text:
1 J. Patrick Atherton, 'The Neoplatonic "One" and the Trinitarian "APXH": the conflict over the unity of the principle and its relation to the "identity" of the absolute in Schelling and Hegel,' in R. Blaine Harris, ed., The Significance of Neoplatonism: Ancient and Modern, vol.1, (Norfolk, Virginia: The International Society of Neoplatonic Studies, 1976): 173–185, at 174.
Article first published online: 6 SEP 2011
DOI: 10.1111/j.1468-2265.2011.00686.x
© 2011 The Author. The Heythrop Journal © 2011 Trustees for Roman Catholic Purposes Registered
The Heythrop Journal
Volume 57, Issue 1, pages 74–83, January 2016
Additional Information
How to Cite
O'NEILL, S. (2016), PORPHYRY THE APOSTATE: ASSESSING PORPHYRY'S REACTION TO PLOTINUS'S DOCTRINE OF THE ONE. The Heythrop Journal, 57: 74–83. doi: 10.1111/j.1468-2265.2011.00686.x
Publication History
- Issue published online: 14 DEC 2015
- Article first published online: 6 SEP 2011
In an article in the first volume of Harris's Studies in Neoplatonism, Patrick Atherton described what he saw as a radical difference between the trinitarian and Neoplatonic first principles. The distinction he draws is seminal: because the first principle, or , produces all things, all that follows from it is determined by its nature. Whereas the unity of what Atherton describes as the 'Neoplatonic One' transcends all relation and difference,
The trinitarian , by contrast, appears as an attempt to reconcile the requirement of unity with that of difference within the principle itself: is now recognised as a moment within the unity, as belonging to the principle as unity. Such a position requires a very different interpretation of the relation between the principle and its derivatives than that found in Neoplatonism.1
Recent scholarship on Porphyry, however, suggests that the important distinction Atherton adverts to is not resolvable into distinctly Neoplatonic and trinitarian camps. What Atherton describes as 'Neoplatonism' is more diverse, as scholars debate the subtle differences between the doctrines of Plotinus, Porphyry, Iamblichus, Augustine, and Proclus, among others. For example, John Dillon and Steven Strange have recently argued that Porphyry's doctrine of the first principle is in fact – as Atherton describes the two positions – 'trinitarian' rather than 'Neoplatonic'. Atherton's characterization of the Neoplatonic describes more narrowly the Plotinian One, for Plotinus is the only Neoplatonist who maintains the absolute transcendence of the first principle beyond all relation and difference. Plotinus's successors, beginning with his own student Porphyry, react against his position and develop within the Neoplatonic tradition different – and perhaps 'trinitarian' – doctrines of the first principle. One need not look outside Neoplatonism to locate Atherton's distinction between Christians and Neoplatonists, for the distinction is to be found within it.
Regardless of which figures fall into which camps and what we wish to call them, Atherton's distinction between these two positions is important and demonstrates not only Plotinus's difference from the Christian Platonists, but in light of recent Neoplatonic scholarship, casts into sharp relief Plotinus's difference and unique status among his predecessors and successors. The dispute over the nature of the first principle on its most fundamental level, whether absolutely transcendent or self-relational, is not so much a matter of Christians versus Hellenic Neoplatonists as it is a matter of Plotinus versus everyone else. Dillon and others are right to see the distinction between an absolutely transcendent and a self-relating first principle occurring within the Neoplatonic tradition, but keeping Atherton's analysis in mind, we must recognize that the first principle of Porphyry and that of Plotinus are fundamentally distinct. The location of this distinction within Neoplatonism means one must refrain from glossing all the Neoplatonists with the same Plotinian brush, but rather underline Plotinus's radical position.
Porphyry's doctrine of the first principle is developed against that of Plotinus. Involving delicate distinctions, however, it is finely nuanced. Porphyry's modifications of Plotinus's doctrine result in a first principle that is utterly distinct from what Plotinus envisioned and I believe would have accepted. Porphyry's solution to the problem of how the One produces brings down the first principle from its Plotinian transcendence and includes within it difference and relation. Because Porphyry's first principle is beyond neither difference nor relation, the human completion of Porphyry's philosophical itinerarium requires no power beyond what the soul alone can achieve through its association with Intellect; this is not true for Plotinus, whose system gestures towards a necessary, but undeveloped, doctrine of grace. Further analysis of the distinctions between these doctrines on the first principle brings out how different Plotinus' thought is from that of other Platonists. Plotinus is a sui generis thinker, and we must be careful not to equate Neoplatonism with him; rather compared to both his predecessors and successors, Plotinus stands alone.
The Plotinian One is utterly transcendent; because it must be the source of all things, it is even prior to and independent of Being, considered either as one among others or as indeterminate Being.2 This speculation of a One-beyond-being is raised in Plato's Parmenides as a hypothesis, which according to Dodds is the clearest – and to his mind, the only – explicit invocation prior to the Enneads of an absolutely transcendent first principle.3 With a few Middle Platonic exceptions, pre-Plotinian Platonists typically identified the first principle with Being or Intellect.4 Plotinus argues against this because he discerns a conflict between this and another piece of Platonic orthodoxy, the doctrine that all multiplicity must derive from a prior unity. Holding to the latter as his starting point, he relegates earlier candidates for the first principle to a lower rank within his metaphysical hierarchy and projects – as did Speusippus before him – a principle prior to Being.5
Plotinus contends that Being cannot be a first principle because it cannot be a unity. Further, in Ennead VI.7.37 he describes what is in effect Aristotle's unmoved mover: self-thinking thought; Plotinus argues that this cannot be the first principle either, because it cannot think itself, or even think at all, for two reasons. First, there is no reason for the One to think, since it lacks nothing. In favor of his candidate, the relation between the One and all other things is asymmetrical: the One is good for all things, being their source, but nothing is good for the One, because it needs nothing.6 The One has no need of activity; thus there is nothing towards which it aims. This is the line of thought behind the proposal of the first principle as the Good. As Socrates claimed, all things desire the Good; it is that towards which all things move. The Good Itself, however, cannot desire itself without falling into a division between subject and object, that is, without becoming at once above and below Itself. The second reason is that thinking requires division and difference, a distinction between what thinks and what is thought about, between knower and object known. The One, as a unity, must be prior to all division. De Koninck explains Plotinus's objection to Aristotle's position:
How can you eliminate all duality from a being whom you describe as thinking about himself ? Can thought remain one and indivisible while considering itself? And if it is one and indivisible (as Aristotle insists God must be), how can it think of this indivisible which it itself must be? It would appear, says Plotinus, that the simplest reality does not think of itself, for it would then be multiple. Hence it does not think of itself and one cannot think about it.7
Plotinus explains that 'the soul […] is not altogether one when it has reasoned knowledge of anything; for a reasoned knowledge is a rational process, and a rational process is many.'8 Elsewhere he asserts that, 'if intellect itself is what thinks and what is thought, it will be double and not single and so not the one.'9 Neither thinking nor Being can be one, since they are, as Plotinus argues, 'all things': 'The one then cannot be all things, for so it would be no longer one; and it cannot be intellect, for in this way it would be all things since intellect is all things; and it cannot be being; for being is all things.'10 Iamblichus makes the same point regarding this division within Intellect: 'Knowledge, after all, is separated (from its object) by some degree of otherness. But prior to that knowledge, which knows another as being itself other, there is the unitary connection with the gods that is natural 〈and indivisible〉.'11 For Plotinus the first principle can be neither a particular being among beings, nor absolutely indeterminate Being, while concurrently preserving its unity. His conclusion is that the One must therefore be prior to Being if it is to be constitutive of Being, and must also be prior to those relations into which Being falls. The Plotinian One is prior to all relation; while we relate to it, it does not relate to us.
Further, because thinking is divided and multiple, the human mind cannot think about it without that principle falling into the division of knower and known and becoming something it is not.12 One cannot think about the One qua One; thought and speech will then be inadequate to its object, which is why the Platonists typically employ analogies and metaphors to elucidate its nature in positive, though admittedly inadequate ways, and negatively through a via negativa. In other words, philosophy, taken as discursive speech, is unable to attain the end it sets for itself.13 Armstrong explains that for Plotinus, 'the complex reality of the Divine Mind is in principle intelligible; its transcendent source, the One, is beyond the reach of thought or language in Its infinite simplicity.'14 This is why for Iamblichus, 'the contact we have with the divinity is not to be taken as knowledge,' considered either as discursive reason which is a process and multiple, or as any kind of intuition in which the division of knower and known is preserved.15 Porphyry describes contact with the One conceived as so radically transcendent as 'apprehension' or 'experience'; again, these words are inadequate. Whatever contact with the One is, it must not involve a distinction between subject and object or a relation of the One to any thing else.
