Since the works of Dee which will
be described in subsequent chapters are concerned mainly with
more particularised problems, the foregoing sections have been
designed to illustrate some of the generalities which helped to
frame the philosophic background of his thought, both from sources
utilised by Dee himself or from those, such as the Cambridge Platonists,
of following generations whose doctrines, though conveniently
more explicit, are closely concordant with his own, and if more
developed are yet related philosophical formulations within a
single intellectual tradition. Something must also be said however
of the ways in which the views and activities of such thinkers
as Dee influenced or proved complementary to the outlook and methods
of the "new" science of the day. One contrast between
this and the older orthodox natural philosophy has been succinctly
shown by Collingwood: "For the Aristotelian doctrine that
change is an expression of tendency, the sixteenth century substituted
the Platonic doctrine - strictly the Pythagorean doctrine for
in essence it is pre-Socratic - that change is a function of structure."(225)
A consideration in terms of structure, that is, the attribution
of causal efficacy only to preceding and therefore probably determinable
structural relationships, suggests at least the possibility of
a complete analysis of apparently disparate entities or "events,"
on some common quantitative scale; for structure is amenable,
as "innate tendency," dependent upon the whole synthetic
form of the object in process of change, is not, to mathematical
description. The differences in the changing object, though accompanied
by widely contrasted qualitative accidents, may in this way perhaps
be reduced to a matter of comparable degrees; it becomes a not
impossible speculation that all observable characteristics may
result from the imposition of a certain intelligible order upon
some primary undifferentiated stuff, of which the only necessary
property is to be "susceptible of arrangement," and
that the secrets of all generation and decay, the reality of all
natural phenomena may be exhaustively expressed, as Dee never
wearied of asserting, in terms of "Number, Measure and Weight."
The sphere in which teleological explanation was admitted - a
philosophy which did not abandon a spiritually significant eschatology
could clearly not dispense with it wholly - became more narrowly
restricted, and action through time increasingly accepted, as
being for the purposes of the natural sciences, irreversibly unidirectional.
The "mechanism" that this suggests as an almost inevitable
consequence may indeed be no more than a teleology a rebours,
but at least possessed the advantage as a working procedural guide
that it did not assume in advance as a working procedural guide
that it did not assume in advance that any of the factors determining
change were, ipso facto, inaccessible to observation.
The evolution of a concept of "structure"
in nature, with such implications, in the Renaissance is best
viewed in relation to two themes, in many respects only artificially
separable. The revival of "the neo-Platonic interpretation
of Plato dominated by the passion for a fully articulated vision
of the world as a structural entity,"(226) and the attempt
to extend as far as possible methods of quantitative analysis
to natural questions which accompanied the rapid progress in the
theoretical development, and the spread of knowledge of mathematics.
The former body of doctrine stood firmly on Plato's declaration
that "we are sure of this....that whatever is completely,
is completely knowable, and what in no way is in everyway unknowable,"
and, by refusing to separate Being from a logical account, developed
such a theory of knowledge as Cusa's: that the function of thought
was not to discover and examine particular discrete and self existing
entities and to build the world from the abstractions drawn from
a grouping of their natures so considered, but to establish intelligible
relations, and a hierarchy of more and more comprehensive laws;
that "vere soire est per nexus soire." The neo-Platonic
picture of the universe of St. Augustine had not in general statement
been very different from that now revived - "une matiere
impregnee d'intelligibilite par les idees divines: tout y est
ordre mesure et nombre, les formes des corps se reduisent a de
certaines proportions numeriques et les operations de la vie se
deroulent, elles aussi, selon les lois intelligibles des nombres.
En droit l'univers est intelligible pour une pensee capable de
la connaitre comme tel."(227) But its revival in the world
of the Renaissance had novel consequences and led to, and was
used in defence of, "a habit of detailed and accurate observation,
based on the postulate that everything in nature however minute
and apparently accidental, is permeated with rationality and therefore
significant and valuable."(228)
The Timaeus hinted at the
metaphysically satisfactory account of the mutual relationships
between meaning or purpose, and discoverable mechanical causality,
which was most compatible with such views. The latter was the
temporal unfolding in discursively intelligible form and therefore
inevitably limited, and bound by necessity arising from the nature
of the selected medium of its expression, of timeless values.
