(1) This very loose cover phrase, meaning little enough without further qualifications, is selected here for its negative virtue of avoiding a too-precipitate definition of a movement - some of the complexities of which it is the purpose of this study as a whole to explore - which would in its narrowness be inevitably misleading. The terms used may, in a general way, be justified, however, by some expansion. The intellectual current referred to, and in which Dee has his place, was, it is true, hardly a "philosophy" in the sense that would imply that it flourished as any uniformly regarded, explicitly forumalated, isolable and complete, systematic body of doctrine. Rather, it exhibited itself in the main, and only so as a whole, through a multitude of partial and particular - frequently idiosyncratic - expresssions by individual thinkers active in numerous, seemingly disparate fields; hence it seems to take on a bewilderingly protean variety of forms as a consequence of such differing selections of and the accompanying changes of emphasis on elements from this philosophy (that is, which organically pertain to it viewed as a whole), and the widely differing types of subject matter with which it was brought into conjunction and applied as a more or less concealed organising framework. At the same time such manifestations have a unity in that there may be traced in them certain characteristic guiding cannons, and they are frequently to be found informed by characteristic, constantly recurring themes. Some of these the present introduction is designed to elucidate, and subsequent chapters, intended to illustrate as they functioned in a number of spheres. The increasing frequency of works in Dee's day that may properly be so analysed testifies to the way in which a number of their common basic assumptions were gaining currency in contemporary culture - though what were perhaps the fundamental reasons ultimately responsible for the directional unity discernable in such particular endeavours, was to find historically only gradual clarification or conscious recognition.
The movement is described as new,
not in order to discount the importance of its very obvious classical
or mediæval roots, or in disregard of such facts as that
many of its exponents were largely obsessed with such themes as
the discovery of the secret wisdom of the ancients, but only in
respect of the wide extent, and previously unexampled fruitfulness,
it attained at this time, and because it would seem to have been
so regarded by the majority of those who adhered to it in any
way; even when believing it to be a "revival" they proclaimed
it as "new" in relation to contemporary thought. Dee
and other such participants in it professedly and proudly looked
upon themselves as "moderns" - in their novel opposition
to many accepted teachings of the day, and seem to have consciously
thought of themselves as reformers; they are on occasion as confident
and enthusiastic as Francis Bacon in envisaging a new era of social,
scientific, and often religious progress, which the innovations
they advocate will contribute to, or initiate. (A good example
of the general spirit is provided by Hakewell, who sometimes quotes
Dee in support of his views; especially his laudatory account
of the "Renaissance" and its various stages from Paulus
Jovius and Boccacio, whom he takes as its initiators onwards -
an historical analysis curiously resembling that of nineteenth
century historians - with his conclusion, "if we descend
to a particular examination of the several professions, Arts,
Sciences and Manufacturies, wee shall surely finde
the prediction of the Divine Seneca accomplished; Multa
venientis ævi populus ignota nobis sciet," and then
quotes a pronouncement of Ramus - whose relations with Dee will
be detailed later - "Majorem doctorum hominum & operum
proventum soeculo uno vidimus, quam totis antea 14 Majores nostri
viderant." A Discourse Apologeticall (p. 261). Its
"vigour," to be gathered from its rapid spread and thw
swift historical realization of its fruitful potentialities, which
become ever increasingly apparent, was assisted by this attitude,
but is chiefly due to the related factor that as a "philosophy"
it proved sufficiently flexible to absorb and adapt itself tot
he requirements of a number of contemporary features of the highest
importance for the development of science - such as a relatively
sudden, renewed interest in mathematical studies, and novel or
unorthodox types of physical speculation - of these it was prepared
to offer an adequate theoreticaly account, and one commensurate
with the high value that individual specialists might attribute
to them, and offered a congenial intellectual setting for their
practise, while towards these older, more rigid systems showed
themselves, at best, indifferent. Its "vigour" is also
to be seen in the way such thinkers as Dee show themselves as
acutely conscious of what they seem quite unequivocally to look
on as a general development taking place in intellectual and more
material fields, and put forward their doctrines as those best
capable of keeping abreast of, or valuably enriching, this process.
Many schemes of educational reform can be associated with this
particular current of ideas, and of the highest significance are
the constant efforts it encouraged, as those of Dee and others,
to convert as far as might be possible, what had hitherto been
neglected as mere "craft" into "applied science"
and to establish mutually beneficial relations between the speculative
theoretician and the uninstructed practise of the artisan and
others engaged in technical and constructive spheres.
(2) How quickly in some respects is graphically illustrated by Campanella's reception in France after his long imprisonment. Preceeded by a considerable reputation as the defender of Galileo, opponent of Aristotle, martyr to reform, on closer acquaintance a new generation of scientists found little worthy of respect in him. Both DesCartes and Cassendi so opposed in many respects, frankly despised him; Mersenne wrote of his disappointing meeting with him "ou j'ay appris qu'il ne nous apprendre rien dans les sciences" - and he was soon consigned to intellectual exile - socially feted and casting horoscopes - at the French court (Lenoble, Mersenne où la Naissance du Mécanisme p. 41 et seq.).
(3) See particularly E.G.R. Taylor
Tudor Geography (1930); F.R. Johnson Astronomical Thought
in Renaissance England (1937).
(4) F.R. Johnson reviewing Tudor
Geography (Isis. XXIII. 1935 p.291).
(5) Huygens has been usually credited
with the origination of this significant - since rapidly popularised
analogy. Boyle writes (Works 1672. Vol. 5, p. 163) that
the Universe is "like a rare clock such as may be seen at
Strasbourg, where all things are so skilfully contribed that the
engine eing once set amoving all things proceed according to the
artificer's first design." However, the comparison would
seem to have a much longer history; Mersenne developed the idea
of God as the Watchmaker - in connection with proofs of his existence
drawn from apparent cosmic design (Lenoble Mersenne p.
250 nl); Ralegh describes "Nature" as that system of
laws infused by God into matter "having no other selfe ability
than a Clocke after it is wound up by a mans hand hath" (History
of the World I, 1, 10 p. 11), and the analogy makes an early
and suggestive appearance in the opening chapter of a popular
work of Christian Platonism by de Mornay that Philip Sydney translated
(also in connection with the argument from design) (Sydney Works
vol. 3, pp.267-8). Early uses are possibly not unrelated to the
considerable interest shown by sixteenth century scientists and
philosophers in the possibility of constructing a mechanical model
of the Universe, based on accounts of Archimedes' "sphere."
(References to this as one of the fruits of mathematical studies
are almost innumerable. Dee quotes Cicero on this work of "Thaumaturgike,"
"For when Archimedes (sayth he) did fasten in a sphere, the
mouynges of the Sonne, Mone and of the five other Planets, he
did, as the God, which (in Timaeus of Plato) did make the world.
That, one turnyng should rule motions most unlike in slownes,
and swiftnes." Preface Ajv). It is not the mere
metaphor or the implied relations of God to the world that is
distinctive and important about its use in the generation of Boyle
and Huygens. These might equally well pertain to any ordered cosmology
- such as that of the Averroists - which aimed to exclude the
element of the miraculous, the irregular, the irrational, from
nature, and indeed many attacks on physical astrology in Dee's
day were made from the theological position that this science
aimed to exhibit the universe as just such a fully determined
system, such a self-sufficient machine as Boyle describes, leaving
God no essential part to play in its general processes and operations
(vide infra Ch. 3). But significant changes occur as regards
the type of causation, the "intelligibility" and accessibility
of the "mechanism" that is supposed to maintain his
His cosmic system. The causal links in the Aristotelian picture
- the transmissionof motion from the primum mobile - remained
inevitably of an "occult" kind, unobservable, incalculable
in detail, unknown, if not inconceivable in principle. Only in
the mid-seventeenth century, if gravity were accepted as a physical
force, able to act at a distance, which could be given exact mathematical
expression, could such an analogy be regarded as holding good
in a strictly "mechanical" sense, and the chain of causes
and effects be thought of as exactly measurable in kind, and the
whole system as mathematically representable, and throughout analysable
and intelligible. (Descartes' plenum with its vortices provided
another pattern of a similar kind, whose entire materiality made
it even more preferable to many.) But this ideal is already significantly
adumbrated in the systems of mathematical neo-Platonists in an
earler age. Dee, for example, in the Aphorisms of 1558
represents the universe as a closed mechanical system, its processes
governed by the "emissionof species" from all entities,
but particularly the heavenly bodies in it; these however he conceives
of as physical forces, which may be if only indirectly, exactly
measured, and their propagation is strictly geometrical, and he
looks forward to a time when scientists might be able, combining
theory and observation, exhaustively to describe the world in
terms of mathematical law.
(6) Bolton: Follies of Science
at the Court of Rudolph II, p.2.
(7) While it remains true that "the
verification of a rationalistic scheme is to be sought in its
general success, and not in the peculiar certainty or initial
clarity of its first principles" (Whitehead: Process
and Reality p. 10) such verification is frequently a lengthy
historical process, distinct from and always subsequent to the
original formulation and acceptance, though it too often intrudes
on, and colours, the examination of the original motives and conditions
which produced such schemes.
(8) Subsequent chapters will explore
some of these interconnections, see also Lenoble's discussion;
its theme, his comment after listing a number of the sciences
considered almost as on equal level in the Renaissance - Mathematics,
Theology, Physiognomy, Cabalah, Argyropeia etc. "Pour les
hommes de ce temps ces 'connaissances' ne sont pas juxtaposées
mais impliqueés, les unes dans les autres" (Mersenne
(9) Hardin Craig: The Enchanted
Glass, p. 14.
(10) Whitehead: Process and Reality,
(11) The argument of Strong's Procedures
and Metaphysics, that science and mathematics developed even
in the Renaissance entirely methodologically, and were only stifled
and impeded by any contacts they made with the Platonism of the
day, which is said to have no direct kinship with philosophies
generated later when the implications of a successful mathematic
were perceived, will be considered in detail in a subsequent study
of Dee's Preface. The present introduction is designed
only to set out and illustrate the point of view from which this
study has been made, but for which, it is believed, later chapters
provide much supporting evidence.
(12) Vision of Piers the Plowman
ed. S. Keat, Oxford 1886 vol. 1, p. 300. B. Passus 10 p. 207-210
(omitted in 3rd version).
(13) Advice to a Son (1658)
ed. Parry, London 1896, p. 14. "My Memory reacheth to the
time," he says of Mathematics, "when the generality
of People thought her most useful Branches, Spells, and
her Professors, Limbs of the Devil."
(14) Blanché: La Science
Physique et la Realité p. 11.
(15) Essays II, 12 "Et
m'a l'on dict qu'en la Géometrie (qui pense avoir gagné
le haut point de certitudes parmy les sciences). Il se trouve
des demonstrations inevitables subvertissant la verite de l'experience,
comme Jacques Peletier me discrit chez, moq qu'il avoit trouvé
deux lignes s'acheminans l'une vers l'autre pour se iondre, qu'il
verifioit toutefois ne pouvoir iamais, iusques à l'infinité,
arriver à se toucher et les Pryrrhoniens ne se servent
d leurs argumens et de leur raison que pour ruiner l'apparence
de l'experience" (quoted Brunschvicg L'Expérience
Humaine et la Causalité Physique, p. 170).