Although Plotinus commits Platonic heresy by projecting a One beyond Being, his claims are nevertheless consistent. Porphyry, by contrast, wavers between two descriptions of the first principle. There is a tension between his endorsement of Plotinus's arguments that the One must be beyond Being and division, on the one hand, and his claims that the first principle is Intellect, on the other. On the first point, echoing Plotinus Porphyry distinguishes between Intellect and the One, recognizing the division within Intellect and stressing that the One must be beyond all partibility: 'Intellect is not the principle of all things; for intellect is many things; but, prior to the many, it is necessary that there should be the one.'16 Dillon points out that 'the whole of ch. 43 of Porphyry's Sententiae […] is devoted to demonstrating that nous cannot be the first principle because nous is multiple, and requires a unity prior to it.'17 He further argues that in the anonymous Commentary on the Parmenides 'we have evidence […] of a One, distinct from Intellect, which is the subject of the First Hypothesis.'18 This is all standard Plotinian doctrine. In a recent article, Dillon considers all the passages of the Sententiae that indicate a Plotinian doctrine of the One and concludes that Porphyry's own conviction '[…] does not involve any radical retreat from the Plotinian position in a "Middle Platonic" direction.'19 Such texts reveal Porphyry to be a faithful heir to and supporter of Plotinus's doctrine of the One. One might expect that if Porphyry deviated from Plotinus's position on the first principle, he would have made his disagreement explicit.20 The tension arises, however, because despite Porphyry's apparent agreement with Plotinus on this point, he also claims that the first principle is Intellect, the second of Plotinus's hypostases, and not a One-beyond-being.
While scholars such as Dillon and Strange have stressed the similarities between the positions of Plotinus and Porphyry on the first principle, others have underscored the difference between them. For example, Wayne Hankey writes that 'For Porphyry, at the level of the spiritual hypostases Being is drawn up into the One.'21 Contemporary scholars who make this point are in good company, for even Proclus, the great diadochos, recognized that the first principle of Porphyry is Intellect. In his Commentary on the Parmenides, Proclus
seems to be assuming that Porphyry is proposing that the first hypothesis, despite its accumulation of negatives, actually concerns the same figure as is the subject of the second hypothesis, that is (in terms borrowed from the Chaldean oracles), the 'Father' of the intelligible triad of Being, Life and Intellect.22
There is textual support in Porphyry's works for arguing that he believed the first principle to be Intellect or Nous. Describing the soul's return to the first principle, he describes the involvement with Nous in ways similar to Plotinian henosis. In his De Abstinentia, for example, 'the return is to one's real self, nothing else; and the joining is with one's real self, nothing else. And one's real self is the intellect [my emphasis], so the end is to live in accordance with the intellect.'23 Viewed within Plotinus's scheme, this would mark merely a stage of the ascent, not its culmination: 'but as one goes to the primary one must lift oneself up from the things of sense which are the last and lowest, and become freed from all evil since one is hastening to the Good, and ascend to the principle in oneself and become one from many, when one is going to behold the Principle of the One.'24 What are we to make of Porphyry's two seemingly contradictory claims regarding the first principle?
Having struggled with the aporias in Porphyry's surviving works, contemporary scholars are inclined to give Porphyry more credit as an expounder of Plotinus's philosophy than their predecessors were. Many now regard Porphyry as a competent philosopher in his own rite who understood his master while contributing to and expanding on the subtleties of Plotinus's doctrine, rather than contradicting or confusing it. Steven Strange warns that we must determine whether or not the distinctions between Plotinus and Porphyry, such as the one mentioned above, represent actual disagreements or cases where 'Porphyry is merely expanding upon or trying to explicate Plotinus.'25 A second option is possible, however, namely that when Porphyry 'thinks he is explicating Plotinus he is really disagreeing with him.'26 That is, commentators on these subtle distinctions and 'mere expansions' seem to gloss over drastic consequences to Porphyry's tinkering with his master's innovation. It would take little effort to give Mona Lisa a moustache, but I doubt that Da Vinci would fail to notice the addition or think it improved her appearance.
Whatever Porphyry's intent and despite his great acumen, I suggest that his clarifications and emendations concerning Plotinus's first principle produce radical consequences, distancing his entire philosophical itinerarium from that of Plotinus. His Plotinian apostasy of returning to the equation of One with Being of Platonic orthodoxy does violence to the equally Platonic maxim that Plotinus stressed, namely, that all multiplicity derives from a prior unity. The extent to which Porphyry retains unity in his first principle is dubious, and his position falls victim to arguments Plotinus wielded effectively against his predecessors. From the Plotinian vantage point Porphyry, though sophisticated, represents a step backwards rather than forwards.
The tension between Porphyry's rival claims stems from his attempt to solve a problem left by Plotinus: how his One, being beyond Being, difference, and all relation, could be productive of anything. Explaining the productivity of the first principle is a fundamental problem for all Platonists, for even Plato inherited this puzzle from the Pre-Socratics. In the Republic Plato provides a poetic metaphor to suggest that the form of the Good is the source of all intellectual and physical light and life, bestowed by a kind of emanation not unlike the power of the sun.27 A philosopher, however, not content with the poetic image and probing the rational substructure beneath this metaphor, attempting to explain precisely how this overflow of goodness occurs, is faced with a formidable task. Nevertheless, the Sun Analogy suggests a way forward to one considering the productive activity of the first principle, and Plato's successors would be occupied by this question long after the master's death.
In a recent analysis, Dillon concludes that, for Porphyry, the 'attempted solution to this conundrum is […] a finely nuanced one, the subtleties of which seem to have been ignored or disdained by his successors.'28 In contrast to his successors who address this problem by a multiplication of the levels of being, Porphyry makes a distinction within the One itself, or at least, a distinction between two ways in which the One should be considered: 'For Porphyry, the One must be viewed in two aspects, according to the first of which it is totally transcendent, simple, and unqualified by any characteristic, while according to the second it is actually the presiding element, or 'Father', of a primal creative triad.'29 Interestingly, Beierwaltes sees a similar idea emerging in the Trinity of Dionysius. He writes,
When we consider the matter philosophically, the Christian concept of God as the Absolute and as the universal origin has its roots in the relationless transcendent One. Yet as an inwardly relational being he has his roots in the second, i.e. reflexive One, so that he could be conceived as an inner trinitarian movement of thinking, (intellectus, sapientia) speaking (verbum), willing and loving (Spiritus Sanctus).30
Dillon explains that Porphyry 'is concerned to keep the two aspects of the Plotinian One, as he discerns them, together, merely striving to introduce some degree of formalization into their relationship with the help of the Chaldaean triad.'31 The first is meant to maintain the Plotinian absolute transcendence of the One-beyond-being, while the second considers the One in its relational, or creative, aspect as productive of Intellect. Although even Intellect must be produced somehow from the One, Plotinus consistently preserves their distinction.
Dillon argues that Porphyry's triad consists of the One, Being, and the skhesis, or relation, between them. These two aspects of the One are not essentially, but rather, conceptually different: 'the One in its purity and One in conjunction with Being.'32 This third element is not a separate hypostasis, but rather is some sort of link that emerges as a kind of difference or otherness, as Atherton points out - ''. While this is a later Neoplatonic development, Dillon suggests it has its origins in Porphyry:
But it is plain that later Neoplatonists, starting with Porphyry, saw this Otherness, or Difference, [of which Plato speaks] also as the third, and linking, element in a triad. It is in fact the skhesis that obtains between One and Being: they are different from one another, and that is the relation between them.33
Atherton, describing the difference between the Neoplatonic and trinitarian first principles, writes,
The primary opposition, then, between the two positions can be characterised as follows: for the Neoplatonists the unity of the is a unity of indeterminateness – just because it is the source of all the differences between things, prior even to the difference of subject and object, the principle excludes distinction from itself and is, in this way, 'one'; on the trinitarian position however, the principle is a self-determining unity – determinateness does not fall outside the unity of the principle: rather, in the completest differentiation the principle returns upon itself, is one with itself.34
Porphyry, as Dillon interprets him, is more trinitarian than Neoplatonic, as Atherton defines these categories. The first principle has a character drastically different from what it has in Plotinus's metaphysics. The One in Porphyry's scheme is beyond neither relation nor otherness, but rather it is the very otherness or difference that links the transcendent and creative aspects of the first principle. Strictly speaking, for Plotinus one cannot say that the One is different from Being, for to say so would be to put the One, which is beyond all relation, into relation. For things to relate to one another, they need to have something in common, and things that are different share this aspect of difference in common and relate to one another.35 From the perspective of the lower looking upwards, the One might be thought of inadequately as being different from all other things, including Being Itself; but one says nothing true about the nature of the One by this assertion, it being prior to difference itself. Dillon sees the One of Plotinus, which Porphyry maintains as the One in its pure aspect, as 'the One which is the subject of the negations of the hypothesis.'36 While Porphyry's first principle is indeed the One of a completed negative theology, this is not the Plotinian One, but rather the One of Christian trinitarian theology.37 The distinction between Plotinus and Porphyry here is clear and of serious consequence for each thinker's itinerarium as a whole.
