PHILOSOPHY PATHWAYS ISSN 2043-0728
Issue number 185 12th May 2014
Edited by Peter Jones
I. 'City in Words' by Lukas Clark-Memler
II. 'Hegel's Dialectic of the Concept' by Martin Jenkins
III. 'The Continuum East and West' by Peter Jones
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In this issue we have discussions of Hegel and Plato focussing on their use of dialectic analysis and the dialectical method. This is the 'Socratic' method or 'method of elenchus'. As a method it is what C.S. Peirce calls 'abduction', a process of inference by which we test the defences of one or more hypotheses in an attempt to eliminate those that lead to self-contradiction, by so doing revealing those that are logically defensible therefore plausible and potential 'keepers'.
It is a strictly cold and rational method of analysis and as such vital to philosophy and the formation of our philosophical theories. Socrates promoted it as the rational alternative to (the worst kind of) sophistry and rhetoric, which is often concerned more with convincing ones opponents, at any cost, than with arriving at truth. Aristotle famously formalised its procedure as a set of three rules. As a method it is concerned directly with knowledge and epistemology, namely the elimination of self-contradiction and inconsistency from our theories in pursuit of a systematic worldview. Yet it may be extended as a principle in ontology also, on the presumption that the world is a mirror of, or even a creation of Reason. The first two essays on the dialectic here illustrate this difference of emphasis.
For a stereotypically 'Western' approach to philosophy the dialectic would be a method of debate and reasoning and no more than this. Its implications would be strictly epistemological. For an 'Eastern' or more 'Hegelian' approach we would have to see it as more than this, for it would describe the formation and functioning of the categories of thought, and thus the formation and functioning of the space-time or psycho-physical universe.
Lukas Clark-Memler begins by arguing that Plato's Republic is an example of the dialectic in action and not, as may often be thought, a naive utopian dream or blueprint for totalitarianism. The latter view, while it may be common, would make Plato a lesser philosopher than the former, and so this alternative interpretation would be the more charitable. Clark-Memler points to the considerable pre-meditation that informs Plato's text as evidence that more is intended than mere political fiction.
In 'Hegel's Dialectic of the Concept' Martin Jenkins explains Hegel's use of the dialectic not merely as a means of arriving at truth in debate or at a 'best' theory of truth, but as revealing the nature of the Absolute. The dialectic process relies on the inevitable truth that for every positive dialectical thesis there will be a positive counter-thesis. It is, therefore, a process of choosing between extreme views. Hegel reduces the categories of thought by a process of transcendence or 'sublation' and is led to conclude that the distinctions and divisions upon which these opposing views depend cannot be fundamental. Reality would outreach the dialectic. Thus a dialectical analysis leads him, much like Kant a little earlier, to a worldview for which at some level the universe would be a unity beyond all difference and division. The dialectic as an analytical method becomes also a guide to ontology.
The Editor's contribution examines an issue that helps us to define clearly the difference between what we call 'Eastern' and 'Western' philosophy. It is the quite different conceptions of the continuum endorsed by the two traditions. Physicist, philosopher and mathematician Hermann Weyl is taken to be authoritative on this topic, and his view is quoted at length and promoted as being correct. It is an issue not unconnected with a discussion of the dialectic, since the two conceptions of the continuum that he discusses would form a pair of opposed dialectical theses between which, as philosophers, we may appear to be forced to choose.
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I. 'CITY IN WORDS' BY LUKAS CLARK-MEMLER
Hermeneutic analysis of Plato's Republic -- interpreting the dialogue as a demonstration of 'dialectic'
'When he [Plato] was about to die, he saw in a dream that he had become a swan and was going from tree to tree, and in this manner he caused the greatest trouble for the bird-catchers. Simmias the Socratic judged that Plato would elude those after him who wished to interpret him. For the interpreters who attempt to hunt out what the ancients had in mind are similar to bird-catchers, but Plato is elusive because it is possible to hear and understand his words in many ways, both physically, and ethically, and theologically, and literally.'
- Olympiodorus, Commentary on the First Alcibiades of Plato
'Nothing is accidental in a Platonic dialogue; everything is necessary at the place where it occurs.'
- Leo Strauss, The City and Man
Sir Thomas More begins his Utopia with an epigraph acknowledging the influence of Plato: 'Plato's Republic now I claim, to match, or beat at its own game; for that was just a myth in prose.' More coined the term 'utopia' from the Greek ou ('no') and topos ('place'): utopia is literally 'no place.' But the etymology of utopia is not so straightforward, for the homophonic Greek prefix eu ('good') can be equally applied to the word; More was a satirist and recognized the ambiguity of the term. Thus, the Western tradition of interpreting Plato's Republic as a utopia is problematic.
Should we consider the constitution of the Republic to be a blueprint for an ideal political state, or is it merely a 'myth in prose,' a 'city in words.'
The orthodoxy holds that Plato's political proposals in the Republic are sincere; this interpretation is strengthened by the clear designation of the Laws as a 'second-best' constitution. However, this reading does not take into account the structural subtleties of the Republic and close examination of both dialogues finds the standard 'literalist' interpretation lacking on many levels. I propose a new interpretation of Plato's Republic, based on the unity and 'form' of the dialogue as a whole.
The purpose of this inquiry is manifold. By considering the flaws in 'literalist' interpretations of the Republic, I can defend Plato from allegations of totalitarianism. Through hermeneutic analysis of the Platonic corpus, I will show the importance of 'action' in the dialogues. And by considering the structural symmetry of the Republic, I can make the impressive claim that the dialogue itself is a concrete example of 'dialectic.' So understood, the Republic does not offer a blueprint for political reform, and should not be interpreted literally as representing Plato's ideal state.
The task at hand is of no small importance. Considering the influence of Plato and his Republic on Western thought, the possibility of two thousand years of misinterpretation is indeed alarming. I must ensure that my argument is clear and comprehensive. Because of the inherently esoteric nature of such an inquiry, the potential for convolution is great; I proceed to outline the essay in appropriate detail. I will begin by discussing the totalitarian implications of the 'literalist' reading, highlighting the danger of misinterpretation. I will then analyze the relationship between the Republic and the Laws, focusing on the oft-quoted 'second-best' passage of the latter. After showing that the Kallipolis is not Plato's ideal constitution, I will begin to develop a new interpretation of the Republic, based largely on the structure and form of the dialogue. The second section of the essay considers the 'action' of the dialogue; I contend that the central theme of the Republic is exemplified by the actions of its characters. The third and final section of this inquiry concentrates on the structural symmetry, or 'form' of the Republic. Upon close reading, we find that Plato uses the various topics of the dialogue to demonstrate dialectic at work; as the text progresses, we witness the ascent of the Divided Line to the Good itself, and the subsequent attempt to use the Forms to impose order on the 'sensible world.' This interpretation takes heed of Friedrich Schleiermacher's maxim that Plato's 'form and content are inseparable.' And it respects Plato's great premeditation in composing the dialogue.
A literal interpretation of the Republic naturally leads to accusations of totalitarianism. The absolute rule of the philosopher-kings and the 'noble lie' have lead philosophers like Richard Crossman to claim that the Republic is, 'the most savage and the most profound attack upon liberal ideas which history can show.' Indeed the rigid autocracy and propagandistic indoctrination of the Republic were echoed in the dictatorial regimes of Hitler and Stalin. Karl Popper, too, is critical of Plato: 'I believe that Plato's political program, far from being morally superior to totalitarianism, is fundamentally identical with it.' Yet neither Popper nor Crossman consider the fact that the political proposals of the Republic are insincere and should not be taken literally.
Before I can discuss my interpretation of the Republic, I must dispel the belief that the Kallipolis is Plato's ideal political constitution. Many scholars see the Laws as representing a revised, more practical manifestation of the Republic's 'utopia,' and that Plato's 'faith in enlightened absolutism' waned in the years between the composition of the two dialogues. This school of thought contends that Plato abandoned the Kallipolis in favour of Magnesia: the more refined, albeit pessimistic, constitution of the Laws. To explain the doctrinal development, scholars point to the downfall of Sparta, as well as Plato's failure at Syracuse in educating Dionysius II. This interpretation is attractive, since Plato's ostensible political maturity matches the chronological order of his political dialogues. The Republic comes first, as the optimistic, idealistic utopia, where a young Plato builds a transcendental society from the ground up, relying only on the Forms. This is followed by the Statesman, which gives the idealistic principles of the Kallipolis a practical dimension; and finally, the Laws, a comprehensive guide to legislation in the ideal society, where divine philosophising is eschewed for practical policy. However, the problem with this interpretation is that it presupposes the Republic to be a sincere political model; this is a position that must be challenged.