(16) B. Jowett, The Dialogues of Plato, trans. with analyses and Introductions (3rd, ed. Oxford 1892) vol. 3 Introd. to Timaeus ch. 8, p. 416. See also ch. 2, p. 388 et seq for his rejection along these lines of Whewell's criticism of the ancients, that they had plenty of ideas and plenty of facts, but their ideas did not accurately represent the facts with which they were acquainted" which Jowett stigmatises scornfully as the crude mistake of an uneducated person!
However, it should be noticed that whatever the defects of Whewell's interpretation of particular points, not the least of the merits of this first great historians of science, is the striking initial analysis he makes of the conditions of scientific knowledge (to which he was led by a neo-Kantian epistemology) in which the "facts" on which all induction bases itself are presented as artificial constructs, already intellectually characterised by the observer's mind. (History of Scientific Ideas, p. 38 et req). "Senstation" he terms the "matter", "Idea" the "Form of Knowledge," and therefore decides that that which is admitted as theory, and that which is accepted as fact, differ merely in the degree to which Ideas are absorbed to the material, the ease and inevitability with which they are felt to organise senstation - i.e., a psychological criterion that prohibits any general and absolute differentiation - "In a Fact, the Ideas are applied so readily and familiarly, and incorporated with the sensation so entirely that we do not see them, we see through them." (Ibid p. 44)
(17) See especially Metzger: Les
Concepts Scientifiques, a detailed examination of the process
of "conceptualisation" - by which differing "objects"
come to be ranged under the same class heading and a study of
the shifting "Analogical criteria that, controlling this
activity, are to be detected in present and past scientific systems.
(It is stressed that the claim that organising class concepts
come spontaneously from the objects themselves, is an undemonstrable
metaphysical assumption; if some appear inevitable, the ultimate
ground for maintainting this is merely "psychological,"
"et c'est en raison de la satisfaction qu'il donne à
notre intelligence et à notre imagination que nous avons
déclaré naturel") and that although
certain "concepts," considered only as terms designating
some particular group of "objects" ("metal"
is an example) superficially seem to have acquired a stability
amounting to permanence through time, yet they have nonetheless
given rise to, or figure essentially in, hypotheses of such widely
divergent characters at different epochs that it is clear that
in a more fundamental sense which in turn determines any view
of the objects they describe, they undergo striking metamorphosis.
Hence the prime difficulty, and perhaps the major task of the
historian of science faced with a particular period, even though
its terminology has obvious overt similarities with others is
"qu'il lui faudra diviner le cortège de penseés
non exprimées que chaque système de concepts évoquait
à telle époque." (pp. 12-14)
(18) Edgar Wind: Experiment and
Metaphysics (Proceedings of the Sixth International Congress
of Philosophy, 1926, p. 609-614 [Offprint p. 221]).
(19) Dingle: Through Science
to Philosophy p. 113 cp. Carmichael: The Logic of Discovery
(a full discussion of the problem of the interaction of theory
and observation from a "postulationist" standpoint)
p. 191. "There is much to be said in favour of the thesis
that natural science should be considered a construct of the mind
rather than a paraphrase of nature wrought out by the mind"
(20) Brunschvicg L'Expérience
Humaine p. 426 quotes an assertion of du Bois-Raymond, "Les
propositions de la mécanique sont mathematiquement demonstrables,
et portent en elles la même certitude apodictique que les
propositions de la mathématique."
(21) From Euclid to Eddington
(22) New Pathways in Science,
C.U.P. 1947 ed., pp. 232-233. The passage continues "But
theory is advancing, and we are beginning to ask, Are these four
constants irreducible, or will a further unification of physics
show that some or all of them can be dispensed with?" (or
again, W.V. Quine comments apropos of the reduction of empirical
sciences to "logic": "Carnap has pursued this
program with such amazing success as to provide grounds for expecting
all the expressions to be definable ultimately in terms of logic
and mathematics, plus just one `empirical' primitive, representing
a certain dyadic relation described as `recollection of resemblance'"
(Truth by Convention p. 116 n. 20 in Philosophical Essays
for A.N. Whitehead, N. York, 1931).
(23) Dr. Seth Demel comments: "Der
mathematische Gedanken indem er unter der unmittelbaren Wirkung
seiner Gestaltung bei Platon den Konkreten Niederschlag in den
des Eukleides findet, wird zu einen mächtigen
Kompenente der abendländischen Geistesbildung. Der Ordo
Geometricus ist das Leitmotiv des Denkens der Renaissance
er erweist in unmittelbarer Orientierung an Platon seine Tragkraft
an der Engfaltung der exakten Naturwissenschaften" (Platons
Verhältnis sur Mathematik p. 143).
(24A) On the Originality of the
Renaissance J.H.I. vol. 4, 1943, p. 51.
(24B) Taylor: Platonism and its
influence, p. 27.
(25) e.g., Sarton, in the Second
Preface to vol. XXII of Isis 1935 The History of Science versus
the History of Medicine, p. 317: "Even as the fundamental
explanation of the universe, so far as any is possible is necessarily
mathematical and cannot even be uttered in non-mathematical language,
even so the fundamental explanation of human progress must necessarily
be focussed on the history of science, itself focussed upon the
history of mathematics....Mathematics forms the very core of human
thought and hence of human life" etc.
(26) Since it can be held that even
general empirical statements of the kind "food nourishes,"
"water drowns," "fire burns" are significant
communications only because they make implicitly recognised reference
to approximate measures of quantity. Discussed Brunschvicg:
L'Experiénce Humaine p. 569.
(27) See Borel: L'Espace et le
Temps, p. 13.
(28) Poincaré: La Valeur
de la Science, p. 7.
(29) Whitehead: Process and Reality,
(30) Its theoretical completeness,
its capaciousness and flexibility is testified to by Mach's assertion:
"The principles of Newton suffice by themselves without
the introduction of any new laws to explain thoroughly every mechanical
phenomenon practically occurring whether it belongs to statics
or to dynamics, difficulties arise only of a mathematical or formal
character." The Science of Mechanics, p. 257.
(31) See Brunschvicg: L'Experience Humaine, p. 53.
(32) E.g., in The Grammar of
Science. Thus "an organism or form of life" Pearson
remarks is "quantitatively described by the numerical values
of the types and variabilities of its several organs, and by their
interrelationships as expressed by the coefficients of correlation."
(op. cit. London, 1900 ed. p. 418).
(33) The Mathematical Way of Thinking
in Studies in the History of Science 1941, University of
Pennsylvania bi-centenary Conference, p. 123.
(34) "Since the dread is considered
to be a complete thing and to comprise the whole essential nature
of the numerical system they assert that the bodies that revolve
in the heavens are ten and there being only nine that are visible
they make the anticthon the tenth." (Aristotle: Metaphysics
I. 5.) It remained unobservable since, having a motion complementary
to the earth's, it remained always on the opposite side of the
(35) The striking material success
of Galileo's work, for instance, obscured even for his immediate
successors and some of his contemporaries, the real nature of
his position and grounds of his methods. On various later occasions,
aspects of his "Platonic mathematicism," his impatient
disregard of the "experience," his opponents were continually
invoking against his conclusions will be relevantly noted. Yet
the completeness of misunderstanding of that was able to arise
among seventeenth century scientists who no longer felt it necessary
to associate their practise with any such metaphysic is illustrated
by Mersenne. Lenoble describes his pragmatic phenomenalist view
of science - that its function was only to search for laws expressing
regular connections between "accidents," but was powerless
to establish any relations between its "true cause"
and any phenomena this being inevitably a metaphysical question.
From this attitude sprang his inordinate admiration for Hobbes
and Gassendi, and with them and without apparently any sense of
disparity he associated Galileo, regarding him as the model of
"the philosopher" as one who merely patiently investigated
facts and avoided all unnecessary discussion (Mersenne,
(36) Metaphysical Foundations
of Modern Physical Science p. 223 et seq. cp also Boutroux
on the transformation of metaphysical notions into mere essential
canons or conventions of procedure, who observes that on the one
hand many scientists declare themselves indifferent to "the
philosophy of science" as having no possible repercussions
on their work, "Et d'autre part ils se montrent si attachés
à leurs propres idées sur la science qu'ils supportent
avec paine de les voir mises en cause; c'est qu'en effet ces idées
auxquelles ils n'attribuent aucune valeur absolue, sont cependant
les conditions indispensables de leur activité scientifique"
(L'Idéal Scientifique p. 7). From similar reasons,
Collingwood has argued that "any attack on metaphysics is
an attack on the foundations of science: any attack on the foundations
of science is an attack on science itself." (An Essay
on Metaphysics Oxford 1940, p. 170).
(37) cp Whitehead, Process and Reality, p. 13. "In their later stages, apart from occasional disturbances, most sciences accept without question the general notions in terms of which they develop. The main stress is laid on the adjustments and direct verification of more special statements. In such periods scientists repudiate philosophy."
A relevant, if restricted, illumination
is provided by Metzger's detailed tracing of the history of the
changing attitude adopted in various periods to one particular
scientific concept - the theme of Attraction Universelle et
Religion Naturelle. The "existence" of Universal
gravitation was established for its advocates "non par des
raisonnements rigoureux la déduisant a priori de la nature
de notre esprit ou de la nature des choses, mais par le succès
de calculs basées sur l'existence de cette force,"
for which Newton had produced the formula (p. 5) and it was bitterly
resisted, as inconceivable, a violation of the character science
must attribute to nature, and mechanical principles by the Cartesian
school. These sentiments were in some sense shared by its supporters
since its existence was extensively invoked by Newtonians for
religious purposes, against a mechanical atheism, as demonstrating
the continual operation of God, or the necessity of supposing
that he had infused this force into matter by special decree,
since it was of a kind that could not be admitted as an intrinsic
property of matter, and properly pertaining to its nature. Increasing
familiarity, the disappearance of rival theories, led eventually,
however, to universal gravitation appearing to astronomers with
no religion at all, such as Laplace and professing materialists,
merely by this progressive assimilation of it to habits of thought,
with no increase or alteration in kind of the evidence for its
existence as entirely "natural," as a notion presenting
no special difficulties or raising further questions if accepted,
to which the mind offered no resistance, as a feature of body
barely separated from the directly perceptible.
(38) L'Histoire des principes
de la Dynamique avant Newton in Revue de Metaphysique et
de Morale. Année 28, 1921, p. 688. The particular
"vue aussi théorique," referred to, is Newton's
assumption that "Les propriétés du mouvement
sont conformes au moule mathématique que nous fournit la
Théorie des Fonctions."
(39) Perhaps the most striking example,
because of its long and still continued importance, forms the
theme of F.A. Lange's History of Materialism, which, emphasizing
throughout the methodological validity of "materialism,"
insists equally strongly on its complete metaphysical invalidity.
