Oreste Delucca's biographical contribution to Gregorio da Rimini filosofo (2003) makes the origins of the nickname Tortor Infantium seem even murkier:
‘Quanto al casato di Gregorio, taluno lo dice appartenere alla famiglia Tortorini, o Tortorucci, o Tortorici; ma non si hanno prove documentarie al riguardo, per cui l'affermazione viene accolta con prudenza, ignorata o addirittura rigettata da molti storici.’ (p. 46)
‘As for Gregory's surname, some say he belongs to the Tortorini, Tortorucci, or Tortorici family; but there is no documentary evidence in this regard, because of which the statement is greeted with caution, ignored, or even rejected by many historians.’
Delucca cites Battaglini (1794), L. Tonini (1880), C. Tonini (1884), and Perini (1929) as being of the former persuasion; earlier we saw Trapp (1980) using yet another variant, 'Tortoricci'.
I'd like to follow up Delucca's references, but the Bodleian – which doesn't even stretch to Gregorio da Rimini filosofo – only has the Perini. The others are all at the Warburg (ENH 360, HNB 174, 175).
Monday, 21 April 2008
Wednesday, 16 April 2008
Leff on Future Contingents
Gordon Leff's Gregory of Rimini: Tradition and Innovation in Fourteenth Century Thought (1961) might be expected to shed light on Rimini's nickname Tortor Infantium, but I'm afraid it doesn't.
I was pleased to read of Auriol's position as ‘somewhat anachronistically described by Michalski as 'three-value logic'’; Leff's wariness is echoed by Schabel in Theology at Paris, p. 3. But the following raised an eyebrow:
‘These two postulates [omniscience and bivalence] are the foundation of Gregory's view of the future; and they constitute an uncompromising repudiation of the two leading ideas among many of Gregory's confrères: that God cannot know future contingents necessarily, and that, as the future is itself undetermined, propositions about it are neutral.’ (p. 115)
Auriol is the only example Leff gives of the "many of Gregory's confrères" who think that propositions about future contingents are neither true nor false. Whether or not a Franciscan and an Augustinian can be said to be confrères, who are the others?
I was pleased to read of Auriol's position as ‘somewhat anachronistically described by Michalski as 'three-value logic'’; Leff's wariness is echoed by Schabel in Theology at Paris, p. 3. But the following raised an eyebrow:
‘These two postulates [omniscience and bivalence] are the foundation of Gregory's view of the future; and they constitute an uncompromising repudiation of the two leading ideas among many of Gregory's confrères: that God cannot know future contingents necessarily, and that, as the future is itself undetermined, propositions about it are neutral.’ (p. 115)
Auriol is the only example Leff gives of the "many of Gregory's confrères" who think that propositions about future contingents are neither true nor false. Whether or not a Franciscan and an Augustinian can be said to be confrères, who are the others?
Tuesday, 15 April 2008
Henninger on Fiorentino on Rimini
Francesco Fiorentino's book Gregorio da Rimini: Contingenza, futuro e scienza nel pensiero tardo-medievale (2004) is riddled with errors. For example, here is n. 16 on p. 9 of the introduction:
‘C. Normore, Peter Aureoli and his contemporaries on future contingents and the excluded middle, "Synthèse", 96 (1993), pp. 83-92. Nel 1999 C. Normore è ritornato sul tema secondo una prospettiva più ampia; cf. C. Normore, Contingenti futuri, in La logica nel Medioevo, The Cambridge History of Later Medieval Philosophy, a cura di N. Kretzmann, A. Kenny, J. Pinborg, Milano 1999.’
An attentive reader working on future contingents will immediately spot three mistakes in this one footnote. The first two are comparatively insignificant: the title of Normore's article begins with ‘Petrus’ and does not contain the definite article. The third is more worrying: the CHLMP was published in 1982, so Normore's 1993 article appeared after his CHLMP chapter, but Fiorentino (presumably using a 1999 translation) tells us that in the latter Normore ‘returned to the theme from a wider perspective’. The worrying thing is that the CHLMP has been the standard handbook of mediaeval philosophy since its appearance over 25 years ago.
Both author and publisher deserve a rap on the knuckles, so I was pleased to discover that Mark Henninger had already reviewed the book in Gregorianum. Pleased, that is, until I read the review.
Henninger is grateful for ‘certain logical principles he wisely provides in the introduction [actually Chapter 1]: the principle of bivalence, i.e., in whatever statement, either its affirmation or its negation is true; the law of contradictories, i.e., for every affirmative statement there exists its contradictory, and vice versa’. Unfortunately, both of these are more or less obvious howlers on Fiorentino's part.
