LEC2HPS.10EEE - Lecture#2 Human Problem Solving(Cont of...

Info icon This preview shows pages 1–9. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Lecture #2 Human Problem Solving (Cont. of Lec. #1) III. Taxonomy of Conceptual Products D. Logical Paradoxes E. Practical Problems F. Games
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 D. Logical Paradoxes A logical paradox is an assertion or line of reasoning contrary to common sense. Type 1 . An assertion that seems true (false) but is actually false (true). Type 2 . A line of reasoning that seems impeccable but leads to a contradiction of logic. The term paradox may not have immediate connections to logic, e.g. a paradoxical personality
Image of page 2
3 A Type 1 Example Consider the following assertion; “You can not draw a ‘perfect map’ of England in a London flat, but you might be able to do it in a New York City pad.” The statement seems false ( you either can do it in both places or you can not do it in either place), but there is an interesting sense in which the statement is true. Most logical paradoxes set in real world settings as opposed to a formal logic setting require a person to interpret things in a certain way to ‘get the point’.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Solution Hint Hint 1- Now just what might be a ‘perfect map’? Hint2- Remember my discussion of the infinite reflection of a person in two mirrors. Of course you could argue as a matter of practical truth that a ‘perfect map could not be drawn anywhere. True, but is there any interesting sense of the problem that would make New York different than London. 4
Image of page 4
Solution Now the difference between being in England and new York is that you would have to depict yourself on the map drawn in London. And what would you be doing? Drawing a map, and you would have to be on that, doing what? etc., etc. 5
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
6 Self Reference Paradoxes There is a long history of logical paradoxes that result from the case where a logical arguments ‘talks about (references) itself.’ A philosopher from Crete in 6 BC named Epimenides exclaimed 'All Cretans are liars!' . If Epimenides' statement is true, then he is a liar and hence his statement is false. A contradiction. If Epimenides' statement is false, then it would be possible to find a Cretan who sometimes tells the truth----- Of course it wouldn’t be Epimenides
Image of page 6
7 The Liar’s paradox So far we do not have a logical paradox, but a small change results in the so-called liar’s paradox. In 4 BC Eubulides of Miletus stated “ I am lying” If true, then he is lying, so his statement is false. If false, he isn’t lying, so the statement is true. In the New Testament of the Bible, Saint Paul warned, “One of themselves, even a prophet of their own, said that the Cretans are always liars.” Later A French philosopher wrote on an otherwise blank page, “ All statements on this page are false.”
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
8 More on the Liar’s paradox Suppose the last sentence in today’s NYT is: ‘The last sentence in tomorrow's edition of The New York Times newspaper is true.’ There seems to be nothing paradoxical about this except tomorrow when you get the paper you see as the last sentence: ‘The last sentence in yesterday's edition of The New York Times newspaper is false.’ This is a bit like the map paradox.
Image of page 8
Image of page 9
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern