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Infinity on the threshold of Christianity: the emergence of a positive concept out of negativity.

1. Introduction

The repudiation of infinity, or horror infiniti, has generally been considered as an insignia of ancient culture. (For a general introduction to the topic, see e.g. Moore 1993, Moore 1990, Maor 1987, de Vogel 1959, and Cohn 1896.) In the same vein it is usually argued that a significant change occurred in the attitude to infinity at the beginning of the Christian era and its newborn religion. As Christians made an attempt to buttress their revelatory experience of God also on the level of rationality, relying in this action on the rich philosophical heritage of the ancients, there was introduced a kind of clash between finitist and infinitist elements into the thought structure of the Christian world. I would like to argue that this substantial conflict provides us with contextual means for investigating not only the concept of theological infinity, elaborated in the Middle Ages, but enables us to look in a historically consecutive way also at the two modern children of infinity - at the idea of physical infinity, starting to emerge in the Renaissance, and at aesthetic infinity, appearing in the second half of the 18th century. In other words, I claim that the history of infinity offers us scope by which to analyze the mutually instigating relationship among faith, knowledge and artistic representation: it reveals how a certain idea, accepted on the grounds of religious arguments, can force the modification of the speculative system of the age and lead, in terms of the modern era, to the foundation of new scientific (experimental) truths, as well as of a new system of artistic representation. Keeping in sight such a project of cultural rhetoric of infinity, I will confine myself in the present article to the topic of the revaluation of infinity in late antiquity and early Christianity.

2. Platonic-Aristotelian concept of infinity

Before going on to tackle the proper subject of the paper, it is necessary to offer some explanatory remarks about the Greeks' disgust of infinity. First, we should make it clearer what we mean by the word infinity because its usual Greek equivalent, apeiron, had a range of meanings not necessarily identical with our sense of the word (Guthrie 1962:83-89, Sweeney 1992:15-28). For example, it is questionable how much we can attribute to it the strictly spatial connotations prevalent in our perception. Aristotle had stated that the belief in the existence of infinity can be motivated in us by five different impressions producing the respective modes of infinity: temporal eternity, infinite divisibility of quantities, the endless process of generation and perishing, the absence of a final boundary line in the corporeal world, the additive infinity in numbers and in our thought (Physics 203b16-269); some steps further Aristotle comes to conclude that infinity as such can exist either by way of addition or by way of division (Physics 204a6-8). As to Aristotle's personal conception of infinity, he coupled it, as is well known, with potentiality pertinent to matter, admitting, quite interestingly, the possibility of endless division as regards spatial quantity, while denying the infinity in space by means of addition (which, i.e. additive infinity, he was in turn ready to admit in respect to time) (Moore 1990: 40-41). In spite of the subtleties we have to consider in speaking about apeiron in various Greek philosophers, I would wish for the moment to stay on the more general plane and to declare simply that the so-called Greek abhorrence of infinity refers to the lowest position infinity as indefiniteness necessarily held, as compared to all finitist conceptions, in traditional Greek thought. In other words, not before Christianity and Neoplatonism (Plotinus), was infinity assigned in the Greek mind a significant cognitive value, let alone elevating it to the position of highest perfection. Nevertheless, even this broad statement needs some qualifications and can be maintained only with the proviso that we limit our scope of vision chiefly to the mainstream of ancient philosophy, i.e. to the Platonic-Aristotelian tradition. Diverging from this orthodox trend was the drift prompted by Greek atomism which had reached the postulation of some progressive, but for later Greeks unconventional, viewpoints, among others, the existence of an infinite void and infinite number of atoms, which has been considered a strong profession in favour of the existence of actual infinity in Greek thought (Sweeney 1992:545, see also Furley 1981, Sweeney 1972:155-173). And of course, we cannot disregard Anaximander, one of the great Milesian monists, who had ushered apeiron into the lexicon of Greek philosophy by his bold conviction that apeiron is the real arche out of which all things have their beginning and into which they all in turn perish--with the implication, similar to that of the atomists', that apeiron is not a deficiency needing to be defeated, but, quite the contrary, the wholeness which comprises all the opposites (Sweeney 1992:544). Nevertheless, our wish to sustain imperfectness as a trademark of Greek apeiron could be vindicated, in the case of Anaximander, by the hylozoistic-pantheistic context of his thought which defies application of certain dichotomies (of matter and soul, of definite and indefinite) essential to the later Greek understanding of infinity; in the case of atomists the justification can be deduced from the fact that the real impact of atomism on Western philosophy was postponed to the 17th century and is thus of auxiliary, not of central, importance for our present research.

In trying to determine a point from which the imperfectness of infinity got fixed in Greek philosophy, we surely have to take note of Pythagoreans. It is interesting to remark that when Hellenic philosophy had started in the form of Naturphilosophie in the Greek Eastern colonies of Ionia, where infinity, missing the opposition to the finite, was rather favoured than condemned, the transition from monistically understood nature to what we can call the dichotomization of principium, was accomplished in the Western side of the Greek colonial world, in the Magna Graecia of southern Italy. Pythagoras, who had left the island of Samos for Croton in about 532 B.C., to escape the tyranny of Polycrates, established the dichotomy of peras and apeiron as a groundwork of his teaching on the universal contrasting principles of the world, linking limit with good and the unlimited with evil. Accordingly, the limit came to be interpreted as a kind of cosmic order that is imposed on the indefinite apeiron breathed in by the limit. (1) This bifurcation of the arche, which from the gnosiological viewpoint surely constituted a progress, as compared to the prime matter of Milesians, is simultaneously characterized by a new search, on the part of Pythagoreans, for the means of expressing the monistic unity of the world. First, it appears, I suppose, in the Pythagoreans' double concept of soul. On the one hand Pythagoreans understood, in line with the Ionians, by soul either the breathsoul (pneuma), conceived mainly in terms of air, or soul (psyche) as a harmony of the material particles of the body - with unavoidable consequence in both cases that soul is mortal and dissolves immediately at death. On the other hand, Pythagoreans have become famous through their doctrine of transmigration of souls, assuming that souls of living creatures are only tiny pieces of one universal soul which are condemned, until they have become purified for joining the divine soul, to search constantly for the bonds of bodily existence (see Guthrie 1962:306-319). The essence of this kind of immortal and transmigrating soul cannot be explicated any longer by the aid of the harmony of elements in the human body, but it demands elucidation on some more abstract level--in the case of the Pythagoreans it means that the divine soul is conceived as numerical harmony of the cosmos. With this concept Pythagoreanism surely took a considerable step towards announcement of the immateriality of the formal principle of the world. Second, the tendency to monism in Pythagoreanism is even more notable in its double concept of the 'one'--true, the idea itself dates from later Pythagoreanism and bears obvious marks of Plato's influence. As an odd number and the first unit of the number-series, one was ranked with limit and other positive qualities issuing from it; at the same time, there is evidence that Pythagoreans divinized the One and viewed it as a monad from which all dichotomies, among others that of peras and apeiron, had got their beginning. (2) Without going into the details here, I simply wish to state that when the negativity of apeiron made its appearance together with the dichotomization of arche, there had loomed, nevertheless, behind this progressive step a 'residual' monistic need to retain the unity of cosmos by the help of an immaterial soul, or by the One which is not even a number but a monad situated out of all oppositions.

The man who can be considered a formulator, as a historical figure, but even more as a protagonist of Plato's dialogue of the same name, of some key concepts of the ancient and early Christian approach to infinity, was Parmenides, a former Pythagorean who became the founder of one more philosophic school in southern Italy--the Eleatic School. The thrust of Parmenides' achievement was the transposition of the issue of peras (i.e. of definitive being) from the mathematical plane to the purely ontological level by asserting that what really exists is 'is' (estin), together with obvious consequence that 'is-not' (ouk estin) cannot exist. Thus, when Pythagoreans, who had imagined generation as a process of drawing in of apeiron by the limit, leading to the multiplication of numbers (and things) separated from each other by the void (i.e. by apeiron), could proclaim that the universe is surrounded by infinite breath (pneuma), (3) Parmenides on the contrary argues that the universe is ingenerated and finite, without any kind of apeiron beyond the heaven. The dismissal of infinity from the cosmos is achieved by the simple reasoning that 'is' cannot be set side by side with its negation, 'not is', and so the apeiron as negativity of being must be excluded from the truth of the universe and attached to the realm of seemingness. As a result, Parmenides acutely restates monism, but not by the argument of some prime matter or divine soul, but by way of eluding the difference, as it has usually been stated, between existential (absolute) and predicative (relational) use of the verb to be, grounding thus his belief in the immovable and same essence ('is') of the cosmos: "But, motionless within the limits of mighty bonds, it is without beginning or end, since coming into being and perishing have been driven far away, cast out by true belief. Abiding the same in the same place it rests by itself, and so abides firm where it is; for strong Necessity holds it firm within the bonds of the limit that keeps it back on every side, because it is not lawful that what is should be unlimited; for it is not in need - if it were, it would need all" (DK 28B8, quot. Kirk and Raven 1957: 276). From the viewpoint of history Parmenides manages to collect the definitive peras under the category of 'is' and so to establish for later Greek philosophy the fundamental distinction between 'that which is' and 'that which is not'. The ontological premise of the construction of this contradictory opposition ('is' and its negation cannot exist simultaneously), complemented by the belief that the definition of things is involved in the absolute 'is' rather than in the copula of the proposition, leads close to the Pythagorean monadic One, with the exception that the Parmenidean One is constituted only by being ('is') itself. (4) Thus stripping being of all its multiplication, i.e. of predicates, and maintaining that this baring of the eon (being) is in fact the true way of operating of the nous, Parmenides constitutes the being as an absolute One which is identified with thinking itself considered in terms of noein--to gar auto noein estin te kai einai ("for it is the same thing that can be thought and that can be"--DK 28B3). (5)

