By using logic I'm pretty sure he could. For example holsing the sphere his hand would from to the sphere whereas holding the cude his band would stay flat. So knowig how he would form his hands to the shape he could use that to decide
I think the question revolves around would he recognize flat and round intuitively. He has a concept in his mind of what flat and round are but no experience with the visual representations of it. Kind of like if you could hear colors all of a sudden would you know what blue and red sound like without anyone telling you which was which.
But for colors you can only see them. There is no way to really describe them without percieving them. But for shapes if he could feel them. He could also understand the characteristics of them and be able to mentally differentiate them. I feel like the comparison to colors in this example wouldnt be right.
This question was actually answered when medical science advanced enough to give some people, who were born blind, the ability to see. The answer is no, they are not able to tell by sight which object is which the first time they are presented with the question.
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