If the meaning of ‘bivalence’ in a logical context is not clear enough from the etymology, even a standard dictionary will define it as the existence of only two truth-values, the corresponding principle being that every statement is either true or false. Worse, Fiorentino goes on (p. 24 n. 23) to cite Łukasiewicz's insistence on distinguishing between the principle of bivalence and the law of excluded middle. A reader following this up will be astonished, given Fiorentino's formulation, to read on p. 82 of Łukasiewicz, Aristotle's Syllogistic: ‘…the so-called principle of bivalence, which states that every proposition is either true or false, i.e. that it has one and only one of two possible truth-values: truth and falsity. This principle must not be mixed up with the law of the excluded middle, according to which of two contradictory propositions one must be true.’
As for the law of contradictories, Fiorentino refers only to Aristotle, De int. 9, 18a28-31. The reader following this up will find a discussion of the truth or falsity of an affirmation and its corresponding negation – not the mere assertion that there is a corresponding negation. And I think the reader checking in Rimini and Auriol will find that the law of contradictories is that if one part of a contradictory pair is false then the other part is true (Rimini), or vice versa (Auriol).
Henninger's verdict is that ‘Fiorentino provides a well-researched, thorough and balanced investigation of the teaching of Gregory of Rimini … In the introduction, Fiorentino sets the context with a helpful historiography of the problem of future contingents and divine foreknowledge as treated mostly by researchers in the last century, as well as a survey of the literature on Gregory of Rimini. … This is a fine work by a fine scholar.’
Sadly, then, Fiorentino's book still awaits a properly critical review.
‘C. Normore, Peter Aureoli and his contemporaries on future contingents and the excluded middle, "Synthèse", 96 (1993), pp. 83-92. Nel 1999 C. Normore è ritornato sul tema secondo una prospettiva più ampia; cf. C. Normore, Contingenti futuri, in La logica nel Medioevo, The Cambridge History of Later Medieval Philosophy, a cura di N. Kretzmann, A. Kenny, J. Pinborg, Milano 1999.’
An attentive reader working on future contingents will immediately spot three mistakes in this one footnote. The first two are comparatively insignificant: the title of Normore's article begins with ‘Petrus’ and does not contain the definite article. The third is more worrying: the CHLMP was published in 1982, so Normore's 1993 article appeared after his CHLMP chapter, but Fiorentino (presumably using a 1999 translation) tells us that in the latter Normore ‘returned to the theme from a wider perspective’. The worrying thing is that the CHLMP has been the standard handbook of mediaeval philosophy since its appearance over 25 years ago.
Both author and publisher deserve a rap on the knuckles, so I was pleased to discover that Mark Henninger had already reviewed the book in Gregorianum. Pleased, that is, until I read the review.
Henninger is grateful for ‘certain logical principles he wisely provides in the introduction [actually Chapter 1]: the principle of bivalence, i.e., in whatever statement, either its affirmation or its negation is true; the law of contradictories, i.e., for every affirmative statement there exists its contradictory, and vice versa’. Unfortunately, both of these are more or less obvious howlers on Fiorentino's part.
If the meaning of ‘bivalence’ in a logical context is not clear enough from the etymology, even a standard dictionary will define it as the existence of only two truth-values, the corresponding principle being that every statement is either true or false. Worse, Fiorentino goes on (p. 24 n. 23) to cite Łukasiewicz's insistence on distinguishing between the principle of bivalence and the law of excluded middle. A reader following this up will be astonished, given Fiorentino's formulation, to read on p. 82 of Łukasiewicz, Aristotle's Syllogistic: ‘…the so-called principle of bivalence, which states that every proposition is either true or false, i.e. that it has one and only one of two possible truth-values: truth and falsity. This principle must not be mixed up with the law of the excluded middle, according to which of two contradictory propositions one must be true.’
As for the law of contradictories, Fiorentino refers only to Aristotle, De int. 9, 18a28-31. The reader following this up will find a discussion of the truth or falsity of an affirmation and its corresponding negation – not the mere assertion that there is a corresponding negation. And I think the reader checking in Rimini and Auriol will find that the law of contradictories is that if one part of a contradictory pair is false then the other part is true (Rimini), or vice versa (Auriol).
Henninger's verdict is that ‘Fiorentino provides a well-researched, thorough and balanced investigation of the teaching of Gregory of Rimini … In the introduction, Fiorentino sets the context with a helpful historiography of the problem of future contingents and divine foreknowledge as treated mostly by researchers in the last century, as well as a survey of the literature on Gregory of Rimini. … This is a fine work by a fine scholar.’
Sadly, then, Fiorentino's book still awaits a properly critical review.