As already stated, the poem of Parmenides and especially Plato's dialogue Parmenides must be viewed as instrumental in forming certain central ideas about infinity in antiquity, but we cannot here go on without taking note of Parmenides' relationship to his supposed ideological antagonist Heraclitus. The opposition between the Eleatic, who insisted on the immovability of one changeless being, and the Ephesian, who postulated a never-ending process of change and movement, corroborated metaphorically again by their descent from opposite edges of the Greek colonial world, induces us, as it were, to see a replication of this antagonism also in their attitude to infinity. In fact it has been shown by Martin Heidegger that the antagonism of ideas at that half-mythological stage of philosophical thought amounts readily to a principal similarity of the farthest ideological positions. (6) In other words, the classical notion of infinity as something related perforce to imperfectness, and consequently to moving, has not yet reached the mind of Heraclitus who can entertain the idea of eternal moving without the slightest intention to yoke it to deficiency. To be correct, even Parmenides, notwithstanding the significant stress he laid on peras, is strictly speaking silent on apeiron and has thus given rise to variant interpretations on his possible understanding of it (Drozdek 2008:41). I should like to guess that the vagueness around the world-views of these two philosophers, as though warranting the reduction of their dissension to a substantial harmony, testifies in a way to the specific nature of Presocratic philosophy (a collection of fragments from later philosophers), which demands that this philosophy has always to be taken as part of certain unavoidably enacted contextualization. Exactly this recognition all but leads us to the underlying proposition of the present article: intending to describe the discourse on infinity, we incline to consider the participating personages, instead of in their historicity, as certain signs (e.g. "Parmenides") engaged in the discourse. From that perspective, I think, the opposition of Heraclitus to Parmenides could well be maintained because Heraclitus obscurus, the great Greek master of apophthegms, was in a way pioneering the Christian antithetical schemes of expression which, as we will see, were supported by negative theology and by the idea of infinity. (7)

The exposition of the monistic ideal in terms of 'is', which bereaved reality, as it were, of its distinctiveness and deposited the truth into the plain fact of existence, formed a decisive background for later Platonic-Aristotelian ponderings on being. The great task before Plato, as initiator of dialektike techne, was to mitigate the resoluteness of Parmenides' postulates which, appearing extremely beautiful in their outmost trust to being, were in fact blocking off the way to the verbal, i.e. philosophical elucidation of the world. In other words, having inherited from Parmenides the highly valuable general concept of being, Plato had to moderate down its absolute nature together with its non-predicative overtones and to graft the negation, dubbed folly by Parmenides, onto the verity of being. This work was to be done by Plato manifestly in his later dialogues, and it is not surprising that to this period belong also, attesting to the flavour of Pythagoreanism (Gadamer 1999b:142), Plato's strictest announcements on infinity, although we cannot put the sign of equivalence between Plato's notions of infinity and 'not-being'.

The metaphysical foundation for relativizing the not-being and for forming from it an idea of diversity (heterotes) that pervades the being and constitutes the logical bedrock for reflections about that what is, was propounded by Plato in his Sophist. Drawing on the Greek discrimination between two kinds of negatives, the relative me on and the absolute ouk on, the dialogue gives proof that to a degree the being is not, while the not-being to a degree is, meaning that "being and the other permeate all things, including each other" (259a); in the last analysis it is demonstrated that the not-being appears to be only a subclass of being itself (260b). The pith of Plato's theory of apeiron is included in Philebus, bearing the subtitle "On pleasure, ethical", which focuses on the question of whether pleasure or knowledge is the seminal part of a good life. The system of the classes of being framed in the dialogue consists of (1) apeiron as a principle of non-measurable quality of pleasure and pain, of (2) peras as something that sets a limit to the apeiron and confers on it the shape of moral life, of (3) meikton as mixture and actual form of existence of infinite and finite in the world, and of (4) aitia as a cause for the occurrence of the mixture (see Striker 1970). Bypassing here the question of the exact relationship between the relative not-being and apeiron, let us state, relying on the account of Alexander Lossev, that Philebus surely continues discussing the metaphysical issues of Sophist on a more subjective plane and with the clear intention to build a correspondence between the ideas as abstract entities (treated in Sophist and Parmenides) and life as an actual manifestation of these ideas (Lossev 1999:516, 522). In any case we can say that in one of his latest dialogues Plato has set forth a theory that expands the Pythagorean dualism of peras and apeiron into the field of individual psychology and morality, and he does it with a suggested wish to implement his former ontological deductions in the region of life as such. Parmenides, a third dialogue grouped together with Philebus and Sophist, is the work to which we will revert time and again, but for the time being it should be remarked that this work complements the Platonic discourse on infinity with an interesting note. In the so-called first hypothesis of Parmenides (137c-142a) it is argued that if, following the line of thought of historical Parmenides, the One really exists, it must be without parts, without beginning and without end, leading to the outmost conclusion that the One must be unlimited (apeiron) (see Moravcsik 1982). In other words, the Parmenidean being as a limited and spherical One turns out to be, as subjected to the scrutiny of logical analysis, an apeiron, because the impossibility of predication, pertaining to the One, cannot be interpreted otherwise. This statement from Parmenides is worth remembering because it contains in embryo some later Plotinian considerations, providing in fact the Neoplatonists, who were ardent to reconsider the apeiron, with a hint of vast importance. As to Plato, we can say that although he had had to modify the Parmenidean being in line with his dialectical aspirations, the absolute One retained, nevertheless, in some corner of his mind, its attractiveness, forcing him to postulate, under the precepts of correctness of thought, the One not as something with a limited being but rather as an apeiron--because of its inexpressibility de facto.

The difference between Platonism and Neoplatonism is usually explicated as a kind of shift from the dialectical interests of Platonism (concentrating primarily on the question of what is what) to the more henological accent of Neoplatonism (focusing on the emanation of the world from the transcendent One). As in fact the perception of difference between Neoplatonism, Middle Platonism, and their common Platonic trunk is comparatively late (happening only in the 18th and 19th centuries), there is good reason to believe that the main presuppositions of Neoplatonism were actually contained in the Platonic heritage and were thus reached simply by extending some Platonic premises to the extreme. The consideration is of importance because the Neoplatonists' foregrounding of the One stood in direct contact with their revision of apeiron and should therefore give us a hint for finding the shoots of their correction already in Plato himself. The most well-known of them stems certainly from the Republic, where (509b) Plato locates the supreme idea, the idea of the Good, outside of being (epekeina tes ousias), intimating its unknowability and resistance to predication. Plato comes close to the same position in the places (see Symposium 210e; Seventh Letter 341c-d; Parmenides 156d) where he describes the Good, or the Beautiful, as the ultimate goal of all dialectical aspirations and concludes that this final step of the dialectical staircase is not to be taken any more by the aid of words but with the help of an intuitive grasp: the apprehension of the good takes place unexpectedly (eksaiphnes) and is equivalent to a mystical turn that combines rest with moving and, as such, defies telling about itself. On the edges of his metaphysical thought, where the seams between ontology and theology had to be accomplished, Plato felt an implicit need to succumb to some lure of incognizability, which in truth prompted him to advance certain assumptions of the apophatic way of thinking, including the premises of the later negative theology (Carabine 1995:32-34). In connection with it Plato simultaneously prepared the ground for the Neoplatonists' reassessment of infinity, because the incognizability of the Good set it necessarily side by side with the indeterminateness of apeiron and thus signalled that apeiron may appear to be a name not only of something that suffers privation of definition, but also of something that in principle exceeds the reach of peras as such.

The contribution of Aristotle to the ancient discourse on apeiron is most succinctly summed up in his concept of dynamis, or potentiality, by which Aristotle launched the meaning of infinity as an oppositional term of energeia (actuality). (See Physics 202b-208a; Muhlenberg 1966:43-57; Duhem 1985:4-5; Ariew 1985:XXV-XXVIII.) Accordingly, Aristotle transformed the Platonic apeiron as a relative not-being, or pleasure principle, into the 'capacity of matter' that is requested to be realized and brought into actual existence by the aid of formal principle or morphe. Attesting thus to the changing realm of matter and its proneness to mutability by way of addition or division, apeiron is a sign of the human mind's capability to think of something as being divisible or addible to infinity. As in reality this process of change can be realized only to a certain measure, by which the infinite necessarily takes a shape of the finite, we are compelled and entitled to conclude that infinity in stricto sensu remains a quality that can never be actualized completely. In fact Aristotle's infinity is characterized by a kind of disproportionality between time and space, between addition and division, and this discrepancy ensues logically from Aristotle's view on infinity as a possibility, in the sense of continuous endless process, which remains always unfeasible in actu (see Moore 1990:40-44.). Thus space, considered without the time factor and distinguished as such by the character of being given all at once, is for Aristotle unavoidably finite, because infinite space would directly imply the existence of actual infinity. On the other hand, time is infinite because its permanent being-in-course cancels any possible reference to its actuality, although time's infinite past, which has been gone through and which thus should be viewed as 'given all at once', seems to pose some questions also about its real immeasurability. The affirmation of the possible infinite division of the bodies, while denying the possible contrary process in the direction of infinite addition, appears to be grounded on similar arguments: the endless accumulation of corporeal substance should bring about the enlargement of the finite space, while ever-continuing division leaves the space untouched and lets infinity appear as an aspect of temporality.

It is significant that similarly to Plato, Aristotle arrives on the margins of his physical and metaphysical thinking, where the bridge to God is intensely needed to be built, to some inconsistencies with his philosophical system that are even more conspicuous than in the case of Plato. The fact that the founder of the law of non-contradiction comes to postulate, as the primary cause of movement, God as the first unmoved mover (proton kinoun akineton--Metaphysics 1074a36ff, Physics 258b), speaks for itself. From our point of view it is of essential interest that in connection with this claim Aristotle refers to the infinite power of the God and so as if suggests, by overriding some of his main assumptions, that both, infinity and dynamis, can be ascribed also to the supreme being (Physics 265a25ff, 267b17ff). (8) We would here like to cleave to the opinion that the supposed collision between the worldly and transcendent section of Aristotle's thought issues simply from the change of register in his expression and thus should not be treated as evidence in favour of Aristotle's Neoplatonist conception of infinity. Without doubt, entering theology where he expected to obtain answers to his final philosophical questions, Aristotle must have been struck by the cracks appearing in his metaphysical edifice, but it all does not disprove the fact that in the last resort God is for Aristotle a pure actuality whose infinite power just mirrors its nature from the angle of the human mind. The critical point for disentangling Aristotelian infinity from the Platonic one, as well as for accounting for the specific Aristotelian influence on the idea of infinity, is contained in Aristotle's understanding of the One. While Plato had paved the way for the apophatic push that aimed at locating the One, because of its linguistic inexpressibility, outside of being, Aristotle, cherishing the hope to level the supposed gap (chorismos) between Platonic ideas and the sensuous world, continues to stroll on more solid ground. Accordingly, Aristotle argues that the One cannot be searched for as only a supreme idea, fuelling human's drive to step into regions of some mystical meditation, but must in a way be encountered also among the onta themselves (Metaphysics 1052a-1054a; see Gadamer 1999b:202, 215ff., Hadot 1972). In more technical terms it means that the One as representation of unity, unemployed by any predicative demands, must be seen as something entailed already in the indivisibility of all existing things themselves. Hand in hand with transforming the Platonic unreal ideas into the immanent formal principles of existing things, Aristotle postulates the One as an internal source of wholeness and a self-integrity of all existing items.

