Schmitt C.B. (ed.) The Cambridge History of Renaissance Philosophy
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Epistemology
of the
sciences
697
Next
Catena considers
the
principles
on
which
all
mathematical
demonstrations depend. These
he
divides into 'common notions' (communes
conceptiones)
and
definitions
of
mathematical entities. Both sorts
are, he
claims,
of the
utmost evidence,
the
former because they
are
preconditions
for
all reasoning,
the
latter
because they deal with
the
perspicuous objects
of
mathematics.
47
The
final source
of
certainty
of
mathematics considered
by
Catena
is
that
which
accrues from
its
method:
In the third place we said
that
the certainty of any discipline is principally made
known
on the basis of method and from the series of demonstrations
that
are
included
in it. For whatever things are arranged so
that
they are interconnected in a
certain close order and so
that
prior things confer solidity and strength on posterior
ones,
posterior things depend on preceding ones and nothing altogether self-
contained and separate from the others is found — such things deserve confident
trust
according to all sound judgements.
48
He goes
on to
assert
that
the
excellence
of
this mathematical method
is
attested
by its
serving
as an
ideal, though
a
scarcely attainable
one,
for all
other disciplines.
49
He
concludes
by
claiming
for
mathematics,
in
addition
to practical utility
and
nobility
of
subject-matter,
the
highest grade
of
certainty
by
virtue
of
the
nature
of
its objects,
the
clarity
of
its principles
and
the sequential
nature
of
its
demonstrations.
50
THE STATUS
OF
ASTRONOMICAL HYPOTHESES
In medieval
and
Renaissance classifications
of
knowledge 'mathematical'
and 'physical' study
of the
heavens
are
sharply separated. Mathematical
astronomy forms
one of the
four mathematical
arts
of the
quadrivium,
whereas physical study
of
the heavens forms
a
specialised branch
of
natural
philosophy.
This
gulf
is
reflected
in
sixteenth-century teaching careers
and
Reliquum
est
tertium genus rerum, quae
re
quidem ipsa materiae inhaerent,
sed
cogitatione nostra
ab
ea
seiunguntur: atque
hae
solae
sunt, quae nobis adamussim cognoscuntur,
nec
mentis aciem
sua
obscuritate tenebris involvunt, neque nimia luce
et
fulgore, earn perstringunt. Itaque trigonum,
tetragonum,
et
alia huiusmodi, quia talia sunt, qualia
sensibus
usurpantur,
et
quia formam ipsam
absque materia contemplamur, neque lignum, ferrum,
vel
quippiam huiusmodi consideramus,
ea
sine
ullis
involucris, ubicunque sumus intuemur.
Atque
haec quidem mathematicarum
disciplinarum,
ex
rebus
ipsis
et
subiectis evidentia, atque certitudo apparet.'
47.
Ibid.,
f. 5
r
.
48.
Ibid.,
f. 6
r
:
'Tertio loco, certitudinem alicuius disciplinae praecipue declarari dicebamus
ex
methodi
ratione, atque
ex
serie
demonstrationum, quae
in
ilia continentur: quaecunque
nam sic
explicantur
ut
denso
quodam ordine inter
se
connectantur, utque priora robur
ac
firmitatem posterioribus
largiantur,
posteriora pendeant
a
praecedentibus, nihilque prorsus,
vel
absolutum,
vel
separatum
ab
aliis
reperiatur, certam sibi fidem, apud omnia solida iudicia promerentur.'
49.
Ibid.,
f. 6
r
~
v
. 50.
Ibid.,
ft
7
V
-8
V
.
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698
Problems of knowledge and action
university curricula.
51
It is reflected also in the genres of literature of the
period concerned with celestial matters. Physical astronomy is primarily
represented in commentary on De caelo and Metaphysics A, and in
specialised
treatises on the substance and
nature
of
the heavens. The primary
texts of mathematical astronomy, Sacrobosco's De sphaera and Peurbach's
Theoricae
novae planetarum, are silent on natural philosophical issues.
