Philosophy 3121.10
Symbolic Logic
Spring Semester 2014
Class time: Wednesdays, Fridays 11:10 – 12:25
Room: 27, 202K.
Professor: Andrea Pedeferri
Office: Philips Hall 510B.
Office hours: Wednesdays – 12.30 – 1.30
e-mail: .
Logic Tutor:
Office: Phillips Hall 510A
Office hours: TBA
E-mail:
Text: Tomassi. Logic, Routledge.
Course Description:
The aim of this course is to study the formal system of deduction called “natural deduction” both in propositional and in quantificational logic. The course will also have a philosophical part where will be discussed some meta-mathematical results of classical logic.
There are three parts to the course. The first is revising natural deduction in propositional logic (a topic that students should recall from their introduction to logic classes). The second part looks at a more sophisticated formal system of logic, and the third part of the course is more philosophical.
In the first part we will review the language of propositional logic and how to translate from natural language into it. We will then look at the system of natural deduction for propositional logic, how it works and its rules of inferences. We will also quickly review the semantics of propositional logic (truth tables and tree diagrams).
In the second part of the course we shall look at a more sophisticated logical language called ‘quantificational logic’ (known also as “predicate logic’ or ‘first order logic’). This formal language is more sophisticated because it allows us to analyze the structure of propositions. We will learn its vocabulary and formation rules and how to translate from natural language into it. We will then turn to natural deduction for quantificational logic. We will introduce new rules of inference and learn how to generate natural deduction proofs in quantificational logic. We will then turn to the semantics of quantificational logic introducing the notion of a counter-example to the validity of an argument.
In the third part of the course we will discuss the limitative results of propositional logic in contrast to those of quantificational logic. We will also present and discuss some classical meta-mathematical results connected with first order logic.
Logic is not like other arts subjects. You have to be organized and meticulous. You must keep up with the homework and with the reading. If you do not do the reading before class, there is a risk that you will not understand the next class and all future classes. It is better to be bored in class, because you understand too well, than be lost in class.
Attendance in class is important. Attendance is not compulsory. The responsibility is entirely yours for catching up on missed classes. It is a good idea to ask a fellow student if you can copy his, or her, notes and discuss the content of the lecture you missed. In the great majority of lectures, new material is covered, and the knowledge is cumulative and cross-referring. That is, you will find it hard to progress if you neglect a part of the course.
The prerequisite for the course is introduction to logic or permission from me.
Learning Outcomes: By the end of the course, you should be able to:
· Translate sentences and arguments from English into Propositional Logic and Quantificational Logic,
· Make Natural Deduction proofs for valid sequents in Propositional Logic and Quantificational Logic,
· Check the validity of a formal argument in P.L. using truth tables
· Check the validity of a formal argument in P.L. or Q.L. using trees,
· Check the consistency of a set of sentences in P.L. or Q.L. using trees,
· Give a counter-example to the validity of an argument in P.L. or Q.L.,
· Give a model for a consistent set of sentences in P.L. or Q.L.
· Have a command of some key notions such as validity, soundness, consistency, information, reasoning, calculation and the undecidability of a formal proof system.
Schedule
Date / Topic covered in class / Readings, Homework, Assignments for next class.15 Jan. / Syllabus, Validity, Syntax and Semantics. The language of Propositional logic. / Read: Tomassi: pp. 1 – 26, pp. 32 – 39.
Exercises: pp.27, #3. p. 42 # 3.
17 Jan. / Translation, arguments and sequents. Natural deduction proofs. Rules of natural deduction: &I, &E, MP. / Read: pp. 42 – 55.
Exercises: .53 #2.2, 2.6. pp. 55 – 56, #1.2, 1.3 #2.(iii), 2.(iv);
22 Jan. / C.P., augmentation, theorems, conditionals versus entailment, Theorem of Deduction. / Read: pp. 56-70.
Exercises: p. 63 #1.3, 1.4, 1.5, 1.6 p.66, #1.2, 1.3, 1.4. p.69 #1.2.
25 Jan. / The biconditional. / Read: pp.74 – 85.
Exercises: p. 69 #1.1, 1.3, 1.4.
31 Jan. / MT, DNE, DNI, VI. / Read: pp. 86- 108..
Exercises: p. 82 #1.1, 1.2, 1.3, 1.6, 1.8.
5 Feb. / VE, RAA; The golden rule: strategies for proofs. / Assignment I set. Due 7 Feb. Handed out in class. Also as homework exercises: p. 109 revision exercise II #1.5, 1.8, 1.9.
7 Feb. / Revision of natural deduction proofs in P.L. / Read: pp. 122 – 126, pp.163 – 176.
12 Feb. / Semantics. Truth trees for propositional logic. / Exercises: p. 167 #1.1, 1.2, 1.3, 1.4.
15 Feb. / Validity trees and counter-examples. / Read: pp.190 – 197, p.202 - 209.
Exercises: p. 176 # 1.7, 1.8, 1.9, 1.10, 1.12.
19 Feb. / Introduction to Quantificational logic. Q.L. interpretations. / Read: pp. 210 – 224.
Exercises: p.209 – 210 #1.(i), 1.(ii), 1.(iii), 1.(iv), 1.(v), 1.(vi), 1.(xii), 1.(xiii). p. 213 #1.(iii), 1.(iv).
21 Feb. / Validity in Q.L. Negation and the interdefinability of the quantifiers. Introduction to relationships in Q.L / Read: pp. 224 - 232.