Friday, 11 April 2008
Rimini as Torturer of Infants
Historians of philosophy like to point out that Gregory of Rimini's views on baptism and salvation earned him the nickname Tortor Infantium, but they are remarkably coy about supporting this with references. The nickname was supposedly derived from Rimini's family name, Tortoricci (Trapp, "Notes on the Tübingen Edition of Gregory of Rimini II", 1980). But when did it first appear in print?
A preliminary search puts an upper bound on the date: 1709, when Leibniz wrote in his Essais de Théodicée (§92): ‘Grégoire de Rimini, général des Augustins, avec peu d'autres, a suivi saint Augustin contre l'opinion reçue des écoles de son temps, et pour cela était appelé le bourreau des enfants, tortor infantum.’
But surely it can't be hard to find something that antedates Leibniz.
A preliminary search puts an upper bound on the date: 1709, when Leibniz wrote in his Essais de Théodicée (§92): ‘Grégoire de Rimini, général des Augustins, avec peu d'autres, a suivi saint Augustin contre l'opinion reçue des écoles de son temps, et pour cela était appelé le bourreau des enfants, tortor infantum.’
But surely it can't be hard to find something that antedates Leibniz.
Frustra fit per plura (III)
Here's another of Auriol's statements of ontological parsimony:
‘multitudo ponenda non est nisi ratio evidens necessaria illud probet aliter per pauciora salvari non posse. Deus enim et natura nihil faciunt frustra’ (S II.14.1.ii)
(Mark Henninger, Relations: Medieval Theories (1989), p. 156 n. 25.)
‘multitudo ponenda non est nisi ratio evidens necessaria illud probet aliter per pauciora salvari non posse. Deus enim et natura nihil faciunt frustra’ (S II.14.1.ii)
(Mark Henninger, Relations: Medieval Theories (1989), p. 156 n. 25.)
Thursday, 6 March 2008
Refugium Miserorum
I like Auriol's dismissal of the theory that the generation of substantial forms requires the intervention of higher powers:
‘Hoc est refugium miserorum in philosophia, sicut Deus est refugium miserorum in theologia.’ (S IV.1.1.iii)
‘This is the refuge of the wretched in philosophy, just as God is the refuge of the wretched in theology.’
(Anneliese Maier, Zwei Grundprobleme, 3e (1968), p. 182 n. 29.)
‘Hoc est refugium miserorum in philosophia, sicut Deus est refugium miserorum in theologia.’ (S IV.1.1.iii)
‘This is the refuge of the wretched in philosophy, just as God is the refuge of the wretched in theology.’
(Anneliese Maier, Zwei Grundprobleme, 3e (1968), p. 182 n. 29.)
Monday, 25 February 2008
Brunellus versus the Brownshirts
Here's an extraordinary story from Gadamer's time in Leipzig:
‘You must understand that during that period one denunciation would come after another, and in my opinion it was pure idiocy – it didn't pay to take it too seriously. But one time a real denunciation did come along. A student wrote about my seminar to her girlfriend who was not there that semester: "I was with Gadamer today. Can you believe he actually said, 'All asses are brown'?" Now, the girl to whom the letter was written was from a family with Nazi parents. She left the letter lying around, the parents saw it, read it, and I was reported to the rector. So I was asked to go to the rector, who was no Nazi sympathizer (no more than I was) but ... he said to me, "So, my dear colleague, how did you come to speak out against the Brown-shirts by saying, 'All asses are brown'? What did you mean by that?" "You don't understand," I replied, "I was merely explaining the first premise of an Aristotelian syllogism with the famous medieval example, 'All asses are brown; Brunellus is an ass; therefore, Brunellus is brown.' For medieval philosophers, all asses are brown, and Brunellus is the name of an ass that they often used." So the rector wrote into the record, "Professor Gadamer was merely explaining the first premise of a syllogism using a medieval example." The rector and I were of similar minds, and there were very few Nazis in Leipzig anyway.’
(A Century of Philosophy: Hans-Georg Gadamer in Conversation with Riccardo Dottori, trans. Coltman & Koepke (2003), p. 104.)
