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6 The Uses of Mathematics in Opus maius, Parts IV-VII: Science Interpreted Moraliter.
Aristotle says in the sixth book of the Metaphysics, mathematics, natural and
divine, the mathematical is of no small importance in grasping the knowledge of
the other two parts, as Ptolemy states in the first chapter of the Almagest’ (Opus
maius, Part IV, 98–99).. Bacon covers a wide area in his application of mathematics, physics, astrology, theology, church history, geography.
For the purposes of this chapter, however, I will focus on the section in Opus
maius IV dealing with Astrology/Scientia Experimentalis: the reason for this is to
indicate that Bacon may well be the one condemned in regard to the charge of
‘Astral Determinism’ in the Parisian Condemnations of 1270, 1277. While Bacon is
not named explicitly, it is clear that some of the propositions cover his doctrine of
universal univocal causation based on the effects of the heavenly bodies on human
bodies and on temperament. And while Bacon does attempt to save freedom of the
Will, it is also clear that he does believe in an astral determination of individual
personality and in the astral determinism of sects and religions. Or better, he clearly
attempts to save Astronomy-Astrology for Statecraft and for the Church by means
of argument and authority: the matter is so important to him that he treats of it in
many places, most notably in Opus maius IV, Opus maiux VI, part three, the
Introduction and Notes to the Secretum secretorum, De secretis operibus naturae
et de nullitate magiae.
Writing on Astrology in the Middle Ages and Renaissance, the renowned
authority on the subject, Graziella Federici Vescovini states:
Roger Bacon was one of the staunchest defenders of the theory of the birth of religions brought
about by the great conjunctions. He Bacon agrees with the astrological theory of religions and
while he strongly advocates Freedom of the Will, he does so at the cost of opposing the latter to
a more strictly deterministic world based on the influence of the stars. Proposition 68, 70,
76, 94 deal with this issue of Fatalism based on ‘Astral Determinism’ (Vescovini 2011, 2014).
I have argued that Proposition 101–107 beginning with the claim that no agency is
open to alternatives; indeed, all agency is determined to one outcome clearly find
warrant in Roger Bacon’s works (Hackett 2000). The diversity of heavenly positions
determines one’s fate. Further, not only is one’s physical complexion is determined
but so also one’s spiritual well-being is determined. Health, infirmity, life and death
are determined by the stars such that the heavenly bodies influence human destiny.
Bacon scientia experimentalis, Part III, and his Moralis philosophia, Part IV,
which Bacon calls the most important part of his Moral Philosophy, are a major
attempt to save Mathematics (Astronomy-Astrology) in regard to contingent
changes on earth and in regard to the human organism. It is the basis for his theory
of prediction of the future and for his astro-sociology of world-religions. A related
approach to Bacon can be found in the works of his younger contemporary, and I
believe his helper, Master Peter of Limoges. This is clear from the sermon De
antichristo (Be´riou 1986).12 Both John North and Graziella Federici Vescovini
See Be´riou (1986). This work reference to a De antichristo by Pierre de Limoges, who was a
Master in Arts at Paris, and then, a theologian, in the 1260s indicates that he had with Roger Bacon
a common concern with astronomy/astrology.
7 From Sapientes antiqui at Lincoln to the New Sapientes moderni. . .
have documented Bacon’s use and dependence of Abu’Mashr’s Liber
conjunctionum, and I have argued for his additional uses of Abu’s Mashr’s Introduction to Astronomy, Pseudo-Ptolemy, Centiloquium, Pseudo-Ptolemy, De disposition sphaerae.
To sum up: Bacon defends a radical opposition between inviolate Freedom of
the Will, and physical laws of nature that are determinate and necessary. Further, all
influence of species in medio are physical (Hackett 2011). There are no spiritual
species in nature. In this, Bacon believes the vulgus in philosophy and theology is
just confused. Bacon believes in Astral Determinism both in respect of physical and
psychological reality. This has been shown in regard to the doctrine of species by
Yael Kedar in her fine Ph.D. work at Haifa University (Kedar 2009). The importance of all of this for the education of the prince as seen in the Pseudo-Aristotle,
Secretum secretorum, Part VII of the Opus maius is connected with the defense of
To appreciate how toxic Bacon’s ideas may have appeared to some contemporaries one need only turn to the Errores philosophorum of Aegidius Romanum
(Giles of Rome, OESA 1944). Written c. 1268–1271, this work is a head on attack
on Greco-Arabian necessetarianism. I have already noted the same reaction to
Bacon’s concerns by the Master-General, Bonaventure.13
Giles of Rome’s work was written between 1269 and 1272 and is exactly
contemporary with Roger Bacon’s writings for Pope Clement IV. Condemned
here are the natural philosophy and metaphysics of Aristotle, Avicenna, Averroes,
al-Ghazali, al-Kindi and Maimonides. With the exception possibly of Maimonides,
all of these thinkers are defended by Roger Bacon. When one turns to al-Kindi and
his theory of universal determinism, radiation and magic, one notices the extent of
Roger Bacon’s dependence on al-Kindi. Aegidius claims (1) ‘al-Kindi erred in
asserting that the future depends simply and without qualification upon the state of
the super-celestial bodies. Hence in this same book in the chapter on the rays of the
stars, he states that “one who knew fully the state of the heavenly bodies would have
complete knowledge of both past and future.”’ (2) ‘Again, he erred in believing that
the effects of all causes in the world extended to every individual.’ (3) Ulterius,
erravit credens omnia de necessitate contingent.
These errors of the philosopher al-Kindi could be directed entirely against Roger
Bacon, and in the context of 1270 they were probably directed against Bacon and
his circle, especially since this circle took the work of mathematics so seriously and
because by means of the scientia experimentalis, the older Bacon and the younger
Magisters Peter of Maricourt (Picardus) and perhaps Magister Petrus de Limoges,
attempted to defend this new form of scientific study in the context of the more
verbal and dialectical education in the arts. The latter had interests similar to Bacon
in regard to the importance of astronomy/astrology, and to their uses in Theology.
See note 34 above.
The Applications of Mathematics: Perspectiva
Richard Newhauser has demonstrated the significant use by Master Peter of Limoges
of Roger Bacon’s moral uses of the study of Perspectiva. He shows the extent to
which this Master drew heavily on the third part of Bacon’s Opus maius, Part V, the
Perspectiva (Newhauser 2012).14 In Roma magistra mundi, the essays in honor of
Fr. Leonard E. Boyle, I provided reasons for thinking that Paris MS BN Lat. 7434
contains a version of the Perspectiva that pre-dates the text of the Perspectiva in the
Opus maius. Further, I believe that it contains the oldest text of the Perspectiva.15
Just recently, A. Mark Smith has shed new light on the nature of Bacon’s
Perspectiva. Smith comments as follows:
Although Grosseteste’s effort to submit the physics of light to geometrical analysis was
only partly successful, he inspired Roger Bacon to bring that effort to fruition. It is perhaps
no exaggeration, in fact, to say that in sharing the same Augustinian theological leanings,
the same desire for broad learning, and the same enthusiasm for applying mathematics to
the analysis of natural philosophy, Bacon was, in a sense, Grosseteste’s alter ego. But
Bacon had one clear advantage over Grosseteste: he could draw on a much wider array of
sources in carrying out his program (Smith 2015).
As Bacon notes in the Opus tertium, there was no knowledge of Perspectiva at
Paris in the 1260s; the subject had been taught but twice, and that was at the
University of Oxford. Smith does a great job in situating the three parts of the
Perspectiva. He devotes more care to part one on the relation of optics and the
psychological process of perception than Lindberg did. Of course, this was the big
bone of contention between both scholars: Was Bacon primarily interested in providing a geometrical theory of vision after the manner of Ibn al-Haytham or was the
concern with optics subordinated to providing for a more comprehensive and better
theory of perception and knowledge. In regard to Roger Bacon, I believe that Smith
has now shown that the latter position is the correct one in the case of Bacon. He
shows that this is not so in the case of Witelo. Here, much more than in Bacon and in
Pecham, one is dealing primarily with a detailed mathematical treatment of optics.