(40) The "problem" is avoided
in the realm of symbolic logics. Here are admitted to a parity
an indefinite number of independent, sometimes mutually contradictory,
tautologous systems, arising from premisses which are not in question,
since they are acknowledged as arbitrary (tough not consequently
random), and which can also serve as regulative fictions - rules
of syntax - setting up a standard of coherence, which alone can
be relevant here. Such systems are empty of "content,"
have no reference beyond themselves, since the entire "meaning"
of any sign employed is merely the totality of its relations to
the other signs within the systems. Most steps in mathematical
reasoning, e.g., (Tan II = Sin II/Cos II) show themselves formally
as being only "a definitional transformation of an antecedent
self identity" (A.V. Quine, Truth by convention in
Philosophical Essays for A.N. Whitehead, London, 1936,
pp. 90-125). But the view that mathematics might be only such
another system, or set of systems, as this, became possible at
only a very late historical stage, for the increasing correspondence
between the structure of various branches of mathematics, the
mutual harmony and apparent inevitability of their premisses,
produced an impression of phoenix-like singleness which had first
to be broken down by the emergence of non-Euclidean geometries,
and Booleian algebras. Platonists insisted, of course, that mathematics
rested on "hypotheses," but not in order to denigrate
at, but to relate it to metaphysics, and so allow of intelligible
explanation for the fact that mathematical results accorded so
well with the intuitional picture of the world.
(41) Cohen: Reason and Nature,
p. 16. The passage goes on to consider what an untrained observer
could have gained, though "experiencing" everything,
at some of "the most famous and epoch making experiments
of modern times," such as those of Hertz or Michelson, in
order to show that "Observations unillumined by theoretic
reason is sterile." (One might add that the results of the
Michelson-Morby experiment had to wait nearly thirty years to
receive any fruitful interpretation. A novel context of theory
in which this data had a logical place was necessary before this
could acquire "meaning" and cease to be merely enigmatic).
(42) cp H. Jeffreys: "It is
sometimes considered a paradox that the answer depends not only
on the observations but on the question, it should be a platitude"
etc. (Theory of Probability preface, Oxford, 1939.)
(43) Collingwood: The Idea of
Nature, p. 42. An excellent detailed illustration, since
it might superficially have been suspected to be an example of
the reverse, is furnished by A.P. Usher's tabulation of the gradual
recognition and solution (the first much the more troublesome)
of successive related problems by Cardan, Porta, de Cause, Toricelli,
Boyle, Guerick, Worcester, Savery, Papin, Huygens, leading "progressively
towards an explicit concept of a steam engine, though no adequate
synthesis was achieved," a process which culminated by clearly
formulating this particular "problem," "and set
the stage for Newcomen's synthesis" (History of Mechanical
Inventions, p. 25 et seq).
(44) Poincaré: La Valeur
de la Science, pp. 24-25.
(45) Illuminating are the shocked
verdicts on Kepler's total work, passed by later scientists, recorded
by Whewell: that he had "miraculous good fortune in seizing
truth across the wildest and most absurd theories," that
this success "may well inspire with dismay those who are
accustomed to consider experiment and rigorous induction as the
only means to interrogate nature with success." Laplace
declared "Il est affligeant de voir ce grand homme même
dans ses derniers ouvrages, se complaire avec délices dans
ses chimériques speculations, et les regarder comme l'âme
et la vie de l'astronomie." Whewell himself, allowing that
Kepler's mysticism apparently did not impede his successful "prosecution
of research," sharply separates the two, saying, in his fertile
mind "weeds and grain throve and flourished side by side
almost undistinguished, and he gave a peculiar appearance to his
harvest by gathering and preserving the one class of plants with
as much care and diligence as the other" (History of Inductive
Sciences, vol. I, pp. 317-320).
(46) See particularly, Burtt: Metaphysical
Foundations of Modern Physical Science, p. 65 et seq. Galileo's
"confident belief in the mathematical structure of the world
emancipated him from the necessity of close dependence upon experiment."
(47) Some typical minor instances are: Columbus' theories, drawn from the Aristotelian physic, of the proportionate distribution of earth and water on the earth's surface; C.M. Hall's invention of achromatic lenses (of different refracting media) which obviated a supposedly irremediable defect of refracting telescopes - resulting from his incorrect views on the structure of the eye and the functions of the humours it contains; Balmer's search for mystic numerical harmonies, which drew him to "discover" along with much nonsense, the regularity exhibited by the wave lengths of the hydrogen spectrum; Hamilton's devising of quaternions - by his own account, from what now appears only a misleading metaphorical syggestion in a fallacious remark of Kant's on mathematics; Carnot's principle - established, as he believed, by a theory of the nature of heat, which soon after refuted, brought the principle into temporary disrepute - until Clausius' vindication of it. Of the relation between the status of the hypothesis and the predictions made from it, "a spectacular instance is the prediction of wireless waves from the electromagnetic theory of light, another the prediction of what is called conical refraction in optics, from the older wave theory of light, another the prediction of the wavelike character (in some respects) of electrons from the newer quantum theory" (E.T. Bell, The Search for Truth, N.Y., 1935, p. 80). An earlier example is the way in which the phlogiston theory had been taken as "proved" by the verification through direct experiment, of various predictions made from it, as for instance that the union of phlogiston (of which carbon ws supposed to consist almost entirely) and of "dephlogisticated metal" should restore the original metal itself (carbon heated with lead calx did, of course, yield lead).
But the striking success in practice
of deductions made from premisses or suggested by representations,
later abandoned as false, is a notable feature of all past science,
indeed if its total history is considered, a very large portion
of all discoveries must have originated in this fashion. An illuminating
discussion of the relations between "théories abstractes
et représentations concrètes dans la physique moderne,"
and of the logical defects, and distortions imparted by these
latter, which nevertheless "ont joué un rôle
des plus utiles dans le dévelopement des théories
physiques, sans elles le progrès de ces théories
aurait été dans beaucoup de cas considérablement
valenti, si ce n'est définitivement entravé,"
is to be found in de Broglie Continue et Discontinu en Physique
Moderne, Paris, 1941, p. 91 et seq. On analogies underlying
past scientific, especially chemical, theories and the predictional
successes of these, see Metzger, Les Concepts Scientifiques,
e.g., p. 43 et seq. on the "success" - in terms of the
discoveries it produced - of a fantastic eighteenth-century theory
of combustion, which took the refractive power of substances as
indices to their "combustibility."
(48) See Nunn: The Aim and
Achievements of Scientific Method, p. 71.
(49) Lovejoy: The Great Chain
of Being, p. 333.
(50) J. Ekehorn, Sherrington's
"Endeavour of Jean Fernel" and "Man on his Nature,"
Comments by.... Pt. I, p. 36, Stockholm, 1947. (Acta Medica
Scandinavia, Vol. 127, Suppl. 187.)
(51) Prost. Les Sciences et les
Arts Occultes au XVIe - Siecle vol. I, Introduction, p. iii.
(52) Their positive contribution
is discussed by E.W. Gudger, The five great Naturalists of
the Sixteenth Century (Isis XXIII 1934/1935, p. 21 et seq.).
(53) Olschki. Bildung und Wissenschaft im Zeitalter der Renaissance, p. 37. Apart from this consideration, Daremberg's verdict may well stand (Histoire des Sciences Medicales: Paris 1870 vol. 1, p. 355 - quoted Zilbourg, The Medical Man and the Witch during the Renaissance, p. 88) that the history of medicine in the sixteenth century is much less significant and theoretically less interesting than that of the preceding one; may in fact "be reduced to the following three points: the humanists busy discussing texts; anatomists scrutinizing nature; and Paracelsus dreaming at high noon and raving delirious whil in full possession of his senses."
Harvey however refers to the heart
as "a piece of machinery in which through one wheel give
motion to another, yet all the wheels seem to move simultaneously"
(Butterfield: Origins of Modern Science, p. 44). The
development of this approach to physiology later in the century
may be seen in the achievements of Stensen and Borelli whose work
On the Motion of Animals has been called "a supreme
example of the application of the science of mechanics to the
study of living organisms" (Ibid p. 100 et seq.). For a
considerable period thereafter it is noticeable how in this sphere
"mechanical explanations," because of their more perspicuous
intelligibility and analogical coherence with other more advanced
or supposedly better founded sciences, are sought in preference
to chemical ones even when these would seem the most natural.
(Huygens typically opens his Traité de la lumière
by defining "la vraye Philosophie" as that "dans
laquelle on conçoct la cause de tous les effets par des
raisons de mechanique" see Lenoble: Mersenne p. 364.)
An illuminating example in the early eighteenth century is Derhem's
treatment of respiration: he notices the difficulties travellers
experience in breathing when crossing the Alps or Andes and continues,
"Thus it appears, that an air too subtile, rare and light,
is unfit for respiration: but the cause is not the subtility,
or too great delicacy, as Mr. Boyle thinks, but the too great
lightness thereof, which renders it unable to be a counter balance,
or an antagonist to the heart, and all the muscles ministring
to respiration, and the diastole of the heart." Later, returning
to this topic, he sets out various chemical reasons that have
been suggested as the purpose of this process, as that "it
conveyeth a nuro-aerial ferment to the blood, to which the animal
spirits are owing, and all muscular motion" - only to dismiss
these and affirm "the principal uses to be, to move, or pass
the blood from the right to the left ventricle of the heart.
Upon which account persons hanged or drowned, or strangled by
catarrhs, so suddenly die, namely, because the circulation of
their blood is stopped." "For the same reason also is
it, that animals die so soon in the air pump." And he appends
a formidable list of experiments, performed by himself and others,
relating largely to the resuscitation of animals by artificial
respiration and blowing air into the lungs, as undeniable proof
of this theory. (Physico - Theology I, 1, p. 41; IV, 7,
(54) E. Ekehorn, op. cit. (supra
n. 50) p. 30; such problems, it is thereupon remarked, and their
successful resolution, may be seen as products of some quite specific
period, for "there must be the means for reply, and enough
collateral knowledge to make the answer worth while."
(55) Given the amount of blood
driven forward at each pulse beat, and the rate of beat,
and the total volume of blood contained in the body, the
heart can be shown to deal with such a volume every few minutes,
and to throw out a weight of blood, exceeding that of a man, in
less time than this quantity could be reasonably supposed to be
freshly created! (In addition to such reasoning and mechanical
considerations regarding the functions of the valves in the veins,
Harvey also appears to have been influenced by preliminary considerations
of the widespread importance of "circularity" and "circular
processes" in the Universe, vide Walter Pagel: Wm. Harvey
and the Purpose of Circulation. Isis, vol XLI, 1950.
(56) An attitude reflected in an
interesting article of J.R. Partington's (in Annals of Science,
Vol. IV, No. 3, July, 1939) on the Origins of the Atomic
Theory, in the Renaissance: no influence or relevance is
allowed to "the overrated Nicholas of Cusa," and "the
speculations of Giordano Bruno" (on the three species of
minima: punctus, atomus, monad) are dismissed as "metaphysical
and of no physical importance. Bruno was a philosopher and not
a scientist." (pp. 200-201) (A more satisfactory picture,
exhibiting the constant interaction and close parallelism of metaphysical
and physical speculation on this subject, and their continuous
progress towards Dalton's conceptions, to which they equally form
the necessary historical background, is given by G.B. Stoner in
Atomic Views of Matter in the 15th, 16th and 17th Centuries
[Isis X, 2, 1927, 445 et seq.].)