To get a better grasp of how the Platonic One, a kind of centripetal point without any extension, gives in the interpretation of Aristotle a way to the extensional but, nonetheless, unitary aspect of the things, we have to take notice of one more Neoplatonist development rooted actually in Plato's theory. Namely, Plato had prepared the ground not only for pushing the One outside of being, but also, as corollary of this act, for situating the One beyond human thought--because something about which cannot be said what it is, is unthinkable. Now, Aristotle declares strictly that his first unmoved mover, that is God, thinks, and does it in a very specific way, namely he thinks, as noesis noeseos, of the thinking itself (Metaphysics 1074b35). Thanks to the inclusion of absolute self-reflectivity as a specific mark of God's actuality in the definition of divinity, Aristotle succeeds in holding the meaning of the One inside of being and, consequently, inside of the domain of thinking. The postulate of the unity of each separate thing, which should in a way reassign Plato's transcendent One back to this world, can thus be seen as a remainder of God's reflective thinking in this earthly life.

We are thus witnessing a certain short-circuit in both Plato's and Aristotle's argument, while they try to formulate some utmost truths of their systems. Plato places, or at least insinuates placing his leg already at the other side of being, whereas Aristotle keeps a more moderate profile, but does it at the expense of challenging his own principle of non-contradiction. As to the idea of infinity, we can state that in spite of the different prospects of interpretations encoded in the texts, neither Plato nor Aristotle testify to the intention of positing infinity at the bottom of their theory of episteme. Surely, in some segments of their thought, related especially to the temporal and numerical aspects of knowledge, infinity plays an important strategic role in their disquisitions, but it does not equal positing infinity as something that exists actually in spatio-temporal terms nor as a kind of absolute negativity that forms the true and primary source of all positive statements.

3. The beginnings of positive infinity in the Greco-Roman world

In mapping the intellectual territory on which the revaluation of infinity started to emerge in the first centuries of the Christian era, we have to take account, on the one side, of the internal monotheistic tendencies of the Platonic-Aristotelian philosophy that were in fact at loggerheads with the overall polytheistic ambience of the Greek world. On the other side we have to consider the ever more powerful Christianity that soon acquired rational ambitions leading it to base its religious truths on intellectual grounds, and, quite understandably, in doing so Christianity stretched out its arm for the rich sources of ancient thought. The junction accomplished in Christian theology between its monotheistic religion and Platonism is of primary importance for the explication of the new attitude towards infinity in the history of Western thought. As tangential phenomena of this major trend, we must view the reconsiderations of infinity induced by the mysteriosophic climate of Hellenism in the areas of Gnosticism and Hermetism.

The key figure in setting infinity to move on the new rails is usually deemed to be Plotinus. In a way, Plotinus' understanding of infinity does not differ much from the example of Platonic-Aristotelian tradition, as it couples in a rather similar and simple way infinity with the incompleteness of matter. However, concurrently with unfolding the henological potentialities of Platonic thought, Plotinus provides the Greek infinity with a new drift enmeshing the word in a double-faced play of meanings: while matter, argues Plotinus, is infinite because of its deficiency (I.8.3-4, II.4.10 et al.), the same quality pertains to the One or God by reason of its being outside of the capacities of human understanding (V.5.6 et al.). (9) This display of the supreme One, from which all creatures have emanated, in the cloak of negativity, hiding the imaginable but not feasible aim of all positive statements, is surely a landmark in the history of negative theology and anticipates the later important distinction between infinitum negativum and infinitum privativum. From the perspective of the conceptual struggles in which infinity got involved in Christianity, two remarks must be made as to the nature of Plotinus' preparatory work in this field. As already noted, Plotinus' glorification of negativity in the human's relationship to the One resulted in his full-scale amplification of Plato's insinuation of 'the One situated outside of Being', which means that in Plotinian, as well as in Neoplatonic thought generally, One became the predicateless not-being--in a word, One was situated there, where Being had ceased to do its job. Second, Plotinus' view that all the beings, from the highest intelligible (nous) to the lowest sensible (matter), had emanated from the unique One entailed a principle of hierarchy and subordination which made Plotinus' universe to be framed by godly infinity above and by its evil counterpart--matter--below. Christianity's subsequent aim of subduing the almost compulsory demand in Neoplatonism to treat the One unexceptionally in terms of absolute aloneness and not-being--which, accordingly, conferred all the emanative being a state of gradual inferiority--, became for at least Western Christianity the touchstone for probing and elaborating its dogmatic self-consistency.

The fact that Parmenides, maybe the most convinced advocate for being in Western thought, became in the shape of Plato's Parmenides a co-founder of Western negative theology, is a curious event that can easily be explained by the convenience by which the systematics of the propositions on the One, offered by Plato in this dialogue, lent itself to the use of Neoplatonists' embroidery on their supreme God (Klibansky 1929:7). As is well known, the interest of Neoplatonists in this maybe experimental, in Plato's intention, dialogue was largely confined to the first of altogether nine hypotheses (Klibansky 1929:9-10), where it is argued that if the One exists as an absolute, it can be neither in a place nor in movement, it can be neither a part nor a whole etc., that is, the One as absolute cannot be at all and as such must be considered unlimited. Proclus' commentary on Parmenides, which had played through its Latin translation from about 1286 a significant role in familiarizing the Latin world (among others Meister Eckhart and Nicolaus Cusanus) with the then quite unknown Plato, had restricted itself also to the explication of the first hypothesis of the dialogue (Klibansky 1929). However, probably the most influential attempt at harnessing Parmenides to the cart of Neoplatonism, stems from the Enneads (5.1.8), where Plotinus had suggested the intimate connection between his three hypostases (One, Intellect, Soul) and the three first hypotheses of Parmenides (see Beierwaltes 1985:194-197). According to this interpretation, the first hypothesis of the dialogue describes the hen on the plane of its absoluteness where nothing about it can really be said. The second hypothesis, the equivalent of the nous, viewed as hen-polla (One-Many) focuses on the apparition of the One in the intelligible world of the Forms where the One reveals itself as Many. The third hypothesis, matching the psyche, postulates already the coordinate existence of hen kai polla (One and Many) and represents the coalescence of the intelligible and sensible world where the 'others' constitute themselves as separate embodied entities dependent genealogically on the One. This triple schema, which was further elaborated by various Neoplatonist (and Renaissance) authors (Beierwaltes 1985:198-225), testifies in a characteristic way to the indirect survival of Plato's, and especially his "Parmenidean" modalities in Hellenistic and later Medieval philosophy, with a consequence of participating in the germination of some strictly modern ideas in the Renaissance when the need to find correspondences between negative theology and empirical reality became urgent (Klibansky 1939, Klibansky 1943, Yates 1991, Koyre 1968). For, it must be emphasized, despite the eminent role attached to geometry in the ancient Platonic tradition, the mathematical quantities were there denied the ability to acquaint us with the greatest arcanum of the universe (Gadamer 1999b:143-145), expressed definitely by Plotinus in his positive reinterpretation of the apeiron:

And it [One] must be understood as infinite not because its size and number cannot be measured or counted but because its power cannot be comprehended. ... it does not think, because there is no otherness; and it does not move: for it is before movement and before thought. For what will he be able to think? Himself? Then before his thinking he will be ignorant, and will need thinking in order to know himself, he who suffices for himself. There is, then, no ignorance about him because he does not know or think himself; for ignorance is of what is other, when one thing is ignorant of another; but the One alone does not know and has nothing of which it is ignorant, but being one and in union with itself does not need thought of itself (VI.9.6, quot. Plotinus 2003:323-327).

Plotinus' threefold schema serves already as an excellent hint for understanding the possible point of affiliation between Neoplatonism and Christianity that built substantially on the dogma of Trinity, but at the moment I would first like to delineate the crux of the dissension in which Christianity very soon got involved with the ancient philosophy. Martin P. Nilsson has pointed out that the conflict between the monotheistic tendencies of Greek philosophy and the overall polytheistic nature of Greek popular religion refers to the 'twofold strain in man's attitude to God':

On the one hand, man needs a God elevated above him, a ruler of the Universe and of fate, who enjoins his commandments upon him ... On the other hand, man needs also a God to whom he can turn, who helps him in his needs and comforts him in his sorrows and anxieties, a Savior from evil, a God in whom he trusts ... It is the great achievement of Christianity to have satisfied them both by introducing a Mediator between the High God and man, and it is proper that Christianity is called by his name (Nilsson 1963:115-116).

Without doubt Christianity can be called a religion of bridges. The first and foremost bridge for Christianity to be constructed was the one between the Old and the New Testament which entailed the hard work of bringing the Judaist foundation of the Holy Scripture into line with the specific world outlook of Christianity. Not less significant was the demand to create a state of cohesion inside the Christian conception of the One, because, as noted by Nilsson, the great innovation of Christianity was to provide the One, or the High God, with its mediator for humans, which means that in fact the One itself was given a form of multiplicity. Now there arises a justified question, if this assumption of multiplicity is not simply a step back to the polytheist, and thus to the humanly more understandable form of unity, because--what else can it by rights be? At this point we have to underscore that it became the historical task of Christianity to prove that exactly the contrary is the case, that is, to demonstrate that the Christian God can have a triple form and still be the One. To be successful in this mission of proof, Christian theology was requested to verify that the One, authenticated as unspeakable in Greek philosophy, can still be talked about, without any kind of degradation of the divine substance, in the form of its mediator, or of the Son, insinuating thus a new type of horizontal equivalence inside the Godhead, which in fact meant a paradoxical compounding of utmost negativity with a chance to the articulation. As a result, the religious drift to the One, residing in the unspeakable edges of Greek philosophy, was in Christianity harmonized with rational forces, in the way that the unspeakable yet speakable God was able to lodge in also fundamental truths of the cosmos.

