lecture9(2) - StatementLogic Recall the distinction between...

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

View Full Document Right Arrow Icon
Statement Logic Recall the distinction between categorical logic and statement logic . 1) All A are B 1) if P then Q 2) No B are C 2) if Q then R 3) No A are C 3) if P then R In categorical logic we use letters to stand for terms; the logical vocabulary is ‘all’, ‘no’, ‘some’, ‘not’. In statement logic we use letters to stand for statements; the logical vocabulary is ‘not’, ‘and’, ‘or’, ‘if…then’, ‘if and only if’. For the next four weeks we are going to be focusing on statement logic. We’re going to develop a simple language which will allow us to make explicit the way in which the logical vocabulary determines whether or not an argument is valid, and which will allow us to use more precise methods for determining validity.
Image of page 1

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

View Full Document Right Arrow Icon
Statements: Atomic and Compound Atomic statements do not contain any other statement as a component. Ex. Manny hit two homers The Red Sox won Compound statements contain at least one atomic statement as a component. Ex. Manny hit two homers and the Red Sox won If Manny hit two homers, then the Red Sox won It’s not the case that Manny hit two homers Manny hit two homers or the Red Sox won We will use capital letters to stand for atomic statements.
Image of page 2
Logical Operators Compound statements can be formed by connecting atomic sentences using ‘or’, ‘not’, ‘and’, ‘if…then’, ‘if and only if’. These words are called logical operators , and we have symbols for each of them: Operator Name Translates Type of Compound ~ tilde not negation dot and conjunction v vee or disjunction arrow if…then conditional double-arrow if and only if biconditional
Image of page 3

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

View Full Document Right Arrow Icon
The Language L So we have a language, L. It has: Capital letters, which stand for sentence letters ~, v, ●, →, ↔, which stand for the operators Parentheses, which function as punctuation marks.
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