But this was only the function of the sense in relation to the individual mind, the general external world built up by perception as it was considered to be chiefly significant by Renaissance neo-Platonism may perhaps best be compared to the diagram in a geometry. They assist the mind in conceiving certain relationships, which they approximately express as far as the limits of their particular natures permit, their failure, insofar as they fall short of the ideal, is not a relevant aspect of them, is not positive at all, but pure "defect." They serve as an intuitive basis for reason and discovery, but they do not embody truths, so much as derive from them, and the system of truths which may be discovered by utilising them is not only independent of them, but is not to be limited in extent and application to what can be, even remotely, represented by them. A purely empirical approach, concerning itself only with naked experience - some schools of medicine were criticised from this standpoint by Platonists - could be regarded as the attempt to establish general propositions by the study of such figures in themselves, by mechanical measurement of sides, angles, etc. an approach which not only is still driven, however it may disclaim it, to employ instruments provided by the mind, while arbitrarily excluding much of the contribution this could offer, but which at best can only arrive with much labour at approximate expressions of truths, which must remain isolated and barren since no rational account can be given of them, and which might more easily be attained by sound analytic methods. "Experience" was highly valued by Renaissance Platonism but, against such a background, evolved towards "directed experiment," and method in observation consciously and closely related to theoretical principles; for what it had come to seek in sensible "images" may be seen to have undergone an important change as compared with the objectives of earlier systems even in the same tradition. When Cusa writes that all the wisest and holiest of men, have with one accord, held that visible things are images of invisible, and reveal their Creator as in a mirror or enigma (171), he is echoing a commonplace, but nevertheless the interpretation he gives it is novel. Cusa is not seeking in the natural world a collection of disconnected emblems of moral or theological maxims such as fill the bestiaries and the catalogue "encyclopedias" of Isidore or Hildegarde, he is seeking to discover in it general laws, combining to form an overall intelligible structure of relations maintaining between its parts. These laws he regards as active products of mind, existing in mind, and knowable by mind, they are not more or less inaccurate conceptual descriptions of real occurrences in the external world, but are themselves the reality of that world. "Les lois ne sont ni des generalisations, bien qu'elles les supposent, et que le sensible en soit l'occasion. Elles sont des applications de l'esprit, des absorptions de l'experience. Le nominalisme de Nicolas, comme celui de l'idealisme moderne, implique l'existence d'un intelligible interieur a l'intelligence, fonction d'intelligibilisation si l'on peut dire."(172)

Such an attitude is connected with the belief in an underlying intelligible unity in the Cosmos. The eternal wisdom (Sapientia) which he identifies with the Logos, and Reason of things, Cusa declares is the Simplicity which relates all forms, and is the entirely adequate Measure of all things (173). But that the world is such an integral structural unity is not here an initial unsupported assumption about ontology, it is rather a conclusion from the verifiable position that mind presented with any disparate entities whatsoever can construct a pattern containing them, unite them under some generalisation (so that these as far as human knowledge is concerned largely condition their natures, defining the aspects under which they are known), taken in conjunction with the belief that the existence of such entities stems from the mind of God - to which man's intellect is, however subordinate, akin - which creates them via such patterns and "generalisations" as are available to man's mind, and by man re-fitted to the "things." Though man received a high and dignified place in such a system, yet a "Copernican" shift in the co-ordinates of reference for schematising the universe was implied. It was no longer to be interpreted, through its direct relationships, practical and moral, to man, a trend inculcated by much previous theology and in general by Christian philosophy hitherto, which took man as primary in its systematisation, and endeavoured to give adequate weight to man as a moral and spiritual being; but was to be considered via general law, the understanding of which was the most proper function of man's mind. Thus Avicenna holds "le but principal que l'etre necessaire se propose en produisant les formes, c'est l'ordre universel."(174) This order embraces a series of spiritual levels, as well as the mechanics of spatially extended phenomena, but it is no longer anthropocentric, the nature and purpose of man make up an object of study to be known through the determination of their logical place in the system. That the world was a single closely organised entity had been a general feature of Stoic writings, but despite the great influence of these in the Renaissance, particularly of the consequent ethics, and also perhaps of the stoic semantics and propositional logic on the new un-Aristotelian logics which spread increasingly, it is nevertheless the fostering of mathematics, and the teaching of the necessity of applying these in the interpretation of the laws and ordering of the universe, a more specifically "Platonic" characteristic, that was of most importance for Renaissance scientific thought. Similarly the ancient atomic systems, which to some extent reappeared, at first sight offered similar "monisms," governed by all pervading necessity, but suffered from similar defects as regards active scientific investigation and ultimate unintelligibility as Aristotelianism. That of Epicurus, in explaining macroscopic phenomena by attributing qualities to the parts - hooked, angular and smooth atoms - drawn from suggestion of sense experience, provided little that was encouraging for further investigation, analysing the sensible world only into another equally inchoate, and almost as multifarious, but quite inaccessible to experience, testing or experimentation (175). Both it and the Democritean version avoided the major problems of Being as presented both to philosophy and science. Concentrating on the nature of individual elemental parts, neither offered any adequate explanation of the emergence, or ingression of "Wholes," neither offered means to a rational analysis of "arrangements," and "integrations," associated with such supervenient wholes or allowed such ideas status as independent, controlling "Principles" which could be derived from, and examined in the light of, a general co-ordinated system of dialectic (176).