However,
the isolation of the two disciplines should not be exaggerated.
Following
Thomas Aquinas, astronomy was often recognised as a scientia
media, a branch of mathematics having special affinities with natural
philosophy.
In judicial astrology, widely taught alongside mathematical
astronomy throughout the period, the two disciplines mingle freely.
Further, though the primary textbooks of mathematical astronomy are
devoid
of
natural philosophy, a considerable number of fifteenth- and early
sixteenth-century commentaries on them discuss the substance and sources
of
motion
of
the celestial orbs. In these commentaries we find discussion of
the potential conflict between mathematical astronomy and natural
philosophy,
a potential conflict
that
arises from the postulation by
astronomers of
epicycles
and eccentrics, orbs whose centres of motion do
not coincide with the centre of place in the universe,
that
is, the earth's
centre.
52
Two
medieval reactions to this perceived tension between astronomy
and natural philosophy deserve mention. In the later medieval period
there
was
widely adopted a most ingenious compromise between the Aristotelian
cosmology
of substantial concentric spheres and the Ptolemaic planetary
models with their epicycles and eccentrics. Though
there
was considerable
variation on points of detail, the basic strategy was to realise Ptolemaic
epicycles
and eccentrics by substantial spheres and spherical shells, the so-
called
'partial orbs' (orbes pardales or particulares). The partial orbs of each
planetary model were embedded in a substantial 'total orb' (orbis totus), a
spherical shell centred on the earth. The total orbs were supposed to form a
plenum and were identified with the Aristotelian concentric orbs.
53
This
compromise proved resilient, providing as it did the framework for the
planetary models of Peurbach's Theoricae novae planetarum, the main
textbook
of'advanced' mathematical astronomy in the Renaissance period.
In marked contrast is the uncompromising stance
of
Averroes
and certain of
his
followers.
54
Here, whilst it is conceded
that
planetary models which
51.
See, for
example,
Westman
1980;
Schmitt
1984, § xiv, and
forthcoming
a.
52. See N.
Jardine
1982. 53.
This
compromise
is
described
in E.
Grant
1981b, § 11.
54. See
Carmody
1952; Dictionary of Scientific Biography
1970-80,
XII, pp. 1-9 ('Ibn
Rushd').
Cambridge Histories Online © Cambridge University Press, 2008
Epistemology
of the
sciences
699
invoke
centres
of
motion away from
the
centre
of the
universe constitute
the only known predictively adequate astronomy,
the
reality
of
such
planetary models
is
denied outright
on the
grounds
that
Aristotle's natural
philosophy
of the
heavens,
as set out in De
caelo
and
Metaphysics
A,
allows
only
orbs centred
on the
earth. Averroes
had
expressed
the
hope
that
someone might succeed where
he had
failed
in
providing
a
predictively
adequate astronomy properly founded
in
celestial physics
and
metaphysics,
and
a
serious attempt
to
construct
a
purely concentric astronomy was made
by
his
near contemporary Alpetragius (al-Bitruji).
55
In the
period with
which
we are
concerned
Averroes'
hope was echoed
by
Alessandro
Achillini
and Agostino
Nifo,
56
and
Alpetragius' attempt
was
emulated
in the
concentric systems
of
Girolamo Fracastoro
and
Giovanni
Amici.
57
In
the
later Renaissance
we
find
a
proliferation
of
noncommittal
and
sceptical
attitudes, involving doubt
or
denial
of
the reality
of
epicycles
and
eccentrics,
but
unlike Averroist concentrism making
no
recommendation
of
an
alternative type
of
arrangement
as the
basis
for a
sound astronomy.
One
such moderately sceptical position
is that
of
Wojciech
(Adalbertus)
de
Brudzewo,
who
taught mathematics
at the
University
of
Cracow from
1474
to his
death
in
1495.
