Does this Fermat's Last Theorem's "Proof" employ circular reasoning?

Question

I happened to find this link which contains a "Simple Proof of Fermat's Last Theorem": http://www.oakton.edu/user/4/pboisver/fermat.html

I don't believe in the "proof" because we can just change III) to be any statement -- even a contradiction -- and still be able derive it. I'm still unsure where a problem with it is. It seems that the system is circular in assuming the truth or falsity of I) in II). Is a problem with this "proof" about circular logic or something else?

Thanks.

Answer 1

Given the note, the proof seems to be a joke. The proof fails because of the circular (impredicative) phrasing of I and II.

Answer 2

Here I can see some aspects that can lead to the understanding of why the prove does not work.

I) At least one of the following two sentences is true.

II) The preceding sentence is false.

III) xª + yª = zª has no positive integer solutions (x, y, z, a) for a > 2.

1.1 There is nothing to support that I is really true.

1.2 Making the II statement feels that the author is trying to poison the well, meaning the rhetoric use of a statement that attempts to discredit something (or someone in more strict sense) without a previous prove.

1.3 Even if I and/or II are true or false nothing of the two statements is related with III and because of that seems that we are facing a post hoc fallacy

1.4 In other words there are formal and informal aspects for making the statement a fallacy

1.5 As you said. Trying any other statement in stead of III like for example "all dogs are animals then Pluto is a planet".