The obvious refutation of the 'literalist' interpretation is that the constitution of the Republic is too politically naive to be taken seriously; for to 'suppose that Plato ever thought that the Republic was attainable would be to suppose him capable not merely of optimism or idealism but of sheer political naivete.' However, the problem with an 'insincere' reading of the Republic -- allowing that Platonic irony leads to a non-literal interpretation -- is that the Laws explicitly discusses only the 'second-best' state: 'The state which we have now in hand [Magnesia], when created... takes the second place.' This leads the 'literalist' school to claim that the Kallipolis is Plato's ideal society and Magnesia is simply the closest any human could come to replicating the perfect model. Analysis of the aforesaid passage reveals the error in this judgement.
The Athenian Stranger describes in detail that the best state will be one of absolute communism: property, family, and honour will be shared by all citizens. To conclude from this statement that Plato endorses the constitution of the Kallipolis is to misinterpret the Athenian's words. In the Republic, Plato restricts communism to the guardians (philosopher-kings and auxiliaries); he allows the 'third class' of merchants and producers to have private property. Sir Ernest Barker considers the Kallipolis to be only 'half communism.' The ideal constitution presented in the Laws is 'full communism,' in which all citizens share everything. Plato scholar Christopher Bobonich discusses this distinction:
The Laws passage presents as the 'first-best' city, not
that of the Republic, but one in which there is, throughout
the entire city, a community of property and of women and
children. So the claim that the city sketched in the Laws
is second-best does not suggest that the Republic still
represents Plato's ideal political arrangement. What the
Laws represents as the ideal... is a city in which all
citizens are subject to the same extremely high ethical
Advocates of the 'literalist' interpretation can no longer use the Laws as evidence that the Republic is a sincere constitutional model. Comparative analysis of the two dialogues shows that Plato instead believed absolute communism to be the ultimate political ideal; the 'second-best' constitution of the Laws is his 'practical utopia.' I can now comfortably reject readings that hold the Laws to be an expression of 'senescent disenchantment' or 'senile aberration' or that it is 'the outcome of a change in Plato's views about human nature.' Only when Plato's Kallipolis is considered to be a sincere political model does it follow that his political theory changed as he aged.
But if the Republic is not a blueprint for an ideal society, then what is it about? This section of the essay has been largely elenchic. In the spirit of Socrates, I have revealed the flaws in common interpretations of the Republic; in doing so, I have forced the 'literalist' to renounce her belief and the conceit of knowledge. In the next two sections of the essay, I will develop a new interpretation based on the structure and 'form' of the dialogue: starting with the 'action' thesis, and concluding with a discussion of dialectic.
There is a tendency in contemporary Plato scholarship to see the dialogue form as a hindrance to philosophical clarity. But to isolate the doctrine from the dialogue is to underestimate the importance of 'form' in Plato's writing; such an act ignores the great premeditation of Plato's composition. We should acknowledge Schleiermacher's insight that in the Platonic dialogue each sentence can only be correctly understood in its place. Hegel's claim, that scholars must 'separate the form... in which Plato has propounded his ideas... from philosophy as such in him,' represents the modern error of anachronistic interpretation. Leo Strauss abjures this variety of analysis and recognizes the 'logographic necessity of every part.' In The City and Man, Strauss outlines his hermeneutic principle:
One cannot understand Plato's teaching as he meant it if
one does not know what the Platonic dialogue is. One cannot
separate the understanding of Plato's teaching from the
understanding of the form in which it is presented. One
must pay as much attention to the how as to the what... one
must even pay greater attention to the 'form' than to the
'substance,' since the meaning of the 'substance' depends
on the 'form'.
In light of this assertion, I will consider the 'action' of the dialogues and how it contributes to the overall meaning. Close examination of the Platonic corpus reveals that the characters of the dialogues exemplify the abstract themes that they discuss. In this way, the dialogues are fundamentally reflexive and self-referential. The Straussian distinction between 'speech' and 'deed' clarifies this aspect of the dialogue form. The speech of the characters is analogous to the 'substance' of the dialogue (the various Platonic doctrines), but the 'deeds' involve the traits of the participants, the manners in which their conversations arise, and the development of character.
An example of this relation will make this thesis clear. In Plato's Meno, the eponymous interlocutor demands an answer to the question, 'can virtue be taught?' Socrates considers the various positions of the argument -- the Gorgian method of didactic instruction, or the virtuous man teaching by example -- but ultimately ends up in aporia. Meno is an excellent example of Socratic elenchus at work, but 'Meno's Paradox' remains unsolved at the finish. While the substance of the dialogue results in no clear conclusion, the form and action of the dialogue shed light on the central theme; while Plato does not define virtue, he shows us virtue.
Over the course of the dialogue we witness the transformation of Meno from irritable and rude, to calm, wise and indeed virtuous. At the outset, Meno rashly accuses Socrates of intentional deception, and interrupts him with frustrated comments; there is little harmony in the conversation. However, towards the end of the dialogue, after Socrates' experiment with Meno's slave, there is a clear shift in attitude. Meno improves in courtesy, wisdom and temperance; he becomes more agreeable and is better able to follow the discussion. From the action of the dialogue we learn that there is at least one way of teaching virtue: Socratic inquiry. The drama, characters and form of Meno answer the central question, while the substance (the 'doctrine') is inconclusive. Such is the power of the Platonic dialogue.
This is the first important aspect of my interpretation of the Republic: the dialogue itself 'acts' on the characters; there is an intrinsic relation of action and theme. For an obvious example of this effect, consider Socrates' 'taming' of Thrasymachus in Book I. We are introduced to Thrasymachus the Sophist by way of metaphor: 'He coiled himself up like a wild beast about to spring, and he hurled himself at us as if to tear us to pieces.' Thrasymachus forcibly enters the discussion and demands a definition of justice from Socrates (much like Meno). And while no conclusion is reached by the end of the first book, the temperament of Thrasymachus has softened. His brief character arc is itself a model of justice. Through engaging in philosophical discussion, Thrasymachus becomes more reasonable and restrained. The 'wild beast' is tamed by justice in action. Strauss writes that, 'the first book surely does not teach what justice is, and yet by presenting Socrates' taming of Thrasymachus as an act of justice, it lets us see justice.'
Similar results hold for the other characters of the Republic. While we are explicitly informed that the 'city is the soul writ large,' and that there is an isomorphism of city and soul, we can implicitly identify the three principal characters with the sections of the tripartite soul. Socrates is unequivocally wisdom embodied. Glaucon -- ambitious, competitive and musical -- represents the 'spirited' part of the soul: he has all the personality traits characteristic of 'thumos.' Glaucon is capable of abstract and theoretical discourse; it is he who discusses the Divided Line with Socrates in Book VI, and the cave and Forms in Book VII. Adeimantus can then be identified with the 'appetitive' section of the soul. He is concerned with empirical observations and concrete proof; he discusses the degeneration of the aristocrat to the tyrant and the problems of poetry.
In the first half of the text (roughly, Books I-VI), there is a tension between the three characters. Glaucon derides Adeimantus and objects to much of what Socrates says. Adeimantus regularly interrupts to voice his dissatisfaction with the abstract nature of the discussion. But after the Divided Line and cave are explored, harmony descends on the trio. Humor takes the place of discord; the interlocutors no longer interrupt, Socrates no longer condescends. The three laugh together, and this transformation -- from heated debate to amiable conversation -- personifies the correct alignment of the tripartite soul (Socrates' definition of justice from Book IV). While Socrates' definition of justice makes use of a metaphorical city, Plato uses his characters to exemplify justice in the soul. The form of the dialogue and dramatic development are essential in interpreting the Republic accurately. Plato constructed a 'city in words' but the reader need only consider the character relations to see justice in action.
So much, so good, but the 'action' thesis does not explain why the Kallipolis dominates the dialogue, nor does it address the structural abnormalities of the text. I now move on to the second tenet of my interpretation: that the aesthetic symmetry of the Republic highlights the art of dialectic, and that instead of simply acting on the characters, the Republic 'acts on' the reader. In her popular work of Plato scholarship, Platonic Ethics, Old and New, Julia Annas questions why Plato wrote Books VIII through X, since the 'ideal' constitution has already been described, and justice in the soul and state identified, by Book VII.