The early Christian controversies over the differentiation within the Godhead, encouraging a variety of proposals as to the explication of the inner-Trinitarian relationship, culminated in the 4th century when the opposition between Athanasius and Arius led to the settling of some of the dogmatic Christological standpoints within Christianity (see Anatolios 2007). Behind the different hereditary, to use the word here in a somewhat ahistorical way, Trinitarian approaches (e.g. Sabellianism, Adoptionism, Modalism, Arianism) had loomed the inconceivability of assigning the Son the same godly nature and status as held by the Father. Consequently, either the Son was demoted to the position of the second God, or the designations Father and Son were treated as mere epithets of the one indistinctive God. As corroborated by the example of Origen, the inclusion of a certain Neoplatonic rationale in Christian theology contributed not to the dilution of the difficulty, but, quite the contrary, had established the hierarchical structure of Neoplatonism as a staple of Christological thinking (Young 2006:453-466, Dillon 1982). Nevertheless, the adhesion of Christianity, in its attempt to prop up the revelatory knowledge by discursive means, to Platonism was very natural because of the kindred cognitive patterns they both fostered. In addition to the emphatic and mystically tinged postulation of the supreme God, the affinity of the positions was suggested by the triadic schemas of thought used by both, and of course, by the comprehension of Jesus as the incarnation of the Word of the God which dovetailed nicely with the Neoplatonic theory of logos, supporting the so-called early Christian logos-theology--in fact a further reason for the consolidation of subordinative argument in early Christianity. Now, when the Council of Nicaea (325) condemned the Arian thesis about the non-divinity of Christ and inaugurated the formula of homoousios ('of one substance') for marking the equivalent divinity of both the Father and the Son, there was necessitated an urgency, inasmuch as Christianity yearned to attune its religious goals with rational prospects, to offer for this unity in multiplicity an explanation also in intellectual terms. It can easily be supposed that the man allotted with this kind of task must have been somebody immersed in antiquity but converted to the new monotheistic religion at some moment of his life, and in fact the task befell Marius Victorinus, a converted classical scholar who furnished with an example also the great reconvert Saint Augustine.

Already the applying of ousia, the central concept of Platonic-Aristotelian tradition, in Christian theology for the designation of the God is a proof of that God's staunch fact of being, which at a stroke eliminated the possibility of his identification with the Plotinian One. The doctrinal formulation of the Trinity, mia ousia, treis hypostaseis, arrived at in the course of the 4th century is thus, from the viewpoint of Greek philosophy, a contradiction in a double sense: on the one hand, it is questionable how the supreme uniqueness can at all be, on the other hand, it is hard to realise how the absolutely unique substance can still consist of three hypostases. Marius Victorinus, an Africa born Roman rhetorician who won renown as translator and commentator of Greek philosophers, converted to Christianity in about 354 A.D., after which he composed, against a background of the synods of Sirmium (358) and Rimini (359), his theological tractates in defence of the positions of Nicaea (see Beierwaltes 1998:25-43, Clark 1982, Hadot 1967: 5-22). Being the earliest attempts to bolster the Trinitarian concept of homoousios with the aid of Neoplatonism, these tracts aim, among other things, at justifying the use of the word ousia, distrusted additionally because of its non-occurrence in the Holy Scripture, for the explanative work about the Trinity (Adversus Arium I.30, see Andresen 1967:158-159; Beierwaltes 1980:60). To understand how Victorinus accomplishes the task, it is necessary to refer to his fourfold classification of not-being which became very successful in later negative theology, being actually rooted in the conceptual displacements of Plotinus. Victorinus argues that not-being can exist in four different ways: (1) as absolute privation of being (matter), (2) as relative not-being (something is not from the perspective of something other), (3) as potential not-being (something is not yet but will be and can be), (4) as perfect not-being (something is not because of its situatedness beyond being) ("Ad Candidum" 4, see Andresen 1967:87-88). While the first mode alludes to the utmost poverty of being, the fourth mode designates the perfectness (the God) that surpasses the being. The task of linking the God back to being entailed, in replication of the hypostatical distinction of the Father and the Son, as well as of the physical distinction of Man and God in Jesus, an introduction of a kind of bifurcation into the fourth mode of not-being. That is, the perfect not-being of God had to be transliterated into the cataphatic alphabet, inasmuch as Jesus and the Holy Spirit are distinctive from the Father, and Jesus pertains to human nature; however, God should remain the non-approachable negative non-entity, inasmuch as the whole Holy Trinity is of the same indistinctive ousia and the two different natures of Jesus exist still inseparably in his one Person (prosopon). The solution offered by Victorinus to this intellectual problem consists in reinterpreting the not-being of the Father as an indefinite esse purum, or pure godly activity, that is not marked off by any specific substantial qualifications and can just by this reason be said to lack any ousia, i.e. to pertain to the not-being in the Greek sense of the word (Adv. Ar. I.33-34, see Andresen 1967:88; 165-166, Hadot 1967:365, Hadot 1962:410-424). Accordingly, Jesus is assigned by Victorinus a qualified substantial being: that what is unmanifest in the Father has become cognitively definite and graspable in the Son. By this move Victorinus completes, hoping to fasten the God to being, a substantial change of meaning in the Greek ousia: the word deemed to designate in Greek something stable, unmovable and morphological, has now been invested with a foggy meaning of potentiality, representing a covert inner force of the world--in a word, ousia as vehicle of upright actuality and condensed reality has been accredited by Victorinus with a new tenor of enigma and mysticism. This change on the conceptual level has its significant correlate on the linguistic plane, as a consequence of the fact that Victorinus acts simultaneously as a translator of Greek terminology into Latin. Namely, the notional split of ousia is also confirmed and attested to by Victorinus' differentiation between substantia (as an equivalent of the traditional ousia) and existentia as esse purum--with a clear intention in his mind to demarcate, at least occasionally, the different senses of being respectively. Thus, as verified by Pierre Hadot (Hadot 1972; Hadot 1968:489), existentia can serve in Victorinus as the Latin counterpart of the Greek hyparxis, of a word which was used by Aristotle and the Stoics to designate a state of appertaining to something (of a predicate to a subject); exactly in this sense of denoting a sheer activity, without any anchor in substantial reality, existentia conveys a contradictive sense as compared to substantia. By launching this usage of being (existentia) in Western thinking, Victorinus can be said to have freed the predicate from its unavoidable insinuation of inferiority and, together with it, to have caused philosophy to reflect the contrary possibility of the primacy of predication (of act, or of moving) over ousia. (10)

The demand of linking the One to being, without demolishing its godly nature, was tied for Victorinus with the not lesser task of convincing the public of the non-substantial, i.e. purely relational, differences between the hypostases of the God. A survey of how Victorinus solves the problem reveals also something about his indebtedness to the Neoplatonic devices he benefited from. The triad of being--life--thought can rightly be said to have its roots in the remote history of Greek philosophy (Hadot 1960, Beierwaltes 1979:106-118). Taking being as the reliable and unchangeable essence of things which, because of its mixedness with matter, appears to us in life always in an inauthentic state of movement, the Greeks understood thinking to be a kind of reflective turn back to the immovable state of being, in the conviction that the real essence of things can be glimpsed by the mind in the elusive transitions between movement and rest. The schema, detectable in various Greek authors, was applied by Plotinus to show that the mind, to know itself, has to multiply and enter the life, for then to move through internal contemplation backwards to the being, the point from where, by his own will, he had started to unfold (see e.g. III.8.8). Victorinus presses the schema into his service by postulating that the Father, the Son and the Holy Spirit are the respective equivalents of being, life and thought. Being, enfolded in the Father, has become evident in the Son as life, whereas the Holy Spirit as thought connects Jesus in a reflective way back to the closed and indefinite essence of the Father (Adv. Ar. III.9.1-3, see Andresen 1967:248-249; Hadot 1967:408-410, Beierwaltes 1980:108-113). The thrust of Victorinus' argument lies, of course, in the message that the three hypostases or persons differ only by a certain relative aspect of actuality and in fact each person contains already, as confirmed by John, the other two in a full and perfect mode: "In the beginning was the Word, and the Word was with God, and the Word was God. The same was in the beginning with God ... In him was life; and the life was the light of men." (John 1:1-3, 5.) Together with showing that the common ousia shared by the three hypostases cannot belong to the homoiousians' order of likeness, to say nothing of the anomoeans' statement about its unlikeness, but must be exactly the same (i.e. homoousian) in all three cases, Victorinus relocates the triad being-life-thought from its Plotinian function of characterizing the action of intellect to the position where it starts to analogize the godly endurance itself. The mystery of the Trinity is posited here as insolubility between a concession to the difference within the Godhead, leading to the possibility of its exposition, at least per analogiam, in positive terms, and the hyper-ousia quality of the God that in fact annihilates its being from the viewpoint of humans. To answer the question of how Victorinus accommodates this suggested parallel between the Trinity and its supposed Greek antecedent with his disposal of definite substance in the case of the Father, we have to take heed of the variations he effects in the Greek triad as he characterizes the different Trinitarian members. While applying for the description of the Son the triad in its nominal form (existentia-vita-intellegentia), Victorinus instantiates the consubstantial Father, in whom all these nominal occurrences are still in a state of latency, by verbal corollary of the triad where all the former nouns are given infinitive mood (esse-vivere-intellegere) and, accordingly, the Father is hinted at as a force without any determinable qualification (Adv. Ar. IV.6, see Andresen 1967:274-275; Hadot 1967:419-424). In the same manner, the Holy Spirit, entailed in the Father in the grammatically infinitive way, has been given a substantive form by the Father's action of begetting his Son, Jesus, to whom the Holy Spirit relates as Jesus' secret and inner reality, although in fact Jesus himself is already life as well as thought, and, accordingly, they both, Jesus and the Holy Spirit, are thereby the same (Adv. Ar. IV.33. 20ff., see Andresen 1967:317-318).

It has been demonstrated by Ekkehard Muhlenberg that the first Christian author who applies 'infinity' in the strict sense of the word, and not in negative but in exactly essential terms, for the designation of the God is Gregory of Nyssa, one of the three Cappadocian Fathers acting in the second half of the 4th century (Muhlenberg 1966, Sweeney 1992:473-504, Carabine 1995:223-258). The philosophical contribution of the three Greek bishops to the elucidation of the Trinitarian doctrine in line with the Nicene formula can be viewed as an Eastern ecclesiastical counterpart of the work done by Victorinus more privately in the Latin side. The flavour of mysticism, increasingly surrounding the Christian God as a result of the attempt to establish its paradoxical triunity, is perceived unfailingly in the Cappadocians who enwrapped the Godhead, by their special interest in the Holy Spirit, in a yet darker cloud of secrecy. The foregrounding of apeiron as an essential epithet of the God in the treatises of Gregory is surely a mark of a compulsion, which he must have felt, to posit the unknowable being of the Christian God--and in succumbing to this demand Gregory in fact infringes the principal law of classical thinking and ushers in, to say it a bit grandly, the age where infinity is beginning to be credited with an epistemological value. The God is, according to Gregory's mystical theology coupled specifically with monasticism, transcendent and infinite, yet not without being, or to put it exactly, infinity itself is the real essence of the God (Muhlenberg 1966:132-135). As our aim here is not to trace the exact verbal signs of infinity in early Christianity, we could at this point conclude that in the 4th century there was reached in the course of the Trinitarian debates, on the Latin as well on the Greek side, and through the appropriation of the Neoplatonic philosophical foundation, the more or less direct positing of infinity as a characteristic of the God, with clear divergence from the Neoplatonists that this God, although featured greatly by non-essential negative terms, was not denied a being.

