PHIL 240.200: Honors Introduction to Logic

Robin Smith, Spring Semester 1999

NEW: a web form with which you can check your grades

Some Basic Things

Who, Where, and How


The textbook for this course is:
Logic Primer, by Colin Allen and Michael Hand (MIT Press, 1992).
At \$15.00, this text is a great buy (for which you have the authors, two members of the A&M Philosophy Department, to thank: they wanted the publisher to keep the price as low as possible). However, it is not a text intended for independent study: it assumes that you actually have an instructor to supply some explanations, discussions, enrichments, and the like. Thus, there is a reason to come to class. There is also web-based support available related to this text at the Philosophy Department's logic computing lab site ( In particular, you will find there a creature called The Logic Daemon with which you can check your solutions to homework exercises. For that matter, you can the text itself online at (but please note that, as the copyright notice on that page specifies, you are not permitted to print off copies). But there's still a reason to come to class.

Formal course work and grading policies

Here are the formal requirements for this course: Exam
Tentative DateProportion of your grade
Exam 1February 2220%
Exam 2March 1220%
Exam 3April 1620%
In a sense, all the exams in this course are cumulative, since the material you learn for each exam is presupposed by the remainder of the course. I also substitute your second-highest hourly exam grade for your lowest hourly exam grade, so you get the opportunity to blow one exam.

Makeup Exams

If you really are prevented from taking an exam for reasons outside your control, and if you give me a good account of those reasons (including University-approved absences), then I will make arrangements for an alternative exam time. However, it is your responsibility to tell me about this as soon as you can. If you're ill, that means the first day you return to class. If it's a University-approved absence, then let me know beforehand.


Doing homework is absolutely essential for learning logic, but I do not keep a record of what you've done. I'll assume you are responsible enough to do it yourself before class (that way, you'll get considerably more out of the discussions of problems in class).

Attendance and Participation

I do not assign a formal percentage of your grade to attendance or class participation. The benefit of attending class is that you learn a lot about logic that will, among other things, be really helpful in taking the exams. If you don't come to class, you will probably suffer.

Academic Honesty and Its Opposite.

Academic dishonesty includes not only getting someone else to do your work (with or without their knowledge) but also knowingly doing someone else's work for them. This applies to take-home assignments as much as to in-class work. Under Texas A&M's policies, students guilty of academic dishonesty may receive lowered grades and other more severe penalties. For more details, see Section 20 of the Texas A&M University Regulations (maintained on the University's web site at

The Content of This Course

We will study two formal systems of logic: a simple system for sentential (or propositional) logic, and an expanded system for predicate logic. For each of them, we will study: (1) the formal language itself; (2) ``translation'' (of a limited sort) from English into the formal language; (3) constructing proofs of validity for arguments in the language; (4) a semantics, or model theory, for the language.

How to Study Logic

Logic isn't actually a very difficult subject. The formal languages we will be studying are very simple---downright primitive, by comparison with natural languages such as English. Most students will find that they can get along pretty well in this course, provided they remember three important rules:
Courses in logic, like courses in mathematics or in a foreign language, are cumulative and require that you learn certain skills. In order to learn any skill, you've got to practice, which in this case means doing exercises. Repetition is extremely important; you'll never succeed merely by reading through the text. It's also essential to have some guidance on how to do logic, and that is what classes are for. Class is also the place to ask questions about what you don't understand. And, since the material is cumulative, it's very, very, very important to keep up: if you get behind, you may wind up staying behind. If you find yourself having trouble with the material, ASK FOR HELP EARLY. If you wait until April to try to catch up, don't expect me not to say I told you so, because I just did, and so I will. Of course, when you do exercises, you'd like to know if you are doing them correctly. There are solutions for some of the exercises in the back of the text, but in the case of proofs there are typically many correct solutions. The best way to check yours is to use the Logic Daemon; this also has the advantages that it will give you instant feedback, without charging you any money, and that it works 24 hours a day.

What Use Is Logic?

Among other things, formal logic aims at representing certain aspects of human reasoning, especially those involved in such processes as deductive inference and mathematical proof. Not surprisingly, then, logic has many applications in areas where these aspects of reasoning are important. In the last few decades, by far the most prominent of these has been computers, which are essentially logic machines. But you say you're not interested in designing any computer circuitry? Well, for most people, the largest benefit of studying formal logic is something quite different. In order to construct deductions in a formal logical system, you need to acquire certain skills that will turn out to be of importance in the kind of strategic thinking you will probably need to do no matter what your choice of career. One of these is figuring out how to reach a desired goal with a given set of resources. Another is the habit of attending precisely to what a statement says (and does not say). A third, more closely linked to the application of logic to natural language, is the ability to see important distinctions. Finally, if you acquire some appreciation for the notion of a valid argument and for the distinction between valid and invalid arguments, then you may find that you are not so easily swayed by the rather large number of atrocious arguments that circulate around us every day. Since this is an Honors section, I'll include in the class lectures some supplementary material about the more theoretical aspects of logic and some discussions of more advanced topics. This syllabus will expand, as the course proceeds, into a fairly extensive set of supplementary notes.

Schedule for the Semester

The table below gives the schedule for readings, exercises, and exams. Nothing about it will be changed except for the parts that get changed. Check the course web site for changes. \flushleft
  Jan. 20, 221.1--1.3: Defining a formal language; expressions and wffs 1.3 
  Jan. 27, 291.3: Translating English into logicalese 1.1, 1.2, 1.3  
  Feb. 1--51.4: What proofs are; the primitive rules; simple proofs  
  Feb. 8--121.5: What sequents are; Derived rules; less simple proofs (look here for hints on how to find proofs) 1.5, 1.6  
  Feb. 15, 171.6: What theorems are; proofs of theorems (moe hints on how to find proofs) 1.7, 1.8 
  Feb. 19 Review for Exam 1: (1) basic notions, definitions; (2) translation from English to sentential wffs; (3) proofs using primitive and derived rules of proof. 
  Feb. 22  EXAM 1
  Feb. 24--262.1: Truth tables for sentences2.1 
  Mar. 1--52.2, 2.3, 2.4: Truth tables for sequents; validity; tautologies2.2, 2.3 
  Mar. 82.4: Indirect truth tables2.4 
  Mar. 10Review for Exam 2: (1) basic truth tables; (2) truth tables for complex statements, arguments; (3)tautologies; (4) indirect truth tables 
  Mar. 12  EXAM 2
  Mar. 15--19  SPRING BREAK (Go home!)  
  Mar. 22--26  3.1: The language of predicate logic. (I will be distributing some supplementary notes on predication) 3.1, 3.3, 3.4  
  Mar. 29, 313.2: Translating English into predicate logic (with supplementary notes on translation) 3.5 
  Apr. 2READING DAY (no class) 
  Apr. 5--143.3: Predicate logic proofs; primitive rules (with supplementary notes on predication)3.5, 3.6 
  Apr. 16Review for Exam 3: (1) predicate logic formulas; (2) translating English into predicate logic; (3) predicate logic proofs with primitive rules 
  Apr. 19  EXAM 3
  Apr. 21--233.4: Derived rules, theorems for predicate logic3.7, 3.8 
  Apr. 26--304.1, 4.2: Semantics for predicate logic: finite interpretations4.1, 4.2, 4.3 
  May 3Review   
  May 4  You may think this is Tuesday, but it's actually Friday, so we have a class. It's our last one.  Review for final 
  May 5, 6READING DAYS (Stay home!)  
  May 10  FINAL EXAM, 8:00--10:00 AM