His
commentary
on
Peurbach's Theoricae novae
planetarum
is
thought
to
have been
a
prescribed text
at the
time
of
Copernicus'
studies there.
In the
course
of
his commentary
on
Peurbach's
model (theorica)
for the sun,
Wojciech
makes
the
following
declaration:
Whether
these
eccentrics really exist
in the
spheres
of the
planets
no
mortal knows,
unless
we are to
declare them,
and
likewise epicycles,
to
have been disclosed
by
some revelation
of
spirits
(as
some claim).
If
not,
then
they have been formed from
the imagination
of
mathematicians alone,
as
Albeon [Richard
of
Wallingford]
testifies
in the
first
part of his
[work]
in
chapter 10, saying:
'Not that there are
amongst
the
heavenly bodies eccentrics
or
epicycles
of
this
sort,
as the
mathematical
imagination contrives
for
itself,
a
thing which
no
educated
man
could suppose
to be
plausible.
It is rather that
without mathematical imaginings
of
this
sort
there
cannot
be
set out the art
concerning
the
regular motions
of
the
stars
which
is so to
establish
their
places
at any
given time
that
they
may not
conflict with
the
ways
in
which
they
appear
to
us.'
58
55. Dictionary
of
Scientific Biography
1970-80, xv, pp. 33-6 ('Al-Bitruji').
56.
Achillini 1498; Nifo 1514. 57- Amici 1536; Fracastoro 1538.
58. Wojciech de Brudzewo 1900, pp. 26-7: 'Qui quidem ecentrici an veraciter existant in sphaeris
planetarum,
nemo mortalium novit,
nisi
fateamur
illos
(ut nonnulli aiunt), similiter et epicyclos,
revelatione spirituum propalatos, si non extunc
sola
imaginatione mathematicorum effictos, sicut
testatur Albeon, in prima sui capitulo decimo, dicens: "Non quod in coelestibus sunt huiusmodi
ecentrici aut epicycli, sicut imaginatio mathematica sibi fingit, quod nullus disciplinatus potuit
verisimiliter putare, sed quia
sine
huiusmodi imaginationibus mathematicis, de stellarum motibus
regularis ars tradi non potest, quae sic earum loca ad quodvis momentum certificet, quod a
nostris
aspectibus non discordent."' Cf. Richard of Wallingford 1976, 1, pp. 278-9
(Tractatus Albionis
no).
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700
Problems of knowledge and action
Elsewhere
in the work
Wojciech
sharply distinguishes between the
concerns of astronomers and those
of
philosophers who study the heavens.
Though
both are concerned with celestial motions, the philosopher is
concerned only with the
nature
and motion of the total orbs. The
astronomer, on the other hand, is concerned to offer an account of the
apparent celestial motions, for which purpose he has to consider in addition
the motions of partial orbs,
that
is epicycles and eccentrics.
59
Wojciech's
doubts about the existence of partial orbs do not extend to the Aristotelian
total orbs. Indeed, he himself ventures into what is, by his criteria,
philosophical
territory, discussing at some length the
nature
of the total
orbs, the causes
of
their motions and the order in which they are arranged.
60
This
combination of attitudes — sharp separation of mathematical
astronomy from natural philosophy, acceptance of the Aristotelian
concentric spheres and licensing
of
mathematical astronomy to employ for
the purpose
of
saving
the celestial phenomena models
that
are, taken at face
value,
doubtful
if
not false
—
becomes widely prevalent in the course
of
the
sixteenth century, being promoted by such influential authors as Erasmus
Reinhold
and Benito Pereira.
61
It is evidently a compromising stance
designed
to stave
off
conflict
and, in didactic contexts, to forestall the asking
of
awkward
questions. There is evidence
of
a connection between its spread
and awareness of Copernicus' work,
62
a plausible supposition
given
that
with
the advent of the Copernican system the area of potential conflict
between
mathematical astronomy and orthodox natural philosophy was
greatly
expanded, and expanded moreover into theologically sensitive
areas.