Taking as granted that the production of the idea of infinite being was a result of monotheistic enterprise acted in unison with intellectual effort to retain a thinkable touch with the One, there arises nevertheless a question of how much the overcoming of Greek abhorrence of infinity was conditioned by something that might be called the absolutely different mental attitude of the Hebrews. In this connection it is relevant to refer to the exciting comparison of Hebraic and Greek thought by Thorleif Boman. Unlike the Greeks, marks Boman, who conceive things as consisting of matter and of form, where the latter is often imagined as an outline or boundary, the Hebrews are very inattentive of these characteristics:

It is a characteristic of the Hebrews that form was an indifferent matter for them to the extent that they constructed no word for form or its synonyms, like outline or contour. To be sure, they have a variety words which can be translated 'configuration (Gestalt)', but none which signifies the form of the object. Israelites were interested in shape only as appearance or something inconclusively expressed: the content of the shape ... They see objects as they are with their colour and shadow, experience their hardness and their temperature with their hands, but they do not see contours, and therefore they employ no words to express this notion. The significance of the outline and form of objects increases to the extent to which all perception is disregarded as the Greek ideal requires or as the Kantian ideal requires still more (Boman 1960:155-157).

A corollary of this Hebrews' devaluation of contour is their very natural and non-problematic relationship to infinity which induces Boman to state that "the born religious man lives in the infinite and eternal world as his home. It is no accident, therefore, that the Semites who can live without boundaries have been responsible for three world-religions; for them infinity or boundlessness is no problem" (Boman 1960:161).

Another evidence of the possible Hebraic underlay of Christian infinity is provided us by Philo, the Hellenized Jewish philosopher, called also the father of allegory, who did much to furnish the later Christian exegetes with hermeneutic devices in their endeavour to reconcile the two Testaments and to bring the Holy Scripture into line with ancient wisdom. Nurtured in the Alexandrian cauldron of multiculturalism, Philo is remarkable not only for introducing the seminal distinction of ousia and hyparxis into Christian exegesis (Carabine 1995:214, Kahn 1966:264), adopted by the Fathers, but also for his obvious apophatic leaning which makes him, for example, a theological forerunner of the problems confronted later by the Neoplatonists. To be exact, stresses Henri Guyot, Philo says only that the God is 'without qualities' (apoios), but nevertheless "the thing [infinity] is there. Following the example of his coreligionists, the Jew puts the God above everything, and the God is indeterminate because his perfection is beyond all determination" (Guyot 1906:55, see also Runia 1995:18). The intermediary role of Philo is exemplified by the existence in his works beside this infinite God also the other type of divinity, the God as almighty person, which, argues Guyot, was inherited from the Greeks or from the Jewish personal representations of Yahweh. Placing as an exegete these two godly images mechanically side by side, Philo left, in the view of Guyot, the conciliatory work to be done for Plotinus who as philosopher "advanced through this action considerably the theory of divine infinity" (Guyot 1906:56). To adduce one more example of the possible Jewish 'stock' of infinity, we could point to Numenius, the Neo-Pythagorean from the 2nd century A.D., who performed an important role in handing to Plotinus, through Ammonius Saccas, the new conjoined form of Platonism he had achieved through tracing Plato's wisdom back to Pythagoras and to diverse Eastern sages, including Moses. Leaving aside the speculations about Numenius' own Jewish background, his keen interest in Jewish and oriental lore is beyond question (e.g. Dodds 1960) and he has been viewed also as a possible link between Philo and Plotinus whose direct knowledge of the first Jewish Platonist has been debated (Carabine 1995:149, Dodds 1970:96, Guyot 1906:99-100). A fact that these few instances of tangible relationship between the idea of infinity and Jewish thought can be complemented with a number of other ones--also from the Middle Ages, say Hasdai Crescas, or from the present day, say Emmanuel Levinas--entrusts us to view the affiliation of infinity with Judaism as an interesting topic, but at this stage it will suffice to subsume the whole issue under the general heading of Greek philosophy's encounter with the system of religious monotheism.

In denoting Neoplatonism and early Christianity as chief advocators in bringing about the exoneration of infinity from its ancient charges, we would still get from the matter a rather contorted picture if we did not add to these central figures some minor agents, not only for the sake of the truth, but also to underscore in a more illuminative way the character of Christian infinity. We have said that the revaluation of infinity was achieved through the 'mystical embraces' of the One which meant, on the one hand, a positing of a former Ionian monistic ideal, as if lost in the halls of Greek rationalism but actually secretly being instilling, in the new form of a unique transcendent God, and, on the other hand, through linking epistemological ideals of philosophy to the aspects of human faith. Although we must be careful in calling Plotinus a mystic, because of the specifically philosophical allure of his unio mystica (Beierwaltes 1985:127-128, Dodds 1970:87, Hadot 1993:54-56), we cannot ignore that he was a practising mystic who attained, according to Porphyry, in six years four mystical ecstasies (Porphyry 2000:69-71). Now, we have to be aware that the efflorescence of mystery religions in the Greco-Roman age, turned at last by Christianity to its own advantage, among other things, by some clever trick of mimicry, was paralleled by the so called mysteriosophical manifestations (see Bianchi 1979:7), e.g. in Hermetism and Gnosticism, from which Christianity had to distance itself in due course as well. The whole matter is pertinent here because these combinations of religion and knowledge entailed an exculpating gesture for infinity too, although with accents different from Neoplatonists as well as from Christians. Plotinus' own stance on Gnosticism has been presented to us in the 9th treatise of the 2nd Ennead entitled "Against the Gnostics". To put it succinctly, even though the evilness remained a clinging characteristic of matter in ancient thought, it never led to the outright contempt of the material cosmos, but, quite the contrary, the latter was usually viewed through the lens of beauty, harmony, and order. It applies all the more to Plotinus as he tracked down all the ontological dualities in the transcendent One, implying thus that even matter in its sensible form, although entirely evil, has retained an imaginable tie with the forces of the Good. The Gnostics derailed from this track of thought by their radical rejection of materiality and by the claim that the material world has not been created by the supreme God himself, nor has it come into existence through some kind of emanation, but the responsibility for its origination rests on the demiurge, a secondary, or fallen God produced by some fateful mishap, which means that a man, to unite again with the divine pleroma, has to turn his back on the material world and to fire up the spark of knowledge (gnosis) deposited in him by the God--this action was deemed to occur in the form of revelation (see Rudolph 1994, Broek 2006a). From the viewpoint of nascent Christianity, which had a complicated relationship with Gnosticism, it entailed a degradation of Yahweh, the Old Testament's creator God, to the minor originator of this world, in a word to Jaldabaoth, while Jesus alone was accredited with the role of a saviour--indeed he too undergoing a bipartition "to the mortal and transient Jesus of Nazareth and to the heavenly-eternal Christ" (Rudolph 1994:166). Thus while Plotinus made an attempt to solve the problems of dualism by the aid of the transcendent One, leaving untouched the structure gained by Greeks through their advances in dialectics, the Gnostics behave very much like those who, to reach divine clarity, discard one pole of the issue (matter, Old Testament). No doubt, the Platonic question about One's relation to Many can be recognized in central considerations of the Gnostics, and their boldness to posit an absolutely unknowable God (e.g. in Basilides) matches the bravest enunciations of Neoplatonists, but differently from these, who notwithstanding all adhere to the speculative traditions of Greeks, Gnostics pose the One in absolute detachment from this world and, as a result, their ponderings on it are arrayed, instead of with the arguments of philosophy, in the acrimonious robe of myths.

Hermetism, an additional Alexandrian heterodoxy, is related to Gnosticism by a similar eschewal of Greek speculative superstructure, but it adjoins to the Gnostic minor key pathos a more optimistic sound by its hope of reaching the knowledge in this material world, on the condition that the signs impressed in matter are deciphered in a correct way (hence the partial overlapping of Hermetica with astrological, alchemical, theurgic and magical treatises) (see Broek 2006b). This attitude of, say, meliorative pseudo-science entails that the search for the One in Hermetism, cast like in Gnosticism and Neoplatonism in the form a transcendent God, is additionally chimed in with a secret wish of ennobling the matter, to use the vocabulary of alchemy, through gradual opus magnum to its highest ontological possibility - ultima materia. At the foundation of Hermetic teaching lay a conviction that the universe, being a mirror image of the God, forms a unified nexus of internal corridors that can by a sage be passed through, from its lowest layer up to the top, and accordingly, every kind of multiplicity found there can be purified and transmuted to the supreme matter (e.g. gold). As demonstrated by Andre Festugiere, Hermetica in fact also contains its pessimistic counterpart which comes in spirit rather near to the Gnostic texts (Festugiere 2006, vol. II:X-XI), but, nevertheless, the intimated similarity between the God and cosmos, characteristic of Hermetism, allowed it to expand the image of divine infinity and incomprehensibility to the areas of physicality unknown to Christians, Neoplatonists, or Gnostics, which obviously explains why the Hermetic magic came to have a significant role in transposing the idea of theological infinity, elaborated in the Middle Ages, to the realm of empiricism during the Renaissance (see Yates 1991:155-156 et al.). All in all we could state that the concept of Christian infinity, conceived to frame the mystery of the Trinity, and employing, in its explicative form, the boons of Greek philosophy, was surrounded in the Greco-Roman world by some other, and complementary, infinitist solution to the problem of world unity: while Hermetists' destiny was to stir the imagination of the pioneers of modern mechanics, the Gnostics probably assisted, by their desperate craving for the other world, to underpin the new Western conception of Romantic desire and love (de Rougemont 1966:78-113).