The 'literalist' would indeed see the second half of the Republic as unnecessary and repetitive, and she would happily stop reading after the education of the philosopher-kings is adumbrated at the end of Book VII. In fact, the latter half of the dialogue is key to understanding the overall meaning. Reflection on the discussion topics of each book of the dialogue, and consideration of the themes synoptically, reveals a distinct aesthetic symmetry. At first this seems strange and erratic, and raises many questions: for instance, why does Plato abruptly return to poetry in Book X? While some translators, so unimpressed by the seemingly random digression, abandon conventional division of the books and opt for their own, more 'logical' order; we must remember that with Plato, 'nothing is accidental.'
The dialogue begins with a descent ('I went down to the Piraeus'), and finishes with one too (Er's descent to the underworld). This is the first instance of symmetry, and the 'descents' of the Republic characterize the structural pattern of the dialogue. The discussion then turns towards the topic of poetry and its role in the education of the guardians. But midway through the exchange Socrates claims that he 'cannot settle the matter at present,' and so the subject of poetry is postponed until the beginning of Book X. In Book IV, the tripartite soul is introduced and justice in the soul is defined. Once again, the same topic returns in Book IX with the haunting metaphor of the 'many-headed beast.' Book V is wholly concerned with detailing the constitution of the Kallipolis, while in Book VIII, Socrates considers the degeneration of the state.
This structural pattern is certainly unusual: the introduction of a theme in the first half is balanced by a return to the same theme in the final half. Why is there this thematic duplication that repeats topics in reversed order? We should note that the two treatments of the topics are not the same; by identifying the difference, we can begin to recognize the meaning and significance of the symmetry.
The first half of the dialogue is characterized by ascent: definitions are given, the state is erected, the discussion rises from 'Becoming' to 'Being'; from the World of Appearances to the World of the Forms. In Books I-VII we may recognize an isomorphism between the levels of discussion and the stages of the Divided Line.
The latter half of the dialogue has the distinct feel of descent: the decay of the Kallipolis to the rule of tyranny, the fall of the 'just' man. The discerning reader should now ask the obvious question: which theme acts as the axis of symmetry? And such a reader should already know the answer, for the peak of the Republic's ascension, the vertex of the Becoming-to-Being trajectory, the apotheosis of the inquiry, is the Good itself; a vision of the Forms marks the completion of the philosopher-king's education.
As we read the Republic and consider the structural symmetry, we witness the power of dialectic. The first five books of the dialogue represent the ascent of the Divided Line -- from eikasia to noesis -- the discussion centers on abstract ideas, without reference to concrete phenomena; the basic templates of justice, the soul, and the state are identified. And then we reach the pinnacle of philosophical inquiry with a vision of the ineffable Good; like the philosopher-kings, we marvel at the majesty of the sun, blinded by the light. But after perceiving the Forms, we must descend back into the cave. A fact that is most often overlooked in Platonic epistemology, is that the dialectical method is not completed once the Forms have been reached; that is only half the journey. For dialectic does not follow an upward sloping line, instead, it takes the shape of a parabola. In the words of classicist James Adam, 'The dialectician's progress involves both an ascent and a descent.'
The second half of the Republic is thus most important, for now that the abstracted topics have been explored, the adequacy of the principles can be tested -- empirically and existentially. The pure theorizing of Books I-VI is applied to the recalcitrant matter of the world in Books VIII-X. The Forms are the ordering principle of the sense world -- they are what give shape and value to all material objects -- but instead of merely describing this process, Plato shows it to us.
Consider the development of the Republic's themes. The account of poetry changes from a meditation on meter and cadence, to the actual effect of mimesis on the soul. The tripartite soul is first identified using the law of non-contradiction, and three corresponding character types are clearly defined -- each perfectly fitted for a role in the 'tripartite society' of the Kallipolis. Compare this to the description of the man, lion and hydra fighting for attention in Book IX; the neat divide of the soul is no longer appropriate once applied to physical beings. The abstract templates inform the sensible phenomena, but must be adapted and molded to accommodate the complexities of human nature.
In sum, the symmetry of the Republic is key to understanding the dialectical process of inquiry. The treatment of themes in the first half is marked by pure rationalism, with the elimination of factors not relevant to the creation of generalized principles. This is reversed in the second half, where focus is given to empirical and existential application. So understood, the Republic depicts dialectic in action, with an actual application of the Forms to the sensible realm -- introducing order to the world, and harmony to the soul. Thus, to 'read it as a practical political proposal is to miss its point.'
Because modern interpretation attempts to isolate a clear philosophical doctrine from the dialogue, the unity of the Republic as a whole has gone unappreciated; key aspects of the dialogue -- the 'action' of the characters, drama, and dialectical process -- have gone unnoticed. The Classical Greek audience would have been able to recognize the aesthetic symmetry of the text and appreciate the irony of the political proposals, though this temperament had largely dissipated by the Hellenistic period. Modern readers ignore the importance of form, which leads to profound misinterpretations; it is absurd to take one section of the text (Books IV-V, the description of the Kallipolis), out of context, as the literal meaning of the Republic. When the dialogue is examined as a whole, it is obvious that Plato's 'utopia' is an 'incomplete abstraction, not a prudential blueprint.'
The 'literalist' school cannot explain why Plato repeats themes, but they clutch to a concrete doctrine, separating the 'philosophy' from the drama, desperate to taxonomize. By focusing on specific sections of the Republic, it is easy to consider the text to be pessimistic -- with its emphasis on the inherent instability of justice in the city and soul, and the perpetual danger of moral degeneration. But by interpreting the complete dialogue to be a detailed account of dialectic, we find Plato at his most hopeful. We are treated to a rare glimpse of the Good, and come to understand that 'there is order to be found when we use the light of the ideal to view the actual.'
If my interpretation is correct, then Plato's Republic should not be considered a work of political philosophy. The construction of the 'city in words' is simply a component of the dialectical inquiry; the political proposals themselves are of little importance to the overall meaning. Yet as an epistemological and metaphysical work, the Republic is the most important dialogue in the Platonic oeuvre, as it is the only account of dialectic in action. While other dialogues take an abstract theme up the Divided Line, only in his Republic does Plato use the Forms to impose order and harmony on the physical universe.
Due to the esotericism of hermeneutic analysis, the present inquiry may be insufficient in defending such a sweeping claim. But in developing a new interpretation of the Republic, I have honored the Platonic tradition by adding one more voice to a two and a half thousand year discussion; a discussion that began with a descent, and continues to progress towards the light.
1. Olympiodorus was a 6th century Neoplatonist who taught at the school of Alexandria. This passage appears in Book II, lines 156-162 of his Commentary on the First Alcibiades of Plato, translated by L.G. Westerink (emphasis added).
2. Page 60.
3. Thomas More, Utopia, vi ('Lines on the Island of Utopia').
4. Plato regularly refers to the Kallipolis (city of the Republic) as a 'city in words' -- Republic 369c, 592a; Laws 739c. From the Greek 'en logoi' -- best translated to 'in words' (though some versions of the Republic translate it to 'in theory' or 'in speech').
5. Laws, 739a-e.
6. 'Dialectic' is the ultimate philosophical activity that leads the capable student to an ineffable vision of the Forms. While Socrates regularly mentions the power of dialectic, he does not offer any comprehensive guide to the method of dialectical inquiry. In Book VII of the Republic, Socrates describes dialectic: 'whenever someone tries through argument and apart from all sense perceptions to find the being itself of each thing and doesn't give up until he grasps the good itself with understanding itself... dialectic is the only inquiry that travels this road, doing away with hypotheses and proceeding to the first principle itself' (532a-533e).
7. 'The safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato' -- Alfred North Whitehead, Process and Reality, 39.
8. A survey of the Platonic corpus finds that this 'self-referential' nature is common -- I will use the Meno as an example of the dialogue 'acting' on its characters.
9. Julia Lamm, 'The art of interpreting Plato,' 103. At this point, I should acknowledge the range of renowned Plato scholars that this interpretation is influenced by. Schleimacher's insistence to view Plato as both an 'artist and a philosopher' greatly enhanced my perspective. Strauss' hermeneutic techniques were of much use in this inquiry. As was the work of translators Allan Bloom and James Adam, who both rejected the notion that the Republic is a sincere political treatise. Robert Brumbaugh and Drew Hyland's unique views on Plato were also significant to the development of my interpretation.
