Logical Reasoning

PT132 · S4 · Q9 If a mother's first child

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If a mother's first child is born before its due date, it is likely that her second child will be also.

Conclusion (so)

It is likely that J's first child was not born before its due date.

Evidence

If a mom's first child is born before its due date, it's likely that her second child will be also be born before the date.

J's second child was not born before its due date.

Evaluate

There is enough symbol repetition here that we could probably beat this question just by diagramming the argument, even if we didn't understand the flaw.

This argument feels like it's almost doing a contrapositive, but because it's working with probability, not conditional logic, that move doesn't work.

Here's the structure:

Prem 1: If 1st born was early, then 2nd was probably early X → probably Y

Prem 2: J's 2nd was not born early. this thing was not Y.

Conc: J's 1st was probably not born early. this thing was probably not X.

Goal

Let's look for something with this structure:

P1: X → probably Y P2: this thing was not Y. C: so, this thing was probably not X

--------------------- If you're curious why this is a flaw, consider this argument: If you live on Earth, it's likely that you've heard of Taylor Swift. Paul has never heard of Taylor Swift. Thus, it is likely that Paul doesn't live on Earth.

9.

The questionable reasoning in the argument above is most similar in its reasoning to which one of the following?

  1. Artisans who finish their projects

    Bad Premise Match

    We're looking for this structure P1: X ? probably Y P2: this thing was not Y. C: so, this thing was probably not X We get a premise saying Finish before ? probably Go X Y The next premise should be talking about someone who did not go to the craft fair. But instead it's saying about someone who did not finish before. Since the second premise is talking about ~X rather than about ~Y, we know this is hopeless.

    4% picked this

  2. All responsible pet owners are

    Bad Premise Match Bad Conclusion Match

    We're looking for this structure P1: X ? probably Y P2: this thing was not Y. C: so, this thing was probably not X This argument only has one premise, so we know it's wrong. And the conclusion is a conditional ("anyone"), while the conclusion of the original argument wasn't a conditional. It just said "J's first kid was probably born early".

    3% picked this

  3. Correct

    If a movie is a

    Why this is right

    We're looking for this structure P1: X ? probably Y P2: this thing was not Y. C: so, this thing was probably not X We get a premise saying Box office hit ? probably Sequel Hit X Y The next premise should be talking about a Sequel that was not a hit, and then concluding something about the first one not being a box office hit. That's exactly what it does. P1: X ? probably Y hit ? probably sequel hit P2: this thing was not Y. Hawkman did not have a sequel hit. C: so, this thing was probably not X Hawman was probably not a hit.

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

    90% picked this

  4. If a business is likely

    Bad Premise Match

    We're looking for this structure P1: X ? probably Y P2: this thing was not Y. C: so, this thing was probably not X We get a premise saying Likely to fail ? won't invest X Y This is already bad because the outcome isn't in probabilistic form. But even if we played along, the next premise should be talking about something where people WILL invest and then concluding that something was not likely to fail. But instead the premise is talking about something that is Likely to Fail. Since the second premise is talking about X rather than about ~Y, we know this is hopeless.

    1% picked this

  5. Tai will go sailing only

    Bad Evidence Match

    We're looking for this structure P1: X ? probably Y P2: this thing was not Y. C: so, this thing was probably not X We get a premise saying Go Sailing ? Weather Nice X Y Once again, it's probably hopeless since there's nothing probabilistic in this conditional. But we would also know it's wrong when the second premise is saying the weather WILL be nice, whereas we're looking for ~Y.

    1% picked this

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