Logical Reasoning

PT112 · S4 · Q14 Joseph: My encyclopedia says

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Joseph: My encyclopedia says that the mathematician Pierre de Fermat died in 1665 without leaving behind any written proof for a theorem that he claimed nonetheless to have proved.

Conclusion (Laura)

Your claim is wrong.

rephrase: Fermat wasn't lying or mistaken when he said he proved the theorem. (i.e. Fermat did prove the theorem)

Intermediate Conclusion

The theorem is provable.

Evidence

Someone has now proved the theorem.

Evaluate

What's wrong with saying, ?

Just because one person was able to prove it doesn't mean that Fermat was also able to prove it. The fact that Lebron can dunk doesn't prove that I can dunk.

At one point Joseph had claimed that the theorem probably cannot be proved. Laura has definitely shown that this is not true, because it has recently be proved.

But the recent proving of the theorem doesn't really shed any light on whether Fermat was able to do so himself.

Goal

Let's find some answer addressing the gap between "it's provable; someone else proved it" and the conclusion that "Fermat proved it".

14.

Which one of the following most accurately describes a reasoning error in Laura's argument?

  1. It purports to establish its

    Self-Contradiction

    The premise is that the theorem has recently been proved / the theorem is provable. That doesn't contradict the conclusion that "Fermat proved the theorem".

    10% picked this

  2. It mistakenly assumes that the

    Bad Description

    Laura never appeals to Fermat's character to vouch for his claim. Her evidence is purely about whether the theorem itself is provable, not whether Fermat was the kind of person who would tell the truth.

    3% picked this

  3. Correct

    It mistakes something that is

    Why this is right

    It's surprising to see the answer testing Nec vs. Suff, since that is a flaw about messing up conditional logic and there weren't any conditional logic premises in Laura's argument. But the conclusion is that Fermat proved the theorem. In order for that to be true, it must be the case that the theorem is provable. No one can do the impossible. Is the author ever acting like "if it's provable, then Fermat proved it"? Yes! In fact, that's basically how Laura's argument goes down. Laura takes the necessary condition (the theorem is provable, as established by today's proof) and treats it as sufficient to conclude that Fermat did actually prove his theorem.

    Skill tested: Flaw · how this choice captures the argument's function is the move to repeat next time.

    63% picked this

  4. It uses the term “provable”

    Bad Description

    This is true but not objectionable, because we know what the word provable means: it's capable of being proven / it's possible to demonstrate its correctness.

    1% picked this

  5. It fails to distinguish between

    Bad Description

    This is a fancy-sounding distinction that does not match the argument. Start with the first chunk -- was the argument ever describing "a true claim that has mistakenly believed to be false"? We could say ... TRUE CLAIM: Fermat proved his theorem Laura thinks that Joseph mistakenly believes this claim to be false. Okay, does the argument then drift into thinking that a false claim is mistakenly thought to be true? Nope, nothing like that is ever happening. Laura just tries to persuade Joseph that he is mistaken to think it's false to say "Fermat proved his theorem" on the basis of the fact that someone else was recently able to prove the theorem. This premise is a true, factual claim. There is no "false claim mistakenly thought to be true" anywhere in the conversation.

    23% picked this

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