Indeed, Smith is quite correct in noticing that with respect to the mathematics, Bacon
does not make advances in the arguments. He simply falls back on Euclid in his
attempt to solve the problem of the angle of incidence. But of course, Bacon was
writing an introductory persuasio to encourage the serious study of optics in the part
of the curriculum of the medieval university, called the Quadrivium.16
See Newhauser (2012) Introduction, xi–xxiii for Peter’s reliance on both Roger Bacon and John
Pecham, but especially, Peter’s use of part three of Bacon’s Perspectiva. Quite significant here is
the fact that Peter nowhere mentions Bacon by name.
See Hackett (1998). I have prepared an edition of this text and am working on a translation of
Might it not have been the case that it was Bacon’s intention by means of his works for Pope
Clement IV to influence the progress of science at the Papal Studium in Viterbo. As we will see
below, the influence of his works there in the mid-1270s has been acknowledged by David
7 From Sapientes antiqui at Lincoln to the New Sapientes moderni. . .
Indeed, Bacon’s advocacy for optics was very successful. In the next decade,
Bacon’s confrere, John Pecham wrote the textbook for the university teaching of
optics, the Perspectiva communis. It is a masterpiece of educational pedagogy.
Thus, Bacon’s plea for the improved study of science in the medieval university
was not a failure; it was a massive success.
I will argue that Bacon’s intense theological concerns condition the manner in
which he sets up the parameters of his scientific account of optics in Part I and Part
II of the text.
The Third Part of the Perspectiva
One issue has bothered students of Bacon’s optics. Why does Bacon make such a
spirited defense of a combination of an intromission and extramission theory of
vision. Now, of course, one could argue that he is combining elements of Neoplatonic Aristotelianism with the straight geometrical optics of Ibn al-Haytham. There
is some truth in that view. However, a review of the Third part of the Perspectiva,
that is the part which deals with the spiritual uses of optics, the part indeed which so
much appealed to the great Master of Preaching, the theologian at the Sorbonne,
Peter of Limoges as can be seen from his Tractatus de oculo morali indicates
another reason for the combining of intromissions and extramission. Here one can
find Bacon’s rationale for his integration of both an intromission theory of vision
and an extramission theory of vision.
Following his remarks on the need for optics in order to know the natures of
things, Bacon writes about the preservation of the spiritual pupil of the eye, that is,
In a comment on this, Bacon lists the seven spiritual gifts, the seven virtues, three
theological and four cardinal virtues, seven gifts of the Holy Spirit and seven petitions of
the Our Father, the eight beatitudes (here, the eyelids provide a convenient eight member to
the seven parts of the eye, ‘so that to the eight spiritual guardians there correspond the same
number of corporeal ones’ (Lindberg 1996).
David C. Lindberg saw Bacon’s combining of the intromission/extramission
theories of vision as a sign of confusion in optical theory. I can see why he would
think so, but I am not so sure that that alone is the issue. Could it not be the case that
Bacon’s theological motivation, namely, the need to find a model for the relation of
grace and free will requires him to have a perceptual theory that unites intromission
and extramission to match what is required in theological doctrine. Is it not the case
that Bacon finds a convenient symbiosis between natural science and the requirements of theology? Indeed, it is the case. That Bacon is motivated by theological
concern is clear from what follows in his text:
It has been said that not only is intromission (of species) required for vision, but also the
extramission and cooperation of its own for vision, but also the extramission and
cooperation of its own power and species. Similarly, spiritual vision requires not only that
the soul should be the recipient from without of divine Grace and Powers, but also that it
should cooperate by its own power. For consent and the exercise of free will are required,
along with the grace of God, if we are to see and gain the state of salvation (Ibid.) [Text 15].