10. Ibid., 73. Further evidence that supports the view that Plato's composition of the Republic was exhaustively premeditated and deliberate, comes from Dionysius of Halicarnassus. In his On Literary Composition he notes that, 'Doubtless the stories about the man's love of labor are familiar to every lover of speeches, especially, among others, the one about the tablet which they say was discovered when he died, with the beginning of the Republic set down in manifold ways' -- in William Roberts (ed.), On Literary Composition, 25.
11. Richard Crossman, Plato Today, 92.
12. Ibid., 9. Crossman deems the Republic a 'handbook for aspiring dictators.'
13. Karl Popper, The Open Society and its Enemies, 84. Bertrand Russell approved of Popper's criticism of Plato, writing in an introduction to Popper's text that the 'attack on Plato, while unorthodox, is in my opinion thoroughly justified.' Russell is also critical of Plato -- in his magnum opus History of Western Philosophy, he aims to treat Plato 'with as little reverence as if he were a contemporary English or American advocate of totalitarianism' (109). Yet we should be reluctant to take Russell's criticism seriously, for he also attacks Plato on theistic grounds (he uses the Benjamin Jowett translation that inaccurately refers to God); since we now know that Jowett was mistaken in his translation -- nowhere in the text does Plato mention a god -- Russell's critique is misguided.
14. Gregory Vlastos, Platonic Studies, 216.
15. Magnesia is the name that Plato gives to the constitution discussed in the Laws -- in the dialogue, Magnesia is to be established in an abandoned part of Crete.
16. In 371 BCE, Sparta was defeated by Thebes at the Battle of Leuctra, ending Spartan supremacy in Ancient Greece. Because Plato was influenced by Laconian society, the decline of Sparta may have led him to revise the Republic.
17. Trevor Saunders, The Laws, 28.
18. Laws, 739e.
19. The fact that it is an 'Athenian Stranger' and not Socrates that dominates the Laws is a significant point, and strengthens the argument that the Republic is not a sincere political dialogue. Many scholars, including Aristotle, simply consider the Athenian to be an incarnation of Socrates, but this is false reasoning. Strauss examines this situation: 'The emphatically political character of the Laws would seem to explain why that work is the only Platonic dialogue in which Socrates does not participate, for Socrates was prevented by his daimonion ['voice of the daimon'] from engaging in political activity' (The Argument and the Action of Plato's Laws, 1). In the Apology (31c-32a) Socrates describes his daimon as an inner voice that alerts him when he is making a bad decision: 'It is a voice, and whenever it speaks it turns me away from something I am about to do.' If the Republic was a political dialogue, then it follows that Socrates' daimon would have prevented him from participating in the discussion. We should not underestimate the importance of character in the Platonic dialogues. Scholars who believe that the Athenian Stranger is Socrates, point to the passage in Plato's Crito, where Socrates alludes to the fact that Crete is the one place he would go if he were to escape from his cell (the Laws takes place in Crete).
20. The best state is one where, 'there is observed as carefully as possible throughout the whole State the old saying that 'friends have all things really in common'... In which there is community of wives, children, and all chattels, and all that is called 'private' is everywhere and by every means rooted out of our life, and so far as possible it is contrived that even things naturally 'private' have become in a way 'communized'... No one will ever lay down another definition that is truer or better than these conditions' (Laws, 739b-d). See Sir Ernest Barker's Greek Political Theory, 370, for an in-depth discussion on the 'three grades of constitutions' -- the best is that of absolute communism, the second-best is Magnesia, and the third best involves all actual constitutions that are closest in kind to Magnesia. The Kallipolis is not even on the list.
21. Ibid. Also see footnote 1 to pages 370-371.
22. Plato's Utopia Recast, 11-12 (emphasis added).
23. Kenneth Moore, Plato, Politics and a Practical Utopia, 82.
24. Leo Strauss, The Argument and the Action of Plato's Laws, vii; Eric Dodds, The Greeks and the Irrational, 216; Trevor Saunders, The Laws, 545.
25. There are a myriad of 'positive' interpretations of the Republic that do not involve a sincere political constitution. Many consider the dialogue to simply be an exaggerated, shocking statement; a catalyst for political discussion. The Roman philosopher Cicero would subscribe to this reading: 'Plato has given us a description of a city, rather to be desired than expected; and he has made out not such a one as can really exist, but one in which the principles of political affairs may be discerned' (De re publica, Book II, Chapter XXX). The French philosopher Jean-Jacques Rousseau considered the Republic to be a text on educational reform -- in Emile he writes: 'Do you want to get an idea of public education? Read Plato's Republic. It is not at all a political work, as think those who judge books only by their titles. It is the most beautiful educational treatise ever written' (Emile, 40).
26. James Rhodes, Eros, Wisdom, and Silence: Plato's Erotic Dialogues, 73.
28. Strauss, The City and Man, 52.
29. Ibid. Strauss' hermeneutics are essential in understanding Plato, and we can ignore his obscurantism without affecting our interpretation.
30. Strauss, The City and Man, 58-61.
31. This is the standard Sophist position of pragmatism -- 'virtue' can be taught, if virtue is understood as the practical means of 'getting ahead in life.'
32. Aporia is a situation typical in the Platonic dialogues, where Socrates objects to all definitions but fails to offer one himself. It is a 'negative' position where elenchic deconstruction results only in confusion.
33. 'Man cannot search either for what he knows or for what he does not know... He cannot search for what he knows -- since he knows it, there is no need to search -- nor for what he does not know, for he does not know what to look for' (Meno, 80e).
34. 'O Socrates... you are casting your spells over me, and I am simply getting bewitched and enchanted, and am at my wits' end... And I think that you are very wise in not voyaging and going away from home, for if you did... you would be cast into prison as a magician' (Meno, 80a-c).
35. Republic, 336b.
36. To those that claim Thrasymachus has merely lost interest in the discussion and has given up on Socrates, I would point out that the transformation from angry abuse to apathetic calm is itself an impressive act of justice. Most modern prisons would consider such a transformation to indicate the success of the 'justice system.'
37. At the end of Book I, Socrates thanks Thrasymachus for becoming more 'gentle' and ceasing harassment (Republic, 354a-c).
38. Strauss, The City and Man, 138 (emphasis added).
39. Republic, 368d-369b.
40. In Book III of the Republic, when the discussion turns to music, Adeimantus departs, and Glaucon is left to consider the intricacies of 'words, harmonic mode, and rhythm.' When Glaucon asks which harmonies are 'expressive of sorrow,' Socrates answers, 'You tell me, since you're musical' (398d-e). In Book VIII, Adeimantus claims that the timocratic man would be 'very like Glaucon... as far as the love of victory is concerned,' to which Socrates responds, 'He'd [the timocratic man] be more obstinate and less well trained in music and poetry' (548d-e).
41. Consider the fact that Adeimantus is satisfied with the 'city of pigs' and agrees that economic interests are the most important. The dialogue might have stopped there had Glaucon not interrupted with the desire to create a 'luxurious city' (372a-373a): 'It seems that you make your people feast without any delicacies... If you were founding a city for pigs... wouldn't you fatten them on the dame diet?' (Republic, 372c-d).
42. Julia Annas, Platonic Ethics, Old and New; Rachana Kamtekar, 'Review of Platonic Ethics, _ Old and New.'
43. Strauss, The City and Man, 60. The passage continues, 'Everything which would be accidental outside of the dialogue becomes meaningful within the dialogue.'
44. Republic, 392a
45. Ibid., 588c-589c
46. Note that Book V begins with an interruption from the long dormant Polemarchus. While Socrates begins to discuss the various kinds of constitutions (and corresponding souls), Polemarchus and Adeimantus demand that Socrates instead elaborate on the constitution of the Kallipolis. Socrates is once again pulled off track by the interlocutors; he returns to his original topic in Book VIII. Why are the interlocutors not ready to discuss the varieties of constitutions and souls? Because they have yet to fully grasp the abstract idea of the Kallipolis itself. They have yet to perceive the Good, and are not ready to incorporate concrete examples into the inquiry.