4. The conceptual fusions underlying the new look at infinity

Our wish to illuminate the intellectual practise of synthesis which made it possible to integrate the idea of infinity into the system of Western onto-theology makes us once again revert to Plato's Parmenides, this time to its anonymous commentary contained in the so-called Turin palimpsest and published by Walther Kroll in 1892. In the 1960s the authorship of this manuscript was attributed by Pierre Hadot to Porphyry (Hadot 1968:107ff.), together with the suggestion that this text and the Porphyrean exposition of Neoplatonism in general must be viewed as a contributory agent in bringing, in the treatises of Marius Victorinus (Hadot 1968:140ff.), the Christian doctrine of Trinity into concord with the Neoplatonic foundation. Hadot's suggestion, having established itself quite well, points us directly to one aspect of the synthesis incurred by infinity - and this is what is usually called the harmonization of Plato with Aristotle. Again, the issue does not confine itself to the historical moment in question, but has a more ample pertinence, as we know, for example, that the first bud of strictly modern infinity, Nicolaus Cusanus' idea of coincidentia oppositorum, which had flashed in the mind of the cardinal during his sea travel (in the winter of 1437-38) back from Greece (Cusanus 2002:100), where he had made serious efforts towards reunification of the Western and Eastern Church, revealed itself to have in addition to the schismatic background also an obvious connotation of harmonizing the two great Greek thinkers (Blum and Damschen 2006:XXX-XXXI). Porphyry's peculiar mission of rescuing the legacy of Aristotle for posterity is traditionally exemplified by his Isagoge, which became in the translation of Boethius a standard textbook in the Middle Ages, but to make sense of his contribution from the viewpoint of Christianity we have to look back at the differences between Plato and Aristotle sketched above. In order to offer Victorinus a clue to integrating the Nicene Trinity with Neoplatonism, Porphyry had to yield something to ward off the Plotinian denial of the being of the One, and this is what he actually did, at least in part aided by Aristotle. The point of Porphyry's grafting of the peripatetic shoot to Neoplatonism is easily grasped when we remind ourselves of Aristotle's concept of God as thinking of thinking itself, entailing a sound reference to God's being as well as to God's inner, self-targeted relatedness. Werner Beierwaltes has characterized this act of conferring on the mysterious One-God a quality of thinking, understood historically as attuning Plato to Aristotle, in the following way: "... he [Porphyry] comprehended indeed God or the One as 'proousion' (pre-being), but at the same time, from a different aspect, equally as pure effectiveness or activity which is the being itself ... The principle of Aristotelian theology had formed--otherwise than in Plotinus and in later Neoplatonism--in association with the divine One the new conception of God. Exactly this structure of thought came to meet the Christian theology: the latter had to understand God not as relationless, and therefore as above-being and above-thinking (uber-seiend und uber-denkend) in itself, but as a thinking Trinitarian relation" (Beierwaltes 1980:61; see also Beierwaltes 1985:198-201). From the perspective of Hadot's study it means that Victorinus' differentiation of esse purum from the determinate being (on), by which he assigned to the infinite not-being (God) a value of being in the form of plain activity, was anticipated and supported by the similar Porphyrean move which partially rested on the exploitation of the trademarks of Aristotelian tradition. At the same time, the pressure on Porphyry from the side of Aristotle to modulate the transcendent sound of the Plotinian God could as well be said to have ensued from Aristotle's distinctive, compared to Plato's, approach to the problem of the One. As noted above, the Platonic One is conceivable as a kind of end result searched for in the process of predication, which entailed that in the long run it led, first, to the self-annihilation of the propositional structure of the statement, and, second, to the positioning of the One in the regions of ineffability. Aristotle's reorientation of his attention to the nominal sentences, reflected in his concept of 'this something' (tode ti) as an unity of three different moments--of the whole (synolon), of indivisible form (atomon eidos), and of proximate matter (eschate hyle)--was supported by his conviction that the One must first of all be understood as a token of indivisibility which is not attained by a predicative search but is taken to be the general aspect of any particular existent (Metaphysics 1029a4-6, 1045b20-22). In other words, together with attaching the Platonic ideas in the shape of morphe to matter, Aristotle highlighted physei onta as proper objects of philosophical investigation and as vehicles of the uniqueness that was ascribed by Plato to the abstract realm of ideas, or even to a Beyond (see Gadamer 1999c:82ff.). This Aristotelian focusing on the particularity of being supposedly assisted Porphyry in formulating his original ontological identification "of hyparxis with einai monon, it is, in identifying the activity of being, the verb 'to be', with pure essence taken in its absolute indeterminateness ... The fundamental distinction here is the one which establishes itself between the 'to be' (l'etre), to act without subject, and the being (l'etant) which is the first subject, a result from the 'be'. The be-infinitive is for the first time in the history of philosophy clearly distinguished from the be-participle" (Hadot 1968:490).

Actually, a certain blending of Plato with Aristotle is witnessed already in Plotinus himself, referring us back to the Platonists' significant adaptation of a peripatetic tenet sometime in Middle Platonism. Namely, despite taking to the extreme Plato's insinuation of the absolute One in his conduct of the first hypostasis, Plotinus displays remarkable kinship to Aristotle in his concept of intellect, i.e. in his treatment of the second hypostasis. It had been a correlative of Plato's insistence on the apophatic qualities of God that Plato's ideas, although a kind of original paradigm of all the existents, were nevertheless already set in touch with the world of multiplicity, and accordingly were situated separately outside of the God. The interesting development that supposedly took place in Middle Platonism was that the ideas got transposed into the divine intellect itself and, consequently, were elevated from the status of an external specimen into something that God himself actively thinks, i.e. ideas became the thoughts of God himself (Armstrong 1960, Meinhardt 1976:61). This coordination of the Aristotelian self-thinking God with Plato's eternal paradigms was deeply entrenched in the 3rd century A.D. Platonism, and so it is no wonder that Plotinus' ideas assumed the same quality of being intelligibles within the intellect emanated from the God. Furthermore, having declared that these intelligibles are the truth and foundation of all realities (V.5.2), Plotinus goes on to state the identity of intellect and thoughts (forms or ideas): "And Intellect as a whole is all the Forms, and each individual Form is an individual intellect, as the whole body of knowledge is all its theorems, but each theorem is a part of the whole, not as being spatially distinct, but as having its particular power in the whole. This intellect therefore is in itself, and since it possesses itself in peace is everlasting fullness" (V.9.8, quot. Plotinus 2001:305-307). The description comes in some way near to the ideal sought by the Christians, i.e. to the formula of unity in multiplicity (trinity), but we must keep in mind that Plotinus' report pertains only to something that is inferior to the God, or to the One, and, on the other hand, is superior to logos which held in Plotinus a position of a mediator between intellect and senses. Thus although Porphyry could find in his teacher, whose works he was destined to systematize and hand down to posterity, a hint of how to set the two great Greeks to cooperate in the name of monotheism--which, as we know, was not at all Porphyry's aim--, but the type of harmony proffered by Plotinus had to be stretched in a slightly other direction to fit the needs of Victorinus.

Another of Aristotle's concepts that underwent a serious change in the Hellenistic and imperial age and formed a background for revaluation of infinity was dynamis. As noted above, dynamis, or potentiality, was for Aristotle equivalent with Plato's infinity and characterized a passivity of an idea as attached to matter. In this sense, dynamis can be taken to be a synonym of a force, but only with a stipulation that Aristotle's dynamis is a force of pull and push that brings another body into motion; to denote the force as immanent capability of the thing itself, Aristotle prefers the word nature (physis) (Jammer 1957:35-36). Considering Plotinus' steps towards attributing apeiron to the God, it is expected to find him revising also the Aristotelian dynamis, and this is what he in fact does, echoing the sensations of imperial Rome. Namely, the agent of this reassessment of dynamis must be seen in the overall rise of occultism and mysticism typifying the era and enforcing upon the Greek idea of ousia a new enigmatic streak. Hans-Georg Gadamer has given a lively description of this break in the tradition:

There is above all the concept of dynamis, of 'force and possibility', that acquires in Plotinus a new accent and a kind of ontological priority. Admittedly, dynamis is essentially related to energeia, as possibility to actuality. This had been the principle of Aristotle's metaphysics. But the Platonic-Aristotelian concept of being, in which the Eleatic legacy continued to live on and which conceived the being as what is present in thinking, gained in the Hellenistic age a new, dynamical connotation. It pointed not to the presentness, but to the restrained and self-manifesting force. Yet the force is a living force - not something that dwindles in its manifestation and then only feebly persists. The living force performs and survives by virtue of its activity. We could call it also an exuberant force, as we see it resulting in the abundance of zest for life, for play, and for dance. Now, it must be gauged in its whole ontological significance. Already in Stoicism this new meaning of force, of breath, and of tension had been anticipated. It was a new turn in the thinking about being which was there in the offing. Being is not anymore a glorious present that is displayed in its reliability to the pensive look as idea, essence or substance--being is now a secret force which slumbers behind all, the being which allows not to be aware of itself, nor to be estimated or exhausted, but which only in its manifestations appears at all (Gadamer 1999d:414-415).

The ascription of dynamis to the substances of the Platonic-Aristotelian tradition is a corollary of the Neoplatonists' attunement of their articulations about God to the scale of negativity; on the other hand, the fact that the Greek ousia is about to assume a quality of a hidden force, indefinite and mysterious, testifies to the change in the assumption about what knowledge is. Connected to this setting forth of the former Aristotelian potentiality as a real essence of things, is a modification in the understanding of matter. We have already referred to the Greek lenient attitude towards matter notwithstanding its principal evilness. This kind of charity was advanced in Plotinus' monistic pursuits and was the basis of his argument with the Gnostics who denied any possibility of illuminating corrupt matter (O'Brien 1981:117-119). Although there exists disagreement about the nature of Plotinus' matter which seems on its sensible level to exhibit an unsurpassable independence (Armstrong 1955:277-278), it is out of the question, first, that matter as a principle of multiplicity applies in Plotinus to all different stages of emanation, and second, that intelligible matter, or noete hyle, pertaining to the first stage, is derived directly from the One and thus has the closest contact with it (Ennead II.2.2-4). This manoeuvre of attaching matter immediately to the intellect, which surely is of great help for Plotinus in reducing the antagonism of Greek thought, draws on developing another trait of the metaphysics of Aristotle: the latter had spoken not only about intelligible matter (Metaphysics 1037a1-5) but had also conceived the relation between matter and form as a kind of shifting intellectual rapport between explicandum and explicans (things situated on the lower existential position relate to the ones on the higher location as matter to form, i.e. they are explicated by the existants of higher formal properties) (Metaphysics 1044a15-30). By dissipating matter over the whole area of existence Plotinus in a way met the needs of Christians (Armstrong 1955:278) who became charged with the historical task of eliminating the evilness of matter, and they accomplished the task, as we know it, by postulating the principle of creatio ex nihilo, i.e. by stating that nothing, not even matter, had existed outside the will of the God.