As Porphyry attempts to account for the productivity of the Plotinian One by bringing the first and the second principles into relation, the first becomes more like the second than the second becomes like the first. This is evident in Strange's interpretation; noting Dillon's connection between the absolute transcendence of the One and its productive activity in Porphyry, he sees Porphyry's One as having a 'dual status'; that is, 'as both somehow being identical with the strictly transcendent One of the first hypothesis and as also having its role as constituent of the One-Being of the second hypothesis, which on the Neoplatonic interpretation is to be identified with the hypostasis Nous.'38 Porphyry understands the transcendent to have an aspect of Nous, which is also Intellect or Being. Evident here is Porphyry's characteristic blurring of the distinction between the first and second hypostases, which remain clearly separate for Plotinus. Further, Porphyry's first principle is relational in the difference between its transcendence and its creative aspect, and is thus not beyond relation altogether, as is the Plotinian One. Dillon has recently argued that 'This does not of course mean that Porphyry has rowed back from Plotinus' epoch-making assertion of a One above Being and Intellect.' However, this is precisely what it means, leaving aside whether Porphyry realised it or not.39 Dillon's article proceeds to inquire into Porphyry's claims concerning the One and Intellect '[…] to see what conclusions we may draw about Porphyry's overall view of the relations between the two'; but, as we have seen, Plotinus's One does not 'relate' to anything.40
Pierre Hadot has shown that Porphyry is the link between Plotinus, who maintains the absolute transcendence of the One-beyond-being, and Augustine, who judges that the first principle is Intellect or Being. Porphyry's shift away from Plotinus's doctrine might account for the former's seeming middle-position between those of Plotinus and Augustine. Pierre Aubenque suggests that besides understanding the first principle to be beyond Being Itself, there is another way to avoid the difficulties of division involved in considering the first principle as Being. Rather than understanding the One as beyond Being Itself, Porphyry deepens (approfondit) 'the notion of being,' as a kind of Being before all determination.41 Aubenque argues that Being, considered as such, is 'absolument simple et indéterminé, puisqu'il est le fondement de toute détermination.'42 Conceptually, it is more accurate to think of the first principle as the 'act of being' (à l'acte d'être), rather than a being. According to either view, the first is not a being; it is either beyond Being (Plotinus), or absolutely indeterminate Being (Aubenque's Porphyry). In either case the first principle is not an object, and therefore not subject to predication, again revealing that Porphyry's doctrine heralds a decisive shift from Plotinian transcendence towards an Intellectual and relational first principle.
These interpretations of Porphyry are insightful and elucidate the subtleties of his doctrine; but again, they do so by distancing his views from those of Plotinus rather than harmonizing them or developing them in consistency from his Plotinian beginning. The relation between the One and what it produces must remain aporetic in Plotinus's philosophy by necessity, given the character of his first principle. Strictly speaking, the productivity of the Plotinian One cannot be explained or even thought, because these activities are relational and discursive. The discursive tools we have at our disposal are inadequate for the job at hand. Dilating on Plotinus's position that the unity of the first principle must be beyond the duality of Intellect, Atherton writes, 'such a view of the principle led to the difficulty that the first derivation could not be logically deduced from it: there seemed to be no logical reason why such an abstractly self-identical unity should divide itself into the subject-object relation of νους.'43 This ineffability of the One and how it produces give rise to what have been identified as 'mystical' elements in Plotinus's philosophy. There is no logical explanation for the One's production because logic itself is discursive, divided, and relational, and thus cannot do justice to the One qua One. Plotinus is a victim of his own achievement: by convincingly arguing for the unity of the One going beyond Being, he has no way back down; having somehow scaled the radically transcendent heights, a descending ladder is unavailable.
While this might not be ultimately satisfactory from a purely philosophical standpoint, so that a shift away from Plotinus's One-beyond-being towards a self-relating principle is necessary to explain emanation and the existence of things, we must still be careful not to confuse what Porphyry understands to be the first principle with what Plotinus projected. By giving Porphyry the credit he is due, Dillon shows how Porphyry's position is perhaps not just a misunderstanding of Plotinus, but rather a reasoned and apparently subtle modification that develops Plotinus's doctrine to answer an essential question.44 As Strange notes, Porphyry's differences from Plotinus indicate 'not so much Porphyry's harmonizing tendency [with Aristotle, etc.] in opposition to Plotinus' more hard-line attitude, but Porphyry's understanding of some of Plotinus' deeper motivations.'45 However, Porphyry's developments are ultimately open to the same criticisms Plotinus leveled against Aristotle and others who did not intuit the necessity for the first principle transcend to Being. Granted that Porphyry is sympathetic to Plotinus's stance on the first principle, nevertheless his alternative explanation moves decisively away from it and pays the price of losing its defining character.
The Porphyrian conclusion is opposed to the Plotinian premise; the subtlety of the move does not compensate for the severity of the result. Porphyry's attempt to explain emanation from the One in a logical and discursive manner reveals Porphyry's difference from Plotinus and betrays his apostasy from the Plotinian doctrine of transcendence. This difference between these doctrines of the One has far-reaching consequences as regards their respective itineraria of the soul. The transcendence of the Plotinian One necessitates that achieving the end requires a power beyond the soul's capacity. Though it is a matter of debate, I believe that implicit in the writings of Plotinus is a doctrine of grace that is necessary if the soul is to reach its end.46 For Plotinus philosophy, taken as discursive reasoning, is a necessary preparation, and perhaps a sine qua non, if we are to attain henosis - but it is not sufficient. Porphyry does not require grace because he lowers the first principle to a level achievable by the unaided activity of the soul; Porphyry's intellectual end requires only an intellectual itinerarium. This also explains Porphyry's dismissive attitude towards theurgy: at best theurgy can purify the lower soul, but the higher soul is purified only by rational activity. The soul must be prepared for its ascent beyond discursive activity toward the final , which is a participation in the multiplicity of Nous, that is, a moving within the noetic realm from one idea to the next.47 The differences between the itineraria of Plotinus and Porphyry have their root in their beginning and their end - in their respective doctrines of the One. These differences are not only theoretical but, as in all things Platonic, concern the juncture of theory with praxis, that is, the necessity that philosophy be a way of life.
2 For a clear and succinct summary of this position, cf. Atherton, 175–79. Cf. also A.H. Armstrong, An Introduction to Ancient Philosophy (Westminster, Maryland: The Newman Press, 1959).
3 Cf. The Parmenides of Plato and the Origin of the Neoplatonic "One"', Classical Quarterly22 (1928), 129–142, at 132., '
4 On the historical development of these doctrines in the Middle Platonic period, cf. John Dillon, The Middle Platonists, (Ithaca: Cornell University Press, 1996).
5 On the first principle of Speusippus, cf. Dillon, The Middle Platonists, 12.
6 Cf. Thomas Whittaker, The Neo-Platonists, A Study in the History of Hellenism, 2nd ed., (Cambridge: Cambridge University Press, 1928), who writes, "[the One] is perfectly self-sufficing; there is no good that it should seek to acquire by volition. It is good not in relation to itself, but to that which participates in it," (57) and John Bussanich, 'Plotinus's Metaphysics of the One,' In The Cambridge Companion to Plotinus, (Cambridge: Cambridge University Press, 1996): 38–65: 'The distinctness of the One from everything else supports the further claim that the One has no relations to other things, whereas the relations of others to the One are real' (43).
