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HPSLEC2.10EEE (1)

# HPSLEC2.10EEE (1) - Lecture#2 Human Problem Solving(Cont of...

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1 Lecture #2 Human Problem Solving (Cont. of Lec. #1) III. Taxonomy of Conceptual Products D. Logical Paradoxes E. Practical Problems F. Games

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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
Can you find any interesting sense of the following paradoxical statement? It is impossible to draw a perfect map of England while standing in a London flat, but it might be possible to do it in a New York City pad. 3 A Type 1 Paradox

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4 The Map Paradox 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. Of course as a practical matter you could not construct one anywhere. But you are invited to find an interesting sense that explains the paradoxical statement. 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’.
5 Self Reference Paradoxes Hint: What exactly is a perfect map? 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

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6 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.”
Eubulides was a contemporary and opponent of Aristotle. He excelled at creating paradoxes that challenged language and logic. The ‘Heap Paradox’: “ A single grain of sand is not a heap. Nor is the addition of a single grain of sand enough to transform a non-heap into a heap; yet when we continue this process of adding a single grain we will obtain a heap at some step.” This gets at mathematical induction and recursion. More later. Language challenges,

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HPSLEC2.10EEE (1) - Lecture#2 Human Problem Solving(Cont of...

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