Argument Structure Questions - - Question 21

Joseph:  My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written...

vawalkey June 8, 2022

How do we differentiate between the subconclusion and the conclusion?

I thought the main conclusion was that the theorem cannot be proved and that Fermat was lying was the subsidiary conclusion supporting the argument that the main conclusion cannot be proved. Can you help me understand why that is wrong?

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Emil-Kunkin June 10, 2022

Hi Vawalkey,

A subsidiary conclusion is a conclusion that is in turn used to support another conclusion. J's argument proceeds as follows:

Fermat dies without writing his proof, yet claimed he had prooved it.
No one has proved the theorem -> SO probably cannot be proved - > SO F was either lying or wrong

The main conclusion is that F was either lying or wrong, and this is supported by the statement what the theorem probably cannot be proved, which is in turn supported by the claim that noone has proved the theorem.