¿What would be Nietzsche opinion on the allegory of the cavern? I am specifically thinking what would Nietzsche philosophy say about the prisoners escape. Would he see anything at all? Is there any reality at all? Was the cave's fiction worst than the fiction outside?
I think Nietzsche would say that the prisoners have exchanged one illusion (life inside the cave or prison) for yet another prison: the forms, I should say fixed forms, which are a new type of imprisonment. Yes, the forms give comfort,and give a fixity as we may see in mathematics, but I believe it is Levinas who has suggested that an ontology is also a power play. Vattimo suggests metaphysics is even violence. Nietzsche overthrows metaphysics, and he asks mankind: can you handle this freedom?
And there is indeed a price to pay. No therapy is without side effects. So both Plato and Confucius might say in response to Nietzsche: for God's sake, and for the sake of all order and stability, rectify the names!! Those who hold the power of saying what reality "is", why they hold everything in their hands, no?
Nietzsche will have none of this, he asks us to give up our illusions of the "is" of the "forms", the "truth", he asks us to throw off the chains of "facts", which under him become only interpretations. So this is a lot of freedom to deal with, and we are far from resolving these issues.
Having read some of Friedrich Nietzsche's philosophical works, as well as the acclaimed biography of Nietzsche by Curtis Cate (which I suggest all those who are interested in Nietzsche should read), I understand that Nietzsche did not view Plato and his philosophy favorably, specifically, the Platonic ideal, and the notion of otherworldly truth and knowledge. Whether or not there is any record of Nietzsche's specific opinion on the allegory, I am unaware of, but I shall still try to opine on the matter. Given his scrutiny of Plato however, I'm inclined to believe it is somewhere out there.
I conjecture that the element of the story that Nietzsche would most approve of is the particular man's escape from the cave, and his venturing out into the 'real' world, out beyond the confines of the cave. Allegorically and in a Nietzschean spirit, the primitive and suffocating cave, and its residents, could represent the mediocrity of the prevailing intellectual and moral system, which would rather continue a fixation with mere reflections of 'reality' than attempt a constructive investigation of ethics and reality. My current understanding of Nietzsche lends me to the belief that this man, who has escaped the mirages and projections of what is real, would posses the opportunity of truly escaping "the herd" that resides within the cave, a term Nietzsche usually uses to describe the prevailing morality of the masses, influenced by Christian dogma as well as ossified by historical inertia. Thus, this lone man (the primordial Übermensch perhaps?), who has escaped (by chance, if I remember the allegory correctly), has triumphed over the rest in his opportunity to grasp the world as it really is. The interesting literary and situational parallels to Zarathustra are many to be considered.
As to whether there was anything 'real' outside of the cave, I believe that Nietzsche would not deny a physical reality 'of the way things are' outside of the projections and pretenses of conventional morality, and how morality influences the worldview. After all, he believed very much so, based upon what I can gather from On the Genealogy of Morality, that science during his time was one of the factors that contributed to the abandonment of traditional knowledge and virtues, so much so that he may have feared its unintended or insidious contribution to cultural nihilism. At any rate, Nietzsche did now infamously quote "there are no facts, merely interpretations", or something to that effect, though there is a greater context to that statement within The Genealogy. Still, Nietzsche was not anti-science, and within the understanding of the allegory, the man's escape from projection and duplicity towards reality and empiricism (after all, he relied upon his senses to absorb and intake the real, outside world) would be consistent with Nietzsche's urging of 'self-overcoming', which is another related concept.
I think Nietzsche's philosophy applies more to group morality - the allegory of the cave is more a picture of individual "enlightenment", perhaps, than group morality, though Nietzsche's philosophy does seem to me to appeal to the category of the individual against group morality, so maybe the allegory does apply to Nietzsche's thinking, too, in that sense. However, the allegory of the cave does not have the same kind of "violence" we could associate with Nietzsche's philosophy, where asserting the independence of the willing self from the normative demands of group morality is a vision enforced through negating the internalised demands of morality through an opposite kind of violence, or "breaking through", by the sheer power of the willing self. In Nietzsche's philosophy, one "is" through "becoming", so what one would "see" through emerging from the cave, is precisely what one is also trying to prove through negating the internal demandingness of group morality - that is, one's own ability to reverse the process of internalising group morality, through purposely or physically expressing one's hatred of its impositions on the willing self. I don't endorse this interpretation of "group morality" (I think his target was Christianity itself), but this is how I see Nietzsche's philosophy relating with the allegory of the cave.