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Mathematician in a vat

Okay, there is an element of satire here, but here goes:

Supposing you think that you have a PhD in mathematics (actually, an ABD will do).  But as a matter of fact, you are really just a brain in a vat being fed electrochemical signals: could it be that all of the mathematical truths you suppose that you know are merely fleeting impressions?  In other words, could it be that you do not really know that 2+2=4, for it merely seems that you do?  What would be the status of your knowledge of laws of nature if knowledge of mathematical truths were not really knowledge at all?

What is the status of our knowledge of math and science if this thought experiment is informative?

Seems to me that one who faces these questions must either grant that he can't really know the truths of math and laws of nature, or he must embrace dualism to preserve at least mathematical truth--OR he might look for a reason for rejecting brain-in-a-vat thought experiments altogether.

I recommend the third alternative.

Next week: philosopher-with-annoying-examples in a vat!

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