There are a number of sixteenth-century writers, however, whose
scepticism
about astronomy goes far beyond
that
associated with this
cautious compromise. For example, in a work of 1586, the humanist poet,
wit
and polemicist Nicodemus Frischlin claims
that
the
true
nature
of the
heavenly
bodies is incomprehensible to us by virtue of their perfection,
simplicity
and great speed
of
motion; and he goes on to make the
following
assertion:
God
the creator
of
things placed
these
bodies so far away from our senses
that
we are
unable to produce principles
of
demonstration
for
them
(as we can in the sciences of
other
things) or to discover what is
natural
and familiar, by means
of
which
we may
afterwards set out the causes of particular appearances. That is why we have
recourse to aids from elsewhere and seek hypotheses from
arithmetic
and
59. Ibid., pp. 17—18. 60. For
example,
ibid., pp. n—13.
61. On the
prevalence
of
this
attitude
see
Duhem
1908;
Blake
1966;
Westman
1975;
Aiton
1981;
N.
Jardine
1984, ch. 7. 62. Cf.
Westman
1975.
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Epistemology of the
sciences
701
geometry. Hence we construct so many lines, we fashion so many circles, we
imagine so many points, we devise so many eccentric and
epicyclic
orbs, and even
little
epicycles
as
well.
63
Frischlin is not content merely to deny the physical reality of astronomers'
planetary models. Such hypotheses are, he maintains, actively misleading if
used for purposes other
than
the calendrical and chronometric uses licensed
by
the Scriptures, for they encourage astrologers and they foster the
erroneous
view
that
the celestial motions really are irregular.
64
In his
Prooemium mathematicum
of 1567 Petrus Ramus
gives
a mocking
history of astronomy in which he denounces it for its unnecessary use of
fictitious hypotheses; and he pleads for the restoration of the pristine
'astronomy without hypotheses' possessed by the Babylonians, Egyptians
and Greeks before Eudoxus.
65
It seems
that
this is a plea for a calculus of
apparent
celestial coordinates, a plea apparently premised on a radical
scepticism about our capacity to acquire knowledge
of
the
true
dispositions
and motions of heavenly bodies.
66
Neither Frischlin nor Ramus offers sustained arguments for the
unattainability of knowledge of the heavens. In Nicolaus Ursus' (Baer)
scurrilous treatise of 1597, written to
rebut
the charge of plagiarism of
Tycho
Brahe's world-system, we find a more systematically defended
sceptical
position.
67
Firstly, Ursus cites the crass absurdity of all past
hypotheses in support
of
his assertion
that
it is scarcely possible in astronomy
to arrive at
true
hypotheses.
68
The history of hypotheses which
follows,
a
history partly derived from Ramus, in which he mocks all the various
world-systems
that
have been proposed, is evidently supposed to substanti-
ate the premise
of
this induction on the history
of
science.
69
Secondly,
there
is
what may, with a degree of anachronism, be called an argument from
observational equivalence. Ursus draws
attention
to the existence of very
different hypotheses: those of Ptolemy, those of Copernicus, those of
Tycho
and those of his own variant of the Tychonic system, all equally
63.
Frischlin 1586, p. 41: 'Cum enim Deus
Opifex
rerum,
ilia
corpora tam procul a sensibus nostris
removerit: ut (quod in aliarum rerum scientiis faceré possumus) principia demonstrationum non
queamus ex ipsis gignere, et oikeia ac vernácula invenire: quibus postea singularum apparentiarum
causas reddamus: ideo nos ad aliena confugimus praesidia, petimusque nobis hypotheses, ex
arithmetica et geometria. Nam hinc tot
lineas extruimus, tot circuios fingimus, tot puncta
imaginamur, tot orbes eccentricos et
epicyclos,
imo etiam
epicycliscos
comminiscimur.'
64.
Ibid., pp. 258-60. 65. Ramus 1567, pp.