(57) For example, see the many surprising,
historically indefensible tributes to the system of Epicurus (the
ethical foundations of which rather inhibited contemporary interest
in the natural sciences, and which adopted a thoroughly reactionary
and hostile attitude towards astronomical studies, one of the
most advanced and fertile departments of Greek science) quoted
by More (Hellenistic Philosophies, p. 51), such as, that
it formed "the creed of men of science," represents
"the most scientific elements of Greek antiquity" (Trezza)
and its advocates "with respect to the laws and principles
of Science come nearest of all the ancients to the science of
our own time." (Walzer.) Boutroux discusses with examples
such false comparisons, e.g., supposed anticipations of Cartesian
geometry in the work of Apollonius, Oresme or Ghetaldi, commenting
that such resemblance "sont souvent de pure forme, c'est
à dire ne portent que sur les manifestations de la pensee
scientifique (énoncés de faits, formules, ou théorèmes)
et non point sur les tendances et l'action creatrice de cette
pensée," he concludes that what is truly of consequence
is not the observation that some particular fact is to be met
with in a particular epoch, but to arrive at an understanding
of how it had then entered a system, what current of speculation
led to its being regarded as important, and what processes of
thought it then served to originate (L'Idéal Scientifique,
p. 11, et seq.).
(58) H. Miller: Philosophy of
Science and History of Science, p. 63, Isis XXX, 1939.
(59) See R. Berthelot: La Pensée
de L'Asie et l'Astrobiologie, Paris, 1938. On the interpretation
of animism and astral-determinism, he writes: "D'un côté
tout serait vivant, même le ciel et les astres; de l'autre,
tout serait soumis a des lois numériques, lois périodiques,
qui seraient à la fois des lois de nécessité
et des lois d'harmonie et de stabilité." (p. 8)
(60) E.g., the seemingly well-attested
phenomena connected with sorcery and magic were accepted indiscriminately
and a view of natural causation that would explain them all was
then sought for. (Typical of "facts" thus admitted,
is Postel's defence of the literal truth of Apuleius accounts
of witches and his own transformation into an ass in his novel,
nothing Postel argues can be urged against their possible
truth, and even if in this case some or all is invented, nevertheless,
"certè similia sunt in experimentis. Nam
quamvis sunt partim a poetis excogitate & fama locupletatae,
tamen omnino falsae esse non possunt: quia impossibile est famosum
esse omnino falsam, ut ait Philosophus, sunt enim famosa secundum
partem necessaria" (De Orbes Terrae Concordia, I,
8, p. 62).
(61) On previous paragraph see discussions
on "Naturalism" in Lenoble's Mersenne, esp. p.
6, et seq. - on its differentiation from later Cartesian mechanist
systems, p. 112, et seq., on Pomponazzi's de Incantationibus
and this movement X. p. 141, on the magnet's importance in such
(62) Mandonnet: Siger de Brabant
et l'Averroisme Latin, pp. 43, 55, 56.
(63) A.N. Whitehead: Adventures
of Ideas (Penguin ed., 1942), p. 139.
(64) P. Duhem: Roger Bacon et
l'horreur du Vide (in Bacon - Commemoration Essays
ed. Little), p. 268.
(65) Emmet: The Nature of Metaphysical
Thinking, p. 216.
(66) Metaphysics II, 995A.
(67) On the Heavens II, 294A,
(68) Rey: L'Apogée de
la Science technique Grecque. Pt. 2, Chap. VI. "La
notion du simple et le développement historique des sciences,"
"l'homme a commencé....par des notions toutes proches
de ses actes habituels, des événements, auxquels
il avait accoutumée d'assister et qui lui importarent le
plus pratiquement." But in the end, what is arrived at is
"le plus simple, c'est....à peu pres ce par quoi on
a commence ces recharches et ce en quoi on a réussi en
premier lieu à satisfaire plus au moins complètement
les tendances profondes...de l'esprit, de l'intelligence et de
la raison." (pp. 232-233)
(69) See Lenoble on the revelation
of the defects of this scheme by criticism based on epistemological
examinations such as that in Mersenne's La Vérité
des Sciences: "en prêtant une valeur ontologique
aux intuitions du sens commun sur l'espace, le grave, le léger,
les éléments et tout le materiels des catégories
il (Aristotle) croyant être assuré de la possession
de principes incontestables. La simple critique des données
sensibles...suffit à faire apparaître l'équivoque."
(Mersenne, p. 348.)
(70) Aristotle, Metaphysics,
(71) Ibid, 1029B.
(72) Ibid, 1043B.
(73) Ibid, 1010B.
(74) Ibid, 1010A.
(75) Ibid, 1063A.
(76) Ibid, 1006B.
(77) Ibid, 1038A.
(78) Ibid, 1025A.
(79) Ibid, 1007A.
(80) See Brunschvicg: L'Expérience
Humaine, pp. 149-153. This feature at once encouraged the
"Naturalist" doctrine previously discussed, and prevented
Aristotelians from making any fundamentally damaging criticisms
of them. Despite the bitter hostility to Naturalism these sometimes
displayed, yet seventeenth century scientists were justified in
looking on them as similar in their powerlessness to give any
satisfactory account of phenomena considered as causes or effects,
e.g., see Lenoble's account of the anti-Paracelsian writings of
the physician and botanist, Thomas Evaste (1824-1883), who strongly
resisted their indiscriminate importation of the miraculous into
nature, trying to present it as an orderly regular system on Aristotelian
principles, but who, although he criticised with sceptical common
sense all supposed operations of occult forms and causes, was
himself unable to suggest the substitution of any essentially
different type of causality (Mersenne, p. 211, et seq.
Lenoble comments, p. 216: "Toute cette critique des arguments
naturalistes est marquée au coin du bon sens. Mais que
propose-t-il à la place? Rien du tout. Il ne connaît
lui-même d'outre action causale que celle des qualités.")
(81) 1556. Avjv-Bjr.
(82) Metaphysics, 1005B.
(83) Discussed Claggett: Giovanni
Marliani and Late Mediæval Physics, p. 59 et seq.
(84) Testimonies as to how satisfactory
this could appear are not infrequent. In 1591 Cattan's translator
declares that the sciences have been almost perfected and exhaustively
explored by man's equiring spirit, for man has in knowledge of
nature "entred so farre, that he hath discovered the essence,
constitution, and mixture of the most parte of things made, the
proportions conveiances and differences of them, and the being
and progresse of the faculties thereof, to what effects they do
come, bringing forth the causes and reasons so manifest, that
they cannot be disproved." (The Geomancie of....Cattan,
Epistle Dedicatory, A2v.)
(85) Dingle: Science and Human
Experience, p. 14.
(86) Dingle: Through Science
to Philosophy, p. 28.
(87) See Claggett: Giovanni Morliani,
(88) A Dialogue Philosophicall,
(89) An excellent example of its
defects in this respect is offered by Porta's Natural Magick.
He sets out to explore nature and to do this experimentally not
merely to understand but to discover, predict and apply knowledge
to practical ends; "I never wanted also at my House an Academy
of curious Men, who for the trying of these experiments cheerfully
disbursed their Moneys, and employed their utmost Endeavours in
compiling and testing the matter of this book. The unit of Cause
in nature he lays down explicitly, on commencing, is the essential
form of things (their virtues he can only explain by giving them
a divine beginning, and referring their operations to divine will).
But he can then only discover as a principle on which these act,
and which is to some extent susceptible of observation, the relations
of sympathy and antipathy which they produce between things "whereof
there can be rendered no probable reason: neither will any wise
man seek after any other course hereof but only this, That it
is the pleasure of nature to see it should be so." This
is then his instrument for the investigation of nature, he expresses
his observations in terms of it, he draws deductions from it as
combined with certain facts that allow him to proceed to other
facts and frequently by predictionof this sort claims the hypothesis
vindicated. A sample of his scientific reasoning in this manner
is - and these are "discoveries" etc. which he has been
led to by it, and claims to have then proved by practical testing:
"The Ape of all other things cannot abide a Snail: now
the Ape is a drunken Beast, for they are wont to take an Ape by
making him drunk; and (therefore) a Snail well washed is a remedy
against drunkenness...The Wolf is afraid of the Urchin; thence
if we wash our mouth and throat with Urchin blood, it will make
our voice shrill, though before it were hoarse and dull like a
Wolves voice," or again, the "love" between the
Moorhen and the Hart, or the Goat and the Partridge is a sign
that either of the members of such pairs may be used indifferently
for the same remedies in medicine, etc. (Naturall Magick...Wherein
are set forth all the Riches and Delights of the
Natural Sciences." Preface; I.5, p. 6, I, 7,
(90) Both quoted Dampier: History
of Science, pp. 181, 184.
(91) De Docta Ignorantia,
(92) Quoted Strong: Procedure
and Metaphysics, p. 76, 89, from Opus Novum de Proportionibus
(93) See Duhem op. cit. (in Note
64), p. 278.
(94) "Adhuc autem gravius est
quod post modum dicit: per rationem concludo de necessitate,
quod intellectus est unus numero; firmiter tamen teneo oppositum
per fidem...Ergo sentit quod fides sit de aliquibus quorum contraria
de necessitate concludi possunt. Cum autem de necessitate concludi
non possit nisi verum, necessarium, cujus oppositum est falsum
et impossibile, sequitur secumbum ejus dictum, quod fides sit
de falsa et impossibile, quod etiam Deus facere non potest."
quoted Mandonnet Siger de Brabant, p. 152 from De unitate
(95) Anagnine, "Pic de la Mirandole"
(In Rev. d'Hist de la Philosophie, 2e Année 1934),
(96) Mandonnet Siger de Brabant,
(97) De Dignitate et Augmentis
Scientiarum lib. 1, cap. 1. "Quare, sicut legi divinae
obedire tenemur, licet reluctetur voluntas; ita et verbi Dei fidem
habere, licet reluctetur ration. Etenim, si ea duntaxat credamus,
quae sunt rationi nostrae consentanea, rebus assentimur, non auctori;
quod etiam suspectae fidei testibus praestare solemus. At fides
illa, quae Abrahamo "imputabatur ad justitiam, de hujusmodi
re extitit, quam irrisui habebat Sarah: quae in hac parte imago
quaedam erat rationis naturalis. Quanto igitur mysterium aliquod
divinum fuerit magis absonum et incredible; tanto plus in credendo
exhibetur honoris Deo, et fit victoria fidei nobilior." (Works,
Vol. II, p. 427.)
(98) Principles of Human Knowledge.
Introd. 3 (London, 1945, p. 6). Aristotle of course uses this
same principle, that capacity will be concordant with appetite,
but by restricting all cognition in man to the sensible, and founding
thought on, and denying that it could be free from, images - and
by denying the operation of the intellect if shown not to involve
these, to be properly a part of man qua man, he implicitly
excludes the desire for ultimate truth, as he explicitly does
that for "eternity," from the class of those natural
appetites that are proportioned to a future actuality. Vide infra
(99) Metaphysics, 995A.
(100) Metaphysics, 1077B.
(101) See J.H. Randall, Jr. Development
of Scientific Method in the School of Padua, p. 198 (J.H.I.
I 1940, 177 ff).
