Logic & Paradox
One Section Available to Choose From:
|Course Dates||Weeks||Meeting Times||Status||Instructor(s)||CRN|
|June 16, 2014 - June 27, 2014||2||M-F 12:45-3:35P||Open||T B D||10630|
Logic is an essential background thinking toolbox for philosophy, mathematics, all sciences, general reasoning, and critical thought, as well as a fascinating and complex subject of study in its own right. Paradoxes, that is, statements which apparently are at the same time true and false, are an exciting and challenging window into the complexities of logic and the places where everyday intuition breaks down. In this course, students will become familiar with the basics of formal logic, a bit of its history, and some of its paradoxes, where simple ideas produce mind-bending results. Students excited by puzzles, interested in building fundamental skills for math, or looking to be surprised by their basic instincts can often find a brief introduction to logic rewarding.
The course will introduce the basic objects and methods in the world of logic, looking to uncover the secrets behind the paradoxes which we will discuss throughout the course. We will also focus on constructing perplexing scenarios from simple thought experiments, then working on their resolution.
We will ask such questions to build logical intuition as: what is the difference between a valid argument and a sound one? What is the difference between using a word and mentioning it? If no elephant is purple, is this the same as there not existing a purple elephant, or there existing an elephant that is not purple? What does it mean to prove a statement?
In discussing the paradoxes which will motivate our study, we will deal with the most accessible and surprising of classical paradoxes, such as the Russell's paradox (does the list of "all lists that do not contain themselves" contain itself?), the liar paradox (is the statement "this statement is false" true or false?), and the knight-knave puzzle (if there are two guides at a fork in the road, one of whom will only lie, one of whom will only tell the truth, and you want to figure out which road to take, what question can you ask to figure out which way to go?). Students will also be introduced to the history of logic and the interesting struggles which have motivated its study. Some more mathematical puzzles, such as the discussion of systems and completeness (what sort of symbols do we need to express everything we might want to say? Why is any form of mathematics necessarily either incomplete or inconsistent?), will also be discussed.
All in all, the course will be fully self-contained and will provide the foundations for more advanced study in logic, as well as some motivation to do so.
Upon completion of the course, students should be able to have a more thorough intuitive understanding of general reasoning, be able to complete rigorous elementary proofs, and should have a better understanding of the universal importance and applicability of logic, as well as an understanding of why logic can be a fascinating and challenging subject of study. Learning formal logic above all is practice in a particular kind of clear and concise thought; at best, students will feel clearer about their thinking & ability to convey their thoughts.
The course requires no previous knowledge, though a degree of comfort with puzzles or difficult reasoning may be helpful.