In other words, Bacon’s fusion of extramission with intromission theory of
vision is motivated by the need to find a natural analogue in vision and perception
for the relation between Grace and human freedom of the will.
Further, citing the relation between the need for proper distance for vision
and spiritual distance, Bacon draws a very tight parallel between perspectival
perception and spiritual perception, in this case drawing closely from Ibn
Since corporeal vision is of three kinds—namely, sense alone [direct impact of the species
of light and color], knowledge of the universal [vague individual] and knowledge by
syllogism—it is likewise necessary for mankind to have a threefold [spiritual] vision. For
by sense alone we gain an insufficient grasp of a few things, such as light and color; and this
cognition is weak, revealing whether things exist and what they are. But by knowledge we
grasp what kind they are and what qualities they possess; whether the light of the sun or the
moon, whether white or black. By syllogism we grasp everything associated with light and
color according to all twenty common sensibles. Therefore, the first cognition is weak, the
second is more perfect, and the third is most perfect. So it is that in spiritual vision; for what
a man knows by his own sense alone is very modest, since he lacks the other two kinds of
cognition, [the first of which is] through teachers, from youth to old age, for we can always
learn them from those who are wiser than ourselves. And [if cognition is by sense alone] we
are also without the third kind of cognition, which occurs through divine illumination
But what is also significant about cognitio per syllogismum is that it has nothing
whatsoever to do with the common Aristotelian use of the term Syllogism as in
formal argument. Bacon is referring to the use of the term in Ibn al-Haytham’s
optics where it refers to direct intuitive perception of singulars. This is the kind of
confirmatory use of intuitive experience that in the Opus maius, Part VI, Bacon
holds is needed to confirm the rational teachings of books and teachers. It has much
significance for epistemology in that it starts a tradition that in Duns Scotus and
William of Ockham and their contemporaries will become central, the intuitive
cognition of singulars (South 2002). This is the source of the doctrine of experience
and intuitive cognition in William of Ockham which has been clearly outlined by
Peter King (2003).17
The remaining two sections deal with the subdivision of vision into direct,
reflected and refracted vision and to its uses in moral persuasion. It also deals
with the application of mirrors to the technology of war.
For the beginning of this account of experience in Roger Bacon, see Hackett (2008–2009).
7 From Sapientes antiqui at Lincoln to the New Sapientes moderni. . .
The Utility of Mathematics: Opus maius VI: De scientia
In this section, I will deal with only one aspect of Bacon’s concerns in his Opus
maius, Part VI. The matter of his relation to the Magister Petrus de Maricourt,
Picardus, has been carefully examined recently by Sylvia Nagel (2012). I will
examine Bacon’s stated concern in the aforementioned text about the nova
translatio of Aristotle’s Meteorologica.
Bacon is quite clear: he does not have time to complete a formal treatise on the
rainbow, halo and related matters. But why in the first place is Bacon so exercised
about the rainbow and halo? What is the big deal? Here we must return to Robert
Grosseteste, and the matter of the translations of Aristotle, especially the translation
of the Book of the Meteorologies of Aristotle.
Roger Bacon’s Criticism of the Translators, Especially
the Translation of William of Moerbecke
Throughout the Opus maius and elsewhere, Bacon talks about the importance of
Book Three of Aristotle’s Metheorologica on the rainbow and halo. Further, the
account of the rainbow and halo provides Bacon with the exemplum for the first
prerogative of his Scientia experimentalis, the confirmation by adequate experiences of the rational claims of the other parts of Natural Philosophy and Optics. But
why pick Book three of Aristotle’s Metheorologica? Surely, there are lots of other
examples from Ibn al-Haythan, Ptolemy and others. What is going on here? Does it
perhaps have to do with difficulties in the translation of Aristotle from Greek into
Latin? (Perspectiva 324–325).