Exercises: pp. 216 - 217 # 1.(i), 1.(iii), 1.(iv) 2.(iv). p.221 #1.
26 Feb. / More on Relationships. / Read: pp.235 - 239.
Exercises: pp.232 - 234 #1.(iv), (v), (vii) (viii), 2.(iv).
28 Feb. / Formal properties of relationships. / Read: pp. 240 - 248.
Exercises: pp. 240 #3 (all).
5 Mar. /
Identity and small finite numbers.
/ Exercises: p.244 #1.(iii), 1.(vi), 1.(vii), 1.(ix), 2.(ii), 2.(iv), p.249 # 1.(iv), 1.(v), 1.(vi)7 Mar. / Revision session. / None.
19 Mar. /
MIDTERM EXAM.
/ Read: pp. 266 - 280.21 Mar. /
UE, UI.
/ Read: pp.281- 286, p. 292 – 302.Exercises: p. 272 # 1.4, 1.6, 1.8, 1.10; p. 281 #1.1, 1.3, 1.6, 1.8.
26 Mar. / EI, EE. / Read: pp. 303 - 314.
Exercises: p.286 #1.5, 1.7, p.292 #1.1, 1.10. pp.302 - 303 # 1.1, 1.2, 1.5.
28 Mar. /
Relations, =I, =E.
/ Read: pp. 315 - 328.Exercises: pp. 309 - 310 #1.1, 1.7; pp. 314 - 315 #1.2, 1.7.
2 Apr. /
Strategies for proof in Q.L. Practicing proofs in Q.L.
/ Read: pp. 334 – 346.Exercises: p. 328 revision exercise I #1.1, 1.2, 1.3, 1.5, 1.9. p.329 revision exercise II #1.4, 1.6, 1.9.
4 Apr. / Trees in quantificational logic / Read: pp.347 – 357
Exercises: p. 346 # 1.1, 1.2, 1.3, 1.4, 1.5, 1.6.
9 Apr. / More on trees, counter-examples. / Assignment II set. (Due 11
April) Handed out in class.
11 Apr. / Revision session. / None
16 Apr. / Problems with Q.L.
18 Apr. / Completeness
24 Apr. / Beyond first order
26 Apr. / Revision class for final examination. / Study.
The date, time and place for the final examination will be announced once known.
GRADING
· midterm exam (35 points out of 100),
· final exam (45 points out of 100);
· homework assignments (20 points out of 100). There will be two take-home tests assigned during the semester. Each assignment worths 10 points. It is the student’s responsibility to turn in the homework assignment by the due date (decided by the instructor). Any homework assignment not turned in on time will count as a failed assignment (0 points). It is the student's responsibility to pick up her/his corrected assignment the day the instructor hands the assignments back. Note that ‘Assignments’ and ‘homework’ are not the same thing. Assignments are handed in, given a grade and count towards your final grade. Homework exercises are set almost every class. These are practice exercises for you. They are not handed in. They are not graded. Often, the solutions to the homework exercises will be discussed in class. If you need more practice, then do the other exercises in the book. If we either did not go over the homework in class, or if you are puzzled about another exercise then go to the logic tutor or me to work through the exercise during office hours.
/ Midterm / Final Exam / Final grade /A / 35 / 45 / 94
A- / 32 / 41 / 87
B+ / 29 / 37 / 80
B / 26 / 33 / 73
B- / 23 / 29 / 66
C+ / 20 / 25 / 59
C / 17 / 21 / 52
C- / 14 / 17 / 45
D+ / 11 / 13 / 38
D / 8 / 9 / 31
D- / 5 / 5 / 24
F / 0 / 0 / Below 24
CLASS POLICIES
Our course requires student engagement with the issues and the student's contribution to the class discussion is essential to the success of the course. Up to three unexplained absences are allowed without affecting the final grade. After three absence, 2 points will be subtracted for each absence from the total of 100 points from the attendance grade. If a student arrives after the attendance has been taken, this will be counted as one-half of an unexplained absence. That is, two incident of tardiness will be counted as one unexplained absence. If the student is absent due to illness and turns in a medical note indicating the exact dates under medical care, an additional two absences will be allowed without effecting the attendance grade.
University Policy on Religious Holidays:
Students should notify faculty during the first week of the semester of their intention to be absent from class on their day(s) of religious observance;
ACADEMIC INTEGRITY
I personally support the GW Code of Academic Integrity. It states: “Academic dishonesty is defined as cheating of any kind, including misrepresenting one's own work, taking credit for the work of others without crediting them and without appropriate authorization, and the fabrication of information.”
SUPPORT FOR STUDENTS OUTSIDE THE CLASSROOM
DISABILITY SUPPORT SERVICES (DSS)
Any student who may need an accommodation based on the potential impact of a disability should contact the Disability Support Services office at 202-994-8250 in the Marvin Center, Suite 242, to establish eligibility and to coordinate reasonable accommodations. For additional information please refer to: http://gwired.gwu.edu/dss/
UNIVERSITY COUNSELING CENTER (UCC) 202-994-5300
The University Counseling Center (UCC) offers 24/7 assistance and referral to addressstudents'personal, social, career, and study skillsproblems. Services for students include:
- crisis and emergency mental health consultations
- confidential assessment, counseling services (individual and small group), and referrals
http://gwired.gwu.edu/counsel/CounselingServices/AcademicSupportServices
SECURITY
In the case of an emergency, if at all possible, the class should shelter in place. If the building that the class is in is affected, follow the evacuation procedures for the building. After evacuation, seek shelter at a predetermined rendezvous location.