211-17.
66.
Ramus' plea for an astronomy without hypotheses has been variously interpreted: see, for
example,
Hooykaas 1958, ch. 9;
Aiton
1975;
Dictionary
of
Scientific
Biography 1970-80, xi, pp. 286-
90 ('Peter Ramus'). 67. Ursus 1597; partial translation in N.
Jardine
1984.
68. Ursus 1597,
sigs.
A iv
r
, B iv
v
. 69. Ibid.,
sigs.
c
ii
R
-D
ii
v
.
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702
Problems of knowledge and
action
adequate for predictive purposes. He even suggests
that
the contrivance of
predictively
adequate hypotheses is an easy business.
70
Given Ursus' tacit
assumption
that
predictive adequacy provides the sole warrant for
astronomical hypotheses, the existence of observationally equivalent
planetary models and world-systems clearly supports his sceptical position.
The
negative and sceptical
attitudes
to astronomy
that
became so
widespread in the
latter
part
of the sixteenth century provoked interesting
defences of the discipline at the
hands
of Christophorus Clavius, Michael
Maestlin and Maestlin's
student,
Johannes
Kepler. Clavius and Maestlin are
both primarily concerned with the question
of
the existence
of
epicycles
and
eccentrics.
Both are cautious in their claims. Thus Maestlin does not try to
defend the literal
truth
of
a particular set
of
planetary models, but maintains
only
that
with the help of geometry we can infer a
posteriori
from the
celestial
phenomena
that
some one of the various possible predictively
adequate arguments of orbs exists 'in
nature'
(Kara
</>vaiv).
71
Similarly,
Clavius
asserts only
that
the existence
of
epicycles
and eccentrics is
credibilis,
given
that
they have the capacity to predict the celestial phenomena and
that
they are not (despite the objections of the
Averroisti)
at odds with the
principles
of
natural
philosophy.
72
Kepler's far more detailed and ambitious
defence
of
astronomy addresses the epistemological problems raised by the
conflict
of the Ptolemaic, Copernican and Tychonic world-systems,
promotes the unification of mathematical and physical astronomy and
defends a view
of
the history
of
astronomy as evincing an accumulation of
truths
about the form of the cosmos.
73
THE
RANGE
OF
EPISTEMOLOGY
OF THE
SCIENCES
The
three
epistemological debates reviewed above concern orthodox
sciences.
It should be emphasised again
that
much of the most
lively
and
original Renaissance debate on questions of cognitive
status
and method
concerns disciplines whose credentials as
scientiae
were perceived as
questionable: the unorthodox sciences and the mechanical and practical
disciplines.
74
In confining our
attention
to orthodox sciences we pass over,
70.
Ibid., sig. A iv
r
. 71. Maestlin 1597 (1st edn,
1582),
pp. 28-9.
72.
Clavius
1581,
pp. 434 ff. On
Clavius'
'moderate realism' see Blake 1966; Wallace
1981a,
pp. 129—
59;
N.
Jardine
1979.
73.
Kepler, Apologia pro Tychone contra Ursum, composed
1600-1,
first published in 1858, text and
translation in N.
Jardine
1984.
74.
On epistemological aspects of unorthodox disciplines see, for example, Pagel 1958a;
Yates
1964;
Nauert
1965;
Walker 1958; Debus 1968;
Vasoli
1974,
pp. 407-75; Copenhaver in this volume, pp.
264-300. On the epistemological aspects of practical and operative disciplines see especially
P.
Rossi 1962; Crombie forthcoming,
part
4.
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Epistemology of the sciences
703
for
example, a whole complex of epistemological doctrines concerning
microcosm and macrocosm, signs and signatures and the 'lights' of grace
and nature, doctrines
that
have sometimes been taken to constitute the
conceptual framework for the most creative thought of the period.
75
The
range
of
debating points in the epistemology
of
natural philosophy is
a wide one.
