{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture04 - PHIL V3411 PHIL G4415 Introduction to Symbolic...

Info icon This preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
PHIL V3411 / PHIL G4415 • Introduction to Symbolic Logic Lecture 4 Sentential Logic: Truth-tables, Logical equivalence
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
INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 4 P. 1 A Puzzle You are on an island where there are two kinds of inhabitants: 1) Knights, who always tell the truth 2) Knaves, who always lie. You meet two of them, Alf and Beth. Alf says: At least one of us is a Knave. What are Alf and Beth? Solution Alf cannot be a Knave, since if he were, what he says would be true (which is impossible: Knaves always lie). So he must be a Knight. But if he is a Knight, then what he says is true. So the other person, Beth, must be a Knave.
Image of page 2
INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 4 P. 2 Formal Explanation Alf’s statement, At least one of us is a Knave, can be expressed as the negation of a conjunction: We are not both Knights i.e. It is not the case that (Alf is a Knight and Beth is a Knight) which has the logical form ¬ ( A B ) We can construct a truth-table for this expression: A B A B ¬ ( A B ) T T T F T F F T F T F T F F F T Note: T means that Alf is a Knight F means that Alf is a Knave Inspection of the table shows that only the second row is possible (since ¬ ( A B ) corresponds to a statement of Alf’s).
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
INTRODUCTION TO SYMBOLIC LOGIC, LECTURE 4 P. 3 How to Construct a Truth-Table (Section 2.1.3) To construct a truth-table for a
Image of page 4
Image of page 5
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