Glaucon uses the word "Supernaturally" to agree with Socrates' assertion that calculation is one of the subjects that is worthy of seeking on the quest to find truth. Merriam-Webster defines "supernaturally" "as of or relating to an order of existence beyond the visible observable universe". This particular definition applies to the text because Socrates is trying to find a way to move beyond the shadows on the cave wall by utilizing learning in a non-mechanical way. In order do do this, one must enlighten oneself to an understanding that cannot be acheived through vision alone. Normally I think of something being supernatural if it is something that is not currently registered in our minds as evidently beliveable. Glaucon is using it as an adverb to advocate that arithmatic and calculation can be considered methods of acheiving a higher state of living.
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