Wednesday, February 27, 2008

math sucks

I read and reread paragraph 4 of the Third Meditation probably about 10 times and could not really get an opinion about whether one can doubt if 2 + 3 = 5. However, after reading Hatfield I landed where I thought I would on the issue.

Paragraph 4 begins by considering simple arithmetic and geometry and how the meditator seemed to see these things clearly enough to affirm their truth. She then recalls her only reasoning for doubt in such matters at 2+3=5 was the deceiving god hypothesis. It seems that when she considers the DGH she must admit how easy it would be for the deceiving god to convince her of these simple truths when they were in fact false. But then she goes into this line of reasoning that confuses the issue. She states that when she thinks about things that are so clear to her (such as her existence and 2+3=5) let whoever deceive her because he can never make it so these things are not true. Given this it seems that she does not think 2+3=5 can be doubted. However, even after this, she maintains that there is still a possibility for a small metaphysical doubt due to the deceiving god hypothesis that she still must investigate and dispell. Given this last point I feel that 2+3=5 is still slightly able to be doubted. The cogito reasoning as Hatfield points out, is able to blanket this DGH concern because of the fact that thinking about the DGH automatically proves ones existence. However, 2+3=5 is not saved in this same way. Therefore, even if it is only a slight reason for doubt, 2+3=5 can still be doubted at the end of paragraph 4. So long as the DGH survives (and it has thus far even though the meditator doubts it heavily), 2+3=5 is possible to be brought under doubt.

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