W HAT IS L OGIC ? logic as good reasoning In this view, logic is - PowerPoint PPT Presentation

P HIL 2310: I NTRODUCTION TO D EDUCTIVE L OGIC Wednesday, 25 August Joel Velasco Wednesday, August 25, 2010 1

A GENDA Introductions Course Information What is logic? Wednesday, August 25, 2010 2

C OURSE I NFORMATION Joel Velasco Language, Proof and joelvelasco@cornell.edu Logic Office: Goldwin Smith 228 Barwise and Etchemendy 2-3pm Tue, 2:30-3:30 W, or email for appointments Software Course Requirements Tarski’s World, Fitch and 30% Homework Boole 20% x 2 for prelims 30% Final Wednesday, August 25, 2010 3

H OMEWORK Assignments Collaboration posted online one week - discuss anything you want before due date: Everything - we encourage working is posted at: http:// in groups! courses.cit.cornell.edu/ jdv55/teaching/2310/ - complete/submit your work without consulting Submission others or group work online: Grade Grinder written: bring to class typically due Monday No Late Work Wednesday, August 25, 2010 4

G RADE G RINDER 1 2 3 Wednesday, August 25, 2010 5

W HAT IS L OGIC ? logic as good reasoning In this view, logic is about the difference between valid and invalid arguments In a valid argument, the conclusion follows from the premises. IF all of the premises are true, then the conclusion is (must be, would be...) true. Equivalently: It is impossible for all of the premises to be true and the conclusion false. Wednesday, August 25, 2010 6

V ALIDITY AND A RGUMENTS (1) If our currency loses (1) If our currency loses value then our trade value then our trade deficit will narrow. deficit will narrow. (2) Our currency will lose (2) Our trade deficit will value. narrow. Conclusion: Our trade Conclusion: Our currency deficit will narrow will lose value Wednesday, August 25, 2010 7

V ALIDITY AND A RGUMENTS (1) If our currency loses P → Q value then our trade deficit will narrow. (2) Our currency will lose P value. Conclusion: Our trade Q deficit will narrow V ALID Wednesday, August 25, 2010 8

V ALIDITY AND A RGUMENTS (1) If our currency loses P → Q value then our trade deficit will narrow. (2) Our trade deficit will Q narrow Conclusion: Our currency P will lose value. INVALID Wednesday, August 25, 2010 9

V ALIDITY AND A RGUMENTS (1) If the continuum P → Q hypothesis is true then the set theoretic universe is constructible P (2) The continuum hypothesis is true Q Conclusion: The set theoretic universe is constructible V ALID Wednesday, August 25, 2010 10

V ALIDITY From these examples we can see that validity as a property of arguments is: (1) topic neutral (2) independent of actual truth and falsity We didn’t need to know any economics or any facts about the world to judge the validity of the previous two arguments. Wednesday, August 25, 2010 11

W HAT IS L OGIC ? logic as good reasoning versus logic as a system First-Order Logic (FOL) computers and programming languages differences between FOL and natural language; the role of formal logic logical consequence and methods of proof Wednesday, August 25, 2010 12

T HIS C OURSE Learn two systems of FOL: propositional logic and predicate logic Convert natural language arguments into FOL Create and assess proofs in FOL Keep in mind advantages of FOL; possible limitations of FOL; relationship between FOL and natural language Wednesday, August 25, 2010 13

Recognizing versus Diagnosing Bad Reasoning Wednesday, August 25, 2010 14