(102) De Crepusculis, 1542,
p. 1. "Porro hec mea demonstrandi methodus alia est fateor
aliquando, ab ea qua prisci illi authoris Menelaus, Ptolemaeus,
et Geber viri doctisimi usi sunt: sed ab Euclide
et Theodio haud quaquam aliena."
(103) On the Heavens, II.
(104) De Rerum Varietate,
1557 lib. IX "de Moribus."
(105) De Subtiltate, 1554,
(106) E.g., the mathematician Tartaglia
published a work on the subject La Nova Scientia which,
although "Euclidean" in form of exposition and strictly
mathematical in procedure, is vitiated by Aristotelian assumptions
on physical questions - as on the rate of fall of bodies, or its
apparent acceptance of the belief that a compound of artificial
and natural motions was impossible, which results in the representation
of the track of a canon ball as a straight line which suddenly
terminates when artificial acquired motion is exhausted, and is
replaced by a vertical line, representing the natural motion of
tendency to the centre that then supervenes. (But Tartaglia is
apparently himself uneasy about this last patently artificial
Aristotelian dogma, and attempts to camouflage the improbable
discontinuity it suggests by inserting a short curved path at
the transitional point, thus allowing stages of violent, mixed
and natural motions to the missile.) Dee, in the Preface
insisting that in a common medium two bodies of the same form
"aequall in quantitie or unaequall will move by aequall space
in aequall tyme," comments "Hereupon, in the feate of
Gunnyng, certain good discourses (otherwise) may receive great
amendment, and forderance." The letters N.T. are set in
the margin - a clear reference to Tartaglia's work and its Aristotelian
(107) A Discourse Apologeticall,
p. 120, and pt. II (new pagination), p. 200.
(108) See R. McKeon, Aquinas'
doctrine of knowledge and its historical Setting, Speculum
III, 1928, p. 426 ff.
(109) By Herlinus and Dasypodus,
1566, Strasbourg (Analyseis geometrica sex librorum Euclides).
(110) John Smith: Discourses,
1673, Disc. IV, chap. 8, p. 101.
(111) Life X and XIII (Rosan:
Proclus, pp. 18, 20).
(112) Thus More: Hellenistic
Philosophies, p. 78 et seq., and Armstrong, The Architecture
of the Intelligible Universe in the Philosophy of Plotinus.
(113) E.g., De. Civ. Dei IX,
10, "Plotinus certae nostrae memoriae vicinis temporibas
Platonem ceteris excellentius intellexisse laudatur" etc.
(114) E.g., in his translation of
the Hymns of Orpheus, 1792 with dissertation on them (Taylor
believed they revealed a true mystical theology) - he states for
example (p. 13): "I shall everywhere deduce my information
from the writings of the latter Platonists as the only sources
of genuine knowledge on this sublime and obsolete enquiry."
Of Plotinus and Proclus he writes, the philosophy of Plato was
indebted "to the former for its restoration and to the latter
for the complete development of all its sublimities and mysteries...(they)
being allotted a nature similar to their master were the true
interpreters of his sublime and mystic speculations" (Introd.
to trans. of Plotinus, pp. XII-XIII).
(115) Life, ch. 38 (Rosan,
Proclus, p. 35)
(116A) E.g., Metaphysics,
(117A) On the Heavens, 303A-304B.
(118A) Metaphysics, 985B.
(119A) Ibid, 987B.
(116B) Noctes Atticae, lib.
111, cap XVII.
(117B) Henrici Ranzouii: Catalogus
imperatorum, regum, ac virorum illustrium, qui artem astrologicam
amarunt, ornarunt et exercuerunt, Lipsiae, 1584, p. 28.
(118B) Cherniss: The Riddle of the Early Academy, p. 83.
(120) The argument is little affected
by whether the original basis of a word's signification be purely
sensible or not, for as its meaning expands within a context,
and its functions as a nexus of relationships are elaborated,
then the sensible element of the experience it may have once indicated
alone, can be viewed, in the Cambridge Platonists' phrase, as
merely "the extrinsical occasion of thought." It is
interesting that even Hume once admitted that although in a very
restricted fashion (which is nevertheless significant here) reflection
on past experience might give rise to new experiential conceptions,
which could not be described merely as a mechanical juxtaposition
of previously known elements, since it was possible, he held,
to imagine a colour if, although never actually sensed,
it be thought of as being intermediate between two known colours.
(Enquiry concerning Human Understanding, II, 16 - it is
true he dismisses it as an instance "so singular that it
is scarcely worth our observing," but admits it as a "proof
that the simple ideas are not always, in every instance, derived
from the correspondent impressions").
(121) Laws, Bk. X, 892A-B.
(122) Fouillée: La Philosophie
de Platon, Vol. I, p. 5.
(123) Beyond Good and Evil,
quoted Urban: The Intelligible World, p. 24.
(124) Opere latine conscripts
II, 2 Florence, 1890, p. 7.
(125) Didascalon, lib 2, cap.
17. See M. Claggett: Some general aspects of Physics in the
Middle Ages, p. 30 (Isis XXXIX, 1948).
(126) B. Kieszowski: Récherches
sur la Philosophie de Jean Pic de la Mirendole, p. 47 (Comptes
Rendus des Séances de la Societé des Sciences et
de Lettres de Varsovie XXIII 1930).
(127) de Docta Ignorantia,
lib. III, cap. II.
(128) Metaphysics 1002A.
(129) Urban: The Intelligible
World, p. 76.
(130) E.g., Strom, II, 4,
13; VI. 7, 57.
(131) Life, ch. XXII (Rosan:
Proclus, p. 25).
(132) Quoted J.R. Halcomb: Synesius
(in Smith and Wace Dict. Christ. Biog. vol. IV, London,
1887, pp. 756-780). (This confusion with the alchemist continued
at least until the eighteenth century, e.g., du Fresnoy's account
in Hist. de la Phil. Hermétique, Vol. I, pp. 40-56.)
Similarly, in the renaissance, Elyot insists that man resembles
God only in understanding; the statement that he was made in God's
image can refer only to his intellect; he adds that the text could
not mean in any way man's shape or bodily constitution for "certes
thanne the ymage of godde were not onely divers but also horrible/monstruouse,
and in some part ridiculouse" (Of the Knowledge which
maketh a Wise Man, ed. Howard, 30r-v=87-8). The whole theme
of this dialogue, one of the most noble and attractive of renaissance
productions in this genre, is the identity of virtue with knowledge,
that he who knows, in the full sense, what is right, will always
act in accordance with it, and that knowledge constitutes an approach
to and imitationof God, beatitude and the soul's eternal bliss
having to do only with the understanding - a thoroughly "intellectualised"
interpretation typical of neo-Platonism. The statement is placed
in Plato's mouth with a marginal reference to Alcibiades I,
that "my profession hath ever been, that no man is happy
except he be wise and also good [that this is a tautology has
not at this stage been established] & that felicitie is in
wisdome and goodnes / and contrariewise / that they which be ignoraunt
and yll / be vnhappy / and that ignoraunce and synne is infelicitie
and misery." (Ibid, p. 15r=45). Now this ignorance which
is the sole cause of sin can only result from body, partially
obscuring the soul's understanding, but this it cannot do unless
permitted by a diseased will, for of itself it clearly cannot
"lette the soule, that is of a divine substaunce, to shew
the effectes and disposition of her nature, whiche is onely
knowledge" (Ibid p. 20v=55).
(133) Commentaires sur le premier
livre d'Éléments d'Euclide, trans. P. ver Eecke,
(134) "C'est un fait capital
pour l'intelligence de l'augustinisme, que la sagesse objet de
la philosophie se doit toujours confondre pour lui avec la béatitude."
(E. Gilson: Introduction à l'étude, Saint Augustin,
Paris 1929, p. 1.)
(135) E.g., Du Mornay, Treatise
on Christian Religion, trans. Sydney, chap. 2 (Sydney Works
III, p. 279).
(136) See W.R. Sorley: A History
of English Philosophy, Cambridge, 1937, p. 81.
(137) Discourses IV, 6, I.
(138) E.g., De Philosophiae Consolationis
V. 5, pp. 389-391. There are four grades: Sense, Imagination,
Reason, and Understanding, under which a thing may be diversely
considered. Each superior form of comprehension embraces the lowwer
but does not depend on or employ them, thus, "Reason when
it considereth any universitality, comprehendeth both imagination
and sensible things without the use of either imagination or senses."
(139) See especially on Avicenna's
epistemology as reproduced here, Goichon: La Philosophie d'Avicenne
et son influence en Europe Médiévale, p. 31
(140) Goichon: Avicenne,
(141) R. McKeon: Aquinas' Doctrine
of Knowledge and its Historical setting, Speculum 111, 1938,
(142) De Idiota Dialogue 1.
(143) Galileo's Platonism
in Studies and Essays in the History of Science and Learning,
offered to George Sarton 1944, New York, 1947, p. 286, et seq.
(144) See Lenoble on Mersenne's relations
to the Augustinian tradition, and adoption of Anselm's ontological
proof "et cela annonce en somme, les Méditations
de Descartes et son argumentation à partir d'une prise
de conscience des données, de l'esprit" (Mersenne,
p. 252), also on history of thesis "Intellectus quodammodo
fit omnia" and its final connections with seventeenth century
intellectualism and mechanism (Ibid p. 344).
(145) A Treatise Concerning Eternal
and Immutable Morality (appended to TIS. 1845, ed. Vol. III)
III, 3, 4 (p. 566); IV, 2, 4 (p. 580); IV, 5, 2 (p. 635). III,
3, 4 continues "so the mind or intellect may well be called
(though in another sense than Protagoras meant it) the measure
of all things." This phrase is popular among Renaissance
Platonists, who in an earlier age are not always so careful as
Cudworth to distinguish the intentions of the originator from
their own applications - Pletho indeed takes Protagoras as a type
of noble certitude - the converse of Pyrrhus, and ch. XXXVII of
Cusa's de Beryllo (Oeuvres Choisis p. 489) is a
vindication of Protagoras on similar lines.
(146) De Fide Catholica:
After denying the emanation of the world from God's own substance,
"nor did he form it after any model lest it should be thought
that anything had already come into being which helped his will
by the existence of an independent nature." (Theological
Tractates, p. 57.)
(147) Phil. Consol. III, 9
(Loeb, p. 265). It is true this is from a poem, and which moreover
is professedly based on the last part of the Timaeus, but
no doubts are expressed in the surrounding text as to its truth.
(148) Against Eutyches and Nestorius
III (Theological Tractates, pp. 87-89).
(149) De Trinitate II (Ibid
(150) Mandonnet: Siger de Brabant,
Vol. I, p. 118.
(151) Despite this resistance to
direct definition, knowledge of it could be taken as nonetheless
certain, since it formed the ultimate value terminating a series
adequated to immediately experienced desires, which could thus
serve to indicate degrees of approach to it, and the "direction,"
as it were, in which it must be. For, "the Good differs
from everything else in a certain respect....a creature that possesses
it permanently completely and absolutely has never any need of
anything else; its satisfaction is complete." (Philebus,
(152) Foullée: La Philosophie
de Platon, Vol I, p. X.