‘You must understand that during that period one denunciation would come after another, and in my opinion it was pure idiocy – it didn't pay to take it too seriously. But one time a real denunciation did come along. A student wrote about my seminar to her girlfriend who was not there that semester: "I was with Gadamer today. Can you believe he actually said, 'All asses are brown'?" Now, the girl to whom the letter was written was from a family with Nazi parents. She left the letter lying around, the parents saw it, read it, and I was reported to the rector. So I was asked to go to the rector, who was no Nazi sympathizer (no more than I was) but ... he said to me, "So, my dear colleague, how did you come to speak out against the Brown-shirts by saying, 'All asses are brown'? What did you mean by that?" "You don't understand," I replied, "I was merely explaining the first premise of an Aristotelian syllogism with the famous medieval example, 'All asses are brown; Brunellus is an ass; therefore, Brunellus is brown.' For medieval philosophers, all asses are brown, and Brunellus is the name of an ass that they often used." So the rector wrote into the record, "Professor Gadamer was merely explaining the first premise of a syllogism using a medieval example." The rector and I were of similar minds, and there were very few Nazis in Leipzig anyway.’
(A Century of Philosophy: Hans-Georg Gadamer in Conversation with Riccardo Dottori, trans. Coltman & Koepke (2003), p. 104.)
Monday, 11 February 2008
Frustra fit per plura (II)
An update to an older post: I have found in Auriol the exact phrase attributed to him by Ueberweg. It occurs in S I.9.1.i, where he asks quomodo se habet generare seu dicere ad ipsam intellectionem. As his third and final negative thesis, he argues quod dicere non sit formam specularem et realem producere, quam intellectus aspiciat:
‘non est philosophicum pluraritatem rerum ponere sine causa, frustra enim fit per plura, quod potest fieri per pauciora. Sed nulla necessitas ducit ad ponendum talem rem ... Ergo si talis forma ponatur, erit absque omni causa et ratione; et per consequens vanum est ponere eam, et superfluum in natura.’
(ed. Friedman 2003; the 1596 edition, p. 319, has 'inducit')
Moreover, I may have found the source of Ueberweg's mistaken citation: Barthélemy Hauréau, De la philosophie scolastique, II (1850). In chapter 27, ‘Disciples et Adversaires de Duns-Scot’, pp. 404–410, Hauréau discusses Auriol. He quotes on p. 406 from Auriol's remarks on prime matter in S II.12.1.i and II.12.1.ii, and then he moves on to discuss Auriol's negative thesis about real specular forms – but unfortunately his subsequent footnotes simply say ‘Ibid.’ And there, on p. 408, is the very phrase quoted by Ueberweg.
‘non est philosophicum pluraritatem rerum ponere sine causa, frustra enim fit per plura, quod potest fieri per pauciora. Sed nulla necessitas ducit ad ponendum talem rem ... Ergo si talis forma ponatur, erit absque omni causa et ratione; et per consequens vanum est ponere eam, et superfluum in natura.’
(ed. Friedman 2003; the 1596 edition, p. 319, has 'inducit')
Moreover, I may have found the source of Ueberweg's mistaken citation: Barthélemy Hauréau, De la philosophie scolastique, II (1850). In chapter 27, ‘Disciples et Adversaires de Duns-Scot’, pp. 404–410, Hauréau discusses Auriol. He quotes on p. 406 from Auriol's remarks on prime matter in S II.12.1.i and II.12.1.ii, and then he moves on to discuss Auriol's negative thesis about real specular forms – but unfortunately his subsequent footnotes simply say ‘Ibid.’ And there, on p. 408, is the very phrase quoted by Ueberweg.
Wednesday, 5 December 2007
Paris University Statutes of 1366
The Parisian Statutes of 1366 show some interesting contraints on students of and lecturers on the Sentences:
‘Item quod scolares librum Sententiarum audientes noviter primis quatuor annis textum Sententiarum portent vel portari faciant ad scolas bachelarii, a quo Sententias audient, ut textum Sententiarum audiant diligenter.
Item quod legentes Sententias faciant honeste et sine verbis offensivis quibuscunque aut elatis sive scandalosis suas collationes et principia, omni injuria cessante servatoque sibi invicem congruo honore.
Item quod legentes Sententias non tractent questiones aut materias logicas vel philosophicas, nisi quantum textus Sententiarum requiret, aut solutiones argumentorum exigent, sed moveant et tractent questiones theologicas, speculativas vel morales, ad distinctiones pertinentes.
Item quod legentes Sententias legant textum ipsarum ordinate et exponant ad utilitatem auditorum.
Item quod nullus legens Sententias legat questionem suam aut suum principium per quaternum aut alias in scriptis. Non tamen propter hoc inhibemus, quin bachelarius possit portare ad cathedram aliquid ex quo possit, si necesse fuerit, sibi reducere ad memoriam aliquas difficultates questionem suam, aut argumenta seu auctoritates aut ad ipsam questionem aut aliquam expositionem pertinentes.
Item statuimus quod nullus magister aut bachelarius qui Sententias legerit, suam lecturam Sententiarum communicet tradendo stationariis directe vel indirecte, quousque sua lectura fuerit per cancellarium et magistrus predicte facultatis examinata.’