47. If we allocate numbers to the themes -- justice is 1, poetry is 2, the soul is 3, and the state is 4 -- we can clearly model the structural symmetry: 1-2-3-4-5-4-3-2-1. I have yet to discuss the axis of symmetry (the fifth topic), but the astute reader will be able to quickly identify it with the analogies of the Forms in Books VI and VII: the Sun, Divided Line, and Cave.
48. While I already acknowledged that the dialogue begins with a descent, it would in fact be more accurate to claim that it begins with an ascent. For Socrates begins his story after having already left Piraeus, and is walking back, up, to Athens when he is confronted by Polemarchus.
49. Robert Brumbaugh, Platonic Studies of Greek Philosophy, 34.
50. 'Quite literally, the Divided Line divides the dialogue, and what comes after it is illuminated by the vision of the intelligible world and its distinction from the sensible world' -- John Bremar, 'Some arithmetical patterns in Plato's Republic,' 78. Note that the Good (through analogy) is the only theme that does not get the double treatment.
51. Republic, 509d-511e. The Divided Line, from bottom to top: eikasia (imagination), pistis (belief), dianoia (thought), noesis (understanding).
52. More specifically, an upside-down parabola where the vertex is the Good, and the corresponding coordinates (sharing the same Y-axis values, but differing X-axis values) form the ascending and descending curves.
53. James Adam, The Republic of Plato, Edited with Critical Notes, Commentary and Appendices, Vol. II., 71. This passage is from Adam's commentary on the Republic 511b: 'Having grasped this principle [the Forms], it [dialectic] reverses itself and, keeping hold of what follows from it, comes down to a conclusion' (emphasis added).
54. Bradley Lewis, The Seventh Letter and Unity of Plato's Political Philosophy, 245.
55. See Bremar, 'Some arithmetical patterns in Plato's Republic,' 78-82, for a discussion on the 'Golden Section' and the mathematical temperament of Ancient Greece. Also consider 'Plato's Number' -- a 'perfect number' that 'controls better and worse births' (Republic, 546a-e) -- famous for its detailed and complex equation that controls the birthing cycle. This highlights Plato's expectation of mathematical and aesthetic competency in the original audience of the dialogue.
56. Brumbaugh, Platonic Studies of Greek Philosophy, 36. Only when read alongside the constitutions of Book VIII does the construction of the Kallipolis have any meaning; a certain 'holistic completeness' is an integral feature of Platonic philosophy, to isolate one 'part' of the 'whole' is to lose the overall meaning.
57. It has become standard in modern philosophy to taxonomize doctrines according to very specific criteria. The obsession with categorisation began with Aristotle and his rigid identification system. The difference in method of Plato and Aristotle cannot be overstated -- we may be reminded of Samuel Taylor Coleridge's assertion that, 'Every man is born an Aristotelian or a Platonist. I do not think it possible that anyone born an Aristotelian can become a Platonist; and I am sure that no born Platonist can ever change into an Aristotelian. They are two classes of man, beside which it is next to impossible to conceive a third' (Specimens of the Table Talk of the Late Samuel Taylor Coleridge, 125).
58. Brumbaugh, 'A New Interpretation of Plato's Republic,' 668.
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(c) Lukas Clark-Memler 2014
II. 'HEGEL'S DIALECTIC OF THE CONCEPT' BY MARTIN JENKINS
The certain unity or identity of human subjectivity (what humans can know) with the objective nature of reality (with what exists), is in essence, the problematic of that Philosophy termed 'German Idealism'. How can we know that what we think and perceive of the world actually is true? Philosophers such as Immanuel Kant, Johann Gottleib Fichte and Frederick Wilhelm Joseph von Schelling were the foremost thinkers of this Philosophy -- each having their own take on the matter. This paper will concern itself with the German Idealism of George Wilhelm Friedrich Hegel (1770-1831) and in particular, his use of Dialectic.
For Hegel, the world 'out there', of tables, houses, mountains, political states and societies, standing beyond the individual human or Subject (as it will now be referred to), is constituted by Reason, Mind, God or what amounts to the same: living Thought (Geist). The thought of human beings gradually and historically recognises that the Rational nature of this 'other world' is in fact, itself and that it itself is also, that 'other world'. This movement of Geist eventually heralds an historically cumulative reconciliation between human subjectivity and the objectivity of the world/ universe in what Hegel terms 'the Absolute Idea'.
This Absolute Idealism differs from the Subjective Idealism of Kant and Fichte in that the latter proposes that the Subject creates or posits the world it perceives whereas the former maintains that the Subject is, by means of a dialectic process merely reconciling itself with an objective world of Reason it has already, unknowingly created yet become estranged from. Hence knowledge has a sounder epistemological and ontological basis with Absolute Idealism.
Understanding and Logic
Hegel made a distinction between Understanding and Reason. Understanding, as it tries to comprehend the world, remains restricted to the binary categories of the Laws of Logic. Consequently, a thing must be what it is and nothing else (Identity), it is either hot or cold (Excluded Middle) and it cannot be true that it is both night and day (Non-Contradiction). For Hegel, this approach cannot and does not account for the nature of reality and for the nature of things; for things change, things become different. Therefore, the rigid dichotomies of the Understanding cannot cognise that being or what is, is also becoming. Hence Hegel employs 'Dialectic' in the application of Reason to account for such change.
Hegel writes that Dialectic has three constitutive moments:
- The Abstract or that of the Understanding
- The Dialectical or Negative Reason
- The Speculative or Positive Reason
As written, the Understanding is limited to cognising binary oppositions, to categories of either/or. The related or second term of a pair is in fact connected and not excluded with the antecedent. For example in The Encyclopaedia of the Philosophical Sciences: Logic (hereafter named Shorter Logic), Hegel famously begins with Being.
Being, Nothing, Becoming
Being is fundamental to everything, it is, what is. Further examination by dialectical or Negative Reason of the nature of Being reveals that as it is so abstract, it is the negative of anything determinate. So it is also Nothing. Whereas Understanding would cognize an outright and mutual opposition between the two terms Being and Nothing and leave the matter thus, Dialectical or Positive Reason sees a connection between the two. As written, Being is so abstract, so indeterminate, it is essentially Nothing; Being is Nothing and Nothing is Being. This interpenetration between the two is mediation or movement or Becoming. The moment of Speculative or Positive Reason in the movement of Dialectic extracts what is common to both terms and creates a higher unity: Becoming. Importantly, this movement is for Hegel, both progressive and cumulative.
Essence: Identity, Difference, Ground
Similarly in the Doctrine of Essence of the Shorter Logic, Hegel examines the essence or nature of things beginning by analysing the immediate -- Identity-in-itself. As we have seen, this, in the traditional logic employed by the Understanding, is the Law of Identity. A thing such as a table is what it is and nothing else; the colour black is immediately black in itself and nothing else. Yet Identity presupposes difference -- that which is not identical with the term. In both cases, something is different from the term, different from itself. The immediate thing is therefore related to some other thing. This is flagged up by Negative or Speculative Reason as difference, other or Negation. Negation is self-repulsion, linked to Identity in the same way as positive is linked to negative, Debt is linked to the Creditor, Black is linked to white and so on. So one term actually requires another: its Negation to be what it is. In sum, the Identity of a thing does not exist in splendid isolation, a things Identity is constructed by what it is not as much as what it is. Determinatio est Negatio. As seen above, the process does not cease with Negative Reason; through mediation both terms become a positive unity. Speculative or Positive Reason furnishes this unity or as Hegel calls it, Ground (Grund). He writes:
That is, either of these two (Positive and Negative) is
stamped with a characteristic of its own only in relation
to the other: the one is only reflected into itself as it
is reflected into the other. And so with the other, Either
is, in this way, the other's own other.
In Hegel's terminology, the 'in-itself' of Identity is possible only through reflection reflecting upon another,' for-another' -- its negation or opposite. Both terms intermediate. By this very movement of dialectic, a term knows what it is with greater clarity. Consider in-itself as me, looking in a mirror. I reflect upon myself, which is also not myself -- so for and through the mediation of another, I perceive what I physically look like: the In-Itself becomes for-itself through another. The Ground is thus the intermediation of reflection-in-itself which is simultaneously reflection-into-another. As CLR James wrote:
The Essence is the fact that something continually becomes
something else and negates it because it isn't what the
thing that is becoming, wants to be.
