Logical Reasoning

PT152 · S2 · Q16 Most pet owners who take

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Most pet owners who take allergy medication are allergic to pets.

Conclusion

If Chuck (a pet owner) develops an allergy to pets, he'll probably take allergy medication.

Evidence

Most pet owners who take allergy medication are allergic to pets.

Evaluate

Whether or not we understand the flaw in this argument, we can map out the structure, by keeping track of quantifiers and overlapping terms.

Premise Most A's who are B are C. Person X is an A. Conclusion If person X is C, they are likely to be B.

The flaw with this argument is reversing the logic of a Most statement.

When we say "Most lawyers are wealthy", then we're allowed to say If Lois is a lawyer, then it is likely that she is wealthy.

But, we're not allowed to say If Lois is wealthy, then it's likely that she's a lawyer.

Goal

The key part of the flaw is that there's a Most statement: Most X's are Y and then the author performs an illegal backwards move, saying If Y, then likely X.

16.

Which one of the following arguments exhibits flawed reasoning that is most similar to that exhibited by the argument above?

  1. Most cars taken to Acme

    Reversed Conclusion / Valid

    This gives us the Most A's that are B are C. But it needs to conclude that, If this A is a C, then it's likely a B. or, equivalently, it it likely that B is true if C is true. The matching conclusion would have been, it is likely that A's car was taken to Acme if it has electrical problems. This conclusion actually is a valid inference from the Most premise.

    15% picked this

  2. Correct

    Most cars taken to Acme

    Why this is right

    We have the same Most A's that are B are C We want a conclusion that's saying likely to be B, if C This conclusion does do that: likely to be Acme, if it has electrical problems What this argument and the original have in common that wasn't noted in our original breakdown of the argument is how the conclusion not only performs the reversed Most move, it also switches to a future tense. The original said, If he develops a pet allergy, he'll be likely to take allergy meds, since most people who take allergy meds have a pet allergy. This answer is saying If the car has electrical problems, she will likely go to Acme, since most people who go to Acme have electrical problems.

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

    73% picked this

  3. Most cars that are taken

    Bad Conclusion Match

    This conclusion involves some truth-value switching that the original argument didn't have. It goes from "do not have electrical problems" in the premise to "does have electrical problems" in the conclusion. And it goes from "do take to Acme" in the premise to "won't go to Acme" in the conclusion.

    2% picked this

  4. Most cars taken to Acme

    Bad Conclusion Match

    This conclusion flips a couple things: the original was saying "it's likely to be B, if C" This conclusion says "it's unlikely to be B, if not C"

    2% picked this

  5. Most cars taken to Acme

    Inferior Conclusion Match

    This is real close. But the conclusion gets into her beliefs: "if she thinks the car has electrical problems". The original didn't say, "if Chuck thinks he has developed an allergy".

    8% picked this

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