76
Major topics include: the distinction between the mode of
consideration of natural things appropriate to natural philosophy and the
modes appropriate to other disciplines; the two types
of
priority operative
in natural philosophy, priority 'for us' and priority 'for nature';
77
the
natures
and sources of knowledge of the different kinds of principles of
demonstration
(dignitates,
suppositiones,
definitiones,
etc.); and the
nature
and
grounds
of
the necessity
that
is required
of
the premises of demonstrations.
There is extensive discussion too of the types of causation, their relative
importance and their relations to demonstration and to the definition of
substances and properties. In this context the Aristotelian tradition shows
considerable powers of innovation. For example, in Zabarella and others
efficient
causation comes to be assigned a dominant role in natural
operations, the agency of material, final and formal causes being mediated
by
external or 'internal' efficient causes;
78
and in Andrea Cesalpino's works
a distinction between entities and processes
that
exist ex
necessitate
and those
which
come about 'for the sake
of
something else'
(alicuius
gratia)
is applied
in novel ways in his discussions
of
transmutation and mixture
of
bodies and
of
the structure and organisation of plants and animals.
79
In the realms
of
methodology
of
natural philosophy
regressus
is
but one
of
a
considerable range
of
topics.
It has, for example, been maintained
that
there
was
an Aristotelian tradition of
treatments
of inference ex
suppositione
or
conditioner
a form of
a
posteriori
inference
that
reveals
verae
causae
and has a
special
role in the subaltérnate sciences: those
that
depend upon a higher
science
for their principles.
80
Further,
there
was a fair amount
of
discussion
of
the various types
oiinductio
(eTraycoyri)
that
figure in Aristotle, discussion
that
generally distinguished sharply between the 'demonstrative' induction
which
leads from individual sense experiences to apprehension
of
universals
and other forms
of
induction, including induction by enumeration. There is
also considerable discussion
of
the status
of
the argument 'from probabilities
75.
See, for example, Foucault 1966, ch. 2;
Yates
1979, part 1.
76.
See Wallace in this volume. 77. See Kosman 1964, chs. 1-5, for a detailed treatment.
78.
J. Zabarella
1607a,
cols.
59off. On later developments of these doctrines see
Reif
1962, ch. 5.
79.
Cesalpino
1571
(lib. 1, q. vii); 1583, p. 23. On Cesalpino's teleology see Aristotelismo véneto
1983,1,
PP-
477-507
(Capecci).
80. See Wallace
1981a,
pp.
129-59;
1981b;
Aristotelismo véneto 1983, 1, pp. 349-78
(Wallace).
Reservations
are expressed by
McMullin
1983, Wisan 1984.
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704
Problems of knowledge and
action
or signs' which figures in the
Prior Analytics,
identified by some commenta-
tors
with the demonstration of the fact of the
Posterior Analytics.
81
The
relation of these discussions to the extensive
treatment
of signs and
signatures
that
occurs in magical, alchemical and medical contexts would
repay study.
82
These and other debates on the
nature
of
method in
natural
philosophy take place against a background of extensive discussion of the
role
of
logic
as a source
of
methods in the
arts
and
sciences,
and
of
the roles of
demonstrative and dialectical methods on the one
hand
and metaphysical
insight on the other in the
pursuit
of
natural
philosophy.
83
It is potentially misleading to describe
regressus
and the methodological
discussions which
surround
it as 'Aristotelian', for throughout the period
they draw on and interact with other traditions. For example, at the be-
ginning
of
his Ars
medica
Galen mentions
three
ways
of ordering material:
analysis,
synthesis and 'division'
(SLOLXVGLS).
84
This cryptic passage greatly
exercised
the commentators. In 'AH Ibn Ridwan's exposition, which
became available in Latin around 1300, Galen's analytic and synthetic
methods are identified with Aristotle's
a-noSe^iS
rov on
and
OLTTOO^L^LS
rov
SLOTL,
respectively; and the analytic method is further identified with the
method of analysis practised by geometers.