7 Aristotle on God as Thought Thinking Itself', Review of Metaphysics47: no. 3 (1994), 471–515, at 477. Atherton also explains this distinction between the positions of Aristotle and Plotinus, cf. Atherton, 176–78. On the incorrect identification of this Aristotelian first principle with Aristotle's God, cf. Jean-Marc Narbonne, Levinas and the Greek Heritage, by Jean-Marc Narbonne (pages 1–96), followed by One Hundred Years of Neoplatonism in France: A Brief Philosophical History, by Wayne Hankey (pages 97–248). Studies in Philosophical Theology (Leuven/Paris/Dudley, MA: Peeters, 2006), at 28–34., '
8 Ennead VI.9.4.1-5. Cf. also Ennead V.3.17.20-5: 'for discursive thought, in order to express anything in words, has to consider one thing after another: this is the method of description; but how can one describe the absolutely simple?' I use the text in Plotinus, Enneads, vols. I–VII, trans. A.H. Armstrong, Loeb Classics Library (Cambridge, Mass: Harvard University Press, 1966–1988).
9 Ennead VI.9.2.35. On Plotinus's opposition to the doctrine that the first principle is a One-being, cf. also Ennead VI.9.
10 Ennead VI.9.2.40-5.
11 De Mysteriis I.3. I use the text in Iamblichus, On the Mysteries, Writings from the Greco-Roman world, trans. Emma C. Clarke, John M. Dillon, and Jackson P. Hershbell (Atlanta: Society of Biblical Literature, 2003).
12 On this, cf. O'Daly's excellent book, Gerard O'Daly, Plotinus' Philosophy of the Self (Shannon, Ireland: Irish University Press, 1973), especially Chapters 3 and 4.
13 Cf. Ennead VI.9.4.1-5.
14 Armstrong, 182.
15 De Mysteriis I.3.
16 Sent. 15. For the English translations I use Porphyry, Select Works of Porphyry, trans. Thomas Taylor (London: University Microfilms International, 1978).
17 John Dillon, 'Porphyry's Doctrine of the One,' In Chercheurs de sagesse. Hommage à Jean Pépin, publié sous la direction de Marie-Odile Goulet-Cazé, Goulven Madec, Denis O'Brien, Collection des Études Augustiniennes, Série Antiquité 131 (Paris: Études Augustiniennes, 1992), 356–66, at 357.
18 Ibid.
19 Intellect and the One in Porphyry's Sententiae', The International Journal of the Platonic Tradition4: no. 1 (2010), 27–35, at 34., '
20 Dillon and Strange also share this view. Cf. John Dillon, 'What Price the Father of the Noetic Triad? Some Thoughts on Porphyry's Doctrine of the First Principle,' in Studies on Porphyry, eds. George Karamanolis and Anne Sheppard (London: Institute of Classical Studies, 2007), 51–59, Dillon, 'Intellect and the One,' 34, and Strange, 20. On the pride that Porphyry seems to have taken in being Plotinus' faithful disciple, cf. Strange, 23–24.
21 The Postmodern Retrieval of Neoplatonism in Jean-Luc Marion and John Milbank and the Origins of Western Subjectivity in Augustine and Eriugena', Hermathena165 (1998), 9–70, at 41., '
22 Dillon, 'Porphyry's Doctrine of the First Principle,' 52. Cf. also Dillon, 'Porphyry's Doctrine of the One': 'Plainly Porphyry was noted in the tradition of the Athenian School for postulating this extreme simplification of the Neoplatonic system of hypostases, apparently retreating even from the relatively simple and fluid system of his master Plotinus, and in effect collapsing the realm of the One back into Intellect,' 357.
23 Porphyry, On Abstinence From Killing Animals, Ithaca, New York, Cornell UP, 2000, 1.29.4; For the text in Greek I use Porphyrius, Philosophi Platonici: Oscula Selecta, ed. Augustus Navck, Hildesheim, Georg Olms Verlagsbuchhandlung, (coll. 'Biblioteca Scriptorum Graecorum et Romanorum Teubneriana'), 1963. Discussing the first principle of Porphyry, Hankey writes, 'At this point, Porphyry, as reconstructed by Pierre Hadot, comes back to mind, for this is most like his primary einai, "to be" simplified beyond predication: "the most intensive possible unity of thought and being without difference."' Hankey, 'The Postmodern Retrieval of Neoplatonism,' 51.
24 Ennead 6.9.3. 18–22.
25 Strange, 18.
26 Ibid.
27 Cf. Republic 517b-d.
28 Dillon, 'Porphyry's Doctrine of the First Principle,' 53.
29 Ibid., 53.
30 Unity and Trinity in Dionysius and Eriugena', Hermathena157 (1994), 1–20, at 5., '
31 Dillon, 'Porphyry's Doctrine of the First Principle,' 54.
32 Ibid., 56.
33 Ibid., 57.
34 Atherton, 174.
35 On the One as being beyond relation, cf. John Bussanich, 'Plotinus's Metaphysics of the One,' In The Cambridge Companion to Plotinus (Cambridge: Cambridge University Press, 1996): 38–65, at 44–45.
36 Dillon, 'Porphyry's Doctrine of the First Principle,' 54.
37 Cf. Beierwaltes, 'Unity and Trinity.'
38 Strange, 32.
39 Dillon, "Intellect and the One," 28.
40 Ibid., 29.
41 Pierre Aubenque, 'Plotin et le dépassement de l'ontologie grecque classique,' in Hadot (éd.) Le Néoplatonisme (Paris: Cent nat de la recherche scientifique, 1971): 101–108, at 107.
42 Ibid., 107.
43 Atherton, 181.
44 Cf. also Dillon, 'Intellect and the One,' 34.
45 Strange, 22.
46 On this debate, cf. John Dillon, '"A Kind of Warmth": Some Reflections on the Concept of "Grace" in the Neoplatonic Tradition,' in Lewis Ayres, (ed.) The Passionate Intellect: Essays on the Transformation of Classical Traditions, Rutgers University Studies in Classical Humanities Volume 7 (New Brunswick, U.S.A.: Transaction Publishers, 1995), 323–32.
47 De Abstinentia 1.29.2.


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|How is Ocala to live in? (22 replies)
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There's all kinds of industry news—exciting, provocative, shocking... boring. And then there's the kind of news that makes you wish things had played out differently.
This morning, Micron CEO Steve Appleton died in a "small plane accident" in Boise, Idaho. He was only 51 years old.
According to Reuters, Appleton was "an avid pilot who flew in airshows and was also an offroad car racer." He joined Micron in 1983 working the night shift, and he rose to the role of CEO in 1994. At age 34, he was the youngest CEO in the Fortune 500 list.
Our thoughts go out to his colleagues, friends, and loved ones.
This discussion is now closed.
|Intel debuts embedded Skylake-R CPUs with Iris Pro graphics
|Fallout 4 gets more love from Bethesda with Far Harbor expansion
|AMD adds refresh-rate ranges to its FreeSync monitor page
|Rumor: Early Broadwell-E benches hint at solid performance gains
|HP refreshes Pavilion consumer PC lineup
|Nvidia teases Pascal GeForces amid GTX 1000-series rumors
|Philips' new 43-inch monitor might make native 4K practical
|Alleged Kaby Lake CPU shows its face in SiSoft Sandra database
|Dell will become Dell Technologies after its EMC buyout
|The entire monitor industry sucks. No consumers know what the hell they're buying, and what the advantages/disadvantages of one tech, price point, or...


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twitter talk
book suggestions
Beezus and Ramona
Author: Cleary, Beverly
Beezus' biggest problem is her 4-year-old sister Ramona. Even though Beezus knows sisters are supposed to love each other, with a sister like Ramona, it seems impossible.
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With three free nights on your hands, you can fly further afield for some holiday fun.
The 14 best places for a four-day short break
Four days off opens up possibilities of relaxing on a cruise through home waters, or a quick trip to a northern neighbour.
The 17 best places for a five-day short break
A five-day break is still a quick getaway, but offers the chance to pack in some action and adventure before head home refreshed and relaxed.
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Michael Gebicki The Tripologist advises on African wildlife, the Italian Lakes and Christmas in Canada.
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Have a couple of days off and want to do something special? Our specialist writers have sampled and reported back on the perfect places to relax and recharge in just a few days.
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Four generations of Merino aficionados gathered to recall their lifelong affection for the time they spent associated with ...


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To show you the most accurate prices, TTPM only displays our pricing tool on products which we've reviewed in the past three years.