These, though "causes," in the sense of providing
explanation required by the soul, did not intrude actively into
the temporal flow of events; though Reason was an agent there,
conceived of as operating as man's mind appears to allow him to
do, rearranging and controlling events, but only in accordance
with Necessity and natural law. The ultimate values could be
thought of as the limit defined by the automatic universal development.
"We must accordingly," says the Timaeus, "distinguish
two types of cause, the necessary and the divine. The divine
we should search out in all things for the sake of a life of such
happiness as our nature admits; the necessary for the sake of
the divine, reflecting that apart from the necessary those other
objects of our serious study cannot by themselves be perceived
or communicated, nor can we in any other way have part or lot
in them."(229) It is probably on this section of the Timaeus
that Boethius bases his version of this doctrine, developed in
terms of Fate and Providence: "For Providence is the very
Divine reason itself seated in the highest Prince which disposeth
all things. But Fate is a disposition inherent in changeable
things by which Providence connecteth all things in their due
order. For Providence embraceth all things together, though diverse,
though infinite, but Fate putteth things by which Providence connecteth
all things in their due order. For Providence embraceth all things
together, though diverse, though infinite, but Fate putteth every
particular thing into motion being distributed by places forms
and times....which although they be diverse yet the one dependeth
upon the other....Providence is an immoveable and simple determination
of those things which are to be done and Fate a moveable connexion
and temporal order of those things which the Divine simplicity
hath disposed to be done."(230) Such a teaching Cusa probably
refers to when discussing The Soul - or Form - of the Universe.
He says that some have called the general type of causality (that
superior nature, which is responsible for all change and process),
Spirit, or intelligence, others the Soul of the World, others
destiny concealed in substance, but the followers of Plato call
it a necessity of structural constitution.(231) Leonardo, who
held that the body is the first great work of the soul, being
its realisation through matter of its ideal of the human form,
found in such views the reconciliation between this thesis, which
involves a hierarchical superiority of the spiritual over the
material, and a theory of nature as exhibiting only mechanically
describable, controllable and mechanically reproducible phenomena,
from which last position he developed his method of investigation.
Charbonnel, who on this point finds Leonardo's thought recalls
both Plotinus and Bruno, thus reproduced it: "La necessite
est le lien eternel, la regle de la nature mais en definitive
elle se confond avec la raison. Ce qu'il y a de primitif, c'est
l'intelligible, c'est la raison vivante souveraine, dont la nature
est l'expression visible. Savoir c'est approfondir l'esprit et
ses lois. Par l'etude des faits nous sommes ramenes du dehors
au dedans, de la realite a l'idee...."(232)
The elevation of mathematics to
the position of the primary instrument of the intellect for the
analysis of nature also found theoretical inspiration in the Timaeus,
even though its particular exemplifications of the results obtainable
by such a method might not themselves be taken over as dogmas.
Atomism always represents the pursuing of uniformity into the
very elements of things, and the geometrical atomism of the Timaeus
exhibited the apparently primary substances of earth, air, fire
and water, still figuring as ultimates in an Aristotelian physics,
as constructs of intelligible concepts; it had also attempted
physical explanation in mathematical terms of such qualitative
phenomena as colour diversity. It suggested a general framework
for thought capable of embracing all things and a uniform language
for the expression of all conclusions, thereby intelligibly and
firmly connecting them together. Its great power and promise
lay in abolishing what in Aristotelian thought sometimes appeared
unbridgeable gulfs between "things," "facts"
and "laws"; for, though on different levels all these
must in essence always be abstractions, they were now abstractions
made on identical principles, and their interrelations capable
of clear examination. What the Timaeus precisely meant
for the scientific mathematicism which began its modern career
in the Renaissance, Brunschwieg has thus described: "En
utilisant par un raisonnement assez insolite ( )
les maigres ressources de la science de son temps. Flaton fait
oeuvre de prophete plus que de precurseur: il delimite du dehors
le terrain ou s'elevera l'edifice de la pensee moderne."(233)
Among a large body of Renaissance
thinkers an increasing dissatisfaction is discernible with the
Aristotelian logic insofar as it laid claim to be of assistance
to constructive thought. A reduction to syllogistic form might
be a useful touchstone for consistency in thinking after any creative
process was over, but its impotence in all other respects became
increasingly remarked: "Logic, it appears to me," declared
Galileo, comparing it unfavourably with geometrical method, "teaches
us how to test the conclusiveness of any argument or demonstration
already discovered and completed, but I do not believe that it
teaches us to discover correct arguments and demonstrations."(234)
The syllogism employed, as its extreme advocates recommended,
as an engine for the investigation of nature involved from an
empirical standpoint a palpably vicious circle, for then interpreted
purely extensively (as forming part of a scheme of class inclusions),
the transition from the universal to the particular could bring
forth no new knowledge, since if the former represented no more
than the invariable association of a set of characteristics abstracted
represented no more than the invariable association of a set of
characteristics abstracted from observation of particulars, these
must previously have been identified as present in the particular,
which figures in the conclusion, when it was subsumed under the
universal in the premise. The form of Aristotelian induction,
associated with such a logical method, was found equally unsatisfactory.