(153) Adamson: The Development
of Greek Philosophy, Edinburgh, 1908, p. 106.
(154) Similarly Philo, after describing
creation as modelled on Ideas (for God saw "that no object
of perception would be faultless which was not made in the likeness
of an original discerned only by the intellect") goes on
to equate the place of the Ideas and the Divine Reason (Logos),
"which was the author of this ordered frame (De Opificio
Mundi IV,  and V ; Works I, pp. 15, 17). On
the transformation of the Ideas, after Plato, until both their
totality and "their place" are simply identified with
the Divine Mind, see Rosan: Proclus, p. 100, et seq.
(155) De Trinitate XV, 13
(trans. Dods. Edinburgh, 1873, pp. 407-411).
(156) Saliba: Étude sur
la Métaphysique d'Avicenne, p. 128.
(157) On Smith see de Boer, Theory
of Knowledge, p. 41. On More, W.R. Sorley, History of
English Philosophy, Cambridge, 1937, pp. 81-82, who quotes
these phrases from An Antidote against Atheism I, 6; Appendix
(158) The Boke named the Governor,
1531, III, 23 (Everyman reprint, p. 273). Similarly in his dialogue
Of the knowledge whiche maketh a Wise Man, Elyot places
an argument in the mouth of Plato, based on the instincts, special
aptitudes and responses to symbols of brutes, to establish that
even they have knowledge that is not drawn from the senses (though
this at the same time is distinguished from the full participation
in Ideas, for the beasts have not that understanding that would
allow them to engage on "nombrynge" unaccompanied by
imagination, p. 29v=74).
(159) This constitutes in fact Galileo's
answer to the charge which he does not in any explicit phrase
accept. He replies merely "What I think of the opinion of
Plato you may gather from my words and actions," and then
that he will allow this deduction of new and positive knowledge
from a priori principles into which he leads the other two speakers,
to stand as an example of "what my opinion is touching the
attainment of knowledge" (Salusbury trans. Vol I, p. 169
et seq. cp. p. 138: "You must know that if a person apprehends
not a thing of himself, it is impossible that others should make
him understand it").
(160) Epistle VII, G.R. Morrow trans.
(Studies in the Platonic Epistles, p. 207).
(161) De Docta Ignorantia,
(162) Ibid I, 12.
(163) Ibid I, 4.
(164) A Sytem of Logic, I,
8.7 (London, 1892, ed. p. 105).
(165) Die Grandlagen der Arithmetik,
II, 26, 28. Breslau, 1884, pp. 36, 38.
(166) C. Ritter: Kerngedanken
der Platonischen Philosophie, pp. 77, 82. Quoted Lovejoy:
The Great Chain of Being, p. 36.
(167) Theaetetus, 1848.
(168) Against the Gnostics,
i.e., Enn, II, 9.16.
(169) Ennead, III, 6, 2.
(170) Antidote against Atheism
(Philosophical Writings, ed. F.J. McKinnon, N.V., 1925,
(171) De Docta Ignorantia,
I. II. The "source" of the form of the expression in
Romans I. 20, "For the invisible things of Him from the creation
of the world are clearly seen, being seen by the things that are
(172) Abel Rey: Introduction to
De docta Ignorantia, trans. Moulinier, p. 20.
(173) Idiota, dial. I.
(174) Saliba: Avicenne, p.
(175) It had a superficial attractiveness,
and has perhaps been useful in contenting the minds of investigators
with a general theory, so allowing them to proceed, psychologically
unhampered, in work on which, in fact, such a theory has no practical
bearing. Thus Cornford quotes from Lemery's Cours de Chymie
of 1675, "The hidden nature of a thing cannot be better explained
than by attributing to its parts, shapes corresponding to all
the effects it produces. No one will deny that the acidity of
a liquid cosists in pointed particles. All experience confirms
this" (Before and After Socrates, Cambridge, 1932,
(176) Bruschvicg, L'Expérience
Humaine, p. 125, expresses the difference very precisely:
"Le type d'intelligibilité, suivant Platon comme
suivant Democrite c'est l'analyse. Mais, suivant l'heureuse
terminologie de Leibniz, l'analyse démocritéenne
est la division en parties, l'analyse platonicienne c'est
la résolution en notions. Le Première laisse
échapper le tout en tant que tout pour ne retenir que les
elements constitutifs; la seconde au contraire, s'attache au tout
lui-meme afin de comprendre ce que le détermine dans sa
totalité. Tandis que Démocrate n'emprunte guère
à la géometrie que l'image encore externe de la
juxtaposition, Platon vise a l'intelligence des relations internes.
Des lors, ce qui va devenir l'objet principal du mathématisme
Platonicien, c'est que l'atomisme laissait inexpliqué:
l'ordre, la proportion, auxquels l'objet est redevable de son
forme esthétique, de son harmonie."
(177) Ennead IV, iii, 4.
(178) Meno, 81C.
(179) Lives IV, 2 (Vol. I,
(180) De Architectura 1, 1,
16, Vol. I, p. 26.
(181) de Boer: Theory of Knowledge
of the Cambridge Platonists, p. 67.
(182) See P. Valéry: Introduction
to the method of Leonardo da Vinci (trans. T. McGreery, London,
1939, p. 13). "For a student of organisms such as he, the
bodyis not a piece of rubbish to be utterly despised. It has
too many properties, it solves too many problems. It possesses
too many functions, is capable of too many resources, not to correspond
to some transcendental necessity that is sufficiently powerful
to construct it, but not sufficiently powerful to be able to dispense
with its complexities."
(183) The Trueness of the Christian
Religion, Sydney trans. (Sydney Works, III, p. 234).
(184) de Boer, Theory of Knowledge,
(185) The positions touched on in
this section are dealth with fully, with some historical reference,
in Wick's Metaphysics and the New Logic. On this particular
question Wick develops (p. 52 et seq) arguments of C.S. Pierce
(On Some consequences of four incapacities) viz. from the
initial denial that we have an intuitive power of distinguishing
an intuition from a cognition inferentially determined by others,
the result may be reached that the conception of anything not
discursively cognizable is a contradiction and cannot be presumed,
while all cognitive activity is, in turn, reducible to the type
of mediate discursive inference, every cognition being determined
by some logically prior cognition. Hence a prime goal of knowledge
becomes the gradual extraction of the informing principles of
whole discursive systems.
(186) Emmet: The Nature of Metaphysical
Thinking, p. 26.
(187) Hence Culverwell's assertion
that we can never have complete intellectual knowledge
of anything - "we can never exhaust the whole intelligibility
of any entity"; meanwhile he justifies partial knowledge
on cherence grounds and by asserting "the experience
of certainty is imprinted on our souls by God along with other
images." Its ultimate foundation is experience, far above
sense, when the soul achieves a level where it can forget "its
wrangling syllogisms" entering an intuitional unity with
its supreme object, see de Boer: Theory of Knowledge,
p. 61 et seq.
(188) Wick: Metaphysics and the
New Logic, pp. 143-143.
(189) Ennead 1, 3, 5.
(190) See Robin: La Théorie
Platonicienne des Idées et des Nombres d'après Aristote,
p. 501, et seq.
(191) Republic VI, 509B.
(192) Jabobi Mazzini: In Universam
Platonis et Aristotelis Philosophiam Praeludia....Venetiis
1597, p. 187, quoted Koyre, Galileo and Plato, p. 400 et
seq J.H. I. IV, No. 4, 1943.
(193) Dialogues Two Principal
Systems, Saldsbury trans. vol I, p. 181.
(194) Sigilli Sigillorum,
Secunda Pars, Cap IV (Opere Lat. Conscripte, Florence, 1890, Vol.
II, pt. II, p. 196-197).
(195) Phaedrus 247C.
(196) Philebus 59C.
(197) Ibid 57C.
(198) Ibid 56A-56B.
(199) Ibid 55.
(200) W.F.R. Hardie: A Study
in Plato, Oxford, 1936, p. 35.
(201) Statesman, 283 and 260B.
(202) Protagoras, 356A.
(203) Philebus, 25-26B.
(204) Protagoras, 357C.
(205) Philebus, 51C-D.
(206) Metaphysics, 1090A.
(207) In Holland trans. of Philosophy
Commonly called the Moral, 1657 ed., p. 834-835.
(208) Metaphysics, 1090A.
(209) Commentary on Euclid.
Introd. Pt. 1, ed. cit. p. 9.
(210) De lib. arbit., II
8, 21, discussed Gilson, Introduction à l'étude
de Saint Augustin, p. 19 et seq.
(211) L'Encyclie des secrets de
l'Eternité, 1571, cited Schmidt, La Poesie Scientifique,
(212) Discourse IV, chap.
(213) Treatise concerning Eternal
and Immutable morality IV, 4, 5 (Appended T.I.S. 1845
ed., vol. III, p. 625).
(214) Meditationes de Prima Philsophia,
Amsterdam, 1678, Med. V. "De essentia rerum materialem,
et iterum de Deo quod existat," p. 31. The conclusion reached
by this is "Atque ita planè video omnis scientiae
certitudinem et veritatem ab una veri Dei cognitione pendere."
(215) C.p. G.H. Hardy, A Mathematicians
Apology, Cambridge, 1940, p. 63-64. "I believe that
mathematical reality lies outside us, that our function
is to discover it or observe it, and that the theorems
which we prove and which we designate grandiloquently as our creations
are simply our notes of our observations," and Russell's
declaration of his former belief "in the Platonic reality
of Numbers, which in my imagination peopled the timeless realm
of Being." (New Pref. to 2nd ed., Principles of Mathematics,
1937, p. X.)
(216) Opus Majus IV, I, 3,
Vol. 1, p. 121-127.
(217) Epistle 79 (Oeuvres,
trans. Druon, p. 508).
(218) Opus Majus, ed. Jebb,
London, 1733, p. 64.
(219) Opus Majus (Burke trans.),
Vol. I, pp. 121-127.
(220) Op. Maj., Pt. V, Vol.
II., p. 499 et seq.
(221) Bib. Nat. M.S. 16089 Printed
R. Steele Isis XX, 1933, Roger Bacon as Professor, A student's
notes, p. 83 et seq. (The arguments are very similar in style
to those in Op. Maj. Pt. IV, Dist. I, Cap. II.)
(222) De Beryllo, Cap. XXXVIII
(Opera 1450, p. 177 - unnumbered).
(223) Dial 3. (Oeuvres Choises,
(224) A sidelight is the establishment
of the compass as the invariable, often the sole, accompaniment
of the emblem of Reason (usually a female figure). A multitude
of engraved title pages from the sixteenth century onwards bear
the two figures, a woman holding a compass (Reason), and another
bearing a Bible (Revelation). Again, De Mornay is full of mathematical
"illustrations" of reason. The "Preface to the
Reader" states that Religion myst be established, and will
thus receive universal assent from Common Principles, developed
in Euclidean fashion, "after the same manner, by this principle:
He that from equall things taketh equall things, leaveth
the remainder equall (Euclid lib. 1, prop. 45); and by a few
other propositions which children learne in playing; the Mathematician
leadeth us gentlie (and ere we be aware of anie mounting) unto
this so greatlie renounced proposition and experiment of Pythagoras
that a Triangle, the side that beareth up the right Angle,
yeeldeth a sqaure quall to the other twayne which at first
sight seemeth impossible, and yet degrees is found to be so of
necessitie. Thus shall the Jew by common principles and conclusions
verifie...(etc.)" Truth can be found and God known by combining
statements of Aristotle and other pagan philosophers "Certesse
in the manner as by Arithmetike, out of two and sixe we draw out
one continuall proportionable line, hidden after a sort in either
of them and yet greater than both of them together which is Eighteene"
(trans. Sydney: Works III, pp. 251-254).