Although Plotinus is mirroring the new dynamis of mysticism and occultism germinating in the age, there exists a perceptible watershed, as regards the secret forces of nature, between his position and the overall attitudes of his era as well as of his Neoplatonic followers, including Porphyry. In spite of the orientation of his whole thought to the ecstatic experience of the One, Plotinus definitely disclaims any relevance of magic and ritual artifice for achieving this aim (Dodds 1970:87- 88), or even shows an outright disdain for such methods. But all this does not hold for Plotinus' disciples. According to Eric R. Dodds, the alteration in the discernment is well manifested "in the wavering attitude of his pupil Porphyry ... Deeply religious by temperament, he had an incurable weakness for oracles" (Dodds 1951: 286-287). Occultism was lent additional wings by Porphyry's own pupil Iamblichus (Dodds 1951:287ff.), who assigned a pivotal role in approaching the One not to contemplation, theory, or theology, but to the magic operations of theurgy which can reveal in a wordless and non-speculative way the signatures of the God in matter. The fact that this stream of irrationality carried weight also with the future Neoplatonists is confirmed by the favour revealed by Proclus and Damascius for theurgic acts, as well as by their elevation of this kind of white magic over the intellectual capabilities of a human (Dodds 1951:283-299, Beierwaltes 1985:158). A special place in Neoplatonist occultism pertained to the Chaldean Oracles (see Lewy 1978, des Places 1996), a revelatory verse collection from the 2nd century A.D., a sort of Bible for Neoplatonists from Porphyry on, which was arguably composed by Julianus (and by his father of the same name), a man who is held responsible also for inventing the designation theourgos, in his intention to distinguish himself as actor upon gods from the merely speakers about Gods, i.e. from theologoi. The historical significance of the Neoplatonists' copious commentaries on the Chaldean Oracles consists, besides lining the speculative kernels with ritual magic, in widening the scope of philosophy and knowledge till inclusion in it the old (as it was supposed to be) hereditary wisdom of the Chaldeans, Orphics etc. Thus setting up a background for philosophia perennis as wisdom which is inherited from the gods and which existed eternally, outside any religious or ethnical borders, Neoplatonists prepared the theoretical ground for the Renaissance enthusiasm of linking together not only Plato and Aristotle, but also various non-Christian and Christian sources (Kristeller 1979:50-59). Yet, despite a somewhat common indulgence of Neoplatonism in magic and mysticism after Plotinus, there must be set a perceivable comma, in its turn, after as well as before Porphyry: the imbrication of philosophy and theurgy in Iamblichus, Proclus and Damascius did not annul the Plotinian trademark of shifting the One outside of being--on the contrary, in some cases it was even considered that the supreme God cannot be named the One and must be taken a step farther still, i.e. into the absolute namelessness (Carabine 1995:161, Hadot 1972:365, Brehier 1955:269-283). Now, we have seen that the implicit chaining of the One to the being was constitutive for the emergence of the Christian infinite God, and there is good reason to believe, as demonstrated by Hadot, that another source of inspiration for Porphyry in prefashioning the schema for Victorinus was, beside harmonization of Plato with Aristotle, the Chaldean Oracles (Hadot 1968:255-272 et al.). As noted above, the hermetic vein, with which theurgy must in some way be connected, is expressed by the meliorative view to matter, explaining why the impact of the oracles on Neoplatonists can most generally be described as inducing them to see the marks of God already in sensible matter (although, it has to be remembered, the Neoplatonic theurgy was a multiplane concept and contained beside lower magic also its highly religious component). In more specific terms, the Chaldean Oracles must be seen as professing strong support for the Neoplatonist vindication of dynamis and, considering especially the case of Porphyry, for applying the concept of the inner enigmatic efficiency of things into the service of bolstering the idea of the indefinite pure being - so that the indeterminate element does not lead to the outdoing of being, nor to the degradation of matter, but allows to keep balance there where it seems logically impossible. To put it yet more exactly, the Chaldean Oracles had enunciated, as a sort of counterpart to the Greek triad of being-life-thought, a relationship of monadic identity between the supreme God (pater), his power (dynamis), and his mind (nous). Porphyry, who lends Victorinus a clue for suiting the old Greek triad to Christian aims, widens in fact the space of possible resonance still by coupling this triad with the Chaldean one, and thus attributes to the whole underlying Neoplatonic theme of God's remaining (mone), procession (proodos), and return (epistrophe) an additional vector of connotation: "... we have already seen that one proper characteristic of Porphyrean doctrine is the identification it effectuates between the One, the original cause of all things, and the Father, the entity of the Chaldean Oracles, the first moment of the intelligible triad. In this tradition the Father is called also hyparxis. Hyparxis, that is, existence, was conceived, according to the theory which extends to Porphyry and is testified to by Victorinus and Damascius, as a pure being (l'etre pur) that antedates all determination. Being (l'etant) and substance, which originate in the association of 'to be' (l'etre) and quality, are thus posterior to the pure being" (Hadot 1968:112). From this perspective we are granted a conclusion that the elements of hermetic magic, re-uncovered in the Renaissance and pointing the way to some highly inventive flights of modernity, had already had a definite role in dismantling the speculative hierarchies of Greeks in Porpyhry and early Christianity.

The third line of thought that conduced remarkably to the formation of the new concept of infinity is to be found in Stoicism. Displaying deep knowledge of Greek philosophical tradition, the Stoics supplied some of its basic notions with a new value. First, moving, which had always been underestimated by Plato and Aristotle as a quality of incompletion, became appreciated in Stoicism as an attribute of God, but with a radical change in the meaning of the concept: considered on the example of tonic tension (of contraction and dilation), moving was not viewed as an alteration of the conditions of a body (from the less perfect to the more perfect one) through an impetus of another body, but as something that is automotoric and complete in its every moment of occurring (Sambursky 1959:29-33, Hadot 1968:226-227,363). The statement about the self-generation and self-perfection of moving was accompanied by some other related announcements on the side of the Stoics: in the same way as kinetic act cannot be considered a moving (from potentiality) towards some future aim (in actuality) situated outside itself, there exists in reality not a past nor a future, but only one temporal localizability--the present; similarly, the real property of existence can according to the Stoics be afforded only to the corporeal presence of things, not to their incorporeal and imaginable localizations in the mind (Goldschmidt 1969:43-44). Second, Stoics succeed in their own materialistic way in overcoming the dualities of Greek thinking. In adopting the Aristotelian thesis about singularity of being as a proper object of philosophical investigation, Stoics manage additionally to eliminate there the antagonism of form and matter clinging to the Aristotelian particular existent: on the basis of their theory of total mixture (krasis di holon) of matter and pneuma, supplemented by the postulate of corporeality of all being, including pneuma and God, Stoics reach materialistic monism where some fundamental Greek polarities have been disposed of (Sambursky 1959:11-17). All this does not deter Stoics from contributing in a very remarkable way to the theory which they themselves considered to have only quasi real or incorporeal existence. All in all, Stoics count four incorporeals--place, void, time and lekton--and from our point of view it is interesting that all these incorporeals are tagged by Stoics also as infinities. (11) To make sense of what the incorporeals, which miss reality, in fact are, we should take a look at Victor Goldschmidt's explication of the Stoics' concept of void. Why must there exist a void in the Stoics' view? As is known, Stoics deny the being of void inside the world, i.e. in to holon, but concede its existence in to pan which includes the world together with its outside space. The reason for this kind of compromise is easily understood: as a consequence of tonic movement, the world goes periodically, through conflagration (ekpyrosis), from the state of contraction, comprising of humidity and cold, into the expanded state of dilation, where it has in fact fully transformed into the fire-based pneuma; because in the latter state the world takes up much more space than in the former one, it was logical and even obligatory to infer that the world is embraced by infinite void. The point of the Stoics' argument is captured by us only when we realize that the existence of void is not a condition for the periodic transformations of bodies (and the world), but, quite the contrary, the empty infinite space exists thanks to the bodies: "... not only that the world needs not the void, but it would be more correct to say that the void is in need of the world in order to be extracted from its non-existence and to be in the form of place ... It is always bodies that condition that incorporeals, inasmuch as they are capable, receive the bodies and limit themselves against the infinities ... not that the world is situated in the centre of void, but the centre of void is there, where is situated the world" (Goldschmidt 1969:28-30). Applied to another incorporeal, time, it means that while the corporeal and sensible present exists, past and future only subsist as our mental constructions whose being is justified and conditioned by the reality of the present: a scar does not signify that somebody has been wounded, but that somebody is having been wounded; a heart wound does not signify that the man has to die, but that the man is having to die (Goldschmidt 1969:44, SVF 2.221). Maybe the most influential has been the Stoics' theory of incorporeals as regards their concept of lekton ('sayable'), which represents an integration of the element of infinity into the theory of semantics. Namely, Stoics posit beside the corporeal signifier (voice or letter), the corporeal signified, and the respective pneumatic (and as such corporeal) state of mind engendered in the listener or reader in the process of signification, as a fourth component the incorporeal sayable or thinkable content of the expression--a kind of conceptus objectivus, to use the language of scholasticism. The best example of what lekton is, is offered by the optative sentences where the merely mental and into the future directed wish ('I wish to drink') constitutes the unavoidably incorporeal aspect of the expression. So, while the Stoics highlighted in their focusing on bodies (in physics) and on subjects (in grammar) the nominal and realistic slant of Aristotle's thinking, their theory of incorporeals can be viewed as a tribute paid to Platonic ideas. From our perspective it is important that in the course of theorizing about the second rank elements of their philosophy, Stoics reached positions that appeared of primary concern in the context of Greek philosophy. The elaborated system of incorporeals proves to be an idiosyncratic way of inscribing the concept of infinity into the structure of ancient thought. In fact Stoics prop up some concepts (place and void) which had experienced weakness in the Greek mind due to their lack of credentials of a strictly Hellenic outlook. By a back-door approach, and maybe thanks to a kind of intentional fallacy, infinity is accredited in Stoicism with a theory that makes it to function as necessary, although not exactly as a full member of philosophic discourse. A new turn was given the process when Porphyry, as argues Hadot, applies the Stoic theory of materialistic monism into the service of Neoplatonic transcendent monism, which entails that incorporeals were also de jure extricated from their inferior rank. While Stoics had pursued the logic that, on the one hand, a void around the world must be infinite, because there is nothing in the void to set it a limit, and, on the other hand, void can be infinite because it is a mental concept without any counterpart in reality, these arguments, especially the second, are invalid for the Neoplatonist. But it did not impede him from tracking the trodden path with a different rationale. What counted was that infinity had been allotted a place in argumentation, which is supposed to have meant in the perception of Porphyry that the concept of unqualified being can be used as reason in delineating the problem of One and of its relationship to the being: "He [Porphyry] had dared to apply to transcendent objects the mode of consideration and the conceptual equipment reserved by Stoics to physical being. The transposition has two aspects: on the one hand, the intelligible substance is described by the aid of the notions applied by Stoics to the physical substance; on the other hand, the incorporeals of the Stoics which held in their system only inferior status were promoted to the rank of transcendent realities" (Hadot 1968:486). How close to the brink of Porphyrean logic the Stoics came is grasped when we look once more at their central concept of corporeality. Without disentangling their ontology from the logic of the sentence, Stoics maintained that bodies are represented in linguistic expression by proper names and general concepts, while predicates (kategoremata), which denote making or suffering, refer only to the thinkable, not to real existence (Rehn 1998:435, see also Brehier 1987:13-25). In this sense, qualities, conveyed by bodies, precede the act of doing. However, there is evidence that at least some Stoics inclined, impelled probably by the concept of tonic movement underlying their theory, to view a quality as a result of a certain act, i.e. of predication (Hadot 1968:365-366). Similarly to the void that englobes and agitates the corporeal world, the Stoic enterprise of nominality is in a way undermined by the notion of tonic movement which, although vividly abolishing the Aristotelian distance between potentiality and actuality, or the Platonic one between copy and original, indicates an act and predicate in a role denied them at the centre of Stoic theory. The step not taken in a clear form by the Stoics was committed by Porphyry who sets a verbal infinitive before the nouns, and thus somehow coordinates the inner dynamism of the Stoic system with its emphasis on corporeality, but more importantly, Porphyry thereby finds the means to support his idea of pure being--with a presumed hint to Victorinus. The act of according legitimacy to incorporeals involved a pretension of authorizing the pure indeterminate activity which in its turn would make it possible to undo the rigorous demand of expelling the One outside of being. In broad terms it all was about preparing ground for the powerful word of the God, which, unlike the Greek logos referring to the stable and preordained world arrangement, creates from nothing and is dynamic in its nature.