The late Joseph Brams once observed that Bacon had spoken strongly against
Guillelmus Flemengus, translator, and that his remarks are compromised by ‘le ton
ironique et le gout de l’exagge´ration.’ Yet, he saw Bacon’s remarks as an issue of
some embarrassment for modern scholars. The newly published critical edition and
study of William of Moerbecke’s nova translation of the Meteorologica of Aristotle
in the Aristoteles Latinus series by Gudrun Vuillemin-Diem makes it possible for
the first time to provide a trustworthy evaluation of Bacon’s remarks in Opus maius
VI on the rainbow (Aristoteles Latinus 2008, X, 2.1/2.2, Meteorologica). Further,
her study of Moerbecke’s translation methods, especially in his translation(s) of the
Meteorologica allow us to prove that Bacon’s strong remarks in 1271–1272 about
Moerbecke as a translator were no exaggeration. They expressed a serious concern
with the first two versions of the translation, which did, indeed, have serious
What are the dates of the three successive translations and which scholars at
Paris first used them? G1a the uncorrected version was done in 1260. It is likely that
Bacon knew this version c. 1266–1267, though he may also have known version
G1b, the second version. This latter version was known to Thomas Aquinas
c. 1269–1271, and GT, the third version, was known at the Papal Court sometime
after 1270. It is the view of Gudrun Vuillemin-Diem that Thomas Aquinas is the
first authentic user of the second version of the translation.18 Or to be more precise,
he may have used G1b (1267), and he certainly knew the third version form 1270.
Unfortunately, we lack the commentary of Thomas Aquinas on Book Three of the
Meterorologica. However, if Thomas Aquinas is the first authentic use of the
second version, G1b, what can we say about Roger Bacon’s use of either the first
or second version? We can state that Roger Bacon knew the translatio nova already
c. 1266–1267, and may have known the second version G1b, thereby preceding
Thomas Aquinas as the first to comment on the new translation of the
Meteorologica. We can also say quite categorically that Roger Bacon, drawing
on his knowledge of Aristotelian commentators from Grosseteste, Adam of
Buekfield and others, wrote on the first prerogative on experimental science as a
correction of Moerbecke’s account of the rainbow: this is what he means by his
appeal to the practice of Robert Grosseteste and the difficulties of the perverse
translations of Aristotle. Like Grosseteste, he intends to use his own experience and
other authors, most notably Seneca and writers on optics to correct and advance the
study of the rainbow. Bacon tries to correct Moerbecke’s Aristotle by a new
treatment of the figure of the rainbow and he shows how an adequate use of
instruments such as the astrolabe one can give precise measurements of the possible
altitude of the rainbow (42 ). He also studies the question of the objectivity of
rainbows and other secondary stars, the role of vision and the nature of the colors.
The question naturally arises concerning Bacon’s move to write on philosophical
topics c. 1260. Did the new translation of Aristotle move him to return to Natural
Philosophy and Logic in order to offer a broad criticism of the new readings of the
text of Aristotle?
But the question remains; could Bacon, the writer of a Greek Grammar and the
commentator in Compendium studii philosophiae of the meaning of Greek words,
have been wrong and just simply prejudiced in a negative manner alone about
Moerbecke; was it a fit of pique that he did not get to translate the Meteorologica?
Was it just a case of corporate professional rivalry? At any rate, according to the
editor of the latter text in the Aristoteles Latinus, it is clear even in version two
(1267), that Moerbecke had trouble with the geometrical figure of the rainbow. A
careful review of all three versions by the editor proves that there are major
problems in Moerbecke’s first two versions: numerous omissions of words, especially syntactical words, mechanical translation from the Greek with assimilation
mistakes, additions by Moerbecke himself, difficulties with unusual (that is, scientific) Greek words, confusion of single words such as those for cloud and fog,
significant failure in reading the text, numerous textual conjectures. Above all,
there was a significant problem with the diagram of the rainbow.
Ibid., Aristoteles Latinus, X, Meteorologica Translatio Guillelmi De Morbeka, 2.1: 349–350.