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DistLectOSU042308 - 1 LOGIC Interdisciplinary Adventures in...

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1 LOGIC: Interdisciplinary Adventures in Mathematics, Philosophy, Computer Science, and Education by Harvey Friedman University Distinguished Lecture The Ohio State University April 23, 2008 I want to thank President Gee for his (overly) kind remarks. I am very glad to see Gordon return to Ohio State this academic year. I also want to thank the Mathematics, Philosophy, and Computer Science and Engineering Departments who thought of me for this honor. Thanks also to the Selection Committee and the Office of Academic Affairs for choosing me for this occasion. In looking over the past University Distinguished Lectures, archived on the OSU website, the topics have generally had a clear and transparent relevance to our daily lives. We have been delightfully treated to Climate History, Legal Aspects of Civil and Human Rights, Superhuman Capabilities of Animals, Psychological Aspects of Cancer, Energy, Food, and Water Scarcity, Americans with Disabilities Act, and The Federal Reserve on 9/11 – just to name a few. Most recently, Kevin Boyle just gave a dramatic Lecture on the Dynamics and Implications of the Sacco/Venzetti Trials. And Marilyn Brewer gave a fascinating Lecture on the Psychology of Social Groups last Spring. Now, I want to warn you that this talk will be relatively painful. For some of you, it’s going to be about 50 minutes too long. So I want to give a very short version of the talk. LOGIC IS EVERYWHERE! Let me make it even shorter: LOGIC EVERYWHERE!
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2 For those of you who have remained in the audience, here is the 50 minute version. There will be a number of words and phrases that I won’t have time to explain in detail. I have displayed these in yellow text, and I think you will find it informative to jot these down and search them on the Internet. You can of course search for LOGIC WIKIPEDIA. I am going to talk about LOGIC as the science of reasoning. We all do reasoning. Some of it is entirely straightforward and second nature. Some of it is highly complex and subtle. And the quality of this reasoning that we all do ranges from obviously valid, to highly questionable – and worse! But doing reasoning is one thing – having a deep understanding of what it is, how we do it, how we should do it – is quite another. We do not have anything approaching a deep scientific understanding of reasoning in most contexts – not in common sense, not in the arts, and not in the sciences. These are wide open topics of research. However, we do have a relatively deep scientific understanding of at least some key aspects of mathematical reasoning. But first, I want to start with some very limited situations in common sense thinking, where we do have a deep understanding. Let us consider the five logical connectives:
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