The Wiffle Ball and Bat comes with a 32-inch yellow bat and a nine-inch regulation Wiffle Ball. With the Wiffle Ball, kids can throw fastballs, screwballs, curveballs, knucklers, and palm balls.
Many parents might remember this from when they were kids, and they'll enjoy sharing the fun of Wiffle Ball with their own kids. The long plastic bat and perforated Wiffle Ball makes it easy for young kids to play, but grown-ups can play, also. This is a great way to get kids having active fun outside.
The Wiffle Ball and Bat is for ages 4 and up.
Additional Wiffle Balls are sold separately.
"Regulation" is a term Wiffle Ball uses. There is nobody that regulates these balls. However, other plastic balls are not as well designed and may not throw as well as the original Wiffle Ball.
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Raspberry Pi unveils camera accessory for credit-card sized PC
February 9, 2013 - 16:18 AMT
PanARMENIAN.Net - The Raspberry Pi Foundation has unveiled a new forthcoming camera accessory for its cheap credit-card sized computer, Digital Spy said.
This week, the foundation started sales of a cheaper Raspberry Pi Model A, packing 256MB of RAM, only one USB port and no Ethernet connection, but costing just £15.95.
In a blog post, Raspberry Pi's Liz Upton also gave a sneak peek of a camera accessory that will be released in 2013.
Upton said that there is still more work to do on the drivers in the camera board, and the team is trying to get the picture quality from "pretty good" to "bleedin' marvellous", before it is released.
But she added: "Everything's looking pretty peachy for the moment. I don't have a release date for you yet, but we're probably at least a month away (and possibly more) from being able to sell these at the moment."
Whilst the exact sensor size of the camera is unknown, Wired reports that official comments on the RPi forums suggest it will be 5-megapixels.
The site says that users won't be able to change the camera lens, add physical filters or zoom, but the camera module will support HD video. It is expected to cost $25 (£15).
Top stories
Disney's ABC, ESPN and Disney Channel are expected to be available on the service along with the Fox broadcast network.
This experience will be similar to a person-to-person call, except that the screen will display the group's name and the list of members.
The week will be full of presentations detailing Apple's new tech, labs and consultations to allow developers to work with Apple engineers.
"The Armenian youth proves to be bright, adamant, committed and persistent," VivaCell-MTS General Manager Ralph Yirikian said.
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Some 90.000 unaccompanied minors sought asylum in EU in 2015 After Sweden, Germany, Hungary and Austria followed as the main destinations for unaccompanied underage asylum seekers.
U2's The Edge makes history with Sistine Chapel performance (video) The Irish four-piece have been working on the follow-up to their 2014 LP "Songs Of Innocence" over the last year.
Azerbaijani President awards fanatic who decapitated Karabakh soldier During the April hostilities the Azerbaijani side made a number of other serious war crimes to be considered by the ECHR.
Zika virus may be more dangerous than previously thought: scientists Most doctors and medical researchers now agree that there is a link between the Zika virus and microcephaly.


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Streaming Now: NBC 5 News
Cub Scout Pack 134 spent last weekend revamping the Haslet Veterans' Memorial Garden at Haslet Park.
In a world of video games and social media, parents may wonder how to keep children active and healthy.
Tuesday, Dallas Mayor Mike Rawlings joins a panel of doctors and community leaders to find a solution...
A multi-million dollar pedestrian bridge, and its intricate wheelchair ramp system, in northwest Dallas is facing criticism.
A man walking on rail tracks was fatally struck by a Trinity Railway Express train Monday night in Dallas, DART police said.
See which cities are ground spraying for mosquitoes and when.
Dallas police say two young brothers last seen leaving their home on foot have safely returned to their home.
A Marine who witnessed and tried to intervene during a domestic shooting Monday was fatally shot by an Army soldier accused in the initial altercation, Arlington police say.
Two weeks to the day since a 45-year-old mother of three was found dead inside a Midlothian church and police continue to search for a killer.
Six dogs who were rescued from a dog meat farm in South Korea by Humane Society International arrived at the SPCA of Texas in Dallas just after midnight on Tuesday.
A longtime McKinney farmer says he'd have to sell his cattle and move if the city approves a plan to build a new road through his property.
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Sir Elton John believes touring is slowly killing him because he's always on the road and never has any time to spend with his husband David Furnish and their two children.
Sir Elton John believes touring is slowly killing him.
The 66-year-old singer is keen to cut down on the amount of concerts he does because he's ''fed up'' of never having any time to spend with his husband David Furnish and their two children, Zachary, two, and seven-month-old son Elijah because he's always on the road.
Speaking to The Sun newspaper, he said: ''The time has come in my life when I will definitely cut back on shows so I have more time with my family.
''That's a conscious decision. I know I'm addicted to playing. I'm addicted to working. I'm addicted to touring. I'm addicted to everything.
''I can't have one bunch of flowers. I can't do one show. That's part of my nature. But I sat down with David and said, 'You know, I'm fed up with it. The travelling is killing me. I can't do it any more. I've never taken enough time to smell the roses'.''
The 'Rocket Man' hitmaker - who was forced to cancel a number of his summer tour dates after being struck down with crippling appendicitis two months ago - admits his time away from touring will allow him to focus on other tasks and try something different.
He explained: ''I want to take my boy to school and I want to spend more time with David. I also want to spend more time on projects that maybe I should have done years ago but never found the time for. This might be a piano album or something just different. If you're going to be Elton John, you have to push the envelope.''
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Amid rumors of ongoing negotiations between Netanyahu and Herzog on national unity government, Habayit Hayehudi chairman says his party views justice portfolio as key to its agenda.09:39 03.05.16 | 1 comments
I applaud President Obama and Israeli President Shimon Peres. This is the first step toward stopping Iran from having nuclear weapons. With all the bluster from right wing elements in The US and Israel, Iran has been moving closer and closer to getting the bomb this is the first step toward reversing that trend


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Linda P.B. Katehi was removed from her position as chancellor of the University of California, Davis on Tuesday after growing cries for her ouster due to alleged violations of university policy. 343 more words
Tags » University Of California-Davis
The Latest: 2nd round ends with a flurry, Sweet 16 field set
The Latest on the fourth full day of the men's NCAA Tournament, including games being played in New York; St. Louis; Oklahoma City and Spokane, Washington. 2,300 more words
Karaitiana leads Hawaii women by UC Davis for Big West title
ANAHEIM, Calif. (AP) — Ashleigh Karaitiana was four years old the last time Hawaii made it to the NCAA Tournament.
Clearly, the senior guard felt like it had been long enough. 894 more words
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Safe space culture stunts young minds and prevents activist students from learning how to debate. Whatever happened to "use your words"?
If one video could perfectly encapsulate the deleterious effect of having students marinate 24/7 in Identity Politics culture, protected by safe spaces, trigger warnings and campus speech codes, it would be this brief video of a scene from a pro-life protest and pro-choice counter-protest at the University of California, Davis. 858 more words
UC Santa Barbara cruises past UC Davis 87-61 in Big West
ANAHEIM, Calif. (AP) — Michael Bryson scored 24 points, Gabe Vincent added 20 and fifth-seeded UC Santa Barbara led the whole way to beat No. 4 seed UC Davis 87-61 in a Big West tournament quarterfinal game on Thursday. 86 more words
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The Guidelines on Voluntary Labelling of GM (Genetically Modified) Food for Hong Kong has been in place since 2006. In a conversation with biz.hk, Alison Van Eenennaam, an expert in genomics and biotechnology and Cooperative Extension Specialist in the Department of Animal Science at University of California-Davis, discusses the safety of genetically modified food for human consumption and challenges associated with mandatory labelling… 1,529 more words
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DAVIS, Calif. (AP) — Luke Nelson hit two free throws with 2.1 seconds left and UC Irvine escaped with a 62-61 win over UC Davis on Saturday night. 146 more words


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ABQ Beer Geek
The 2010 New Mexico IPA Challenge
From 10 breweries and hundreds of judges, one beer emerged victorious
By ABQ Beer Geek
Thanks to my nightly ritual of "adult NyQuil," also known as beer, I rarely have a hard time sleeping. But the eve of the New Mexico IPA Challenge always brings an uncomfortable night of rest. Mixed with humid weather that left my swamp cooler helpless, the looming challenge had me tossing and turning all night. Last year's judging in Albuquerque was held at Il Vicino Tap Room, and seating was scarce—most people sat on empty kegs. I was afraid if I didn't get to this year's competition early enough, I wouldn't be able to get my fill of the best IPAs our state has to offer.