Only induction by a simple and exhaustive enumeration could be
formally valid, but to escape the difficulty here by asserting
that although this could rarely be done with particulars it might
be with species, or else to rely on the rational intuitions, possessed
by gods (or rather separated spiritual substances such as angels,
for Christian Aristotelians) and men, as being able properly to
extract from a few cases a universal of this kind that could operate
as a middle term in argument, proved especially in purely physical
questions (relating to motion for instance) merely misleading.
Again though all definitions amount to the enunciation of some
particular properties selected as characteristic, yet those of
mathematics by permitting an exhaustive "construction"
of the entity described, involved implicitly all other truths
about it, which though initially unknown or unobserved, might
thereupon be validly deduced from the implications of the definition
itself - at the same time, since often many alternative definitions
of equal adequacy were here possible a practical refutation of
Aristotle's claim that all things had a single "essence"
that could be expressed in one "true definition" only
was provided. On the other hand if deduction claiming to establish
genuine new knowledge were attempted syllogistically, employing
synthetic definitions of the kind Aristotle recommended then it
would in fact appear successful only when an unjustified importation
of "meaning" into the terms figuring in the premisses,
in excess of that attributed to them by definition, had unobserved,
by psychological sleight, taken place. (An attack on the claims
for the syllogism made by Aristotelians, along these lines occurs
as Morsenne's Verite des Sciences - it embodies, Morsenne
argues, no implications of ideas or causes but only a formal arrangement
of elements observed as usually empirically associated. If man
possessed Intuition equal to that of the Angels, both the minor
and the conclusion would be seen to be unnecessary, they would
be known immediately as present in the major; as it is, this last
is established only by an induction from particulars, a procedure
which has not been universal, else there would be no new particular
to appear in the minor to which the conclusion relates - and hence
remains always to some degree uncertain (235).) The "purely
verbal" nature of syllogistic reasoning which while by its
form it seemed to compel the reason, yet in its matter all too
frequently remained thoroughly unconvincing for the understanding,
became glaringly apparent in the light of many of the acute and
genuine problems of sixteenth century thought.
