CHAPTER I. RENAISSANCE METAPHYSICS AND THE HISTORY OF SCIENCE I. Dee a representative sixteenth century scientific figure — the endeavour after a new philosophical synthesis (n.i) and neoplatonism — his scientific importance chiefly due to his assumption of the role of a propagandist for mathematics — this championship derived from metaphysical doctrines, not considerations of utility — the essential unity of his thought, though only some discrete elements of it historically survive as significant — and the Elizabethan world order — in what sense Dee is a philosopher — the need for a philosophical defence of mathematics in his time. II. Impossibility for mere empiricism in sixteenth century to found a successful science — necessity of a preliminary framework of concepts and uniform methodology in any examination of nature — the fact constructed or determined by such contexts — in these the only means to achieve one constant goal of science, to organise its constituent knowledge into a deductive system — such systems differentiated by such contexts — in these the only means to achieve one constant goal of science, to organise its constituent knowledge into a deductive system — such systems differentiated by their fundamental criteria of the significant or intelligible — importance in this respect of the Renaissance for later scientific thought — the subsequent progress of mathematical domination of science first adumbrated then — emergence of fundamental assumptions of Newtonian Science in the Renaissance — the apparent transformation of metaphysics into methodology — ultimate dependence of all practise on theory; and the experimental method — history of science the gradual clarification of ideas not accumulation of facts — contrast between actual development of a science through time and its late formal elaboration — consequent necessity for studying the thought of a period as a "whole" and in its own terms. III. The main schools of Renaissance metaphysics — inevitable defects of such sketches as present, excessive schematisation, over-simplification, too clear cut distinctions — subsequent chapters correctives to these generalisations — actual picture especially blurred by extensive permeation of naturalism — the plausibility and scientific impotence of this. IV. The services of the Aristotelian revival of the thirteenth century for later thought — important as preparatory organisation of scientific knowledge — as a system rapidly, and by the Renaissance, fully, exploited — the inadequacy and dangers of its qualitative analysis of nature — its standards of Reality fatally divorced from intelligibility — doctrine of essence and accident and assumption of a direct access to facts through language — ascription of causal efficacy to quiddity — its wide appeal to experience and qualitative "experiment" — inadequacies of Aristotelianism as an overall scheme of correlation — it represented a merely contemplative ordering of knowledge, providing no assistance to applied science — doctrines of causality — species and teleology — discontinuities it established in nature — separation of the realms of faith and reason and consequent low estimate of powers of mind — the rational and the natural and the depreciation of mathematics. V. The evaluation of mathematics one of principal matters in dispute between Aristotelian and neoplatonist schools in Renaissance — restricted nature of empirical evidence producible against Aristotelianism — but general superiority of mathematical procedures to verbal methods of investigation. VI. Tradition of scientifically orientated neoplatonism of Dee — its critical but not hostile attitude to Aristotelian doctrines — conciliation of Plato and Aristotle a perennial characteristic of neoplatonism — lack of any differentiation between Plato and his followers — Pythagoreanism. VII. The constant characteristics of neoplatonism in all its varieties — insistence on the mind's direct access to truth — the status of the universal — ultimate grounds of knowledge placed at opposite end of scale of being to sensible — the Idea of the Good, Union with the One and intellectualism of Christian neoplatonism — the a priori — revelation and the levels of knowledge — thought always directed towards being — transformation of Platonic Ideas into modes of considering objects — and operational conventions — Ideas become essentially functional for Galileo — reconstitution by scientific neoplatonism of Renaissance of "objective" as that of which a logical account can be given. VIII. The sensible world and neoplatonism — it awakens individual minds to latent conceptual knowledge — its derivation from intellectual truth — its consequent rationality and the new ideal of discoverable natural law — intelligible unity of the cosmos in neoplatonism of Renaissance — universe no longer crudely anthropocentric — the "parts" of the universe — superiority of neo- Platonic mathematical approach over qualitative atomism — the natural fact considered as a theorem in geometry pertaining in the same way to a system — Platonic tradition of the unification of all sciences — and the new stress on detail and exactitude — the revaluation of nature — the unity of the natural and intelligible following on the view of the Real as the logically representable — dialectic and reality in Platonism. IX. The a priori and mathematics — sixteenth century stress on mathematical doctrine as fundamental distinction between Plato and Aristotle — mathematics for Plato — fusion with Pythagoreanism — the entire certainty of mathematics — mathematics as the type of objectivity — general sixteenth and seventeenth century adoptions of these teachings — Roger Bacon's ideal of "verifying" all the sciences by mathematical means and John Dee. X. The connections between neoplatonism and new science in sixteenth century — structure gradually replaces tendency as key concept in analysis of nature — the reconciliation of belief in overall Divine Providence and acceptance of universal mechanical causality — inspiration given by the Timaeus — superiority of new mathematical methodology over Aristotelian induction — beneficial results of spread of Ramus' logic directed towards psychology rather than "substance" — its connection with mathematical approach to nature and general advantages of this — idealism of relation replaces realism of substance — germs of subsequent science clearly present in Renaissance — Galileo's neo-Platonic mathematicism — his confidence in reason even when opposed by experience — the scientific inspiration of Archimedes' works in sixteenth century — effect of his apparent success in applying purely a priori methods to establish synthetic results. XI. The replacement of quality by quantity as what is taken as fundamental in nature — difficulties of such an attitude in sixteenth century — lack of pragmatic support for it — primary and secondary qualities in neo-Platonic tradition — consequent gradual abandonment of claims of intuition — but necessity in Renaissance of a Pythagorean metaphysic for defending alternative doctrine — the new Reality of Renaissance Science — its standards of value — particular dangers, as evidenced by Dee, of theory of world as an exemplification of mathematical truth. XII. Divinity as the head of the hierarchy of sciences — consonance of Platonists and Christian doctrine — views on the nature of God and the soul inseparable from Renaissance scientific theory — consequent place of qualitative experience in Dee's mathematics — the Renaissance synthesis and its multivalent appeal — rational, mathematical, aesthetic, theological — its intention to be wholly adequate to all the capacities of man. I. 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