Mina's Dish
By Mina Yamashita
Nostalgia With a New Mexican Kick
I grew up the oldest of six kids in a Japanese-American family. My mom honed her cooking skills working at her aunt and uncle's diner in Los Angeles' Little Tokyo, where she met my dad, a truck driver who delivered produce. It was 1940, and she was 18.
Ask Ari
Dual-Season Gardening
By Ari LeVaux
Q: In harvesting some of my earlier crops, like lettuce, and in pulling bolting crops like spinach, I've opened up some holes in my garden. With what should I plug these holes?
EVENT HORIZON (Saturday, May 7)
Día de las Madres
Tequila, Taco and Cerveza Fest
By Rini Grammer
A showcase of diverse Mexican alcohols, unique local taco recipes, live bands, water pong, Chihuahua racing and much more.
via compfight
EVENT HORIZON (Sunday, May 8)
Yas Queen
Mother's Day Afternoon Tea
By Taylor Grabowsky
Menu includes savories, scones and sweets.
Tomorrow's Events
Fundraiser Night at Flying Star Café
Benefiting Companion Animal Rescue and Medical Assistance which is a non-profit organization that helps with the adoption and placement of rescue animals.
Tasty Wednesdays at the Farm Shop at Los Poblanos Historic Inn & Organic Farm
Cinco de Mayo Celebration at M'Tucci's Cocina GrillMore Recommended Events ››
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ok, so i am obviously new here (and to Linux). i tried out an Ubuntu 7.10 Live disc and liked it enough to wanna play with it more...and then Hardy came out. i was due to reformat my laptop anyway, so i partioned off my 100gb hard drive into a approximately 10gb for Windows XP, 80gb as a stoarage space for my files (that both OS's can access) and left 10gb as unformated free space for a future Ubuntu install.
as of now, i have used Wubi to install Ubuntu 8.04 under XP, just using 4gb of space while i tried some stuff out. i really like how easy Wubi was, and i like the option of the dual boot. i am gonna want to move/reinstall Ubuntu to the free space i left for it and i was curious if it would be better to format the free space and tell Wubi to install there, or use the regular Live CD and install it that way?
if i go with the Live CD, will it automatically detect and set up just the free space accordingly? or do i need to create a formatted partion out of it first? if i format, should i go FAT32 or NTFS, or will Ubuntu reformat the space to the appropriate format? how hard will it be to keep the dual boot as it is with XP first (and auto) and Ubuntu as the alternate choice?
if i go with a reinstallation using Wubi, would there be any sort of performance difference since it would now be on its own partion instead of Window's? would it matter if i formatted the partion as FAT32 or NTFS?


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All Work and No Play and a Yellow Spider on a Pink Tulip
28 minutes ago
Good luck on your show--it sounds very interesting. The tiara made me smile :)
Wow, that's interesting. I would have had no idea. How ingenious of them.
Very nice. Interesting background, too.
Eternal recycling!
Nice thing!


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Aero Theatre
1328 Montana Ave,
Santa Monica, CA 90403
(323) 466-3456
Movie Times
Rush to War
Chimes at Midnight
Another Nice Mess: The Restored Laurel and Hardy, Volume 2
Bonnie Scotland
Another Nice Mess: The Restored Laurel and Hardy, Volume 3
Business Details
in Business
- Hours:
Regular Hours
Weekdays, doors open at 6pm Weekends, doors open at 12pm or 3pm
- General Info:
- Screen Count: 1
- Extra Phones:
Primary Phone: (310) 260-1528
Phone: (310) 260-1528
- Payment method:
- master card, visa
- Neighborhoods:
- North of Montana, West Los Angeles
American Cinematheque
American Cinematheque at the Aero Theatre
- Other Link:
- Category:
- Movie Theaters
- Other Information:
Price Range : Average
Parking: Street
Thanks to technical genius' like Bill Hogan this theater has one of the best sound systems in the city of L.A. If you ever have the chance to see a well mixed film in 70mm or DTS, it is highly recommended, the sound will b low you through the roof! By all accounts this is one of the last great neighborhood cinemas left, with regulars including Popeye's Dad, Jeffrey the angry critic, Gera the German volunteer and countless others. Every celebrity on the planet has visited, been a guest ...view moreand/or a regular patron of this theatre including an often drunk Sean Young and occasional visit from Spielberg himself. If Cassavetes was still alive he would probably be hanging out nightly. The Aero is one of those magical places where almost anything can happen, and often does. The annual Halloween Horrorthons are an orgiastic marathon of eclectic clips, free food and frenzied audiences, with the occasional Packard short often met with groans from the elderly. You can even expect an occasional riot or two when Tom Cruise or Peter Falk show up.\r
Do yourself a favor and pay a visit to Clint Eastwood and Mel Brooks' favorite theatre, the Aero, where deals are made, film is projected and pretty girls are easy to pick up in the lobby.view less
This is what movie theatres are supposed to look like, or at least used to look like. This place has a really classic feel, and is obviously a pretty significant Santa Monica landmark. They definitely offer a variety of pretty eclectic films from art house to documentary to Sleepless in Seattle. It's not always easy to find show times, and the whole thing seems to be a little un-organized at times, but none the less a veritable classic and a great stop on Montana.


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Microsoft was flaming fast in fire-fighting a major Office 365 flawTechRadar Pro
The security hole affected some big-name companies including BT and IBM.
The security hole affected some big-name companies including BT and IBM.
HP's pro-level, 13-inch Chromebook takes on the Dell Chromebook 13 and Chromebook Pixel.
Samsung's about to launch the Artik 10, a cool looking Pi rival.
Early testing of DNA as a storage medium is proving promising indeed.
UpdatedApple's refreshed MacBook yet is even more of a joy to use, but it's not for everyone.
A smart little gadget that's equally useful for businesses and end-users.
Google and HP have teamed up to create one of the most gorgeous and capable Chromebooks to date for your office.
Can this cheap MFP cope with all your printing and copying needs?
Wired for the IoT and able to produce its own electricity, the automated building is coming to save us all.
OpinionThe rise of premium Chromebook laptops could have something to do with the Surface
Round upFive of the best apps for your PC, curated from the Microsoft Store.
AirBnB's plan to use the 'mythical' tech for digital identities goes against its very spirit.
UpdatedWant to know what you can do with a Raspberry Pi? Here are some fun projects to get you started.
As much as we love our Macs, there are some things that niggle, but a solution is usually close to hand.
Windows 10's Tablet Mode (previously known as 'Continuum') ensures the new OS adapts to the device you're using.
You don't need reminding that your Mac is an awesome machine, but here's some features you might have forgotten about.


text:
The Dyson Supersonic was just unveiled in Tokyo and with no doubt; the name immediately stirs up imagery of an ultra high-speed vacuum or fan. And while I'm sure some of their existing technology is in this new product, James Dyson and his crack team of 100+ engineers and 30 in-house motor specialists have come up with what they think is the ultimate fast, focused and intelligent hair dryer and the answer to all hair drying problems.
Archive for the 'Gadgets' Category
Cool CreoPop pen lets you draw in 3DGreg Gazin - April 23rd, 2016
If you think 3D printers are cool, then how about a pen that allows you to draws objects in 3D that's truly cool? It's called CreoPop from a Singapore-based company of the same name originally funded through Indiegogo. The pen uses specially designed ink made from photopolymers that flows freely from the pen and solidifies when exposed to LED diodes.
AirJamz wearable brings your Air Guitar to lifeGreg Gazin - April 16th, 2016
Who doesn't like to play air guitar? If you do, then you may be interested in AirJamz a new wearable by Zivix, the creators of jamstik+ that takes those moves you got so good at and turn them into music.
Why mop floors when Braava jet can do it?Greg Gazin - April 9th, 2016
Regardless as to how meticulous you are the floors in your house need to be mopped once in a while. It's no secret, mopping up is one chore that most of us hate doing, so it's great news to hear that iRobot has added a complementary cleaning gadget to go along with the Roomba robotic vacuum, the Braava jet 240 Mopping Robot, a compact high-tech hard surface cleaner.
iRig BlueTurn wirelessly turns your pageGreg Gazin - March 12th, 2016
Accessing your computer or mobile device while on stage for artists or presenters can often be a pain. This is especially true if your hands are full and all you want to do is turn a page on your sheet music, change a setlist or move through a presentation. This is where the new iRig BlueTurn comes in. It's a compact wireless page turning gadget that utilizes your foot rather than your hand.