Again, this movement is subject to the Negative and its Dialectical mediation onto a higher Positive unity. Inherent to this dialectic is contradiction.
Returning to the aspect of Negative Reason as mentioned above, this time intermediation in positive unity between the In-Itself and For-Itself or Ground announces contradiction:
The proximate result of opposition (when realised as
contradiction) is the Ground, which contains Identity as
well as difference...
The Ground is the site of a dialectical process between the in-itself and the for-another motivated by contradiction. Here, Negative Reason is overcome or superseded and preserved (aufgehoben) by Positive Reason. This movement is a process, a dialectical process that is progressive and cumulative. Progressive as the movement overcoming contradictions ultimately contributes to the end goal of Absolute Knowing; cumulative in that each contradiction overcome contributes to and is an essential part of the larger process-like individual bricks contributing to the whole structure. The lesson of the Doctrine of Essence is that What is -- Being -- proceeds to its fullest reality from out of itself by means of its other, by reflection upon that other, by means of overcoming contradiction with that other. Why, in the process of dialectic, does the moment of Negative Reason need to be superseded by the higher one of Positive Reason? The answer is found with Hegel's theory of the Concept, Notion or Idea (Begriff).
The Concept is the immanent, organising and driving force behind the architecture of the universe, of reality. It underlies all processes of thought. It is not merely a category of thought but the fundamental, dynamic law behind reality, the architectonic. Through progressive stages of dialectic leading to the Absolute Idea, the realisation of the Concept is realisation of everything: the identity of human subjective thought with itself in its other or objectivity; the overcoming of all contradiction. This movement is at the same time also referred to as the progress of Geist.
Consider the Concept as the blueprint which guides and informs the construction of a building; each stage in construction is a realisation of a stage of the Concept. The completion of the whole building is the adequate realisation of the Concept with itself i.e. the Absolute Idea. The in-itself of the blueprint has informed a building which as for-another, now stands before me. The moment of Negative Reason is human consciousness' understanding of the inadequacy of the Concept at a particular moment in its realisation. As seen already, this contradiction between the Concept and itself in its otherness is overcome (aufgehoben) by means of Positive Reason: the operation of Dialectic. These are no mere categories of human thought as the Concept is the ontological and dynamic force behind all reality. Hence the central problematic of German Idealist Philosophy -- the relation between human subjective knowledge and the nature of reality -- is realised and finds its solution in the successive fulfilment of stages of the Concept and its culmination in the Absolute Idea:
The Idea is in short, what contains all the earlier
categories of thought merged in it. It certainly is a form
but an infinite and creative form which includes but at the
same time releases from itself, the fullness of all
The dynamic driving this is the realisation of the Concept by means of dialectic.
The Idea is itself dialectic which forever divides and
distinguishes the self-identical from the differentiated,
the subjective from the objective, the finite from the
infinite, soul from body. Only on these terms is it an
eternal creation, eternal vitality, eternal spirit. But
while it passes or translates itself into the abstract into
the understanding, it remains forever Reason. The Idea is
dialectic which makes the mass of understanding and
diversity understand its finite nature and the
pseudo-independence of productions which brings the
diversity back to unity.
So in the Shorter Logic, we begin with the Doctrine of Being. This begins from the most abstract sense of Being and ends with Determinate Being -- i.e. a thing, an object and similar.
A Determinate Being becomes, in the Doctrine of Essence, self-Identity. Here, a thing is shown to actually exist in its non-identity, involving an otherness, as highlighted by Negative Reason. This otherness of the thing is overcome and incorporated (aufgehoben) by Positive Reason thereby augmenting what the thing is in a higher, more advanced unity until this process of dialectic begins anew. In the Doctrine of the Concept, the process of dialectic is shown to occur with the parameters of the Concept. The Concept strives to be fully adequate or identical with itself, the end state of Absolute Knowledge being the cumulative overcoming of all stages of inadequacy by dialectic reaching full adequacy or total Identity of the Concept with itself.
The dialectic of the Concept toward Absolute Knowledge is teleological. In essence, the process is one of the Concept, from beginning to end, overcoming its own externalisations, incorporating them into a higher unity ultimately ending in the Absolute Knowledge of itself. This knowing of itself by itself is for Hegel, human finite knowledge of infinite Living Thought or God, God understood by Hegel as the living Concept of what exists.
1. Immanuel Kant (1724-1804)
Johan Gotleib Fichte (1762-1814)
Frederick Wilhelm Joseph von Schelling (1775-1854).
2. The practice and philosophical perspective of Dialectic can be traced back to ancient Greece. Essentially, in for example a discussion the subject matter develops through interaction with its opposite, through criticism and from out of this emerges common ground, a conclusion or a new thesis. German Idealists used dialectic to account for the development of the human mind in its construction and understanding of reality, a task they felt philosophical materialism was unable to perform.
3. #96 GWF Hegel. Encyclopaedia of the Philosophical Sciences. Part One: Logic. (Shorter Logic) Oxford University Press 1975.
4. Doctrine of Being. Opus cite above.
5. In a letter written in 1674 discussing figures in space, Spinoza argued they are determined, limited by negation, hence et determination negation est: Determination is Negation. This insight becomes integral to Hegel's dialectic. See Chapter 10 Eckart Forster and Yitzhak Y. Melamed Spinoza and German Idealism. Cambridge University Press 2012.
6. #119 Shorter Logic op cite above.
8. In the rest of the Doctrine of Essence, we see the dialectical movement of the moments of In-itself and for-another becoming the stages of Ground and Existence, Existences and Things, Things and Matters, Matters and Form, cumulating in Form and Content of the Appearances of things. From here we have the dialectical movement between the Phenomenal and Appearance, Content and Form, Relation and Correlation, Form and the Expression of Form, the Inward and Outward nature of things developing into Actuality.
9. #119 Shorter Logic op cite above.
10. Mike Marchetti The Concept. http:--- proposes the origins of Hegel's Concept is found in Aristotle's attempt to understand the nature of things. Dunamis (potentiality or Matter) mediates with Energeia (Actuality or Form) by means of Entelechia (inner purpose or teleology) so an object can become what it is.
11. #160. Ibid.
12. #213. Ibid.
13. This conclusion became contentious with the followers of Hegel. It gave the impetus for the developments of Old, Young, Right and Left Hegelian tendencies. Old or Right Hegelians generally maintained Hegel's conclusions in the interests of religious and political conservatism. Young and Left Hegelians interpreted Hegel in a liberal, Humanistic, individualist and materialistic direction; the most notable being David Strauss, Ludwig Feuerbach, Max Stirner and Karl Marx respectively.
(c) Martin Jenkins 2014
III. 'THE CONTINUUM EAST AND WEST' BY PETER JONES
This essay examines the relationship between mysticism, for which Buddhism's Middle Way doctrine would serve here as a defining example, and what, for want of better word, we call 'Western' philosophy. This is an issue of general interest to philosophers, since sooner or later in our investigations we must all decide whether the 'Western' kind of philosophy makes more or less sense to us than the 'Eastern' kind.
One obstacle we face in trying to make this decision is the difficulty of discerning clearly the defining characteristics of the two philosophies, those features that lead us to make such a final and definite distinction between them in the first place. We commonly speak of 'Eastern' and 'Western' philosophy, but are not so commonly able to say quite what we mean by this. The relevant issues are profound, mind-bending and probably inexhaustible. They need not be complicated, and they are often quite simple, but they are always immensely challenging.
One of these simple (stripped of the details) yet challenging issues would be the true nature of the continuum. The discussion that follows outlines the view of physicist, mathematician and philosopher Hermann Weyl. Weyl makes a careful distinction between the 'arithmetical' continuum, the continuum conceived of as an extended object, as it must be for the real numbers and space-time, and the 'intuitive' continuum, the empirical continuum of experience, which is not extended, and he demonstrates that when we set out to define what we mean by 'Eastern' and 'Western' philosophy, the foundations of analysis would be a good place to start. The interconnectedness of all the relevant issues at a foundational level, for all roads lead to Rome, means that we may as well start where we like, but mathematics takes us immediately to what might be the most clearly discernable and easily described difference between the two philosophies and worldviews, perhaps also the most general and profound, namely their entirely different conceptions of the continuum.
As there is just one source for each author quoted here I have not added numbered references but just tried to make it clear who is talking. Italics are always original.
