Throughout the latter half of the sixteenth century John Dee enjoyed a thoroughly European reputation for profound scholarship: his opinions were widely consulted, his authority invoked in many diverse fields of speculation and research. Yet, without minimising the value of his personal influence and attainments, the justification for a detailed study of these must depend less on the limited value of the accompanying attempt to assess Dee's own claims as an original thinker or direct contributor to scientific discovery, than on the fact that he may be significantly considered as the representative - and in some respects the spokesman - of an age. Dee in his life and writings championed a certain vigorous "new philosophy" which flourished in the late Renaissance(1), and though this philosophy, or rather the particular form which it then assumed, fell later into barren obsolescence (2) yet some of its offshoots of that time were to bear rich, and unexpected fruit in succeeding centuries. Dee's surviving works are perhaps only fragmentary illustrations of certain aspects of the general body of doctrine he maintained, yet an examination of them is illuminating since, however limited or idiosyncratic their subject matter, they exemplify a typical approach to various problems, and they also occasionally give clear expression to broad statements of principle, which should, Dee believed, provide a foundation for a multitude of particular applications. In these respects, they throw some light, if only indirectly, on much contemporary endeavour and achievement, even in fields discussed not at all, or only incidentally, by Dee, since these may often properly be regarded as related and comparable effects arising from a common intellectual tradition.

The movement to which Dee contributed may be described rather broadly as striving after a new philosophic synthesis which should fully express and relate, as far as they could be known from the data of reason, revelation, and experience, both the capacities of men and the processes of nature, and which should relegate neither to a subordinate or derivative position in regard to the other. It has a natural place, frequently acknowledged by its exponents, in the general stream of neoplatonism, but it is more particularly associated with that current, which embracing much of later Greek endeavour in astronomy and mathematics, stemmed from Alexandria, notably preserving thereafter, from this source, the characteristic emphasis on the natural powers of the Intellect to arrive at truth, and on the value of dialectic, with the corresponding lack of stress on the immediate importance of "ecstasy" (reflected in the Greek patristic writers' comparative neglect of the doctrines of Original Sin and Grace), and ran through much of the scientific thought of the Arabs; which current, by insisting that the Cosmos was a logical and necessary unfolding of intelligible principles, emanating from and manifesting the nature of God, gave strong support and encouragement to the study of the natural sciences and mathematics. That other aspect of neoplatonism - the only one of much influence in the Latin speaking world during the middle ages, represented by the writings of the Pseudo-Dionysius, and to some extent those of St. Augustine, which stressed, or was inclined to value above all else, the personal mystic experience - to which all knowledge and philosophy was considered at best, merely a propaedeutic, since true knowledge was essentially revealed and not attained to - this aspect was of course incorporated into the scientific neoplatonism of the Renaissance - to have excluded it would have introduced incoherency and inconsistency into a doctrine relying so much on the assertion of the mind's ability, owing to its relationship with the creative thought of God, to determine a priori, at least criteria of, truth. Nevertheless it was overshadowed in the sixteenth century by the rediscovery of, or by the increased attention then given to, the works of later Greek Platonists - the mathematical and metaphysical commentaries of Proclus for example, whose writings make up one of the chief single influences on Dee's thought in general - as well as ancient scientific writings either associated with these, or at least having little relation with and frequently running counter to Aristotelian doctrines - and the theological writings of the Greek Fathers, who presented a much more explicit synthesis of Christianity and pagan philosophy, the essential harmony between which was affirmed by Justus, Clement, Gregory and others, than any of the Latin Fathers had been prepared to do. The form this Neoplatonism assumed and the applications of its doctrines, in the late Renaissance, of which Dee's work is here considered to be representative, and which were to give a new character to the scientific, or philosophical, approach to Nature in his time, bore fruits in fields far removed from Dee's own immediate interests; for while his own practical achievements, in kind and in extent, remained somewhat narrowly limited, the principles from which they sprung, and the method by which they were developed, were widely proclaimed and accepted as possessing universal validity throughout the "natural," "intellectual," and "spiritual" worlds, and as providing guiding canons for practice of the various arts as well as invention or discovery in mechanics and natural sciences.

