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Plato's allegory of the cave is a story in the Republic about prisoners who mistake shadows for reality, used to illustrate education and the ascent of the soul toward knowledge.
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Descartes meant that the act of doubting or thinking cannot be doubted. Whenever I think, I must exist. Scholars still debate whether this is an inference or an intuition.
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Nietzsche did not claim a deity had died. He meant that belief in the Christian God had become unbelievable, leaving Europe's morality and values without their foundation.
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