Month: March 2015

A recent reading quiz question in the area of problem solving confused a student. The student wrote:

Dr. Leighton,
Could you please explain to me why this is wrong? I was confused by the book, because it does say that you can have a “valid but incorrect conclusion” if the “premises use terms inconsistently or ambiguously”, which the term environmentalist is very broad and could be considered ambiguous in the question, so I am not really sure what the correct answer is.

This is a good question. Here is the question and answers from the quiz:

Mr. Smith is running for Congress. Alejandro does not know much about Mr. Smith, but he has heard that Mr. Smith is an environmentalist. Because Alejandro cares about the environment, he votes to send Mr. Smith to Washington. After the election, Alejandro finds that Mr. Smith does not act like an environmentalist, and he regrets having voted for him. Alejandro’s mistake was forgetting that:

Question	Mr. Smith is running for Congress. Alejandro does not know much about Mr. Smith, but he has heard that Mr. Smith is an environmentalist. Because Alejandro cares about the environment, he votes to send Mr. Smith to Washington. After the election, Alejandro finds that Mr. Smith does not act like an environmentalist, and he regrets having voted for him. Alejandro’s mistake was forgetting that:
Answers	A. a conclusion is true only if the premises are true B. a conclusion can be valid without being true C. premises with ambiguous terms lead to incorrect conclusions D. both B and C

The student thought both B and C should be correct. The correct answer is A. Why? Here’s what I wrote to the student:

This is a good question. Lets walk through the example.

Remember that a syllogism has a premise and conclusion. In this case, what’s the premise and conclusion?

I think the premise is that Mr. Smith is an environmentalist. I think the conclusion is that Mr. Smith will act like an environmentalist.

I don’t think that “environmentalist” here is ambiguous. What I think the issue is whether the premise is correct. So, what is the basis for the premise?

The basis for the premise is what Alejandro heard about Mr. Smith. That’s a pretty suspicious basis for the premise – so I think the weakest part of the example is whether what Alejandro heard about Mr. Smith is true.

The evidence that Mr. Smith does not act like an environmentalist indicates that the conclusion is incorrect, and thus the premise is not true. Thus, the conclusion is only valid if the premise is true.

Does that help?

Lets use another example.

Instead of “environmentalist” we substitute something more ambiguous: how about “can fly?” Then we can get something like:

Alejandro does not know much about Mr. Smith, but he has heard that Mr. Smith can fly. Because Alejandro thinks it would be awesome to have someone with superhuman powers in congress, he votes to send Mr. Smith to Washington. After the election, Alejandro finds that Mr. Smith doesn’t have feathers and has never been seen flying around the capitol, but instead is just an airplane pilot, and he regrets having voted for him.

Now we have a conclusion (Mr. Smith has superhuman powers) that is based on an ambiguous premise (Mr. Smith can fly).

Make sense?