In contrast, "parts," says Plotinus, may be assumed, and thought of, in such organized wholes as the soul with its various faculties, which he is here primarily discussing, or the universe, "in the same manner as a theorem is part of science; the whole science indeed nevertheless remaining; but the separation into parts, being as it were the utterance and energy of each. In a thing of this kind, however, each possesses the whole science in capacity, but the whole nevertheless continues to be the whole."(177). The universe as a system of interconnections, the key to which may be found in the mind, appears in Plato's own dictum, "for as all nature is akin, and the soul has learned all things there is no reason why we should not, by remembering one single thing - an act which men call learning - discover everything else, if we have courage and faint not in the search."(178) The manner in which "one thing" truly known may be pressed into unlimited service in revealing natural or spiritual mysteries is a key to many Renaissance treatments of symbols, especially so far as some of these are considered as the summary of some all embracing scheme of analogies, and it epitomises much of the theoretical foundation of the Lullian Cabalah, Dee's Monas or Bruno's "mnemonics."

Diogenus Laertius records that Speusippus who "adhered faithfully to Plato's doctrines" was accredited as being "the first to discern the common element in all studies, and to bring them into connection with each other so far as that was possible."(179) The historical appearance of theories laying man emphasis on such a "common element," as the most significant and profitable clue for investigating various sciences rather than concentrating primarily on those aspects of the nature of their subject matter which differentiated and particularised them, while not invariably associated with Platonism - it is a characteristic feature of thought drawing inspiration from mathematics or mechanics - represents generally an approach divergent from Aristotelianism. Pronouncements like "Thus through all the sciences (Music, Medicine, and Astronomy have just been correlated) many things or indeed all are in common, so far as theory is concerned," are to be found in Vitruvius (180), a source consulted and applied by Renaissance theoreticians, whose interests were far other, or extended much further than, practical Architecture. Again Raymond Lull, whose writings seem to have undergone a revival, with the spread of teachings of Pico, Reuchlin, Agrippa, etc., had aimed in the Ars Demonstrativa at inventing an art, a combination of a metaphysic and a calculus, by means of which all sciences should be demonstrable, universally and incontrovertibly: the principles of no single one were enumerated, but a method, mechanically based on an algebraic expression of syllogistic reason, is taught for discovering their common principles, on which those more particular to each may be shown to depend. In the Renaissance the De Arte Cyclognomica of Cornelius Gemma, a prominent mathematician, Copernican and acquaintance of Dee's - to name one of a multitude of works in this genre that then appeared - also presented, with a liberal use of illustrating emblems and geometrical diagrams used as metaphysical analogies, a universal method of enquiry into, and reasoning on natural, intellectual and spiritual matters. For Truths, said Culverwell, summarising the underlying dogma here, "love to spin and thread themselves into a fine continuity," and this carries as a corollary, it has been observed that "our grasp of that continuity assures us that we are sharing in the divine thought."(181) As this continuity extended through the whole of the natural world, what is perhaps a valid criticism of the original Platonic system, that it was not open to correction from experience, is inapplicable to much Renaissance Platonism, for which exactitude in material measurements, and accuracy of natural observation was frequently of the highest importance, though the real significance of the results, it might be held, was to be sought elsewhere. Its idea of the law that was to be found there led such neo-Platonism in the Renaissance to a revaluation of the external world. For the same reasons as those on which Plotinus had attacked the Christians for despising astronomical phenomena, the Cambridge Platonists ventured to criticise Plato himself for denigrating the body. That intelligible order was to be found in nature accounts for Leonardo's reverence and devotion to factual detail - so that for example he could but himself to the considerable difficulties of obtaining and dissecting ten corpses in order to trace the course of certain veins - and could proclaim the body as an organism so much a miracle that the soul, "itself a thing divine, only separates from it eventually with the greatest suffering and grief."(182) Thus de Mornay, defending Pagan Philosophy as expressing true religion unconsciously (for as he later states "the voice of nature is the voice of truth), and, it would seem, criticizing the Averroist position, writes "To be short the marke that our faith looketh at, is the Author of Nature, and principle of all principles. The rules therefore and the principles of Nature which he hath made, cannot be contrarie unto himselfe. And he is also the verie reason and truth itselfe. All other reason then, and all other truth dependeth upon him, and relieth upon him, neither is there or can there be any reason or truth but in him: So far off is it that the thing which is trewe and reasonable in Nature, is or can be false in Divinitie...."(183) Culverwell, in the seventeenth century then, elaborating the argument that Nature is an "order or work of order" in which Eternal Law "is not really distinguished from God himself,"(184) is at once, reflecting an attitude that contemporary science was formulating with self-professed independence and originality, and yet writing well within a speculative tradition of long continuance.

