Logical Reasoning

PT138 · S3 · Q24 In the Riverview Building

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In the Riverview Building, every apartment that has a balcony also has a fireplace.

Evidence

For all apartments at Riverview,

If an apartment has a balcony, A → B it also has a fireplace.

None of the ones with A → ~C balconies are 1-bed.

Conclusion

None of the 1-beds C → ~B have a fireplace (B → ~C)

Evaluation

Since both conditionals have the same trigger (A), there's no way to conclude any conditional connection between their outcomes (B and ~C).

If a 1-bedroom had a fireplace, that wouldn't contradict any premises (unless that 1-bedroom also had a balcony, but it's possible that there's a 1-bedroom, with no balcony, but with a fireplace).

Since this argument is highly conditional / quantified logic, we can probably match our way to the correct answer whether or not we understand why the structure is flawed.

Goal

Two conditional premises with the same trigger. A conclusion that makes a conditional relationship between the two outcomes.

24.

The flawed nature of the argument above can most effectively be demonstrated by noting that, by parallel reasoning, we could conclude that

  1. every fish has fur since

    Bad Conclusion Match

    We do have two conditional premises with the same trigger: Cat → Fur Cat → ~Fish The conclusion does create an illicit conditional relationship, but it isn't between those two outcomes. To match the original, we'd want to see a conclusion look like: Fur → ~Fish or Fish → ~Fur Instead, we get Fish → Fur A matching conclusion would have sounded like, "Nothing with fur is a fish".

    6% picked this

  2. some cats lack fur since

    Bad Conclusion Match

    The original conclusion was conditional, so the correct answer's conclusion should also be. This conclusion, meanwhile, is a Some statement.

    2% picked this

  3. Correct

    no dog has fur since

    Why this is right

    We have two conditional premises (an All and a No), with the same trigger: Cat → Fur Cat → ~Dog And we have a conclusion that builds a No conditional relationship between them: Dog → ~Fur

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

    67% picked this

  4. every cat is a fish

    Weak Premise/Conclusion Match

    If we wanted to, we could make both conditional premises have the same trigger: Dog → ~Cat Dog → ~Fish But (C) is already a better match, since it better replicated the mix of All and No premises we had in the original. The conclusion of this argument does create a conditional relationship between the outcomes, but it is an All relationship, whereas the original was a No relationship.

    17% picked this

  5. no fish is a dog

    Bad Premise Match Valid Logic

    We do not have two conditionals with the same trigger. We can put Mammal on both sides, but we have a positive and a negative version, so it doesn't match. ~Mammal → ~Dog Mammal → ~Fish So there's no reason to keep reading this one. If we did, however, we would see that it's actually valid logic.

    8% picked this

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