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Department of Philosophy

Symbolic Logic I: PHIL 120 - 851 (Remote)

Winter 2023

Description

We can think of logic as the study of consistent sets of assertions, as the collection of all valid inferences, or even, albeit less thematically, as the rules that govern our reasoning. In this course, we will take all these definitions into account, with the fundamental premise that our inquiry will aim at formal logic, that is, a mathematically precise method of framing those concepts. This is what  "symbolic"  stands  for,  a  rigorous  translation  of English  into  a  formal language through unambiguous mathematical symbols.

Accordingly, our first goal will be to formalize sentences with an increasing degree of complexity by  dealing  first  with  the  syntax  of propositional  logic  and then predicate or first-order logic. Secondarily, we will investigate the semantics of these two systems by effectively using truth tables and Tarski's interpretations. This part will tackle notions of "satisfiability" and "logical truth" of a sentence, as well as "validity" and "soundness" of an argument. We will then proceed to define and put to practical use a proof system for first-order logic.

Course Objectives

This course covers both truth-functional logic’ (or sentential logic, or propositional logic) and first-order logic (or predicate logic, or logic of quantifiers). In each of truth-functional logic (TFL) and first-order logic (FOL), the three main areas we will explore are

Syntax

Semantics

Derivations

At the end of the term, you will be able to:

1.   Understand the specific logical sense of a sentence, an argument, and premises and the conclusion of an argument;

2.   Distinguish deductive arguments from other types of arguments;

3.   Understand fundamental concepts of deductive reasoning, such as validity, soundness, logical consequence, theorem, and axiom;

4.   Analyze the meanings of sentential connectives, such as “and” , “or”, “if-then”, and “not” ,  and quantifiers, such as “all” , “some”, and “none”, in English and distinguish their specific meanings in symbolic logic;

5.   Learn a symbolic language characterized by mathematical precision;

6.   Translate sentences from English into that symbolic language;

7.   Interpret sentences in the symbolic language, and apply those interpretations to determine the validity of arguments;

8.   Learn rules of inference and analyze how they determine the meanings of sentential connectives and quantifiers with mathematical precision;

9.   Apply those rules and construct derivations or proofs to analyze how the information of a      conclusion can be extracted from the information contained in the premises step-by-step with mathematical rigour;

10. Have some basic understanding of the metatheory that frames the main properties of elementary logic.

Course Format:

This course is delivered remotely; no classes, office hours, or exams are currently held on campus. Each week our routine will be as follows:

-     On Tuesdays, we have an online session (synchronous class) on Zoom from 6:00 to 7:30 PM.  Attending  Zoom  sessions is not mandatory, and all the sessions are recorded and posted on eClass, but it provides an opportunity to get involved in live discussions over the weekly topics. The Zoom link for the live session is on the main page of eClass.

-     On Wednesday, we do not have a live online class; instead, I will upload material relevant to the current topic (exercises, short video lectures, etc.).

-     The  free,  digital  textbook,  notes,  and  class  exercises  are  provided  on  eClass.  Also,  all assignments and exams are held on eClass.  So, no platforms, applications, or software other than eClass are needed.

Textbooks:

The required textbook for this course is Forallx Calgary: An Introduction to Formal Logic. This textbook is  available  online  for  free. It  can be  found on  eClass  or downloaded  from this link: http://forallx.openlogicproject.org/forallxyyc.pdf.

The  main  textbook  is  paired  with the  exercise book Forallx Calgary: Solutions to Selected Exercises,  which,  likewise,  is  uploaded  on  eClass  and  available  for download  from this link: http://forallx.openlogicproject.org/solutions/forallxsol.pdf.

Additional Course Fees: N/A

Important Dates:

First Day of Class: January 10th

Add/Delete Deadline: January 18th

50% Withdrawal February 6th

Midterm Exam Date: February 14th

Withdrawal Date: April 4th

Last Day of Class: April 11th

Final Exam Date: April 11th

Date of Deferred Final Exam: N/A

Lecture Schedule & Assigned Readings:

Week

Dates

Topic

Readings (textbook)

1

Jan. 9 – Jan. 15

Introduction

Part I, Part II

2

Jan  16 – Jan  22

Truth-functional logic (TFL): syntax

Part II

3

Jan. 23 – Jan. 29

Truth-functional logic (TFL): semantics

Part III

4

Jan. 30 – Feb. 5

Truth-functional logic (TFL): derivations

Part IV

5

Feb  6 – Feb  12

Truth-functional logic (TFL): derivations

Part IV

6

Feb. 14

Midterm Exam

RW

Feb. 20 – Feb. 26

Reading Week

7

Feb  27 – Mar  6

First-order logic (FOL): syntax

Part V

8

Mar. 6 – Mar. 12

First-order logic (FOL): syntax

Part V

9

Mar. 13 – Mar 19

First-order logic (FOL): semantics

Part VI

10

Mar. 20 – Mar. 26

First-order logic (FOL): semantics

Part VI

11

Mar. 27 – Apr. 2

First-order logic (FOL): derivations

Part VII

12

Apr. 3 – Apr. 7

First-order logic (FOL): derivations

Part VII

13

Apr. 11

Final Exam

Components of Course Grade:

Component

Weighting

Date Due

Take-Home assignments (4)

20% (each assignment worth 5%)

Jan 31st, February 7th, March 21st, April 4th

Midterm exam (by submission on eClass)

35%

Tuesday, February 14th

Final exam (by submission on eClass)

45%

Tuesday, April 11th

In this course:

Homework assignments: There will be 4 assignments each of which is worth 5% of the course grade.  Assignments  questions  are  uploaded  on  eClass  5  days  before  the  due  date  of each assignment (Typically: posted on Friday and to be submitted by the following Tuesday). Answers should be submitted on eClass by 6 PM of the due date according to the above schedule. For the policy for late assignments, see below.

Midterm exam: The  midterm  exam  will  contain  a  set  of multiple-choice  or  short-answer questions. It has a 60 minutes time limit. The midterm will be opened at 1 PM and closed at 9 PM on February 14th . You are free to start the exam whenever you please between the hours of opening, but from the moment you start the timer cannot be stopped.

Final Exam (tentative): The midterm exam will contain a set of multiple-choice or short-answer questions. It has a 90 minutes time limit. The final will be opened at 1 PM and closed at 9 PM on April 11th . You are free to start the exam whenever you please between the hours of opening, but from the moment you start the timer cannot be stopped.