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Minoru Itoh is a senior faculty member at Tokyo University of Science. Dr. Itoh is also Dean of the Graduate School and is also involved in teacher training.
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Dave: Welcome back to Rationally Minded Podcast. Irrational or poor patterns of reasoning are called fallacies. Each week, we invite an EFL educator and expert critical thinker to discuss different kinds of fallacies that come up in our everyday lives. We also discuss how you can learn to recognize fallacies and respond to other people’s fallacious statements and arguments with common and useful English expressions. I’m David Gann and this is Rationally Minded Podcast. Today we’re pleased to have with us, Dr. Minoru Itoh, a senior faculty member at Tokyo University of Science. Dr. Itoh is also Dean of the Graduate School and is also involved in teacher training.
Minoru:Yes, I’m advisor of the Super Science High Schools. Now, Japanese society is a knowledge oriented society. We have to make students more Internet savvy, and to–not only the sciences, but also the liberal arts and humanities. [Tokyo] University [of Science] students have a lot of training for the science oriented skills and knowledge, but they need the skills of critical thinking. So I am training, not only the pedagogy, but also the way of thinking . . . like logical thinking and critical thinking in their educational fields.
Dave:So that brings us to you and what you can tell us about this fallacy called the undistributed middle. It sounds difficult.
Minoru: The undistributed middle is just another form of a broken syllogism. The first thing is to understand what a middle is. A typical syllogism goes like . . .
All A’s are, have, or do B.
C is an A.
So this C is, has or does B.
Dave: Now if that is difficult to understand, especially on radio, let’s dress it up like this:
Green tea contains caffeine.
Hojicha is a kind of green tea.
So, hojicha contains caffeine.
Very little caffeine but yes, it does. A regular coffee or stronger green tea drinker might not even notice the caffeine level in hojicha, but there is caffeine. Anyway, though, as for the middle term in this syllogism, you can see that in the first premise, Green Tea is term A . . . and Caffeine is term B. And in the second premise, the new term Hojicha is introduced, and that’s term C. And the premise says that Hojicha (C) is a kind of (A), that is Green Tea.
Minoru: The MIDDLE term is the word that appears in the first AND second premise but doesn’t appear in the conclusion.
Dave: Okay, that’s a very important point so let’s repeat that: the MIDDLE term is the word that appears in the first AND second premise but should not appear in the conclusion. So, listeners, listen again. What term do you hear in the first and second premise?
Green tea contains caffeine.
Hojicha is a kind of green tea.
So, listeners, of course, it’s . . . green tea. And that’s what makes it the middle term.
Minoru: Yes, but to be sure, we have to look at the conclusion and make sure that the middle term IS NOT included. Let’s look at the conclusion again.
So, hojicha contains caffeine.
Do we find the term green tea in that sentence?
Dave: We do not. So, that means that the middle term is correctly distributed.
Minoru: Okay, here’s another example.
The City Office has confirmed that all the houses on Madison street have security systems installed.
The yellow house on the corner of Madison street and Delaware avenue is listed with an address on Madison and not Delaware.
Therefore, the yellow house on the corner has a security system installed.
Minoru: The MIDDLE term is the word that appears in the first AND second premise but does not appear in the conclusion.
Dave: So listen again and tell me, what word do you hear in both the first and second premise?
All the houses on this street have security systems installed.
The yellow house on the corner is on this street.
Listeners, what did you hear? You should have heard the words “on this street” twice. In the first and second premise. Let’s hear that conclusion again.
Therefore, the yellow house on the corner has a security system installed.
Listeners? You should have heard “yellow house” which was also in the second statement; and “security system” which was also in the first statement, but not “on this street”. Not in the conclusion. And that is what makes “on this street” a properly distributed MIDDLE term. That’s the power of syllogisms in reasoning. By arriving at a conclusion that does not use the middle term, we can reason our way to new information that was not in the first or second premise. Okay? How about this one?
No person under 30 years of age may become a U.S. Senator.
Patricia Vanderbilt just turned 29 today.
Hence, Patricia Vanderbilt may not become a U.S. Senator.
So, can Patricia Vanderbilt become a U.S. Senator? Not until she turns 30.
And as we said earlier, it’s the term that is distributed in the first and second premise.
Minoru: You could have just said, Patricia Vanderbilt is under 30.
Dave: Hmm, I see what you mean. There isn’t one, exactly, worded the same, but being under 30 and being 29 are the same thing. And It doesn’t really matter if she’s 9, 19 or 29. The point is that being under 30 is the middle term. And it’s in the first and second premise.
Minoru: And not in the conclusion.
Dave: So, is that all there is to it?
Minoru: Okay, we have to talk about two grammatical terms, “subject” and “predicate”.
Dave: Listeners, do you understand the difference between a subject and predicate?
Generally, a subject is the main focus of the sentence and the predicate is what comes after. It’s easier to give an example.
The girls are good at math.
In this sentence we have the subject, “The girls” and the predicate “are good at math”.
Minoru: So if you understand that the Middle term must be the subject in one premise and the predicate in the other premise then you can analyse the following argument.
Dave: So, let’s hear the rest of that sample argument.
All the girls in this class are good at math.
Cindy is good at math.
Therefore, Cindy is a girl in this class.
Listeners, do you see the problem? There’s no reason why Cindy couldn’t be in a different class, in a different school, in a different country and be good at math. We can understand that the logic in this argument is broken just by seeing the premises are true, but the conclusion is false.
Minoru: But we can also analyze the structure and see the middle term is the predicate in both sentences.
Dave: And that is why the argument fails. Let’s look at an argument that includes the same information but which correctly distributes the middle term.
All the girls in this class are good at math. Z>B
Cindy is a girl in this class. Y>Z
Therefore, Cindy is good at math. Y>B
Listeners, I hope you can see that this is a good sensible argument.
And that is because the middle term has changed to “is a girl in this class” which is now in the position of predicate in the sentence.
Minoru: So your listeners should now why an undistributed middle leads to an invalid conclusions.
Dave: Yes, to have a correctly distributed middle, the middle term must be the subject of one premise, the predicate of another premise and must not appear in the conclusion. And on that note, I think we are getting close to the end of this part. Before you go, Minoru, is there anything you would like to say about the future importance of critical thinking in the curriculum at Tokyo University of Science?
Minoru: Our students need to know the basic skills of critical thinking that will help them to be competitive in global society. And also, because of the Internet, and how easy [it is] to get good or bad information, it’s going to be more and more important here and at universities throughout Japan.
Dave: Alright, thanks for that. I think you helped us to make sense of the undistributed middle. Now normally, we have you, our guest, stick around for a game of Name that Fallacy, but this episode we are having a review quiz over all the kinds of fallacies that we have learned in these first several episodes. So, I’m going to say goodbye to you now, and I really want to thank you for appearing on the show.
Minoru: Thank you for having me, and keep up the good work!