85
Pietro d'Abano, in his
immensely influential
Conciliator differentiarurn philosophorum,
composed
around 1310, further conflated these methods with the two procedures
mentioned by Aristotle at the beginning
of
the
Physics,
the one proceeding
from particular to universal, the other from universal to particular.
86
This
collage
of methods was elaborated and modified at the
hands
of
a
series of
medical writers, including Torrigiano dei Torrigiani (the
Plusquam
Commentator),
Gentile da
Foligno,
Jacopo da Forli and Ugo
Benzi,
all much
concerned to establish the credentials of medicine as
scientia.
87
In a
brief
but masterly work of 1508 the humanist scholar and physician
Niccolo
Leoniceno brought philological expertise and knowledge of the
classical
commentators to bear on the issue
of
the number and
nature
of
the
methods of medicine and
natural
philosophy.
88
Leoniceno distinguishes
sharply between
ways
of ordering the contents of an
entire
discipline for
81.
Prior Analytics
11.27.
This identification derives from the classical commentators: see references in
Bottin 1972; N.
Jardine
1976.
82. On signs in these contexts see, for example, Arber 1938, ch. 8; Pagel 1958a; Hacking 1975, ch. 5.
83. Risse 1964, pp. 201-439. See also Corsano 1958-63, 41:
507-17;
Papuli 1967; Poppi
1972a.
84. Galen 1821, 1, p. 305. 85. 'Ali Ibn Ridwan 1487, f 151™. 86. Abano 1504, ff. 9
v
-i2
v
.
87. See, for example, Randall 1961; Philosophy and
Humanism
1976, pp. 283-305 (W. F. Edwards);
Siraisi
1981, ch. 5; Scienza e filosofia 1983, pp. 375-94
(Movia);
French 1985.
88. Leoniceno 1532 (De tribus doctrinis ordinatis secundum Galeni
sententiam
liber; 1st edn, 1508). On this
work
see Philosophy and
Humanism
1976, pp. 283-305 (W. F. Edwards); Mugnai Carrara 1983.
Cambridge Histories Online © Cambridge University Press, 2008
Epistemology of the
sciences
705
teaching purposes
(ordines docendi)
and procedures for investigating
particular questions
(modi doctrinae).
89
To the first category he assigns the
three
procedures of Galen's Ars
medica.
In the latter category he recognises
syllogistic
demonstration together with
three
'Platonic' methods for
hunting down definitions,
resolutio
(which he is at pains to distinguish from
other resolutive procedures, including the resolutive or analytic method of
the geometers
90
),
divisio
and
definitio.
Much of the extensive sixteenth-
century Italian writing on medical method
follows
Leoniceno in this
classification.
91
The Paduan physician and Galen editor Giovanni Battista
da Monte makes interesting use in his account
of
therapeutic method
of
the
investigative
procedures recognised by Leoniceno together with inference a
signo
which, he claims, is needed to relate the general conclusions
of
medical
science
to particular patients.
92
It has been shown
that
da Monte's account
forms a
part
of
his programme for a reform of the teaching of therapeutic
medicine designed to bring it more into line with the doctrine of Galen's
Methodus
medendi.
93
Where
there
is a substantial secondary literature on Italian debates in the
epistemology
of natural philosophy,
there
is a dearth of recent studies of
'northern'
developments. For example, the epistemology of Philipp
Melanchthon and its influence have received little recent attention, despite
the great intrinsic interest of his De
anima
and the likely historical
importance
of
the
views
of
the
Praeceptor Germaniae
94
Similarly, although
the methodological innovations of Petrus Ramus have been the focus of
considerable scholarly attention,
95
the works of his French and German
Aristotelian opponents have been little studied.
96
When we
turn
to the epistemology of mathematical science we find
again a considerable diversity of topics. Catena's
Oratio
pro
idea methodi
is
but one of a number of works of the latter
part
of the sixteenth century
which
set up the deductive hierarchy
of
geometry as a model
of
perspicuous
organisation for other disciplines.
