Logical Reasoning

PT153 · S3 · Q11 Studies have shown that those who take daily

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Studies have shown that those who take daily doses of vitamin C are less likely to contract colds than are those who do not.

Conclusion (thus)

If a person contracts a cold, he or she probably doesn't take daily doses of vitamin C.

Evidence

Studies show those who take daily doses of vitamin C are less likely to contract colds than are those who do not.

Evaluate

At first this might seem like pretty sound reasoning. Since taking vitamin C daily seems to make one less likely to get a cold, we might think that someone with a cold probably doesn't take daily vitamin C.

If we don't understand the flaw, we can at least focus on the structure, and the structure may be enough to get us to the correct answer.

Since the ideas of "vitmain C" and "contracting a cold" appear in both premise and conclusion, this argument lends itself to an algebraic representation.

Prem: People who do X are less likely to have Y happen

Conc: If Y happens to someone, then they probably don't do X

Why is this actually a flawed argument? It's because there might be way more people who take daily vitamin C than those who don't. So even though taking vitamin C makes you less likely to get a cold, there will still be a ton of people who take vitamin C with colds.

Here's an analogy. Say there are 300 million or so natural born citizens in the U.S. and maybe 20 million naturalized citizens (i.e. they were born elsewhere but at some point moved to the U.S., passed the citizenship test, and got U.S. citizenship).

Foreign-born citizens of the U.S. are usually more likely to know American history (because they had to learn it to pass the citizenship test) and usually more likely to know formal rules of English grammar (because they had to learn English mainly through classes, not through informal conversation).

So we could probably say that natural born U.S. citizens are less likely to know American history or less likely to know formal rules of grammar.

But does that mean if we find an American who happens to know history or grammar, that they are probably not a natural born citizen?

Or to put it another way, does that mean that

No, it doesn't. Even though foreign-born Americans are more likely to know that stuff, they are vastly outnumbered in raw totals by the quantity of natural born citizens, so it's still the case that .

Goal

Anywayyyy, since that is a tricky statistical flaw to understand, we are probably best served by taking our algebraic recipe into the answers.

Prem: People who do X are less likely to have Y happen

Conc: If Y happens to someone, then they probably don't do X

11.

The questionable reasoning in the argument above most closely parallels that in which one of the following?

  1. To be classified as a

    Bad Conclusion Match

    Since the original conclusion is a conditional claim with a "probably" strength, this conclusion here doesn't look at all tempting. It could be written as a conditional, but it would have a certain outcome "are not hurricanes". We can bail for that reason on a first pass. If we needed to dig deeper, we would see that the premise is a rigid "to be X, you must be Y" rule. Our premise was "people who are X are less likely to be Y".

    1% picked this

  2. Everyone who ate the tuna

    Bad Evidence Match

    The conclusion is making a "probably" prediction, so this is worth reading. However, the evidence isn't giving us a claim like, "People who are X are more/less likely to be Y". It's giving us a Universal: All who ate tuna got botulism.

    1% picked this

  3. Laboratory rats given an extremely

    Bad Conclusion Match

    This conclusion is not a "probably"-strength prediction, so we can bail on a first pass. If we looked deeper, we'd also notice a switch from evidence about "rats" to a conclusion about "people". The original argument definitely didn't contain any category switch like that.

    1% picked this

  4. People who train diligently to

    Bad Conclusion Match

    The conclusion is a very strong, categorial claim: People owe their success to X alone We're looking for a softer conclusion: People who are X are probably Y That's reason enough to bail on a first pass. If we looked deeper, the premise is not at all of the form "people who are X are more likely to be Y".

    0% picked this

  5. Correct

    Automobile engines that undergo regular

    Why this is right

    Good news -- the structure was enough! Our original algebra was like this: P: ppl who are X are less likely to be Y C: something that is Y is probably not X P: People who take daily C are less likely to have cold. C: So someone that has cold is probably not taking daily C. This argument is saying, P: Engines that get regular oil changes are more likely to be problem free. C: So engines with problems probably don't have regular oil changes. We would just have to rearrange how that first sentence gets expressed to line up the same "less likely": P: Cars that get regular oil changes are less likely to have engine problems. C: So if a car has an engine problem, it probably doesn't get regular oil changes. And just like the original argument (and our analogous one about U.S. citizens), this logic doesn't have to hold. There might be way more cars that get regular oil changes than don't. So even though those oil changes make you less likely to have an engine problem, there are still going to be a ton of cars that have regular oil changes that still end up with engine problems.

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

    96% picked this

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