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April 22, 2004 - 'Logic Made Easy' by Deborah Bennett - 2004-04-22

Broadcast on COAST TO COAST: April 22, 2004

AA: I'm Avi Arditti with Rosanne Skirble, and this week on Wordmaster -- we talk to Deborah Bennett, a mathematician and author. It seemed only logical for her to combine her interests in a new book. It's called "Logic Made Easy: How to Know When Language Deceives You."

BENNETT: "Most of us do not like to be considered inconsistent or contradictory, and those things that you do or say that appear contradictory violate the, quote, 'laws of logic.' I guess another thing that bothered me was all these talking heads [analysts and commentators] on TV that appear to give a logical argument. People need to understand what is and is not logical so that they can weed out the arguments that are not valid, that do not follow."

RS: "Are there some red flags that go up when you're listening to those talking heads, for example? Can you give us some practical idea of how we would identify ... "

AA: "There are laws to this, right? As a mathematician, you must see violations left and right of the traditional laws of logic."

BENNETT: "Right. OK, if I say 'all mothers are women,' it's not necessarily true that all women are mothers. But people will reverse that all the time. For example, maybe just in office conversation or something, you know, maybe somebody will make the claim 'all women are pacifists.' And a man says 'well, I'm a pacifist and I'm not a woman.' But that's the error of the converse. You can do the same thing with an 'if-then' statement."

RS: "Give us an example."

AA: "Because in your book, you call if-then -- [you say] it's been referred to as the 'heart of logic.'"

BENNETT: "Right, right. OK, I just did my taxes. OK, so there's one stipulation that says if you make more than -- I'll probably get the numbers wrong -- ten-thousand dollars in dividend income ... if you make that, then you must fill out Schedule B. It's not the case that if you're filling out Schedule B, it's necessarily because you have more than [ten-thousand dollars in dividend income]. So that would be one example."

RS: "Which is very much like a mathematical equation."

BENNETT: "Yes, any time you're having to agree or disagree to a statement or vote on something in voting referendums, they do this all the time. A statement that's worded in the negative, you'll have to be really careful what voting 'yes' means. So the flags for that are, you know, 'do you want the repeal of the term limits [on elected officials]?'"

RS: "Yes or no."

BENNETT: "So if you vote yes, then you are against term limits. 'Are you in favor of the ban on smoking?' So again it's a negative -- the repeal, the ban. The one I like is, 'do you favor the repeal of the ban on assault weapons?'"

RS: "How should that statement be written?"

AA: "Or was it written a certain way to try perhaps to ... "

BENNETT: "Some people think they are written in such a way so that people will be confused. How should that [be written]? I'm not a lawmaker, I'm not sure I could. But if you wanted to know, I guess, the will of the people, you know, 'do you favor ownership, under certain conditions, of assault weapons?'"

RS: "You're a mathematician. What did you learn about language by writing this book?"

BENNETT: "Well, I learned that language doesn't necessarily follow the same -- the way we use language, the definitions are not exactly the logical definitions. So it's no wonder, really, that people don't always understand."

AA: "What do you mean by that?"

BENNETT: "OK, like you can take an easy word like 'or.' In logic, 'or' means either/or or both. You can say, you know, 'I bet you're an aunt or a mother,' all right? Well, you could be both. But we use the word 'or' all the time -- 'are you coming or going?' So sometimes we use it in what's called the exclusive sense, where [it means] take one or the other, but it can't be both. And yet if you interpret 'or' that way in, say, a logic test or on one of these national tests to get into college or law school or whatever, then you'd be wrong."

AA: Deborah Bennett teaches mathematics at New Jersey City University in Jersey City. Her newest book is called "Logic Made Easy: How to Know When Language Deceives You."

And that's Wordmaster for this week. If you have a question about American English, then here's the logical place to send it: Or visit our Web site: With Rosanne Skirble, I'm Avi Arditti.