In The Continuum: A Critical Examination of the Foundations of Analysis, Hermann Weyl points out that the extended space-time of physics and ordinary perception is, in the same way as the number line, a construction of reason and not intuitively or empirically given. He addresses a problem that arises in different guises but with an equal vengeance in religion, physics, mathematics and metaphysics. It is the problem of modelling a continuum as an extended series of discrete locations or 'things', as we do must do for the number line, geometry and arithmetic, space and time, and even for our very concept of the continuum, when a series of discrete locations or 'things' is exactly and precisely what a continuum is not.
A continuum cannot be extended as a series of points or moments for the reasons Weyl gives below, and yet it must be in order for anything to be extended in space and time. This causes a problem in philosophy. It would be a 'first-order' metaphysical problem or 'antinomy', a straight choice between two ideas neither of which work. It would be closely connected with the question of how many angels can dance on the head of a pin, of how small we can make an angel before it becomes the 'ghost of a departed quantity'. The various problems and paradoxes to which the intellectually-constructed continuum of the arithmetical line gives rise has no impact on the usefulness of mathematics, which is wholly dependent on this conception, but it indicates that the continuum of space-time is not an equivalent case and is, rather, a true continuum. As such, it would not be a set of locations but a unity. A unity has no parts. This would suggest that space and time are conceptual imputations and that Reality, whatever is truly and independently-real amongst all the smoke and mirrors, is not in fact extended. This is a difficult idea but not a new one, and it is widely popular in religion. When theoretical physicists say 'distance is arbitrary', perhaps they are suggesting something similar. It might at least help to explain how a Big Bang can appear to have occurred before there is, was or ever will be a time or a place for it to have happened. For an ultimate view it would not have happened. If the continuum cannot have parts then all co-ordinate systems are emergent.
Here is Tobias Dantzig, Einstein's favourite mathematician, introducing the issues:
Herein I see the genesis of the conflict between
geometrical intuition, from which our physical concepts
derive, and the logic of arithmetic. The harmony of the
universe knows only one musical form -- the legato; while
the symphony of numbers knows only its opposite, -- the
staccato. All attempts to reconcile this discrepancy are
based on the hope that an accelerated staccato may appear
to our senses as legato. Yet our intellect will always
brand such attempts as deceptions and reject such theories
as an insult, as a metaphysics that purports to explain
away a concept by resolving it into its opposite.
While a series of points serves perfectly well for the continuum of the number line and arithmetic, on examination it is a paradoxical idea that must be rejected in both metaphysics and physics as a model of space-time. The continuum of physics is, at this time, extended as a series of points and moments, and as such no sense can be made of it. Viewed as a real phenomenon a continuum so-defined would either be paradoxical or fail to qualify for the name. We have every right to define the continuum for mathematics as we currently do, and if our idea is paradoxical then it is only a problem when we investigate the foundations of analysis. When we define the continuum for mathematics we are not making a claim about the nature of Reality. Elsewhere it would be a different matter. In metaphysics we certainly cannot adopt a priori an arithmetical definition of the continuum. Insofar as it relates to metaphysics this might be the central message of Weyl's book. At the same time, physics and ordinary perception are heavily theory-laden, dangerously so. Our usual everyday theory is that time and space are extended in just the same way as is the number line, such that space- and time-points can be represented as locations in an extended co-ordinate system. But is there any evidence that space and time are extended objects? What is it that our wristwatch is actually measuring? Are we quite sure that our usual theory of extension, for which space-time would be a 'classical' or Newtonian phenomenon, is fundamentally correct? Is it a metaphysical conjecture, a testable scientific theory, something we know from experience or a highly evolved misinterpretation? For our Western tradition of philosophy this would be a famously undecidable problem. Here the continuum appears to be paradoxical, for it cannot be extended ex hypothesis, and yet, by some magic, it is. Or it seems to be. For the Eastern tradition this everyday theory of space-time would be testable and it would fail the tests, being refutable in logic and falsifiable in experience. The continuum would be a unity, just as its name implies.
Weyl reduces the conceptually extended continuum of mathematics and traditional physics to what he calls the 'true' or 'intuitive' continuum, where the latter is carefully distinguished from the former. The intuitive continuum, the continuum as we experience it, is not extended as a series of moments or points. We do not experience time and space as consisting of moments and points, or, if we do, it is only ever the same moment and point. We are always here and now. What is more, there is actually something very odd about the idea that space and time are 'grainy' in this way. The length of ten thousand points would be equal to the length of one point, for a start, so no amount of points would be sufficient to construct basic geometry, let alone a piano. In the same way, no amount of moments would be sufficient to account for motion and change. Space and time are explanatory theories, Weyl proposes, generated by reason and imagination, not empirical phenomena.
For an orthodox view of space-time here is a passage from Wikipedia from the entry for Hermann Minkowsky:
This new reality was that space and time, as physical
constructs, have to be combined into a new
mathematical/ physical entity called 'space-time', because
the equations of relativity show that both the space and
time coordinates of any event must get mixed together by
the mathematics, in order to accurately describe what we
see. Because space consists of 3 dimensions, and time is
1-dimensional, space-time must, therefore, be a
4-dimensional object. It is believed to be a 'continuum'
because so far as we know, there are no missing points in
space or instants in time, and both can be subdivided
without any apparent limit in size or duration. So,
physicists now routinely consider our world to be embedded
in this 4-dimensional Space-Time continuum, and all events,
places, moments in history, actions and so on are described
in terms of their location in Space-Time.
Dantzig explores the origins of this co-ordinate system:
The notion of equal-greater-less precedes the number
concept. We learn to compare before we lean to evaluate.
Arithmetic does not begin with numbers; it begins with
criteria. Having learnt to apply these criteria of
equal-greater-less, man's next step was to devise models
for each type of plurality. These models are deposited in
his memory very much as the standard meter is deposited at
the Bureau of Longitudes in Paris. One, two, three, four,
five...; we could just as well have said: I, wings,
clover, legs, hand... and, for all we know, the latter
preceded our present form.
He goes on to observe that the staccato of the numbers is not empirical or intuitive, but a superimposition.
It is possible to assign to any point on a line a unique
real number, and, conversely, any real number can be
represented in a unique manner by a point on the line.
This is the famous Dedekind-Cantor axiom. This proposition,
by sanctifying the tacit assumption on which analytical
geometry had operated for over two hundred years, became
the fundamental axiom of this discipline. It defines a new
mathematical being, the arithmetical line. Henceforth the
line -- and consequently the plane, and space -- ceases to be
an intuitive notion and is reduced to being a mere carrier
In the following passage Dantzig notes the paradoxical nature of the arithmetical line. This matters little in mathematics, but when the arithmetical line is taken to be a model of the true continuum it renders Reality paradoxical and causes philosophical havoc, in particular a deep rift between two quite different traditions of philosophy:
The axiom of Dedekind -- 'if all points of a straight line
fall into two classes, such that every point of the first
class lies to the left of any point of the second class,
then there exists one and only one point which produces
this division of all points into two classes, this severing
of the straight line into two portions' -- this axiom is just
a skilful paraphrase of the fundamental property we
attribute to time. Our intuition permits us, by an act of
the mind, to sever all time into the two classes, the past
and the future, which are mutually exclusive and yet
together comprise all of time, eternity: The now is the
partition which separates all the past from all the future;
any instant of the past was once a now, any instant of the
future will be a now anon, and so any instant may itself
act as such a partition. To be sure, of the past we know
only disparate instants, yet, by an act of the mind we fill
out the gaps; we conceive that between any two instants -- no
matter how closely these may be associated in our memory -
there were other instants, and we postulate the same
compactness for the future. This is what we mean by the
flow of time.
