#11 - Studies have shown that those who take daily doses of

[Administrator]

Please post your questions below!

[danimcca]

Hi,

Can someone please explain the flaw in the question. I see the conditional reasoning as;

Vit C /cold/
Contrapositive: Cold /Vit C/

The flaw being that there could be many other reasons for contracting a cold, just as Answer E, there could be many other reasons that the engine is not working. Is this correct?

Thanks!

[Frank Peter]

Hi Danimcca,

I think your diagram below is correct, as is your understanding of why answer choice (E) is correct. There is a conditional reasoning aspect to this question as you have diagrammed, but it is possible to have conditional reasoning that works on a formal level without actually making much sense in the real world. There's also a cause-and-effect aspect to the logic here, and that's the problem. It's entirely possible for someone to get sick even if they are taking daily doses of vitamin C, just as it is possible for an automobile to have engine problems even if it gets regular oil changes.

[gwlsathelp]

I see the first sentence's probabilistic reasoning, then mixed causal conditional in the second sentence; but I don't see the quasi-causal-conditional reasoning in the automobile parallel. How would one suss this out to be conditional?

[Rachael Wilkenfeld]

I wouldn't treat either the stimulus or the answer choice as having a strong conditional aspect here, gw. I think the fact that both the premises and conclusions have likelihood language rather than certainty language would make this a non-conditional statement. But that doesn't mean there's not still an error here. The big error is population size. We don't know how many people take vitamin C. We don't know how many people get colds. It could be that only 5 people take vitamin C while 50 million people get colds. That's the same error we see in the automobile case. We don't know how many cars have oil changes and how many have engine troubles.

Let's look at some example numbers to see why this is a flaw.

Let's say 1000 people take vitamin C and 10 people don't. If you have 100 people with a cold, at least 90 of them will have taken vitamin C. Most of the people with the cold would have taken vitamin C, even though most of the people who take vitamin C wouldn't get a cold.

Hope that helps!