97
Further,
there
is an interesting body of
late sixteenth-century speculations on the
nature
of'universal mathematics'
(mathesis universalis),
speculations inspired by reflection on book v of
89. Leoniceno 1532, p. 69. 90. Ibid., pp.
62ff.
91.
On sixteenth-century treatments of medical method see N. W. Gilbert i960, pp.
102—5;
Wightman
1964, 1973; Wear 1973; Bates 1977.
92.
Da Monte 1558, pp. 83fF., ii2ff. (Methodus medicinae universalis). For a detailed account of Da
Monte's
methodology see
Bylebyl
forthcoming. 93.
Bylebyl
forthcoming.
94.
See, however, Sartorius von Waltershausen 1927; Maurer 1962; Kessler in this volume, pp. 516-
18.
95. See especially Ong 1958a;
Vasoli
1968a, pp. 333-601.
96.
In particular Jacob
Schegk's
massive De demonstratione would repay further study: see Risse 1964,
pp.
256-9; Schilling 1969, p. 44. 97. Schilling 1969; see also De
Angelis
1964.
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7o6
Problems
of knowledge and action
Euclid's
Elements
and passages from Proclus'
Commentary on the First Book of
Euclid's
Elements
which suggested the existence of a mathematical master
science
prior to arithmetic and geometry and concerned with order and
proportion.
98
Proclus' commentary on Euclid plays a major role too, both
as source and as
foil,
in Ramus' radical but often obscure pronouncements
on the
status
of
mathematics, pronouncements which range from 'Platonist'
claims
about the certainty, intuitive evidence and edifying power of
mathematics to remarks which imply
that
he viewed mathematical
propositions as precepts derived from observation for practical purposes of
measurement, calculation and prediction. Both the content and fortunes of
Ramus' epistemology
of
mathematics deserve further study.
99
Yet
another
Proclean topic with an
interestingfortuna
is geometrical analysis. Consider-
able
attention
was paid to the cryptic passages in Aristotle, Pappus and
Proclus,
which describe geometrical analysis as if it were a method for
working
back from problems or theorems to the principles by which they
may be solved or proved.
100
I have already mentioned the importance of psychology, and in
particular the De
anima
commentary, as a context for questions about the
means of attaining scientific knowledge.
101
Certain other issues in
Renaissance intellectual history deserve mention as contexts for the
epistemology
of
the
sciences.
The period is one in which substantial changes
occurred in classification and subordination of the
arts
and sciences both as
expressed in encyclopaedias and compendia and as embodied in university
curricula. The large
literature
on classification, subordination and prece-
dence in nobility and certitude of the sciences provides a major context
for
the epistemology of the sciences.
102
A second
important
context for
epistemology
is
that
provided by Renaissance discussions of ordering and
disposition of material within particular disciplines.
103
It would be
anachronistic to regard this
literature
as merely concerned with teaching,
98.
Crapulli 1969.
99.
On Ramus'
views
on method in mathematics see Verdonk 1966, ch. 6; 1968; Schilling 1969, pp.
I03ff.
On the didactic context see Margolin 1976.
100.
On the classical sources see Hintikka and Remes 1974.
101.
On Renaissance De anima commentary see Platon et Aristote
1976,
pp.
359—76
(Cranz); Kessler in
this volume.
102.
On the connections between epistemology and classifications of the
arts
and sciences in the
sixteenth and early seventeenth centuries see the major study by Schmidt-Biggemann 1983.
Wallace
1984,
pp.
126—48,
considers some late sixteenth-century Jesuit discussions
of
classification
and subordination
of
the
sciences.
The importance
of
the literature on precedence as a context for
epistemology
is noted by
Vasoli
1974, p. 425.
103.
This literature is surveyed by N. W. Gilbert i960;
Vasoli
1968a.
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