It may well be, as F.C.S. Schiller
insisted, that the sole alternative to a logic which comes to
terms with psychology (thus ultimately abandoning any claim to
be absolute and eternal) is one enslaved to grammar (236). It
would seem that much of the popularity of Ramus' logic, among
Platonists, humanists, and the new scientists, was due to the
impression it gave at the time (as distinct from any final historical
judgment on it as a system) of being a method directly drawn from,
and remaining much closer than the Aristotelian to, observable
natural mental process, of truing to base itself on the way terms
are in fact used in thinking, and of being a new and profound
attempt to investigate actual meanings, and evolve a formal method
which should take into account that these are always relative
to purpose. Nevertheless a logic "enslaved to grammar"
offers the great advantage of providing absolute, demonstrable
certainty through formal manipulation made in accordance with
merely syntactical considerations. Such a system, having such
advantages, the Renaissance found in mathematics, and this moreover
apparently resolved the antinomy which syllogistic reasoning was
incapable of doing, that if a logic is to be of value it must
be able to produce conclusions which are of intelligibility -
an example is Malebranche's declaration that that could only be
accepted as a true cause, between which and its effect the mind
perceived a necessary connection as clearly as it did the equivalence
that a series of substitutions could establish between two terms
of an equation in algebra (239). It was an ideal suggested by
mathematics and which applied to physical questions - and it is
problems of method in natural philosophy that Malebranche was
here treating of - it led inevitably, though not immediately,
to mechanism ("Le mecanisme" it has been claimed "prend
comme terrain solide de construction l'unite profonde de l'intelligible
et de l'experience, du pensable et du representable, du
rationnel et du perceptible"(240)). However much it might
represent the limit of already acquired knowledge in some subjects,
an inference of cloven hoofs from the observation "horned"
by way of the form "ruminant" functioning as cause,
was no longer in even remote conformity with the, ideally, demanded
pattern of scientific procedure. The Cambridge Platonists were
to receive more encouragement from the practical science of their
day in believing that the division into "forms" and
"matter" could be dispensed with yet in rejecting these
as false and artificial, and replacing them by the terms "body"
and "spirit" and removing all teleological considerations
from "body," they were developing the position of many
predecessors in the Renaissance. But conscious life which could
be observed to act in relation to an end - though only in accordance
with the prior representation the mind framed of this, which alone
and not the "end" itself could therefore properly be
regarded as "causal" - this class of conscious volitional
actions, taken together with that of physical phenomena mechanically
explicable, did not suffice to entirely account for natural change
and generation. The solution usually adopted by those who forsook
Aristotelianism was to ascribe what remained to the "seminal
reasons," which the stoics had employed and which combined
the advantages and avoided some of the difficulties of both the
Democritean atoms and the Ideas of Plato (certainly in the original
form in which these had been put forward). Augustine had made
large use of this concept and it had subsequently had a lengthy
and respectable history in philosophic thought. Sir Thomas Browne
still found it a useful hypothesis, offering, for want of better,
a plausible shadow of explanation (241). It at least avoided
the dangers of a theory which would have directed speculation
towards considering the final entelechy of a form rather than
observation towards conditions of development.
Aristotle had thought it a cogent
argument to urge against the Pythagoreans that number could not
be admitted as the essence of things nor the cause of the form,
for the reason that essence was always a ratio (as the essence
of skin and bone was to be three parts fire and two of earth)
and number was merely adjectival, signifying an amount of matter,
an intensity of quality (242). This could not serve as valid
criticism against the procedure of the Renaissance neo-Platonists,
who were not solely, or perhaps chiefly concerned in subsuming
a thing under some one cardinal number, binding them together
in a mesh of allegory, and so interpreting nature through the
supposed mystic properties of the numeral system. Rather they
accepted this statement (implied for example in Dee's treatment
of medicine graduation), but turned its force against Aristotle,
by asserting that all that could be certainly known of the nature
of the terms figuring in the ratios compounding essence was in
turn merely other determinable ratios that they observably entered
into. The key to nature was therefore still mathematical, but
it lay in the application of what Dee always referred to as "The
Divine Science of Proportion" - a title originated by Paccioli.