Furthermore, paradoxical though this may seem, the present
is truly irrational in the Dedekind sense of the word, for
while it acts as partition it is neither a part of the past
nor a part of the future. Indeed, in an arithmetic based on
pure time, if such an arithmetic was at all possible, it is
the irrational which would be taken as a matter of course,
while all the painstaking efforts of our logic would be
directed toward establishing the existence of rational
In other words, the Dedekind sense of the word 'present' is irrational. Space-time cannot have the properties he assigns to the number line unless the Cosmos is irrational. This is the problem addressed by Weyl. He deals with it by making a clear distinction between the intuitive or experienced continuum, the intuition of the continuum that for all of us is an empirical phenomenon, and the intellectually constructed faux-continuum of Dedekind's arithmetical line. They could hardly be more different:
To the criticism that the intuition of the continuum in no
way contains those logical principles on which we must rely
for the exact definition of the concept 'real number,' we
respond that the conceptual world of mathematics is so
foreign to what the intuitive continuum presents to us that
the demand for coincidence between the two must be dismissed
He points out that the usefulness of the arithmetical line has no bearing on its plausibility as a model of the space-time continuum:
Whichever view of the relation of mathematics to nature one
takes, there is no independent physical conception of the
continuum on offer in all this, since all the mathematics
is filtered through the real number system (or Hilbertian
geometry as a surrogate). Moreover, I don't see that any
argument can be made from the enormously successful
applications of mathematics in natural science to the
conclusion that one or another of the mathematical
conceptions of the continuum surveyed above is uniquely
singled out as the 'real one'. In any case, the work on the
reach of predicative mathematics cited at the end of the
preceding section shows that the properties of the
continuum needed for its applications in natural science do
not require it to have a definite reality in the platonistic
Here is extract from an essay on Weyl and the continuum by John Bell:
...Weyl regards the experienced continuous flow of
phenomenal time as constituting an insuperable barrier to
the whole enterprise of representing this continuum in
terms of individual points, and even to the
characterization of 'individual temporal point' itself. As
'The view of a flow consisting of points and, therefore,
also dissolving into points turns out to be mistaken:
precisely what eludes us is the nature of the continuity,
the flowing from point to point; in other words, the secret
of how the continually enduring present can continually slip
away into the receding past.
Each one of us, at every moment, directly experiences the
true character of this temporal continuity. But, because of
the genuine primitiveness of phenomenal time, we cannot put
our experiences into words. So we shall content ourselves
with the following description. What I am conscious of is
for me both a being-now and, in its essence, something
which, with its temporal position, slips away. In this way
there arises the persisting factual extent, something ever
new which endures and changes in consciousness.'
We see here that an examination of the foundations of analysis leads us immediately into the realms of psychology, physics, metaphysics, religion, consciousness studies and more. Bell continues:
Weyl sums up what he thinks can be affirmed about
'objectively presented time' -- by which I take it he means
'phenomenal time described in an objective manner' -- in the
following two assertions, which he claims apply equally,
mutatis mutandis, to every intuitively given continuum, in
particular, to the continuum of spatial extension:
1. An individual point in it is non-independent, i.e., is
pure nothingness when taken by itself, and exists only as a
'point of transition' (which, of course, can in no way be
2. It is due to the essence of time (and not to contingent
imperfections in our medium) that a fixed temporal point
cannot be exhibited in any way, that always only an
approximate, never an exact determination is possible.
The fact that single points in a true continuum 'cannot be
exhibited' arises, Weyl continues, from the fact that they
are not genuine individuals and so cannot be characterized
by their properties. In the physical world they are never
defined absolutely, but only in terms of a coordinate
system, which, in an arresting metaphor, Weyl describes as
'the unavoidable residue of the eradication of the ego.'
In particular, he found compelling the fact that the
Brouwerian continuum is not the union of two disjoint
nonempty parts-that it is, in a word, indecomposable. 'A
genuine continuum,' Weyl says, 'cannot be divided into
separate fragments.' In later publications he expresses
this more colourfully by quoting Anaxagoras to the effect
that a continuum 'defies the chopping off of its parts with
Weyl's book on the continuum delves little further into metaphysical issues than is necessary for his examination of analysis. Elsewhere he says more, and we find a clear connection between his mathematico-philosophical views and Buddhism's theory of emptiness and doctrine of dependent origination. As far as it goes his book on the continuum could be read as a mathematical explanation of the universe of the perennial philosophy, and of how it differs from that of the Western tradition in at least one vital respect. Bell makes the correlation clear.
In The Open World (1932), Weyl provides an eloquent formulation of his philosophical outlook, which quickly moves beyond its initial echoes of Schopenhauer:
The beginning of all philosophical thought is the
realization that the perceptual world is but an image, a
vision, a phenomenon of our consciousness; our
consciousness does not directly grasp a transcendental real
world which is as it appears. The tension between subject
and object is no doubt reflected in our conscious acts, for
example, in sense perceptions. Nevertheless, from the purely
epistemological point of view, no objection can be made to a
phenomenalism which would like to limit science to the
description of what is 'immediately given to
consciousness'. The postulation of the real ego, of the
thou and of the world, is a metaphysical matter, not
judgment, but an act of acknowledgment and belief.
But this belief is after all the soul of all knowledge. It
was an error of idealism to assume that the phenomena of
consciousness guarantee the reality of the ego in an
essentially different and somehow more certain way than the
reality of the external world; in the transition from
consciousness to reality the ego, the thou and the world
rise into existence indissolubly connected and, as it were,
at one stroke.
Any comparison of 'Eastern' and 'Western' approaches to philosophy must eventually end up here, examining the question of whether the continuum of space-time is arithmetical and paradoxical, or whether it would make more sense to say that spatio-temporal extension is an interpretation of appearances, a relationship between appearances, and not an empirical or even truly real phenomenon. Whichever way we decide this question, an examination of these issues will reveal a clear and crucial difference of opinion between East and West over the ultimate nature of Reality.
It is absurdly misleading to use the words 'Western' and 'Eastern' to describe two philosophical camps, and really it is dualism and nondualism that we are comparing here, both of which appear all over the world. Whatever words we use, mathematics can help us to pin down our definitions in important respects.
Weyl summarises his view as follows:
The category of the natural numbers can supply the
foundation of a mathematical discipline. But perhaps the
continuum cannot, since it fails to satisfy the
requirements [mentioned in Chapter1]: as basic a notion as
that of the point in the continuum lacks the required
support in intuition. It is to the credit of Bergson's
philosophy to have pointed out forcefully this deep
division between the world of mathematical concepts and the
immediately experienced continuity of phenomenal time.
The view of a flow consisting of points and, therefore,
also dissolving into points turns out to be false.
Precisely what eludes us is the nature of the continuity,
the flowing from point to point; in other words, the secret
of how the continually enduring present can continually slip
away into the receding past...
...When our experience has turned into a real process in a
real world and our phenomenal time has spread itself out
over this world and assumed a cosmic dimension, we are not
satisfied with replacing the continuum by the exact concept
of the real numbers, in spite of the essential and
undeniable inexactness arising from what is given. For, as
always, there is more at work here than heavy-handed
schematizing or cognitive economizing devised for
fulfilling our practical tasks and objectives. Here we
discover genuine reason which lays bare the 'Logos'
dwelling in reality (just as purely as is possible for this
consciousness which cannot 'leap over its own shadow'). But
to discuss this further cannot be our business here.
Certainly, the intuitive and the mathematical continuum do
not coincide; a deep chasm is fixed between them...
...The reflections contained in this section are, of
course, only a slightly illuminating surrogate for a
genuine philosophy of the continuum. But since no
penetrating treatment of this topic is at hand and since
our task is mathematical rather than epistemological, the
matter can rest there.
For a book on analysis it would have been inappropriate for Weyl to say more about this. If we are examining the pivotal questions on which Eastern and Western philosophies are divided, however, then the matter cannot rest here. The former philosophy makes a claim about the continuum that is denied point-blank by the latter. It may still be true that 'no penetrating treatment of this topic is at hand', at least outside of the 'mystical' literature, but this would not reflect on the importance of this topic across all of philosophy, and it need not prevent us from forming a view on which of these two philosophical approaches gives the most plausible description of space and time.
Is space-time extended or is it a continuum? Weyl suggests that we cannot have it both ways. Nagarjuna's Middle Way Buddhism, which is infuriatingly stubborn when it comes to endorsing extreme views on any topic, would say that the question is not quite answerable in this straightforward form. There would be a sense in which it is neither and a sense in which it is both. There is not a straightforward disagreement between East and West on the answer to this question, therefore, with the two sides adopting equal and opposite views. All the same, it seems true to say that the very different answers they give to this question reveal one of the most crucial and far-reaching differences between these two traditions of philosophical thought.
Bell, John L, 'Hermann Weyl on intuition and the continuum'. http:---
Dantzig, Tobias, Number -- The Language of Science, (Pearson Education 2005 (1930)
Weyl, Hermann, The Continuum: A Critical Examination of the Foundations of Analysis, Dover (1987)
(c) Peter Jones 2014
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