So the metaphor of the Sun is basically stating that by having light that is provided by the Sun you are able to see the truth. This is because the light gives you visibility and this allows you to see the truth. Without the sun their would be darkness and you wouldn't be able to see clearly and the truth wouldn't be visible. This part relates also to the allegory of the Cave. The Sun is also connected to the Good and the Good is science and the truth. The Good is also responsible for all existence but with out the sun the Good wouldn't be apparent. In that way the Good and the Sun both depend on each other and can't exist without the other.
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