The change of orientation that was initiated in the Renaissance,
and has since, evolving persistently, maintained ascendancy by
this new approach, has been delineated by Blanche: "En l'adoptant,
la pensee transformait du meme coup sa propre structure et s'obligeait
a une revision intellectuelle totale. La hierarchie allait desormais
se renverser entre les sens et l'entendement, entre les choses
et les rapports. L'idealisme de la relation allait se substituer
au realisme de la substance et a l'idealisme de la representation,
et une forme nouvelle de realite se faire une place entre le monde
anthropomorphique de la perception et le monde transcendant de
la speculation, entre le phenomene et la chose en soi....Le concret
ce n'est plus le qualitatif, dans sa diversite pittoresque, et
d'ou l'abstrait se forme par reduction, c'est un entrecroisement
de determinations intellectuelles...Le reel n'est plus au point
de depart, mais au terme de la connaissance. Il n'est plus donne
a la sensibilite par les qualites d'une substance il est construit
par l'intelligence comme un systeme de rapports."(243) The
Renaissance mathematicisation of the world already contains in
embryo the definition of scientific knowledge of Eddington - that
any account of the external world "involves unknowable actors
executing unknowable actions," which are nonetheless a vehicle
for "The knowledge we can acquire [which] is a knowledge
of a structure or patter, contained in the actions."(244)
The new methods in action and the
visible manifestation of their power are more clearly apparent
in a generation later than Dee's. But the same doctrines, for
which Dee out of faith was a largely theoretical propagandist,
were held by the much greater and more creative Galileo, who refashioned
the world out of them in a way that could not be ignored. Mathematics,
Galileo asserted in the Dialogues of the Two Principle Systems
was the one type of knowledge in which man's knowledge though
less in extent was necessarily the same in kind as God's
(245); it was therefore a domain in which reality and God's thoughts
could be immediately attained. "La filosofia," he declared,
"e scritta in questo grandissimo libro, che continuamente
ci sta aperto innanzi a gli occhi (io dico l'universo) ma non
si puo intendere se prima non simpara a intender la lingua e conoscer
i caratteri, ne'quali e scritto. Egli e scritto in lingua matematica
e i caratteri son triangoli, cerchi ed altri figure geometriche,
senza i quali mezzi e impossibile a intenderne umanamente parol,
senza questi e un aggirarsi vanamente per un oscuro laberinto."(246)
He seems to have consciously accepted without serious doubts,
that the mathematical methods he employed were inseparable from
a Platonic theory of knowledge and metaphysics (247); and recent
research has corrected older views on the empirical elements in
his work and its supposed contrast with earlier science, in showing
that where ever he rejected the Aristotelian physics or method,
Galileo's "did not revert to mere observation but on the
contrary reverted to a more vigorous form of Platonic rationalism,
in which observed nature is merely an instance of a universal
geometric order of infinite complexity."(248) "On pourrait
dire," Professor Koyre has written of Galileo, "...qu'il
n'a aucune confiance en une observations non verifiee theoriquement.
L'epistemologie galileenne n'est pas positiviste. Elle est archimedienne."(249)
A statement strikingly illustrated by the true version of the
Pisa episode, which exhibits Galileo as unshaken in his faith
in the reasoning which demonstrates contradiction in the Aristotelian
position - two equal weights tied together cannot double their
rate of fall merely by being so conjoined if their single rates
were equal when they were separate, since the velocity of neither
can increase that of the other; while a lighter weight attached
to a heavier, should on the Aristotelian premisses both result
in a faster rate of fall, and by composition of their respective
velocities, a slower - and presents him as merely referring to
this argument when his opponents claim to vindicate Aristotle
by experiment from the leaning tower, dropping wood and lead of
equal volume, the lead reaching the ground invariable three cubits
in advance of the wood (250). Galileo's attitude is exactly that
expressed in the declaration made by Descartes after dealing with
the laws of shock: "Et les demonstrations de tout ceci sont
si certaines qu'encores que l'experience nous sembleroit faire
voir le contraire, nous serions neanmoins obliges d'ajouter plus
de foi a notre raison qu'a nos sens."(251)
An inspiration and a model for Galilean science was the successful and apparently a priori method followed by Archimedes in mechanics. Indeed those very features were fixed on in the Renaissance as being of the highest value in it that have been singled out for criticism by a later positivism; thus Mach, from the general thesis that mathematical reasoning is powerless to discover experimental facts, criticises Archimedes' treatment of the lever, for disguising his premises as definitions and axioms claiming to be self evident, when they can be no more than the results of general resumes of and abstraction from common experience (252). Nevertheless it was through the use of similar methods, that Galileo, Stevin and others were able to complete the foundations on which the edifice of all later mechanics has been raised. In contrast to the vast collections of "cases" recommended by Baconian induction, the small number of experiments that was here found necessary is significant, and many of these were, or in the unfamiliar formal exposition could be replaced by, such as were of an entirely "Ideal" character - that it was not necessary to realise, since the result was evident as soon as their conditions were stated. Such an experiment is that by which Stevin demonstrated the principle of the composition of forces, after which "le developpement complet de la statique n'etait plus desormais qu'un probleme purement geometrique et analytique."(253) The general appeal to experience made by Aristotelianism, only analysed in accordance with concepts based on synthesized perceptions, cannot, as these purely theoretical demonstrations can, be granted the title of "experiment," in the same manner in which the term is applied today to scientific technique in even its most empirical aspects.