Logical Reasoning

PT103 · S2 · Q20 Martha’s friend, who is very knowledgeable

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Martha’s friend, who is very knowledgeable about edible flowers, told Martha that there are no edible daisies, at least not any that are palatable.

Conclusion

What Martha's friend told her must be incorrect.

rephrase: There are some palatable daisies.

Evidence

Some daisies are a kind of chrysanthemum, and there are some palatable chrysanthemums.

Evaluate

Our first job was to translate the Rebuttal conclusion "her friend is incorrect" into a specific claim, "There are some palatable daisies".

We see a lot of symbol repetition in this argument. There are two instances each of 'palatable', 'daisies', and 'chrysanthemum'. Thus this argument is ripe for turning into algebra.

P1: Some daisies are a type of chrysanthemum Some A's are B

P2: Some chrysanthemums are palatable. Some B's are X

C: Some daisies are palatable Some A's are X

We can talk about the bad Quantifier Logic this argument is employing. A valid argument would say, All A's are B Some A's are X Thus, Some B's are X

That works because the overlapping idea in the premises ("A") is the trigger of the All statement. If Some X's are A, then automatically that means that Some X's are B, since every thing A is B.

In this argument, by contrast, the premises are just saying Some, so no overlap inference can be made. We can never prove from "Some A are B" and "Some B are C" that "Some A are C".

We could also just conversationally argue with the argument. Just because some daisies belong to a category, some of which is palatable, doesn't mean that daises are palatable.

Tomatoes belong to the category of fruit, some of which are made into popsicles, but that doesn't mean tomatoes are made into popsicles.

It's possible that tomatoes are an example of a fruit that doesn't get made into popsicles.

It's possible that daises are an example of a chrysanthemum that isn't palatable.

Goal

Let's look for something with this type of structure: P1: Some A's are B P2: Some B's are X C: Some A's are X

20.

Which one of the following has a flawed pattern of reasoning most like that in Martha's reasoning?

  1. Jeanne is a member of

    Bad Conclusion Match

    We can tell this is off the mark because it lacks the symbol repetition of the original. If we're saying "J is a part of the city chorus group, and the city chorus group has the trait of being renowned", then the matching conclusion would say something like, "J is a renowned singer". That would still be off somewhat, but closer. But since this argument is using a different idea in the conclusion, we know this doesn't match up. (excellent vs. renowned = skilled vs. famous)

    10% picked this

  2. Rolfe belongs to the library

    Bad Premise Match Valid Logic

    We were looking for this: P1: All A's are B (or A is a member of B) P2: Some B's are X C: Some A's are X And this argument is giving us this: P1: Rolfe is a member of the library group. P2: All library group members are X C: Rolfe is X. That's a valid argument! The original argument was flawed because some chrysanthemums are palatable and some aren't (and it's possible that daisies are entirely among the ones that aren't). In this case, every single library group user is an avid reader, so we know that every member is an avid reader.

    7% picked this

  3. Correct

    Some of Noriko’s sisters are

    Why this is right

    This matches our formula nicely. P1: Some A's are B Some N-sisters are on debate. P2: Some B's are X Some debate are poor students. C: Some A's are X Some N-sisters are poor students. Just like, P1: Some A's are B Some daisies are chrysanthemums. P2: Some B's are X Some chrysanthemums are palatable. C: Some A's are X Some daisies are palatable.

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

    69% picked this

  4. Most of Leon’s friends are

    Weak Premise Match Valid Logic

    The quantifiers on the two premises are off, which makes the argument actually have a pretty valid conclusion. P1: Some A's are B Most of L-friends are good swimmers. P2: Some B's are X All good swimmers are quite strong. C: Some A's are X Some of L-friends are quite strong. If we say "most of Paul's friends are NBA players, and NBA players are quite tall. Thus, some of Paul's friends are quite tall", that seems like valid logic.

    8% picked this

  5. Many of Teresa’s colleagues have

    Weak Premise Match Bad Conclusion Match

    The quantifiers on the two premises are off, which already make this inferior to the correct answer. P1: Some A's are B Many of T-colleagues have written books. P2: Some B's are X Most books written by T-colleagues are on the subject of good writing. C: Some A's are X Some of T-colleagues are good writers. But the conclusion is also a bad match. It is a flawed conclusion, because you can write a book on good writing without being a good writer yourself. But that's a different flaw. This argument introduces a new concept into the conclusion. The original argument did not.

    6% picked this

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