A Quick Review

Author
Affiliation

David W. Agler

The Pennsylvania State University

Abstract
A review of chapters 1 and 2.

Course Administration

Exam

You will take Exam 1 in Pollock Testing Center

  • On Monday, you will get an email from them to schedule
  • Pick date and time: Monday (9/28) and Tuesday (9/29)
  • The exam is on Canvas in the Center

Exam Contents

You can find a sample of the exam questions on my website: Practice Exams

NoteCommon Mistakes
  1. Semantics: If \(v(P)=T\) and \(v(D)=F\), then what is the truth value of \(P\to D\)
  2. Translation: Translate the following sentence into the language of propositional logic: ‘Bob is happy and Vic is ambitious’.

Homework

  • For Homework 1, complete Exercises 1.1-1.8, 2.9-2.26.
  • You may skip Exercises 2.27, 2.28, and 2.29.
  • Staple / paperclip your homework together

Give it to me either 9/25 (Friday) or 9/28 (Monday)

NoteCommon Mistakes
  • Not doing every exercise set
  • Skipping an entire chapter or exercise
  • Not stapling it

Why Ch3?

Exam 1 covers chapters 1 and 2. Why are we starting Ch3?

  • Reason 1: Scheduling issues
  • Reason 2: Potential Upside

Advice

  1. Do the homework now!
  2. Look over the practice exam sample questions: Practice Exams
  3. Email me if anything is unclear.
  4. You want mastery not just competency

Questions?

Quick Review

Ch1

This chapter focused on four things:

  1. What is Logic?
  2. Identifying three criteria for evaluating arguments: C follows from Premises, Relevance, Truth
  3. Getting more precision about “C follows from Premises” through the concept of validity
  4. Showing that informal tests for checking for validity (intuition and imagination) are bad

Key Takeaway

  • On their own, people can identify good and bad arguments but the methods are not reliable
  • Logic is useful because it will make us better at identifying good and bad arguments

Ch2

This chapter focused on two things:

  1. The language of propositional logic (PL): Symbols, Syntax, Semantics
  2. How to translate from English into PL and vice versa

Key Takeaway

We can take certain arguments in Englisn and translate them into PL:

  • P1. Tek is a good dancer iff he has flexible ankles.
  • P2. Tek has flexible ankles.
  • C. Tek is a good dancer.

Translation

  • P1. \(G\leftrightarrow F\)
  • P2. \(G\)
  • C. \(F\)

Continued

We then can use tools to check if this argument is valid

  • P1. \(G\leftrightarrow F\)
  • P2. \(G\)
  • C. \(F\)

Every argument that has this structure will be valid: \(G\leftrightarrow F, G\) therefore \(F\)

Continued 2

Eventually you’ll (1) see the logical structure in the English and (2) know it is valid because you know it has a valid structure

  • P1. Tek is a basketball player iff he is tall.
  • P2. Tek is a basketball player .
  • C. Tek is tall.