfecto. Subiectum vero locutionis est subiectum quo ad grammaticum, et est illud quod redit suppositum verbo. Unde in ista ‘cuiuslibet hominis asinus currit li ‘hominis’ est subiectum propositionis et distributionis, sed iste terminus ‘asinus’ est subiectum locutionis, tarnen se tenet ex parte praedicati loquendo de praedicato propositionis.” W. Burley, De Puritate Artis Logicae. Tractatus Longior, St. Bonaventure, N.Y.: Franciscan Institute 1955, p. 41.
This twofold possibility was already suggested in the Ars Meliduna: “Hoc etiam non nisi ab his dicendum videtur qui dicere consueverunt substantivum terminum supponere, verbo adiectivo circa eius rem determinante proprietatem.” (f. 237va, quoted in De Rijk, Logica Modernorum, vol. II, part I, p. 368). See also the text of R. Kilwardby quoted in n. 17.
“Ideo litem de media tollentes dicimus quod suppositio potest fieri turn per obliquum, ut sit propositio singularis, turn per orationem ex obliquo constantem et recto, ut <sit propositio> indefinita. Singulari autem agitur de aliquo discrete, ut de Socrate, de quo dicitur sui asinum esse album.” Ars Meliduna, quoted in De Rijk, Logica Modernorum, vol. II, part I, p. 369).
“Et dixi ‘manens syncategorematica’, quia si dictio syncategorematica fieret pars extremi, quod contingit quando disponit partent extremi, tunc talis dictio non tenetur syncategorematice nec manet ut syncalegorema, et lunc non habet virtutem confundendi terminum communem mediate sequentem confuse tantum.” W. Burley, De Puritate Artis Logicae. Tractatus Longior, p. 21.
The linkage of the functions of terms to their position in the proposition seem to find its root in the framework of the doctrine of conversion, a doctrine which is of extraordinary logical importance, both for its relevant role in the development of syllogistic doctrine, and for the important role which, without doubt, it played in the constitution and development of the doctrine of the suppositio.
To the subject term ‘homo’ there corresponds, in the universal, a confused and distributive suppositio, and, in the particular, a determinate suppositio, by virtue of the different syncategoremata (‘omnis’ / ‘quidam’) which in each case, and by virtue of the fact of their concordance, affect it. To the predicate term ‘albus’ there corresponds, in the universal, a suppositio confusa tantum, and, in the particular, a confused and distributive suppositio, but, ordinarily, in order to justify the attribution of this species of suppositio, we no longer appeal, as we might have done, to its function as a predicate affirmed or denied with respect to a subject taken in distributive or determinate manner, but rather presupposing the order subject-copula-predicate to be the normal order, we appeal to its position with respect to the syncategoremata, ‘omnis’ or ‘non’, that precede it. In this manner, we attribute to the sign ‘omnis’ a distributive effect over the term that immediately follows it and a confusive power over all the terms that follow it in a mediate manner, and to the sign of negation ‘non’ a distributive power over all the terms that follow it. Thus the way is open for new forms of propositions; for example, in the proposition ‘quidam homo albus non est’ — which initially could have been considered as a synonym with the negative particular — in so far as the predicate ‘albus’ does not follow the sign of negation, we can no longer say that its predicate is distributed, but rather determinate, and therefore the latter constitutes a new type of proposition which is distinct from the four types A, E, I, O that are usually considered.
“Ad hoc dicendum quod haec ‘cuiuslibet hominis asinus est albus’ duplex est, ex eo quod suppositio huius termini ‘asinus’ potest multiplicari vel non. Non autem ostenditur causa ex vi locutionis quare debeat simpliciter multiplicari, sed quod multiplicetur hoc est ab intentione loquentis.” Tractatus De Propietatibus Sermonum, quoted in De Rijk, Logica Modernorum, vol. II, part II, p. 719. “Unde ad hoc est magna diligentia adhibenda utrum rectus precedat obliquum vel e converso. Et quandocumque ponitur aliqua propositio ab aliquo philosopho vel doctore, recto precedente obliquum vel e converso, semper trahenda est ad bonum sensum intellectum […] Et ideo quando aliqua propositio alicuius philosophi vel doctoris allegatur contra regulas scientie logicalis, communiter solet distingui, et bene, quod talis propositio dupliciter potest sumi, quia vel de virtute sermonis vel de bonitate intellectus, vel quod idem est, potest dupliciter sumi, scilicet, vel in sensu quern facit vel in sensu in quo fit.” Vincent Ferrer, Tractatus De Suppositionibus, p. 139.
For example, it is not enough to say that the difference between the propositions ‘cuiuslibet hominis asinus est albus’ and ‘asinus cuiuslibet hominis est albus’ is located in the fact that ‘asinus’, in the first proposition, has a suppositio confusa tantum, because it mediately follows the universal syncategorema ‘cuiuslibet’, whereas in the second proposition it has a determinate suppositio because it precedes it, since ‘albus’ also follows, in both cases, the syncaregorema ‘cuiuslibet’, and yet the suppositio confusa tantum which in virtue of such a criterion would correspond to it, is not assigned to it in both cases.
Such moments or stages possess, without doubt, a clear chronological component, but they could also have geographical components or be linked to certain schools.
“Quando haec dictio ‘omnis’ preponitur orationi constanti ex recto et obliquo, tunc comprehendit omnia appellata illius orationis, ut ‘omnis filius hominis currit’. Si vero interponatur recto et obliquo ita quod precedat rectum, tunc comprehendit omnia appellata illius recti, non absolute tarnen, sed respectu unius appellati obliqui, ut cum dicitur ‘hominis omnis filius currit’. Si vero precedat obliquum, comprehendit omnia appellata illius obliqui, ut ‘videns omnem hominem currit’.” Tractatus Anagnini, quoted in De Rijk, Logica Modernorum, vol. II, part II, p. 299.
