LR Bible 2015, page 507, ex. 3

[DlarehAtsok]

"Most people ...". In the Answer Key (p510) it is claimed that there is a division error. While this makes some sense, I believe it is more about a problem with numbers. More precisely, we know that most people who shop ... buy prepared frozen dinners. Also, we know that most people in Hallstown shop for groceries no more than three times a month. Most people in Hallstown can include from 50.00001% to 100% of the population of Hallstown. However, even if most people who shop no more than three times a month in Hallstown buy prepared frozen dinners regulars that does not mean that most people of Hallstown do. 50.0001% of 50.00001% would not mean most, right?

[Nikki Siclunov]

Hi DlarehAtsok,

Thanks for your question! The argument is structured as follows:

• Premise: Shop for groceries max. 3 times/month Buy frozen dinners
  
  Premise: Hallston Shop for groceries max. 3 times/month
  
  Conclusion: Hallston Buy frozen dinners

There are several ways of looking at this logical flaw. Yes, it's an Error of Division. The statement "most people who shop for groceries no more than 3 times a month buy prepared frozen dinners regularly" is a statement about a class of people having a certain attribute. Since Hallston is a member of that class, the conclusion depends on the erroneous transference of the attribute from the class onto a member of that class.

It's also helpful to recognize this as a Formal Logic error. Just because most people in general do something doesn't mean that the people in Hallston will do it. After all, it's entirely possible that 49% of the people who shop for groceries no more than 3 times/month do NOT buy frozen dinners, and that everyone living in Hallston is part of that 49%. There is actually no conclusion we can draw about the people of Hallston: it's entirely possible that NONE of them buy frozen dinners regularly.

As a general rule of thumb, we cannot "cross" two arrows in a chain (A B C) and expect to arrive at a logically valid deduction (A C is not a valid conclusion). This is an issue discussed in the Formal Logic chapter of the LRB.

Hope this clears things up!

Thanks,