#23 - Research indicates that 90 percent of extreme

[kenlars5]

Hi there,

Is it correct to approach this question as a formal logic question and set it up like this:

Extreme insomniacs consume large amounts of coffee

Therefore you can see that the conclusion that because Tom drinks a lot of coffee does not necessarily mean that it is likely he is an extreme insomniac, simply because that’s not what the premises show? In other words it’s only talking about the percentage of insomniacs who drink large amounts of coffee, not the percentage of coffee drinkers who are insomniacs?

I did this as a formal logic question and was able to get the right answer, but just wanted to make sure that this was an appropriate approach to questions like this.
Thanks!

[Adam Tyson]

That's a perfect approach, kenlars5! It is indeed a Formal Logic flaw, and Formal Logic usually fits into the larger category of Numbers and Percentages. While you can take a diagrammatic approach to Formal Logic, as you did here with accurate results, you can also take the approach of using numbers - imagining, for instance, that there are 10 insomniacs but 100 coffee drinkers - to see that the conclusion is not warranted. I also look at arguments like this and make quick analogies to show how silly they are: "90% of my children are in the Navy. Tom is in the Navy, so he is probably my child." "90% of my pets are dogs. Tom is a dog, so he is probably my pet."

Well done!

[simonsap]

9/10 insomniacs drink 100L of coffee per day
1/10 insomniacs drinks no coffee

Tom drinks 100L of coffee per day, so he's probably an insomniac.

He could be an insomniac, however, e also could be highly insensitive to coffee and get great sleep despite his coffee intake.
The argument falsely presumes the former.

Answer A is wrong because the argument does not care about the % of people who drink large amounts of coffee, only about the percentage of people who are insomniacs. We don't know if its only 10% of extreme coffee drinkers who are not insomniacs, the number could be much higher, for example.

B - other causes, we don't care
C - says we don't know how often extreme coffee intake results in insomnia (this is the corollary to A)
D - there is no reverse generalization; more like reversed logic
E - doesn't say this

[augl2023]

Would this be like a sampling flaw?

[Rachael Wilkenfeld]

It's not a sampling error, augl2023, it's a problem with using the data they have. A sampling error would mean they are asking the wrong people the question. For example, if you asked high school students how much they pay in monthly rent, then drew a conclusion about rent prices overall in the country. High school students are the wrong sample to draw a conclusion about the country as a whole. They aren't going to give a representative sample.

This issue is different. This is taking data that was sufficient to show one thing and use it to show another. We have no reason to think that the research done on extreme insomniacs was flawed as to extreme insomniacs. However, we can't use that data to draw the conclusion they attempt to draw about coffee drinkers, for the reasons Adam describes above.

Hope that helps!