The limits detected are not limits that are intrinsic to the positional criteria in themselves, but rather they derive from the particular and restricted usage which medieval logicians made of them. Due to requirements of grammatical concordance, they could not apply positional criteria with all the freedom that is required in order to solve the problems they were faced with.
“Et secundum istum intellectum debet fieri punctuatio et pausa inter ly ‘pater’ et ly ‘patris filii’. ita quod punctuetur sic ‘omnis pater. patris filii est pater’.” Albert of Saxony, Sophismata, sophism VII. See also n. 22.
“Solutio: Ad primum dicendum quod verum est, sicut probatum, cum ille terminus ‘asinus’ respiciatur mediate ab hoc signo universali ‘cuiuslibet’, unde confunditur exiliter, et ita, secundum exigentiam locutionis, stat pro pluribus particularibus asinis pro quibus locutio vera est. Ad hoc autem quod postea infertur ‘ergo asinus cuiuslibet hominis currit’, dicendum quod non valet <quia> cum ille terminus ‘asinus’ precedat signum, non confunditur ab ipso, et indeterminate tenetur pro aliquo, pro locutio est falsa. Et in tali argumentatione est fallacia figure dictionis, scilicet, univocatio ex mutata suppositione termini, quia ille terminus ‘asinus’ primo confusam habet suppositionem, in conclusione vero determinatam.” Dialectica Monacensis, quoted in De Rijk, Logica Modernorum, vol. II, part II, p. 614.
See n. 22.
“Verbi gratia sic dicendo ‘videns omnem hominem est animal’, in ista propositione non stat iste terminus ‘animal’ confuse tantum sed determinate; sequitur enim ‘videns omnem hominem est animal, ergo animal est videns omnem hominem’, et econverso; et in ista ‘animal’ supponit determinate, et ideo supponit determinate in alia.” W. Burley, De Puritate Artis Logicae. Tractatus Longior, p. 21.
This is the reason why the sophisms ‘ab omni homine enuntiatum est verum’ and ‘ab utroque istorum enuntiatum est verum’ cannot have the same solution. See Peter of Spain, Tractatus, called afterwards Summule Logicales, ed. L.M. De Rijk, Assen: Van Gorcum 1972, pp. 222-4.
J.R. O’Donnell, “The Syncategoremata of William of Sherwood”, Mediaeval Studies 3, 1941, pp. 46–93. Sherwood’s texts will be quoted from this edition.
N. Kretzmann, William of Sherwood’s Treatise on Syncategorematic Words, Minneapolis: University of Minnesota Press 1968, pp. 32–4.
L.M. de Rijk, “Each man’s ass is not everybody’s ass” (see n. 17 above), pp. 221–230.
p. 52.
p. 33, n. 61.
p. 222.
P. 51.
“Sherwood’s fundamental objection is that the alternate analysis supposes that there are two admissible readings of these expressions. His own position is, in effect, that Rule [IV] makes only one reading admissible” (Kretzmann, op. cit., p. 34, n. 63); “For that matter, when dealing with the above sophism Sherwood rejects the opponents’ analysis simply by appealing to the plain structure of the sentence (i. c, word order) which admits of one interpretation only.” (De Rijk, op. cit., p. 221).
p. 34, n. 64.
p. 221.
Kretzmann, p. 33, n. 60; De Rijk, p. 222.
Kretzmann, p. 34, n. 64; De Rijk, pp. 221-5.
“The sophisma requires that ‘each man’s ass is running’ be taken in two senses: [a] for each man x there is an ass y such that x owns y and y is running’; [b] ‘there is an ass y such that each man owns it and it is running.’ Sense [a] is the one supported by the hypothesis, but sense [b] is the one that supports ‘Brownie is running’, which is false; and in sense [a] ‘ass’ has merely confused supposition while in sense [b] it has determinate supposition.” (Kretzmann, p. 33, n. 61)
“It is therefore tempting to assume that our MSS wrongly read ‘cuiuslibet hominis asinus’ (rather than ‘asinus cuiuslibet hominis’) in the assumption.” (De Rijk, p. 222)
See n. 47.
“Sherwood says that our sophism falls within the scope of the previous ones, because the supposition of the word ass is changed in a similar way as there. Indeed, in the first premiss of the syllogism ass (asinus) is taken in merely confused supposition, confuse tantum, in the assumption in determinate supposition. […] Sherwood most certainly must refer to the word order (see his Rule IV) as supporting the determinate supposition of ass in the assumption.” (De Rijk, p. 222)
“The point of Sherwood’s solution could, it seems, have been made at least as readily and perhaps more in keeping with his previous solutions if he had put it in terms of determinate and merely confused supposition rather than in the roughly corresponding terms of hoc aliquid and quale quid.” (Kretzmann, p. 33, n. 60)
See n. 50.
“Sherwood, however, rejects energetically this latter interpretation — he even calls it nonsense (hoc nichil est) — giving in fact two reasons for his rejection: first, a reference to the rule given: ‘when the phrase “each man’s” precedes the word “ass” (i. e. in “cuiuslibet hominis asinus”) the sign “each” has power over the nominative case “ass”, and so the phrase “cuiuslibet hominis asinus” is to be judged starting from the distributive sign’; in other words, taking asinus, too, as confused by cuiuslibet, not only man; and so any determinate supposition of asinus is excluded, and, accordingly, any ambiguity of the phrase ‘cuiuslibet hominis asinus’ as well.” (De Rijk, p. 223)
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d’Ors, A. (1993). Hominis Asinus/Asinus Hominis. In: Read, S. (eds) Sophisms in Medieval Logic and Grammar. Nijhoff International Philosophy Series, vol 48. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1767-8_22
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