Logical Reasoning

PT2 · S2 · Q20 All savings accounts are interest-bearing

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All savings accounts are interest-bearing accounts.

Premise 1

All savings accounts are interest-bearing accounts.

Premise 2

Some interest-bearing accounts have tax-free interest.

Conclusion

Therefore, some savings accounts have tax-free interest.

Evaluate

The structure: All A are B. Some B are C. Therefore, some A are C. This is invalid. The "some B" that have property C might be the B's that are not A. (For example: All cats are mammals. Some mammals are dogs. Therefore, some cats are dogs — clearly bad.) The flaw is that "some B are C" does not specify which B's — they could be the B's outside of A entirely.

Goal

Find an answer with the same structural form: All A are B. Some B are C. Therefore, some A are C.

20.

Which one of the following arguments is flawed in a way most similar to the way in which the passage is flawed?

  1. All artists are intellectuals. Some

    Bad Validity Match

    This argument is valid. All artists are intellectuals. Some great photographers are artists. So those photographers (who are artists) must also be intellectuals. The structure is "All A are B. Some C are A. So some C are B" — and this is logically airtight. We need a flawed argument matching the original's flawed structure.

    7% picked this

  2. All great photographers are artists.

    Bad Validity Match

    This argument is also valid. All great photographers are artists. All artists are intellectuals. So all great photographers are intellectuals — and certainly some are. The structure transmits the property cleanly through universal claims. The original's flaw came from a "some" premise pointing to an unspecified subset of the larger group; this argument has no such weakness.

    6% picked this

  3. Correct

    All great photographers are artists.

    Why this is right

    This matches the original's flawed structure exactly. All great photographers are artists (All A are B). Some artists are intellectuals (Some B are C). Therefore, some great photographers are intellectuals (Some A are C). The "some artists" who are intellectuals could be artists who are not photographers at all — say, sculptors. The argument has not actually shown any photographer to be an intellectual. Same flaw as the original: the "some B are C" premise tells us nothing about which B's, so it cannot be moved over to A.

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

    77% picked this

  4. All great photographers are artists.

    Bad Validity Match

    This argument is valid. All great photographers are artists. Some great photographers are intellectuals. The "some great photographers" who are intellectuals are also artists (since all photographers are artists), so it follows that some artists are intellectuals. The structure is "All A are B. Some A are C. So some B are C" — which is fine. The original's flaw was different.

    9% picked this

  5. All great photographers are artists.

    Bad Validity Match

    This argument is valid. All great photographers are artists. No artists are intellectuals. So no great photographers are intellectuals (and thus some are not). The structure uses a universal-negative premise, which is not the original's pattern, and it follows correctly. Not a parallel flaw.

    1% picked this

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