Symbolic Logic I: PHIL 120 - 851
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
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.
2023-03-02