text:
Contextual Approach to Quantum Formalism / Edition 1by Andrei Y. Khrennikov, A. 'Iu Khrennikov
Pub. Date: 05/18/2009
Publisher: Springer Netherlands
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum… See more details below
The aim of this book is to show that the probabilistic formalisms of classical statistical mechanics and quantum mechanics can be unified on the basis of a general contextual probabilistic model. By taking into account the dependence of (classical) probabilities on contexts (i.e. complexes of physical conditions), one can reproduce all distinct features of quantum probabilities such as the interference of probabilities and the violation of Bell's inequality. Moreover, by starting with a formula for the interference of probabilities (which generalizes the well known classical formula of total probability), one can construct the representation of contextual probabilities by complex probability amplitudes or, in the abstract formalism, by normalized vectors of the complex Hilbert space or its hyperbolic generalization. Thus the Hilbert space representation of probabilities can be naturally derived from classical probabilistic assumptions. An important chapter of the book critically reviews known no-go theorems: the impossibility to establish a finer description of micro-phenomena than provided by quantum mechanics; and, in particular, the commonly accepted consequences of Bell's theorem (including quantum non-locality). Also, possible applications of the contextual probabilistic model and its quantum-like representation in complex Hilbert spaces in other fields (e.g. in cognitive science and psychology) are discussed.
Product Details
- 9781402095924
- Publisher:
- Springer Netherlands
- Publication date:
- 05/18/2009
- Series:
- Fundamental Theories of Physics Series, #160
- Edition description:
- 2009
- Pages:
- 354
- Product dimensions:
- 9.21(w) x 6.14(h) x 0.88(d)
Table of ContentsPart I: Quantum and Classical Probability
Chapter 1: Quantum Mechanics: Postulates and Interpretations1.1 Quantum Mechanics 1.1.1 Mathematical Basis 1.1.2 Postulates 1.2 Projection Postulate, Collapse of Wave Function, Schr\"odinger's Cat 1.2.1 Von Neumann's Projection Postulate 1.2.2 Collapse of Wave Function 1.2.3 Schr\"odinger's Cat 1.2.4 L\"uders Projection Postulate 1.3 Statistical Mixtures 1.4 Von Neumann's and L\"uders' Postulates for Mixed States1.5 Conditional Probability1.6 Derivation of Interference of Probabilities
Chapter 2: Classical Probability Theories2.1 Kolmogorov Measure-Theoretic Model 2.1.1 Formalism 2.1.2 Discussion 2.2 Von Mises Frequency Model 2.2.1 Collective (Random Sequence) 2.2.2 Difficulties with Definition of Randomness 2.2.3 $S$-sequences 2.2.4 Operations for Collectives 2.3 Combining and Independence of Collectives Part I I: Contextual Probability and\\ Quantum-Like Models
Chapter 1: Contextual Probability and Interference1.1 V\"axj\"o model: Contextual Probability 1.1.1 Contexts 1.1.2 Observables 1.1.3 Contextual Probability Space and Model 1.1.4 V\"axj\"o Models Induced by the Kolmogorov Model 1.1.5 V\"axj\"o Models Induced by QM 1.1.6 V\"axj\"o Models Induced by the von Mises Model 1.2 Contextual Probabilistic Description of Double Slit Experiment 1.3 Formula of Total Probability and Measures of Supplementarity 1.4 Supplementary Observables 1.5 Principle of Supplementarity 1.6 Supplementarity and Kolmogorovness 1.6.1 Double Shasticity as the Law of Probabilistic Balance 1.6.2 Probabilistically Balanced Observables 1.6.3 Symmetrically Conditioned Observables 1.7 Incompatibility, Supplementarity and Existence of Joint Probability Distribution 1.7.1 Joint Probability Distribution 1.7.2 Incompatible and Supplementary Observables 1.7.3 Compatibility and Probabilistic Compatibility 1.8 Interpretational Questions 1.8.1 Contextuality 1.8.2 Realism 1.9 Historical Remark: Comparing with Mackey's Model1.10 Subjective and Contextual Probabilities in Quantum Theory
Chapter 2: Quantum-Like Representation of Contextual Probabilistic Model 2.1 Trigonometric, Hyperbolic, and Hyper-Trigonometric Contexts 2.2 Quantum-Like Representation Algorithm QLRA 2.2.1 Probabilistic Data about Context 2.2.2 Construction of Complex Probabilistic Amplitudes 2.3 Hilbert Space Representation of $b$-Observable 2.3.1 Born's Rule 2.3.2 Fundamental Physical Observable: Views of De Broglie and Bohm 2.3.3 $b$-Observable as Multiplication Operator2.3.4 Interference 2.4 Hilbert Space Representation of $a$-Observable2.4.1 Conventional Quantum and Quantum-Like Representations2.4.2 $a$-Basis from Interference2.4.3 Necessary and Sufficient Conditions for Born's Rule2.4.4 Choice of Probabilistic Phases 2.4.5 Contextual Dependence of $a$-Basis2.4.6 Existence of Quantum-Like Representation with Born's Rule for Both Reference Observables 2.4.7 &'grave;Pathologies'' 2.5 Properties of Mapping of Trigonometric Contexts into Complex Amplitudes 2.5.1 Classical-Like Contexts 2.5.2 Non Injectivity of Representation Map 2.6 Non-Double Shastic Matrix: Quantum-Like Representations 2.7 Noncommutativity of Operators Representing Observables 2.8 Symmetrically Conditioned Observables 2.8.1 $b$-Selections are Trigonometric Contexts 2.8.2 Extension of Representation Map 2.9 Formalization of the Notion of Quantum-Like Representation 2.10 Domain of Application of Quantum-Like Representation Algorithm
Chapter 3: Ensemble Representation of Contextual Statistical Model 3.1 Systems and Contexts 3.2 Interference of Probabilities: Ensemble Derivation 3.3 Classical and Nonclassical Probabilistic Behaviors 3.3.1 Classical Probabilistic Behavior 3.3.2 Quantum Probabilistic Behavior 3.3.3 Neither Classical nor Quantum Probabilistic Behavior 3.4 Hyperbolic probabilistic behavior Chapter 4: Latent Quantum-Like Structure in the Kolmogorov Model 4.1 Contextual Model with &'grave;Continuous Observables'' 4.1.1 Measure-Theoretic Representation of V\"axj\"o Model 4.2 Measure-Theoretic Derivation of Interference 4.3 Quantum-Like Representation of Kolmogorov Model 4.4 Example of Quantum-Like Representation of Contextual Kolmogorovian Model4.4.1 Contextual Kolmogorovian Probability Model 4.4.2 Quantum-Like Representation 4.5 Features of Quantum-Like Representation of Contextual Kolmogorovian Model 4.6 Dispersion-Free States 4.7 Complex Amplitudes of Probabilities: Multi-Valued Variables Chapter 5: Interference of Probabilities from Law of Large Numbers 5.1 Kolmogorovian Description of Quantum Measurements 5.2 Limit Theorems and Formula of Total Probability with Interference Term Part III: Bell's Inequality Chapter 1: Probabilistic Analysis of Bell's Argument 1.1 Measure-Theoretic Derivations of Bell-Type Inequalities 1.1.1 Bell's Inequality 1.1.2 Wigner's Inequality 1.1.3 Clauser-Horne-Shimony-Holt's Inequality 1.2 Correspondence between Classical and Quantum Statistical Models 1.3 Von Neumann Postulates on Classical$\to $ Quantum Correspondence 1.4 Bell-Type No-Go Theorems 1.5 Range of Values (&'grave;Spectral'') Postulate 1.6 Contextuality 1.6.1 Non-Injectivity of Classical $\to $ Quantum Correspondence 1.6.2 Bell's Inequality and Experiment 1.7 Bell-Contextuality and Action at Distance
Chapter 2 : Bell Inequality for Conditional Probabilities 2.1 Measure-Theoretic Probability Models 2.1.1 Conventional Probability Model and Classical Statistical Mechanics 2.1.2 Bell's Probability Model and Classical Statistical Mechanics 2.1.3 Confronting Bell's Classical Probabilistic Model and Quantum Mechanics 2.2 Wigner-Type Inequality for Conditional Probabilities 2.3 Impossibility of Classical Probabilistic description of Spin Projections of Single Electron
Chapter 3: Frequency Probabilistic Analysis of Bell-type Considerations 3.1 Frequency Probabilistic Description of Models with Hidden Variables for EPR-Bohm Experiment 3.2 Bell Locality (Bell-Clauser-Horne Factoribility) Condition 3.3 Chaos of Hidden Variables does not Contradict to Stabilization of Frequencies for Macro-Observables 3.4 Fluctuating Distributions of Hidden Variables 3.5 Generalized Bell's Inequality 3.6 Transmission of Information with the Aid of Dependent Collectives
Chapter 4: Local Realistic Representation for Correlations in the EPR-experiment for Position and Momentum 4.1 Space and Arguments of Einstein, Podolsky, Rosen, and Bell 4.1.1 Bell's Local Realism 4.1.2 Einstein's Local Realism 4.1.3 Local Realist Representation for Quantum Spin Correlations 4.1.4 EPR versus Bohm and Bell 4.2 Bel&lgrave;s Theorem and Ranges of Values of Observables 4.3 Correlation Functions in EPR Model 4.4 Space-Time Dependence of Correlation Functions and Disentanglement 4.4.1 Modified Bel&lgrave;s Equation 4.4.2 Disentanglement 4.5 Role of Space-Time in EPR Argument Part IV: Interrelation between Classical and Quantum Probabilities