(225) The Idea of Nature,
(226) A.E. Taylor: Platonism
and its Influence, p. 12.
(227) Gilson: Introduction de
l'Étude de Saint Augustin, p. 116.
(228) Collingwood: The Idea of
Nature, p. 95. Elsewhere Collingwood returns to this theme
to emphasise the importance of a Christian theology combining
with a Platonic mathematician to produce this novel evaluation
of the particular. For an emphasis on an omnipotent creator implied
that nature could not merely be an imperfect approximation
to an ideal realm, if the natural line was not exactly straight
then it was exactly something else as God intended it, and it
was the business of scientists, confident of the rationality of
God, to discover why; hence, in some respects, Collingwood affirms
"The Platonism of Renaissance natural scientists is not fundamentally
Platonic, it is fundamentally Christian," and in this lay
its power. (An Essay on Metaphysics, Oxford, 1940, p.
(229) 68E-69. Trans. Cornford, p.
(230) De Cons. Phil IV, 4.
(231) De Doct. Ign. II, 9.
(232) Charbonnel: La Pensée
Italienne au XVIe siècle, p. 444.
(233) Le Progrès de la
Conscience, p. 39.
(234) Two Principal Systems,
Salusbury trans. Vol. II, p. 137. The distinction he insists
on between "logic" and "demonstrations" is
not unimportant in this context. Earlier it is said (Ibid p.
23) that just as the composition of poetry can only be properly
learned from the reading of poetry itself "Demonstration
is learned from the reading of Books full of demonstrations, which
are the Mathematical not the Logical" - in which once more
a Platonic view of the limitations and method of education in
relation to the prior potentialities of the mind seems to be assumed.
(235) See Lenoble, Mersenne,
(236) The general thesis of Formal
Logic, London, 1912.
(237) Système du Monde,
1799, V, 5, quoted Boutroux, L'idéal Scientifique,
(238) Euthyphro 7 b-c.
(239) Récherche de la Vérité
discussed Brunschwicg: L'Expérience Humaine, p.
5 et seq.
(240) Abel Rey (Théorie
physique chez le physicien contemporary, 1905), quoted and
discussed, Metzger, Les Concepts Scientifiques p. 156 et
(241) "In the seed of a plant
to the eye of God and to the understanding of man, there exists
though in an invisible way the perfect leaves flowers and fruit
thereof; for things that are in posse to the sense, are
actually existent to the understanding" (Religion Medici,
I, 50. Works, II, p. 74). It was in the field of biology
that the assumption of "Legions of Seminal Ideas" that
had yet to put on "the coats of their forms" seemed
most requisite to supplement lack of demonstrable knowledge.
(242) Metaphysics, 1092C.
(243) Blanché: La Science
Physique et la Realité, p. 3 & 33.
(244) New Pathways in Science,
Cambridge, 1947 ed., p. 256, cp. p. 262, "what physics ultimately
finds in the atom or indeed in any other entity studied by physical
methods is the structure of a set of operations."
(245) Salusbury trans. Vol. I, pp.
86-87. Human knowledge comprehends little "extensively,"
but some things absolutely intensively; such are propositions
in Geometry and Arithmetic, "in which Divine Wisdom knows
infinite more propositions, because it knows them all; but I believe
that the knowledge of those few comprehended by human understanding
equalleth the divine as to the certainty objective, for
that it arriveth to comprehend the necessity thereof than which
these can be no greater certainty," for though a difference
may be said to be that God knows them without a discursus, at
least of a temporal kind "as to the truth of which Mathematical
demonstrations give us the knowledge, it is the same which Divine
Wisdom knoweth." The position rapidly becomes commonplace,
and is met with frequently in allusions, thus Osborne, in passing,
refers to "Mathematicks, the Queen of Truth"
as "this Angelicall Knowledge," and after referring
to the certainty of the demonstrations, declares it "the
only knowledge we can on Earth gain, likely to attend us to Heaven."
(Advice to a son, 1656, ed. Parry, London, 1896, pp. 13-14.)
(246) Il Saggiatore (Opere
VI, 1933, p. 232).
(247) See Koyre, Galileo and Plato,
J.H.I. IV, no. 4, Oct. 1943. "It is obvious that for the
disciples of Galileo, just as for his contemporaries and elders,
mathematicism meant Platonism" p. 424.
(248) P.P. Wiener, The Tradition
behind Galileo's Methodology (Osiris I, 1936), p. 743.
(249) La Loi de la Chute des Corps
Descartes et Galilée. (Revue Philosophique, Année
162, 1937, p. 153, separate publication as Études Galiléennes,
(250) The legend has been examined, and ascertainable facts brought to light by Lane Cooper: Galileo and the tower of Pisa (N.Y., Cornell University Press, 1935) and A. Koyré, Galileo et l'expérience de Pisa (Annales de l'Université de Paris 12, 1937).
(251) Principes 11, 82, see
Brunschvicg: L'Experience Humaine, p. 185.
(252) See on Mach's criticism of
Archimedes Emil Borel: L'Evolution de la Méchanique,
Paris, 1943, p. 24 et seq. Arnold Raymond's view that "the
path followed by Archimedes in mechanics, though an admirable
method of demonstration, is not a method of investigation,"
(History of Science in Greco-Roman Antiquity, London, 1927,
p. 295) may be admitted without impugning the position that such
formal expression is nevertheless the commonly desired end in
the presentation of results previously determined by no matter
what psychologically helpful method of "discovery."
(253) Borel, L'Espace et le Temps,
(254) De Caelo, 303B-304B.
(255) Eva Sachs: Die fünf
Platonischen Körper, Berlin, 1917, p. 206.
(256) Ennead 111, 6, 13 et
(257) Saliba: Avicenne, p.
(258) Crescas' Critique of Aristotle,
p. 307, Prop. XXXII.
(259) Francesco Patrizzi: On
Physical Space (trans. B. Brinkmann from Nova de Universis
Philosophia 1593, J.H.I. 4, 1943 p. 221 et seq).
(260) Crescas: Critique of Aristotle,
(261) Commentary on Euclid,
(262) Vorrede to Metaphysische
Anfangsgrunde der Naturwissenschaft (1780) Werke, ed.
Cassirer, Vol. IV, 1922, p. 372. Particular sciences rely on
the apodeictical certainty of reason, which rests on a priori
elements in thought. Science must construct its concepts
to correspond with the given and "Nun ist die Vernunfterkentniss
durch Konstruktion der Begriffe mathematisch"; philosophy
is taken as less fundamental, by a distinction which reappears
in the Introduction to the Logic of 1800, for it is "Rational
Knowledge from mere Concepts," while mathematics is "Rational
Knowledge from the Construction of concepts."
(263) Ignatius his Conclave
(Nonesuch Donne, London, 1929, p. 363).
(264) The Nature of Truth,
1640, p. 104, he continues with a criticism of the senses: "When
the nimble jugglers play their pranks you see and heare yet neither
see nor heare," etc.
(265) Burtt: Metaphysical Foundations,
(266) La Monde, ed. D.R. Paris,
1664, Chap. 1.
(267) True Intellectual System,
Pref. to Reader, Vol. I, p. XXXII.
(268) De Boer, Theory of Knowledge,
(269) Our Knowledge of the External
World, London, 1914, p. 110.
(270) The Mysterious Universe,
Cambridge, 1930, pp. 140-141.
(271) Borel: L'Espace et la Temps,
pp. 151, 154.
(272) A Mathematician's Apology,
Cambridge, 1940, p. 68. Cp Martin Johnson: Science and the
Meanings of Truth, London, 1946, p. 11: "Nearly every
recent writer on the philosophy of science has endeavoured to
captivte or to scandalize his readers by pointing out that a lump
of material is hard, cold, motionless, unpenetrable in the nonscientific
account but....(in the scientific account)...reduces to points
of singular intensity of electric field in empty space, its constituents
totally inaccessible to the sight, touch, smell, hearing of our
individual explorations of the world."
(273) Cp, however, Mersenne on the
same topic in Questions Théologiques, "il semble
que la capacité des hommes est bornée par l'ecorce,
et par la surface des choses corporelles, et qu'ills ne peuvent
penetrer plus avant que la quantité, avec une entière
satisfaction. C'est pourquoy les anciens n'ont pen donner aucune
demonstration de ce qui appartient aux qualités" (See
Lennoble, Mersenne, p. 353).
(274) Thus Dee dwelt sometimes on the immense possibilities of mechanical development guided by mathematics. But perhaps the most complex machine actually in use in England in the 16th century was William Lee's stocking frame. Cardan's works dealing with machines still tend to treat tham as isolated "mirabilia," they amaze or amuse, rather than assist useful work; the designs of Beason might stimulate the imagination by grandiose claims,but would only have brought discredit on the new scientists' prophecies had an attempt been made to realise them. (They most assume, neglecting the weight of the structure, an increase in power directly proportional to size; they are purely ideal in their indefinite multiplications of pulleys and cogged wheels and screws.)
(275) It is hardly necessary to labour
this point. Many examples are given by E.T. Bell: The Development
of Mathematics, N.Y., 1940. Thus, pp. 21-22: over a century
and a half "before anyone had dreamed of an electric dynamo
the necessary mathematics of dynamo design was available."
The Pythagoreans investigated polygonal numbers which only recently
became of practical importance (in insurance and statistics);
"the Conic sections were substantially exhausted by the Greeks
about seventeen centuries before their applications to ballistics
and astronomy, and through the latter to navigation, were suspected."
"The fact is," wrote W.K. Clifford of mathematical research
(Lectures and Essays, London, 1886, p. 70), "that
the most useful parts of science have been investigated for the
sake of truth and not for their usefulness," and adds a similar
and pointed contemporary mathematical example.
(276) G.H. Hardy: Some Famous
Problems of the Theory of Numbers, Oxford, 1920, p. 4.
(277) Through Science to Philosophy,
p. 159. He has just quoted Eddington's phrase: "a thing
may be said to be real if it is the goal of a type of enquiry
to which I personally attach importance."
(278) Metaphysical Foundations
of Physical Science, p. 300.
(279) In Somn. Scip., I, 6,
19. "Esse autem dicimus intelligibilia videri, esse, corporalia
omnia seu divinum corpus habeant sen caducum"; "Number,"
Macrobius declares, is "the first perfection of the incorporeal"
(Ibid I, 5, 13; Opera, p. 15. See Whittaker, Macrobius,
Cambridge, 1933, p. 59 et seq).
