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I'm still confused about the wording of C, and more generally about sentences that take up the construct "mistakes X for Y ." Whenever we see such a construct how do we know which element is the one the respondent believes in? It's understood he or she mistook something for something else, but which is the one they now believe in? And grammatically or structurally, how do we know which element that one is?

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 Adam Tyson
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We have to play a bit of a matching game, Sunshine. I would start by asking myself "what is Laura's conclusion?" The answer is that Joseph is wrong, and Fermat was neither lying nor mistaken. In other words, Fermat was telling the truth.

What does Laura think ensures that conclusion? That the theorem is provable. Laura thinks that because it is provable, Fermat must have been telling the truth. But that's not necessarily true. If Fermat was telling the truth, that would mean the theorem must be provable, but the theorem being provable doesn't guarantee that Fermat was telling the truth (he still might not have proved it and could have been mistaken about it or lying about it). Laura has confused a necessary condition (that the theorem is provable) for a sufficient one.
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So I have a question in regards to the flaw in reasoning for Laura. However, it may not be completely related to the correct answer. What I am about to explain is my first prediction at what the flaw is. However, it turned out not being the main flaw, which was determined to be C.

So, at first glance of reading the two arguments. I thought Laura has misinterpreted Joseph's conclusion. Joseph's conclusion is that. "It is likely that Fermat was either lying or else mistaken when he made his claim."

Laura's argument mentions how someone proved the theorem recently. I thought that she misinterpreted his conclusion to being just "It is likely that Fermat was either lying or else mistaken," and so current evidence could prove to disprove his claim. More specifically, Laura was making the mistake in assuming that because someone proved it today (or recently) showed that the claim that Fermat made back then was wrong. I don't know if this makes sense. However, let me explain it in terms of a different example.
Let's say Joseph said someone along the lines of "Benjamin Franklin is alive in 1788." Using the same reasoning that I mentioned, Laura could have misinterpreted it and said, "That is wrong. He is dead right now. "

So, in other words, I thought Laura made a mistake in reading his argument and I thought that current evidence does not disprove a claim that was made about a specific time period.
Let me know if this is a flaw in the argument or if I was completely off-base.
 Rachael Wilkenfeld
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Hi Renee,

The problem with your reading of Laura's statement is that it doesn't really apply to the situation. Mathematical theorems are truths about how the world works. They don't just apply during specific time periods (as someone's lifespan would). It couldn't be the case that it wasn't true in the past, but it is true now. Just like addition was just as true a million years ago as it is now. It doesn't matter that there weren't people yet to put a name to the concept. It still existed. Two velociraptors plus two velociraptors equals four velociraptors. I can see cases where disproving something today does not disprove it in the past, but that doesn't apply to this question.

Hope that helps!

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