Such a view of Nature, before its retrospective justification in use and application, found a congenial setting and apology in the Platonic metaphysic with which it indeed historically is most frequently conjoined. For perhaps the most fundamental characteristic of "Platonism," wherever and whenever it appears, has been its uniform refusal to separate the "logical" from the "factual," consistently regarding the essence of "things" or "facts," as that by which they become intelligible, and which is not to be looked for in the sense experiences connected with them, in their "usualness" of occurrence, or in the "customary" way of accepting them generated by habit in daily life. The foundations of knowledge are not a set of Aristotelian "first intentions," or what Russell has defended as "basic perceptive propositions." A correspondence theory of truth is replaced by a view in which all confirmation becomes a function of coherence (185). A "fact" for such a philosophy, it has been observed, "is not something objective that we apprehend outside our experience (taken as a whole), it is an interpretation of a part of experience, which other coherent interpretations of experience oblige us to believe,"(186) a view which may be developed so as to imply the denial that any specific fundamental distinction can validly be drawn between "data," and what is inferred form this or even the very process of inference itself, and to imply that they are all ontologically on a parity, and therefore only to be artificially differentiated. Thus a "thing" is real only as a "part" of a system, and considered in itself reduces to a nexus of relations (187). To be simple, to be self-subsistent belongs only to the Whole, the One, the Good, which is strictly ineffable, for being in all respects positive, embracing the full extent of the positive, it cannot ever be properly represented by discursive thought as indeed the neo-Platonic Negative Theology always taught - for which all positive assertions acquire their meaningfulness only by the implied denial made by their terms that some certain range of qualities can belong to the "entities" they refer to, since to discriminate - which is to know within such a system - is to limit and restrict. The Aristotelian objection, applicable to all purely contextual theories of signification, that to base Reality on such an unattainable absolute, leads to an infinite regress in a series of progressively more abstract discursive systems, is not particularly damaging, since the successive levels engendered by dialectic describe, as they employ more and more general and inclusive principles, an asymptotic approach to, what is defined as, the Whole. Thus from the Theaetetus it appears that, while the term "knowledge" can be applied with varying reservations relative to the status of the particular system, at a variety of levels, what is meant by "to know," without qualification of such a contextual type, cannot be accurately specified. For Plato then, it has been said, "Dialectic....while incidentally providing terms convertible in predication with "being," is not primarily a knowledge of being int he manner of Peripatetic metaphysics. It is primarily a method or an `art' of analyzing discourse by generalizing from contingent and arbitrary modes of signification so as to achieve a context free from such contingency."(188) But "dialectic" represents also the activity, and thus the actualisation of, the Intelligence, as "logic" it reveals, and has for its object, the laws governing the operations of the mind; it exhibits, which is what knowledge aims at, the conditioning principles of the patterns of relationships through which the universe can be conceived of as ordered and intelligible. Thus "dialectic" writes Plotinus, must not be fancied to be merely the instrument of the philosopher "since it does not consist of mere theorems and rules, but is conversant with things and has beings as it were for its subject matter," and "it proceeds in a path to beings, possessing things themselves together with theorems."(189) In this way an analysis of the syntax of logic, of the structure of discursive knowledge, is converted into a metaphysic. "Being" and the "True," "Non-being" and the "False" are equated by Plato (190) - "Non-being" representing that "deficiency" which particularises or differentiates anything, producing multiplicity, preventing the Universe from appearing a Parmenidean One; and though that which is the "True" without qualification, the ultimate Form of all discourse, is transcendent, nevertheless from it, through mediating dependent systems of discursive thought, "the objects of knowledge not only receive their being known, but their reality and essence."(191)