(280) E.g., Whewell (History of
Scientific Ideas, p. 106 et seq) develops the thesis that
mathematics is not merely a matter of definitions and assumptions
logically organised, but is founded firmly on certain necessary
truths corresponding to Ideas or Intuitions, natural to the mind,
which exclude all alternative systems, thus on the Euclidean concept
of parallels he observes, it is "a geometrical doctrine of
which we see the truth with the most perfect insight of its necessity"
(281) Continu et Discontinu en
Physique moderne, Paris, 1941, pp. 87-88.
(282) "May not the Harmony and Discord of colours arise from the proportions of the vibrations propagated through the fibres of the Optick Nerves into the Brain" exactly as the harmonies and discords of sounds have a numerical basis? queries Newton (Optics, 1704, pt. 2, p. 136, Query 14). It was of course only with the appearance of his work that "the science of colours became as truly mathematical as any other part of Optics" (Burtt, Metaphysical Foundations, p. 206).
(283) De Anima II, 1. He
argues elsewhere (On the Sense, ch. 4) that qualities cannot
be so reduced as they are often contraries (as hot or cold) which
figures and numbers cannot be.
(284) Showing this kind of sensation
experienced depends not on the mode of stimulation of the nerves,
but on the nature of the sense organ: light, pressure, mechanical
irritation, acting on optic nerve or retina all producing luminous
sensations (see Dampier, History of Science, p. 275).
(285) Karl Pearson's The Grammar
of Science is one of the earliest of the very many modern
presentations of this view, in support of which Varhinger's analyses
of the self contradiction inherent in many of the most useful
scientific concepts were also made.
(286) An example of H. Jeffries (Theory
of Probability, Oxford, 1939, p. 343). "There are three
main quantum theories, but all make the same predictions...The
theories themselves are not the same and indeed each contains
referencies to things that have no meaning on another.
The treatment of them as equivalent refers on ly to the observable
results and not to their actual content." Poincaré
observes (Science et Hypothèse, p. 167) that an
infinite number of "mechanical explanations" may be
given for any finite set of phenomena, as long as no limit is
set on the degree of theoretical complexity involved. Sir Edmund
Whittaker similarly remarked in the Tarner lectures of 1947 (From
Euclid to Eddington, p. 30) that space can be equally well
mapped on either Euclidean or non-Euclidean principles "provided
we make the requisite changes in our physical laws. It is purely
a question of convenience whether we prefer to have an easily
intelligible geometry with complicated physical laws, or a less
intelligible geometry with simply physical laws."
(287) C.I. Lewis, Mind and the
World Order, London (printed USA), 1929, p. 204.
(288) Harmonices Mundi (1619).
The square of the periodic time of a planet is proportional to
the cube of its mean distance from the sun (i.e., if these quantities
are both taken as 1 in the case of the earth, to provide a standard,
then for each of the other planets, both quantities will be represented
by the same number). It is clear that while simple lengths of
time, or distance, or even multiples of them, may figure in equations
and still convey an intuitive impression of representing or describing
what may be conceived of as effective "things," existing
in nature, whatever the reference may be of the quantity obtained
by squaring or cubing them, it provides no support at all to such
an attitude, Kepler sought esoteric significance in the mathematical
harmonies themselves to account for so perfect and complex a relationship.
Additional psychological support was the realisation that every
quantitative relation among phenomena can be put into a form which
asserts the constancy of some quantity which can be calculated
from the phenomena, but that this constant, this unchanging "quantity"
is not in any of the individual phenomena taken singly, they are
in continual change, only they vary proportionally and in accordance
with, as though themselves governed by, this purely abstract quantity.
(cp Burtt, Metaphysical Foundations, p. 53. Kepler "thinks
of the underlying mathematical harmony discoverable in the observed
facts as the cause of the latter, the reason he usually puts it
why they are as they are.")
(289) Republic, Bk. VII, 529-530.
(290) One of the major themes of
the Preface, where the familiar doctrine of the three worlds
is given an epistemological interpretation. The lower world is
that known by sense experience and imagination supplied by the
senses, the upper is that in which the soul attains adequate intuitions
of spiritual entities, knowledge in both involves a relationship
between the mind and an external perceived reality. The mediant
region is that of mathematics in which the mind may draw its whole
matter for discourse from what it already possesses, and without
any reference beyond itself may discover in this region the laws
and patterns that will allow it to comprehend phenomena in both
upper and lower worlds. The doctrine is given an apt emblem by
Cornelius Gemma in De Arte Cyclognomica, which is set on
the title page (and also reproduced and discussed at times in
the text). From a winged heart rises a pillar surmounted by a
circle (eternity) over which is set a pyramid (God) giving forth
living fire. About the pillar of man's central nature coil two
winged dragons as round a caduceus, forming three circles increasing
in proportions from lowest to highest. The mouths of the dragons
feed on the fire from the pyramind. The top and bottom circles,
however, are not complete but open - the upper open toward the
pyramid, the lower open towards the inferior heart, but the middle
where their bodies twice cross, is complete in itself. The three
are labelled "Virtus Imaginatrix," "Ratio"
and "Intellectus" (see pt. I, p. 11 for some verbal
interpretation - where Man is described as planted by God in the
earth, rooted inthe lower regions with his upper parts - "comam
vero atque perpetuo frondente verticem...supra caeli extremam
circumferentiam ad nunquam interituros ambitus religauit"
(291) Ennead I, 5, 8, states
that an individual should live an amphibious life -
- between the spiritual and sensible worlds.
(292) Communsa Mathematica
II, 3, 3 (Opera hact med., Fasc. XVI, ed. Steele, 1940,
p. 117), cp also I, 1, 7, pp. 16-17, on the utility of mathematics
and the general object of all philosophy.
(293) Christ's Tears over Jerusalem
(Works II, p. 125).
(294) Cornelius Gemma gives an elaborately
drawn emblem to illustrate the process of the way in which by
"illumination" true "Ideas" are to be gathered
through the medium of even the least of natural things (which
also illustrates the manner in which "mathematical"
propositions were applied analogically to reveal metaphysical
truths). A round temple represents the human mind. It is blocked
from the sun by a large outer wall with a small circular window.
The rays of the sun enter through this (as in a pinhole camera)
to cast an image much larger than the orifice through which they
passed onto the temple (reflected light from this also renders
visible the outer wall - or sensible things - from the temple).
Gemma commnts "Ita & idearum influxus a superna vita
in inferiorem derivati ex augustissimus maximè in angustiam
particularem rediguntur, donec a materie atque corporibus reflexi
iterum in humanos animos, ex singularibus facti universales, amplitudine
pristina potiantur" (De Arte Cyclognomica, Pt. II,
pp. 89-90). The source of this proposition seems to be the Pseudo
Euclid De Speculis, prop. 9. "Ex hoc quoque ostendam,
quod, cum sol intrat per fenestram, illud luminis eius, quod ingreditur
et super terram cadit, magis est amplium quantitate fenestrae"
(Alkindi Tideus und Pseudo Euklid. Drei optische Werke,
ed. Bjornbo and Vogl, Berlin, 1912, p. 102, see also p. 112, for
the same theorum used by Witelo, Optics, and by Baconin
Opus Majus II). The same symbol makes an interesting appearance
in Chapman's Sir Giles Goosecap II, 1, the narrowness of
the circle here representing the low worldly estate of Eugenia's
suitor that Lord Momford is arguing should, rightly regarded,
prove no impediment: "The bigness of this circle held too
near our eye keeps it from the whole sphere of the sun; but could
be sustain it indifferently betwixt us and it, it would then without
check of one beam appear in his fulness" etc.
(295) Lives III, 63 (Vol.
I, p. 33).
(296) Dialogue with Trypho,
2, Works, p. 73.
(297) The Practise of Chymicall
and Hermeticall Physicke, A.4r.
(298) Confessions, VII, 9;
de Civ. Dei X, 29 (Vol. I, 303-305). But de Civ. Dei
VIII 9 (Vol. I, p. 233-234) discussed Platonism and Pythagoreanism
under the heading "Oft that philosophy that comes nearest
to Christianity," while on the manner of the soul's restoration
to a body after death he declares: "Plato and Porphyry held
diverse opinions, which if they could have come to reconcile they
might perhaps have proved Christians" (Ibid, XXII,
27, Vol. II, p. 397).
(299) Protrepticus VI (Works
I, p. 69, et seq). Clement's own doctrine of God has been said
to be based on an "essentially heathen conception."
He has not asked what is Spirit, or what is the Idea of the Good,
but "what is the simplest thing conceivable? And he assumes
that this is, and that it is the cause of all that exists."
(Bigg, The Christian Platonists, p. 95.) Such a doctrine
it may be noted, is also the starting point of Dee's Monas.
(300) Opus Majus II, 16, Vol.
I, p. 68.
(301) Ibid, VII, Vol. II,
(302) Taylor: Platonism and its
Influence, p. 14.
(303) Trans. Sydney (Sydney, Works
III, p. 365).
(304) Diogenes Laertius, Lives,
Bk. 1, 9 (Myson, 600 BC) (Vol. I, p. 113).
(305) "Nay Nature itself invites
us to be geometricians: it presents us with Geometrical Figures,
with Circles, and Squares, with Triangles, Polygons and Spheres,
and proposes them as it were to our Consideration and Study, which
abstracting from its usefulness is most delightful and ravishing."
(Constantin Huygens, The Celestial World Discovered, 1698,
(306) Thus Butler writes of "a
Mathematician": "His Art is only instrumental and like
others of the same kind, when it outgrows its use becomes a mere
curiosity; and the more it is so the more impertinent it proves....His
Forefathers passed among the Ancients for Conjurors, and carried
the credit of all Inventions, because they had the Luck to stand
by when they were found out, and cry'd half's ours."
Geometry he says, is to inventions in mechanics only what grammar
is to the original use of language: "Mathematicians are
the same Things to Mechanics as Markers in Tennis Courts are to
Gamesters," and any that say that inventions are due to mathematics
"are as wise as those that say no man can play well that
is not a good marker." (Characters, p. 79.)
(307) A typical sixteenth century
statement is Postel's "Certissimum est, quum omnis compraehensibilia
ad hoc creavit Deus, ut de illis agnoscatur, ametur, laudeturq
in aeternum datur infinitus, opus fere, ut omnia creata clarissimi
sint ad intellectus nostri adoequationem per uentara: Nam ahoqui
frustra essent condita." (Absconditorum Clavis A3r)
cf. Boyle "I see no necessity that intelligibility to a human
understanding should be necessary to the truth or existence of
a thing" (Works IV, p. 450, quoted Burtt, Metaphysical
Foundations, p. 179).
(308) "The capital fault of
materialism lies not in its belief that the primary qualities
- or some of them - are objective, but in its denial that the
secondary qualities are so. It seeks to replace the presented
facts of experience by other alleged facts of which the former
are explained to be only appearance." Nunn: The Aim
and Achievements of Scientific Method, p. 16.
(309) Klibansky: Continuity of
the Platonic Tradition, p. 29.
(310) The same interests are frequently
found united in later thinkers such as Descartes or Malebranche,
who owe a debt to this tradition of thought. Even of Mersenne,
Lenoble records "Il n'a jamais écrit que deux pages
de véritable lyrisme, l'une pur chanter la vie religieuse,
l'autre les automates" (Mersenne, p. 81).
(311) Klibansky, op cit., p. 29.