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Not infrequently in recent years, attention has been given to Dee's scientific importance (3), and recognition of this has led to the demand for a re-examination of his work that will once more accord him "his rightful place as the central figure in the beginning of modern science in England." (4) Dee's historical significance in this sphere is chiefly due to the fact that he became one of the principal propagandists in England for an approach to nature which proved of immense value in the hands of later experimentalists, and laid the foundations of the methods of modern physical science. Yet Dee supported these views not from any intuitive precognisance of the profitable results - their pragmatic justification - which would follow from their extensive application in succeeding centuries, but rather because they formed an intrinsic part of a general scheme of thought, which was largely evolved and defended by as pure an a priori theorising as the most involved logistic subtleties of that earlier scholasticism which Dee's intellectual legatees of the seventeenth century, in conscious superiority, so frequently and vociferously derided. There were other philosophies of the day, seemingly as cogent, offering much greater favourable empirical evidence, than this stubborn assertion of discoverable, all-permeating numerical harmonies which flew frequently in the face of "common sense" in its interpretations of observed fact, and of which the few demonstrable advantages were almost ridiculous compared with the vastness of its pretensions, and though, finally, these rival systems fell into entire discredit it was only because they were found not to be so congruent with the mechanical world, which the later unification of scientific theory, accompanying material progress, seemed increasingly to insist on.

Moreover it is to be observed that many of the apparent eccentricities of Dee's thought, the intricate and unprofitable mazes of cabala and occultism in which he inextricably involved himself, were, in some respects, no more than rigorously derived consequences of the general philosophy he had so heartily embraced; and though this, in other hands, provided the framework for the ordered world of Newton, the watch-universe of Huygens (5), there was not to be found implicit in its premisses, as Dee accepted them, any just cause for an invidious division between mathematical activities concerned with quantitative measurement of natural phenomena, and esoteric numerological fantasy. Those of his contemporaries who achieved a greater measure of practical success, or who did not involve themselves so deeply as Dee in these fields, were men who were more fortunate or less consistent in their employment of the "new" methods. The charge has been too often reiterated that Dee "allowed his imagination to dominate his scientific knowledge, and he adopted the baseless superstitions of the day." (6) Only by an unjustifiable application of the standards of modern knowledge, (7) is it possible to separate as intrinsically different those elements in Dee's work which survived the test of "usefulness" in future generations from those sterile speculations which to him, and to his age, seemed to be fully as necessary in completing a coherent picture of the world.(8)

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The Elizabethan World Order, it has been said, "was at once theological, legal, scientific, psychological and moral. It was designed to provide for everything." It was felt as "a poetry at work in the world preparing a grand solution of the problem of human existence," (9) rather than expressed as a formal body of doctrine; and thus, though it embodies specific features possessed of high survival value and considerable fertility, examination of these and the particular systems of thought of the day which produced them, must be conducted with reference to this general background. Moreover, although Dee's works are set, quite consciously, within a fairly clearly discernible philosophic tradition, no one of them sets forth explicitly, in ordered and comprehensive form, a total philosophical system. Whether such an adjective in its modern sense is properly applicable to them is doubtful. Dee for instance seldom touches on epistemological problems; he has made certain assumptions, from which he is inclined to dogmatize about the foundations of knowledge, and seems only ever concerned with the problem of the possible range and extent of its content. Compatible with his assumptions and his efforts to determine these is characteristically an extensive and eager syncretism, in which he attempts to absorb with an almost voracious credulity, vast areas of data and ideas discovered by various recourse to myth, tradition, theology, authority, reason and experience; his criteria of their validity being only the potentialities they may exhibit for being brought into coherent arrangement within a framework whose pattern takes its inspiration from what he believed to be the methods of mathematics and the dialectic of Plato. But such tests he did, with considerable strictness, apply, and thus may be allowed to have followed "the true method of philosophical construction which is to frame a scheme of ideas the best that one can, and unflinchingly to explore the interpretation of experience in terms of that scheme," (10) and his works may be legitimately considered in the light of such an implicit scheme.

