Firstly, I must congratulate you for your diligent, disciplined endeavour: you have written a week what most people never manage to force themselves to write down in a month.
Secondly, I must apologise if any of my critiques of the critique sound harsh. I am as guilty of the sins I am about to denounce as you are, if not more. (The Gospel teaching "la paille et la poutre" is somewhat relevant there.)
And now for the comments on the piece itself.
Generally, I found your writing hampered by your reading. In the body-analogy, one could feel Plato cramping up your hand. (Presumably you were thinking of his nous, thymos and epithymia trichotomy.) Most of the critique followed your (admirably, laudably wide) readings, but too closely. The essay as a whole lacked, I feel, personality, individuality. It is best I think, to use your own style rather than the Cartesian or Kantian style - or rather Philosophy doing Philosophy will be superior to Philosophy doing Descartes and Philosophy doing Kant. Use your own voice and ideas, and do not rely on the authorities of others: what you say has as much weight as what Plato says.
There was something about your critique which was strangely hybrid: neither a wholy personal development of idea, nor a close reading of various works. Like your preface, it will strike a reader as a lack of confidence - and why should you, Philosophy, lack confidence? Speak like a king, and not a beggar. You have things to say, say them loudly, shout, say "I, I, I" and hide not from your reader the shape of your thought behind a pile of names.
A second problem I felt was probably due more to the lack of time than anything. Much of your essay has an unprecise quality. As a mathematician for example, I found your mathematical example on the unboundedness of the natural numbers inaccurate or weak. More time I feel should be spent sharpening the edges of your writing, making sure that all is said in an effective manner.
"for they have not seen such, for the idea was proposed, and was declined" is confusing, ineffective.
The head of state as "head" but not "source" of happiness was beautiful and effective
One of my greater faults is my tendency to use too many words. too many adjectives, and I feel in you a fellow sufferer of that disease. Economy of means, and a concern for the necessity of the words one uses are amongst the difficult literary and philosophical virtues most difficult to acquire.
Lastly, and this, perhaps is the greatest problem, the looseness I noted in your words seems to be reflected in your ideas. You use words like "peace, equality, justice" without worrying about what they mean, without helping the reader see what it is you see in them.
Is equality logical equality, equivalence or something else, like an equal dignity as a human being: you are white, I am black. We are not equal, for we have different characteristics. Yet I will look upon you and you on me with the same, equal respect. I will recognise in you a human being, and treat you as being equal in humanity to me... ?
There are also your grand, flamboyant assertions:
"That is to say, in a fantastic society such as this philosophocracy, the idealisms of equality, justice, and liberty are warranted by its reasoning and logical foundations and, therefore, there should be no slave who is unwillingly forced to perform tasks for the philosopher-king. "
How is it warranted? Are you sure equality, justice and liberty are compatible? Why should no slave disobey?
"Reasons in logic shall shine upon the political head of state and gives him the truth of philosophy as a tool for him to govern his people in a phenomenal fashion that which cannot be comprehended by most men"
You have not explained how it shall shine, you have not explained what truth of philosophy you are speaking of: your read feels his is a vulgar mind, like the common man you deride, the man who cannot comprehend.
If I say these things, it is not that I am an ennemy of the ideas you advance. Indeed I have more than some sympathy for some of them (Is my fate not tied to France, that land of utopian exaltation and dreamers?)
It is only that a reader faced with your essay will either not understand your ideas, or not see any justification for them in your writings.
When it comes to the ideas I must mention the fact that you seem to be misreading Aristotle's too famous "man is...", and that your essay suggests a belief in a manichean world of Logic, Truth &Philosophy on the one side, Ignorance & Logical Fallacies on the other. This black/white divide lacks in subtlety. Moreover, your vision of Tao as the way forward (to ataraxia and beyond!) needs more explanation and defense: it is presented as crede, unappealing to the unbeliever.
Finally, your description of utopia lacks somewhat in restraint. You are speaking of what you see as utopia; heaping enthusiasm and adjectives on it will make the reader smile and enjoy this lyrical passage in your essay. However, it has little philosophical worth because of its vagueness. Details are necessary here - your utopia has structure and justifications, it must not be Pepperland. Rather than state how wonderful the utopists are, explain their routine, the way they are educated, what laws they live under... something like Rabelais's description of the Abbey of Thelemes would be optimal.
I do not want however to end on this critical note. I must congratulate you on your fine effort, and on your first production. Some rewriting needs to be done, perhaps, but the writing is there, the will to think and write, and that is precious and praiseworthy.