LR Problem Set #2, Q 173

[smile22]

Is this question (regarding tenured faculty, full professors, and linguistic faculty members) a case of formal logic? If so, how do I properly diagram it? And, could you please walk me through why C is the correct answer?

[Adam Tyson]

I expect I can help you partway here, although the diagram might be a challenge due to the constraints of this forum. I'll do my best!

First, yes, this is formal logic. Some might approach it with a Venn diagram (we generally don't use those in our course, but they can be helpful) - two overlapping circles, one of which represents Tenured Professors and one of which represents Full Professors. The portion that overlaps would be those professors that meet both criteria (and be aware that there might be some or there might be none at all). You can also do this with a version of the double not arrow from conditional reasoning, adding the word "all" above the center of the arrow, which would just tell you that there is not a complete overlap of the two groups (and again there may in fact be no overlap) (It may also be that every Full professor is tenured, but that there is at least one Tenured that isn't Full).

With all that in mind, let's analyze the argument. We know that we do not have complete overlap of the two big groups (Tenured and Full). The author then tells us that we cannot have complete overlap of a subset of the Tenured group, the professors in the linguistics department, and the Full group. Is that supported by the premises? Nope, it's not - it could be that all the linguistics profs are Tenured and Full, and all the philosophy profs are Tenured and Full, and all the law profs are Tenured and Full, and on and on and on - as long as there is at least ONE Tenured Professor who is not a Full Professor (in, say, the Music department).

The flaw, then, is a form of a Flaw of Division, assuming that what is true of the whole (Tenured Profs) must be true of all the parts (the Tenured Profs of any given department).

Answer C might not look the same at first glance because they have altered the language to hide the similarity. The first sentence could easily be re-written as "Not all buildings designed by famous architects are well proportioned" to mirror our stimulus better without changing the meaning. Follow that through and you will find the same flaw - the author assumes that what is true of the big group (buildings designed by famous architects) must be true of a subset of that group (gov't buildings). Isn't it possible that all gov't buildings are well proportioned, and that the only famous-architect-designed building that isn't well proportioned is a non-gov't building (say, a commercial office building)?

A long answer, I know - I hope it was a helpful one!

[smile22]

This explanation is great. Thank you for helping me understand this question.