That the new science grew up within the confines of a metaphysic is not surprising (11), for one of the most striking characteristics of this metaphysic is its view, radically differing from that of other schools of thought, of the status, functions, and potentialities of mathematics. And mathematical studies stood in dire need of such organised philosophical encouragement and support. Without it the fulfillment of the rich promises held out by contemporary rediscovery of many ancient scientific works might have been much longer delayed. The difficulties of obtaining adequate instruction in mathematics was a grave discouragement; their study penetrated only slowly and in the face of many obstacles into the curricula of the universities; an established and orthodox Aristotelian science, by relegating mathematics to a wholly inadequate place in the universe of knowledge, provided no inducement to a prolonged and arduous study of them, since it largely denied the prospect of any valuable results to be achieved thereby.

Moreover mathematics still suffered under the unenviable reputation, deeply entrenched in the learned as well as the popular mind, of being a branch of necromancy, or at least of being intimately connected with such forbidden lore in its more recondite aspects. Such suspicions Langland had voiced - the words are supposed to be those of Dame Study - in the fourteenth century:

"As astronomye is an harde thynge and yvel for to knowe,
Geometrie and geomesye is gynful of speche,
Whoso thenketh werche with tho two thryveth ful late,
For sorcerye is the sovereyne booke that to the science longeth." (12)

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In Dee's day far from diminishing they had rather, in some respects, increased and become more acute, they were encouraged by the all too easy misunderstanding of the approach to natural magic and theories of ceremonial magic adopted by many of the new school of "neo-Platonic" mathematicians. They survived hardily into the age of Francis Bacon, long after Dee's death, so that after the Savilian and Sedleian chairs had been established in 1619 at Oxford, Francis Osborne records that one effect of the University's encouragement of this study was that "not a few of our then foolish Gentry" thereupon refused to send their sons to it "lest they should be smutted with the Black Art." (13) It was a reputation kept alive by the inevitably somewhat isolated and individual activities of mathematicians, many of whom undeniably engaged in a variety of "magical" practices, in an attempt to attain wider benefits or more concrete results from their study, than it directly indicated.

Of theories recognising the importance of mathematics, it has been acutely observed "Les uns adoptent le mathematisme en considerant d'ou il vient; il ne faut pas les confondre avec ceux qui l'adoptent en considerant ou il permet d'aller." (14) In the sixteenth century the second consideration was perforce still largely a matter of faith, a faith which might be sustained by the promise held out by its supposed importance for ceremonial magic or belief in hidden spiritual knowledge contained in formal numbers, but one which insofar as it related to the physical or applied sciences could be based only on a particular interpretation of a restricted range of data, which opponents had no trouble in discounting. The general defence of mathematics could be far more effectively conducted, therefore, by appealing to the absolute certainty attendant on its demonstrations, its apparently a priori source, and the doctrine that the intellect of man was, in the sphere of pure reason, a reflection of the creative intellect of God (which together may be said, broadly, to make up the argument of Dee's Preface). Since moreover it rapidly became obvious that many conclusions reached in this field were in flagrant contradiction with accepted teachings, or views arising from seemingly natural modes of thought, some such philosophical justification as this was required if the results were to be accepted as a true picture of "reality"; otherwise they could only teach such a lesson in scepticism, with its accompanying lessening of interest, as Montaigne drew from the information that the "certain" logic of geometry had produced the impossible conclusion that lines could asymptotically approach each other (15). An imperfect understanding of mathematical operations, especially as regards their application to physical phenomena, posed questions which demanded answers, seemingly only to be found in non-mathematical fields - even in the solution of simple Archimedean problems of weights and balances difficulties would seem to have been encountered in conceiving these otherwise than as involving the intellectual performance of the, physically, clearly impossible operation of multiplying a "weight" by a "length" - indeed it is very striking how far in needless complication, techniques of calculation, based on "ratio" and proportion went as a rule to avoid such a suggestion when dealing with such problems. It is this inhibition against "mixing" different qualities in the same term that perhaps accounts for the fact that while in certain early thinkers, such as Leonardo, clear and exact statements of lever problems, even of those considering the bent arm lever, and requiring the concept of the "potential arm" are to be found, yet the idea of turning moments about a point, though to us it appears obviously to be already essentially involved in the correct expression, which they had arrived at, of the relationships they were considering and indeed to be only a transformed equivalent of this, is conspicuously absent. Another example is Dee's treatment of problems of medicine graduation in the Preface, in which both measures of volume and degrees of temperament were concerned, and in which he goes to some lengths, in working them out, to avoid multiplying coefficients of these two distinct "qualities" together.

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