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P H I L O S O P H Y   P A T H W A Y S                   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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IV. New PhiloSophos philosophy search engine



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

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.

Peter Jones

Email: peterjones2345@btinternet.com

About the editor:



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

  - Olympiodorus, Commentary on the First Alcibiades of Plato[1]

'Nothing is accidental in a Platonic dialogue; everything is
necessary at the place where it occurs.'

  - Leo Strauss, The City and Man[2]


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.'[3] 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.'[4]

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'[5] 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.'[6] 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,[7] 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.[8] 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.'[9] And it respects
Plato's great premeditation in composing the dialogue.[10]


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.'[11] Indeed the rigid autocracy and propagandistic
indoctrination of the Republic were echoed in the dictatorial regimes
of Hitler and Stalin.[12] 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.'[13]
Yet neither Popper nor Crossman consider the fact that the political
proposals of the Republic are insincere and should not be taken

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.[14] This school of thought
contends that Plato abandoned the Kallipolis in favour of
Magnesia:[15] the more refined, albeit pessimistic, constitution of
the Laws. To explain the doctrinal development, scholars point to the
downfall of Sparta,[16] 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.'[17] 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.'[18] 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[19] describes in detail that the best state
will be one of absolute communism: property, family, and honour will
be shared by all citizens.[20] 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.'[21] 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.'[23]
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.'[24] 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?[25] 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.[26] Hegel's claim,
that scholars must 'separate the form... in which Plato has
propounded his ideas... from philosophy as such in him,'[27]
represents the modern error of anachronistic interpretation. Leo
Strauss abjures this variety of analysis and recognizes the
'logographic necessity of every part.'[28] 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'.[29]

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

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,[31] or
the virtuous man teaching by example -- but ultimately ends up in
aporia.[32] Meno is an excellent example of Socratic elenchus at
work, but 'Meno's Paradox'[33] 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,[34]
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

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.'[35] 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.[36] His brief character arc is itself a model of justice.
Through engaging in philosophical discussion, Thrasymachus becomes
more reasonable and restrained.[37] 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.'[38]

Similar results hold for the other characters of the Republic. While
we are explicitly informed that the 'city is the soul writ
large,'[39] 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[40] -- 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.[41]

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.[42]

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

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,'[44] 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.'[45] Book V is wholly concerned
with detailing the constitution of the Kallipolis,[46] 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.[47] 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:[48]
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

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.[50]

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[51] -- 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.[52] In the words of classicist James Adam,
'The dialectician's progress involves both an ascent and a

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.'[54]

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[55] 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

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.[57] 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.'[58]

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

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.

27. Ibid.

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

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

51. Republic, 509d-511e. The Divided Line, from bottom to top:
eikasia (imagination), pistis (belief), dianoia (thought), noesis

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

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.


Adam, James. The Republic of Plato, Edited with Critical Notes,
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Bobonich, Christopher. Plato's Utopia Recast. Oxford: Oxford
University Press,2002. 

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available: http://plato.stanford.edu/entries/plato-utopia/
[accessed 10 September 2012]. 

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Journal of Philosophy 64, no. 20 (1967): 661-670. 

------. Platonic Studies of Greek Philosophy: Form, Arts, Gadgets,
and Hemlock. Albany, NY: SUNY Press, 1989. 

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Samuel Taylor Coleridge. New York: Harper,1835. 

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California Press, 1951. 

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------. 'Taking the longer road : The Irony of Plato's Republic
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A Critical Guide,ed. Christopher Bobonich, 51-70. Cambridge:
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G. M. A. Grube,
2nd ed. Indianapolis: Hackett, 2002. 

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(c) Lukas Clark-Memler 2014

Email: lukasclarkmemler@gmail.com



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.[1]
This paper will concern itself with the German Idealism of George
Wilhelm Friedrich Hegel (1770-1831) and in particular, his use of

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

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[3]

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.[4]

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.[5] 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.[6]
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.[7]
Again, this movement is subject to the Negative and its Dialectical
mediation onto a higher Positive unity. Inherent to this dialectic is


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...[9]

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

The Concept is the immanent, organising and driving force behind the
architecture of the universe, of reality. It underlies all processes
of thought.[10] 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.[12]

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.

In Conclusion

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.[13]


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.

7. http://www.marxists.org/archive/James-clr/works/dialecti/James.htm

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://www.GWKHegel.org Marchetti
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

E-mail: martinllowarch.jenkins@virgin.net



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
     of numbers.

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

     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
     as absurd.

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
     he says,
     '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
     understood mathematically);
     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
     a hatchet.'

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'.

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

Email: peterjones2345@btinternet.com




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