(Chartularium Universitatis Parisiensis, vol. III, §1319, pp. 143f.)
‘Item quod scolares librum Sententiarum audientes noviter primis quatuor annis textum Sententiarum portent vel portari faciant ad scolas bachelarii, a quo Sententias audient, ut textum Sententiarum audiant diligenter.
Item quod legentes Sententias faciant honeste et sine verbis offensivis quibuscunque aut elatis sive scandalosis suas collationes et principia, omni injuria cessante servatoque sibi invicem congruo honore.
Item quod legentes Sententias non tractent questiones aut materias logicas vel philosophicas, nisi quantum textus Sententiarum requiret, aut solutiones argumentorum exigent, sed moveant et tractent questiones theologicas, speculativas vel morales, ad distinctiones pertinentes.
Item quod legentes Sententias legant textum ipsarum ordinate et exponant ad utilitatem auditorum.
Item quod nullus legens Sententias legat questionem suam aut suum principium per quaternum aut alias in scriptis. Non tamen propter hoc inhibemus, quin bachelarius possit portare ad cathedram aliquid ex quo possit, si necesse fuerit, sibi reducere ad memoriam aliquas difficultates questionem suam, aut argumenta seu auctoritates aut ad ipsam questionem aut aliquam expositionem pertinentes.
Item statuimus quod nullus magister aut bachelarius qui Sententias legerit, suam lecturam Sententiarum communicet tradendo stationariis directe vel indirecte, quousque sua lectura fuerit per cancellarium et magistrus predicte facultatis examinata.’
(Chartularium Universitatis Parisiensis, vol. III, §1319, pp. 143f.)
Saturday, 1 December 2007
Gregory of Rimini on the Eternity of the World
Gregory of Rimini's treatment of the paradoxes of infinity (S I.42-44.4) allowed him a swift response in S II.1.2.i to an Aristotelian argument that an endless world could not have had a beginning.
Here is the core of the Aristotelian argument:
‘Probatur minor, quia si detur oppositum, sequitur quod erit infinitum maius infinito. Nam tempus aeternum ex utraque parte super utrumque aeternum ex altera tantum addit reliquum tempus aeternum ex reliqua parte, ut super aeternum in praeterito tantum addit tempus aeternum in futuro tantum, et econverso. Cum igitur omne aeternum in futuro sit ens tempore infinito, sequitur quod fuit etiam ens infinito tempore praeterito.’
And here is Gregory's response:
‘Ad secundam rationem principalem nego minorem, et dico quod probatio aeque militat contra Philosophum, qui posuit tempus aeternum in praeterito et in futuro, cum tamen aeternum in praeterito sit infinitum, et similiter aeternum in futuro, et aeternum ex utraque parte utrumque comprehendat. Quia tamen, secundum quod inferius dicam, possibile fuit tempus esse aeternum, quamvis de facto habuit initium, ac per hoc fuit possibile infinitum comprehendere in se plura infinita, dico quod hoc non est inconveniens, sicut in primo libro distinctione 44 declaratum est. Et pro nunc sufficiat exemplum de aliquo continuo, cuius utraque medietas continet infinitas partes proportionales alias ab his, quas reliqua continet.’
The tu quoque here is a nice move.
Here is the core of the Aristotelian argument:
‘Probatur minor, quia si detur oppositum, sequitur quod erit infinitum maius infinito. Nam tempus aeternum ex utraque parte super utrumque aeternum ex altera tantum addit reliquum tempus aeternum ex reliqua parte, ut super aeternum in praeterito tantum addit tempus aeternum in futuro tantum, et econverso. Cum igitur omne aeternum in futuro sit ens tempore infinito, sequitur quod fuit etiam ens infinito tempore praeterito.’
And here is Gregory's response:
‘Ad secundam rationem principalem nego minorem, et dico quod probatio aeque militat contra Philosophum, qui posuit tempus aeternum in praeterito et in futuro, cum tamen aeternum in praeterito sit infinitum, et similiter aeternum in futuro, et aeternum ex utraque parte utrumque comprehendat. Quia tamen, secundum quod inferius dicam, possibile fuit tempus esse aeternum, quamvis de facto habuit initium, ac per hoc fuit possibile infinitum comprehendere in se plura infinita, dico quod hoc non est inconveniens, sicut in primo libro distinctione 44 declaratum est. Et pro nunc sufficiat exemplum de aliquo continuo, cuius utraque medietas continet infinitas partes proportionales alias ab his, quas reliqua continet.’
The tu quoque here is a nice move.
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