5. Conclusion

The new concept of infinity was achieved out of the disquisitions on the One where intellectual agents combined indistinguishably with religious ones. Three constituents must be distinguished in this process. First, there was the philosophic soil of Platonism embedding a vigorous seed of infinity which sprouted easily in the benign conditions of the Greco-Roman age. Second, the monotheistic claim of Christianity conveyed a principal message of infinity which performed an instrumental role in inserting the concept into the theological and metaphysical structure of Western thinking. Third, the whole process was underpinned by diverse fusions of Platonism with Aristotelianism, with theurgy and with Stoicism. However, at the base of these syntheses must be the blending of theology with philosophy which was in fact highly encouraged by the Trinitarian mysticism of 'unity in multiplicity'. The aim of the present article has been to chart, drawing especially on the studies of Pierre Hadot, the mutual triggering of belief and knowledge, out of which appeared the concept of positive infinity, in Neoplatonism and early Christianity, keeping in mind a further aim to show, in the form of the rhetoric of culture, how infinity instigates the cooperation between different segments of human perception in the Renaissance and in modernity.

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(1) See DK 58B28: "Further, the Pythagoreans identify the infinite [apeiron] with the even. For this, they say, when it is taken in and limited by the odd, provides the things with the element of infinity. An indication of this is what happens with numbers."(Quot. Kirk and Raven 1957:243.)

(2) For an overview see Guthrie 1962:240-251. As stated by Guthrie, it is unlikely that the concept of the two 'ones' derives from the primitive Pythagoreanism or from the time of Plato; rather, he argues, the theory is surely Platonic in character (as we know, Plato was often associated with the Pythagoreans, or even treated as their direct spokesman). Eric Dodds has in a more concrete way seen the origin of the monadic One in Plato's Parmenides from where it made its way into later Pythagorean philosophy and Neoplatonism (Dodds 1928:139 et al.; see also Trouillard 1960:194).

(3) See DK 58B30: "The Pythagoreans, too, held that void [kenon] exists and that breath and void enter from the Unlimited [epeisienai ... ek tou apeirou pneuma] into heaven itself which, as it were, inhales; the void distinguishes the natures of things, being a kind of separating and distinguishing factor between terms in series. This happens primarily in the case of numbers; for the void distinguishes their nature." (Quot. Kirk and Raven 1957:252.)

(4) As noted already, the backward connection between Parmenidean and Pythagorean absolute One is supposed to be, through Plato's Parmenides, a historical reality, so we are here somewhat consciously muddling up the facts.

(5) For Martin Heidegger's fundamental discussion of Parmenides' proposition see Heidegger 1959:115-122.

A separate issue, as regards the Greek infinity, is the one concerning Melissus. Included among the school of Eleatics, Melissus proposed in some vital aspects views bitterly at odds with the position acclaimed to be Eleatic. The central and most remarkable point of divergence with Parmenides is contained in the fact that by maintaining the integrity and oneness of being, Melissus, nevertheless, claims it to be infinite, both in time as well as in space. The controversy in the attitude of two representatives of the same school has often been attributed to the Ionian background of Melissus (see Sweeney 1972:124-135, Drozdek 2008:40-47). According to the latter hypothesis, Melissus, having been born on the island of Samos, continued to advocate the Ionian philosophical predilections which, underpinned by hylozoism and the theory of prime matter, had debarred Mileasians of seeing anything but imperfection in infinity. From this point of view it has been argued that Melissus ostensibly advanced for the designation of the perfection of being a term more convenient for him, i.e. the apeiron.

(6) Heidegger's look at Heraclitus and Parmenides as at two kindred philosophers who both tell authentically about 'being' before it fell into oblivion in Western metaphysics, is expressed succinctly in his Introduction to Metaphysics: "Even today it is customary in describing the beginning of Western philosophy to oppose the doctrine of Heraclitus to this doctrine of Parmenides ... Actually Heraclitus, to whom is ascribed the doctrine of becoming as diametrically opposed to Parmenides' doctrine of being, says the same as Parmenides. He would not be one the greatest of the great Greeks if he had said something different." (Heidegger 1959:82-83.)

(7) Consider at this point the position of Hans-Georg Gadamer (1991a) who sees behind Heraclitus' way of bringing all opposites to unity an original, in the context of Greece, theory of abrupt change (plotzlichen Umschlages). By Heraclitus, argues Gadamer, it goes not about discovering some solid being, like soul, under flickering appearances of the world, but Heraclitus is concerned directly with the paradox of a momentous transition (e.g. from life to death), i.e. with the suddenness of change itself. Thus, diverging from the overall Greek religiosity, which focused on moderating the anguish of death through, for example, a transmigration of souls, Heraclitus anticipated, according to Gadamer, the Christians' aim of facing death with open eyes, the latter being a corollary of a belief in the resurrection of body as signalled by the redemptive act of Christ (Gadamer 1991a:66).

The antithetic schemes of expression (including the theory of typological structure of history), characteristic of Christian discourse, allow one to relate it rhetorically to the epigrammatic use of contrast in the proverbial prose of Heraclitus (see Villwock 1992). In this connection it is also interesting to remark that Heraclitus has often evoked in history discussions about his possible connections with the non-European thought traditions (see Schleiermacher 1998:241, West 1971, Kahn 1979:297-302)--as if in a further evidence of the track he was allotted to take between the diverse (geographical and philosophical) opposites.

(8) The thesis that Aristotle actually had in mind two concepts of infinity, the one connoting defection and the other perfection (and thus as if foretelling the later Neoplatonist and Christian understanding of infinity) was propounded by Rodolfo Mondolfo (L'infinito nel pensiero dell'antichita classica 1956). Both Muhlenberg (56-58) and Sweeney (1992:157-163) tend to discard this kind of interpretation and their position is adopted also in the present article.

(9) For infinity in Plotinus, see Armstrong 1954, Sweeney 1992:167-256. Although Plotinus implies in many places the infinite quality of the One, he in fact avoids directly identifying the One with apeiron. Leo Sweeney has therefore argued that Plotinus' implied attribution of infinity to the One must be categorized as 'extrinsic denomination'. In his reply to Sweeney's discussion of Plotinus (first published in 1957) Norris Clarke has claimed (Clarke 1959) that this kind of interpretation tends to ignore the actual role Plotinus had in overthrowing the classical disdain for infinity.

(10) The necessary question to be posed here is the following: how, and if at all, can we differentiate the existential use of 'being' launched by Victorinus and Christian theology from the Parmenidean way of estin which is also traditionally characterized, as stated below, by its absolute, or existential, use of 'is'? The same kinds of considerations seem to lie behind Cornelia de Vogel's opposing of Etienne Gilson's thesis (de Vogel 1958, 1961) that the philosophical concept of absolute being resulted from the original Christian input unto the lexicon of Western philosophy (for Gilson's discussion of existentia, from a strictly Neo-Thomist viewpoint, see Gilson 1987). In other words, de Vogel claims that absolute being was averred unerringly already by Parmenides. In connection with that I would first like to refer to Charles H. Kahn who has argued that in the case of the Greek we cannot really speak about the true existential uses of einai, because all the Greek uses classified intuitively as such are in fact underpinned either by veridical, durative, or locative value of the verb to be: "the most fundamental value of einai when used alone (without predicates) is not 'to exist' but 'to be so', 'to be the case', or 'to be true'." (Kahn 1966: 250; for a thorough discussion of the topic see Kahn 2003; see also Popper 1998: 129-130.) Second, it seems to be clear that (1) in Neoplatonism the One was stripped of being and that (2) Christianity had invented a unique concept of unity in the Trinity: the application of Neoplatonism into the service of Christianity should therefore necessarily result in some kind of historically novel conceptual output. Thus, even if debated, there must surely be a definite distinction between the existential usage attained in Christianity and the one implied possibly by ancients, including Parmenides.

(11) Cf.: "Just as anything corporeal is finite, so the incorporeal is infinite, for time and void are infinite. For as nothing is no limit, so there is no limit of nothing, as is the case with the void. In respect of its own subsistence it is infinite; it is made finite by being filled, but once that which fills it has been removed, a limit to it cannot be thought of." (SVF 2.503, quot. Long and Sedley 1987: 294.) As to the place, which accounts in Stoicism incorporeal as well but is, nevertheless, said to be finite, it must noted that the Stoic place is a kind of younger brother of the void which appears, from the viewpoint of the world, always to be occupied and defined by bodily substance--in fact, place as something separable and distinguishable from body doesn't exist for the Stoic.

Rein Undusk

The Under and Tuglas Literature Centre, Tallinn

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