Chapter 1: Discrete Time Dynamics 1.1 Discrete Time in Newton's Equations 1.2 Diffraction Pattern in a Single Slit Scattering 1.3 Interference in the Two Slit Experiment for Deterministic Particles 1.4 Physical Interpretation of Results of Computer Simulation 1.5 Discrete Time Dynamics 1.6 Motion in Central Potential 1.7 Energy Levels of Hydrogen Atom 1.8 Spectrum of Harmonic Oscillator 1.9 General Case of Arbitrary Spectrum 1.10 Energy Spectrum in Various Potentials 1.11 Discussion and Conclusion
Chapter 2: Noncommutative Probability in Classical Disordered Systems 2.1 Noncommutative Probability and Time Averaging 2.2 Noncommutative Probability and Disordered Systems
Chapter 3: Derivation of Schr\"odinger's Equation in the Contextual Probabilistic Framework 3.1 Representation of Contextual Probabilistic Dynamics in the Complex Hilbert Space 3.2 Characterization of Schr\"odinger Dynamics through Dynamics of the Coefficients of Supplementarity Part V Hyperbolic Quantum Mechanics 297
Chapter 1: Representation of Contextual Statistical Model by Hyperbolic Amplitudes 1.1 Hyperbolic Algebra 1.2 Hyperbolic Version of Quantum-like Representation Algorithm 1.2.1 Hyperbolic Probability Amplitude, Hyperbolic Born's Rule 1.2.2 Hyperbolic Hilbert Space 1.2.3 Hyperbolic Hilbert Space Representation 1.3 Hyperbolic Quantization 1.4 Experimental Verification of Hyperbolic Quantum Mechanics
Chapter 2: Hyperbolic Quantum Mechanics as Deformation of Conventional Classical Mechanics2.1 On the Classical Limit of Hyperbolic Quantum Mechanics 2.2 Ultra-distributions and Pseudo-differential Operators over the Hyperbolic Algebra 2.3 The Classical Limit of the Hyperbolic Quantum Field Theory 2.4 Hyperbolic Fermions and Hyperbolic Supersymmetry
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We expose slave masters and people smugglers in suburban Britain.
Is there more to life than money?
09 Aug 2010 09:01 GMT
"She said in the night she had been awakened by men knocking at her door that said they had been sent to her by Charles Taylor, and they had given her a very huge diamond," Farrow told the court.
Farrow said Campbell had then said she intended to give the diamond to the Nelson Mandela Children's Fund.
'Mildly flirtatious'
Campbell testified last week that she had received "dirty-looking stones" at the 1997 dinner. But she told the court that said she did not know who the gift was from.
Prosecutors had called the model to testify in the hope that she could provide evidence that Taylor had handled diamonds allegedly used to purchase weapons during the 1991-2001 Sierra Leone civil war.
Taylor is on trial on charges of murder, rape, mutilation, sexual slavery and conscription of child soldiers during wars in Liberia and Sierra Leone, in which more than 250,000 people were killed.
The court is also to hear testimony from Carole White, Campbell's former modelling agent, who is expected to challenge Campbell's version of events as well.
White told prosecutors in May that Taylor and Campbell were "mildly flirtatious" throughout the dinner, and that she heard him promise the model a gift of diamonds.
Campbell later seemed disappointed with the "pebbles" she had received, White said in a statement.
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Campbell said last week that she told White and Farrow about the gift, both of whom assumed the stones were diamonds.
"One of the two said 'that is obviously Charles Taylor' and I said 'yes I guess it was'," she told the court, adding that she later gave the stones to Jeremy Ratcliffe, a representative of a Mandela charity.
Ratcliffe, the trustee of Nelson Mandela's charity in South Africa, testified before the court on Friday, saying he handed over to authorities three alleged "blood diamonds" given to him by Campbell.
Musa Zondi, a the spokesman for the special investigations unit of the South African police, confirmed the authenticity of the diamonds.
"They are real diamonds, handed back to us now, and the investigation begins."
Source: Agencies
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We expose slave masters and people smugglers in suburban Britain.
South Africa's Julius Malema talks to Al Jazeera
Special series | 25 Jun 2014 09:01 GMT | Business & Economy, China, Elections
After centuries of western dominance, the world's centre of economic and political weight is shifting eastward.
In just 30 years, China has risen from long-standing poverty to being the second largest economy in the world – faster than any other country in history.
From angry farmers to weary migrant workers, powerful politicians and everyone in between, what China says and does has become of undeniable importance to the entire world.
Although no other country in history has risen so quickly from poverty to prosperity as China has, for many in the world's most populous nation, those advances have come at a price.
The economic reforms that made the People's Republic's rise possible have also led to a harshly divided China. Divisions whose impacts could easily spread from disenfranchised indviduals to threaten the economic growth contemporary Chinese society has come to be based upon.
In the opening episode of this four-part series, we tell the stories behind these divisions, from the rising urban middle class to impoverished rural areas and the precarious existence of hundreds of millions of migrant workers on the fringes of some of the world's fastest growing cities.
From the ruling Communist Party to filmmakers and bloggers, more and more people in China are looking to get their voices heard.
As blogs look to exploit their political potential and grassroots protests and mass incidents continue to increase in numbers, we analyse how the country run and how do the people get their say.
In this episode of China Rising , we look at how the people of one of the world's most powerful yet closed states, manage to reach the masses.
We interview authors who struggle with censorship and self-censorship, and examine the country's thriving film industry, which seeks to top Hollywood.
Following the revolution of 1949, legislation regarding equality was passed, which was a huge step forward for China at the time.
And the economic reforms of recent decades have further improved the lives of women, yet it is the only country in the world where more women than men commit suicide, according to the World Health Organisation.
So, as China surges forward, how will society change and what role will the new generation play in this new global powerhouse?
China's economic role in the world is growing at a record pace, and it is also now a key player in world politics,
The country has no doubt become a global manufacturing giant, but how will it deal with issues on the home front such as increase in pollution and water shortages?
Although it has been confronted with tough environmental problems, efforts are being made to solve these.
In the final episode of this series, through a range of interviews from Africa, the EU, the US, and China, we find out how it is positioning itself as a major global player.
Source: Al Jazeera
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Region's first brick-oven pizza parlour hopes to inspire entrepreneurs and move the DRC beyond cycles of violence.
Africa, Democratic Republic of Congo
Will Department of Justice reforms change a culture of violence in the New Mexico police department?
Magazine, Racism, Gun violence
Child inmates are left to languish in prison with no visitors or legal assistance as many wait years for a trial.
Is a communist village in Andalusia where most villagers work for a cooperative really as utopian as it seems?
We examine how cyber thieves are hacking the world's financial architecture and why it's not just about money.
Business & Economy, Science & Technology, Crime
We follow the journey of Kenyans seeking justice for Britain's role in the torture during the 1950s Mau Mau uprising.
Kenya, United Kingdom, Africa
People & Power investigates the environmental consequences of palm oil plantations in equatorial Africa.
Environment, Africa, Cameroon
Five years on, Misratans reflect on the siege of their city and how it played a role in the downfall of Gaddafi.
Libya, War & Conflict, Muammar Gaddafi