Welcome to Elementary Logic
An introduction to formal logic, propositional and predicate. The study of various forms of inference, theorems, derivations and proofs. And a little metalogic thrown in for good measure. McDaniel Plan: QR
About
This course fulfills:
- Old Curriculum: nothing
- New Curriculum: QR
- Phil Major: required for all majors
Quick: here's a problem that will remind you of the SAT:
| Math | : | Physics |
| | : | Philosophy. |
The answer, of course, is Logic. Democritus, the Ancient
Greek philosophy who inspired Socrates to pursue Philosophy, held that the
starting point for the study of all things was the study of the mind. The mind
is our starting place, our point of departure, from which we investigate the
world. In order to understand the world, we must understand how we investigate the world. And in order to understand how we investigate the world, we must first understand
how we reason - and that is the subject of Logic. In short, in order to
understand how we understand, we practice philosophy. And in order
to understand how we reason - either about the world or about our
minds - we study Logic.
The questions 'How do we reason?' and 'How should we reason?' are fundamentally different. And the difference between these two just is the difference between Critical Thinking and Logic. In Critical Thinking classes, we learn 'informal' reasoning: we learn how to analyze and create particular instances of arguments. In Elementary Logic, we learn formal reasoning. We learn how to reason about reasoning itself, regardless of the accuracy of the particular argument at hand.
For example, suppose I claim that "If it is raining, I will carry my umbrella." And that "It is raining." What can you deduce about my actions? Why? Are you certain?
You should be able to say - with absolute, unequivocal certainty - that if my two statements are true, I will be carrying my umbrella. Now suppose that it turns out that I am not carrying my umbrella. Then, with absolute certainty, we should be able to say that one of my first two statements must have been false. There is just no possible way in which my two statements could have been true and the conclusion (that I will be carrying my umbrella) false!
Notice that you need to know nothing about the weather to make these claims. It doesn't matter if it is raining or not - all that matters is that if my first two statements are true, then I must be carrying my umbrella. If one of my two statements is false, well, we can deduce nothing about my umbrella-carrying habits.
Why Study Logic?
When asked this question, my Logic professor in Grad School would retort "Because it is the ultimate practice for life - it's really, really hard and ultimately pointless."
Hysterical. But he does have a point: studying logic sharpens the mind in a way few disciplines do. It's a kind of intellectual calisthenics that we pursue not because it serves some greater purpose, but because it's kind of fun to work your mind. The fact that logic provides the intellectual foundation of arithmetic, provides the theoretical underpinnings of the theory of computing, and opens the entire world of reasoning to its students is really just a side benefit. We study logic because it is interesting. The fact that it applies to just about every intellectual endeavor - well, that's just a bonus.
And if you don't agree with this line of arguing, just remember that operating brain cells burns 6 times more calories than operating muscles. Take Logic! Lose Weight! ;)
Syllabus
Phil 2233 Section 1
BMC 100
MWF 1:50-2:50
Dates and Times
MWF 1:50-2:50,
BMC 100
Description
An introduction to formal logic, propositional and predicate. The study of various forms of inference, theorems, derivations and proofs. And a little metalogic thrown in for good measure. McDaniel Plan: QR
Structure
It is all about the homework. Do it, and the course will run well. Don't, and you'll be lost, the class will be awfully painful, and we'll all struggle.
Here's a rough outline of the course:
- Mondays will be dominated by doing problems from the homework over the weekend.
- Wednesdays may continue that trend, but hopefully will be the day we introduce new material.
- Fridays will be for discussions, queries, etc. Much of the latter half of the semester will be a matter of doing problems together. It is vital that you keep up with your homework and come to class with problems that need to be solved.
Honor Code
As members of the McDaniel college community, I expect that we are all committed to upholding and abiding by our honor system. That means that I will do everything I can to make possibly ambiguous assignments clear and that you are obligated to report any violations. I require that all written work be submitted with the signed honor pledge "I have neither given or received unauthorized aid on this piece of work, nor have I knowingly tolerated any violation of the Honor Code". I will not grade any assignment without such a signature.
Finally, when in doubt, ask. There will be cases, if not in this class, then in others, where the line between citation and plagiarism is vague. And there will be cases in which the line between helping a friend and doing their work will be crossed. Your best bet in finding the line is to ask me. If you ask before hand, you have nothing to worry about. If you wait until after, it might be too late.
Objectives
- To develop the ability to analyze bad reasoning, produce instances of good reasoning, and know the difference.
- To understand and use propositional logic both semantically and syntactically.
- To develop a formal, abstract, analytic skills.
- And most importantly: to question everything.
Materials
Note: the pictured book is the 4th edition. The 5th edition is preferred - the chapters on deductions (which is the hardest part of this course) are much improved.
Requirements
The college believes that "liberally educated men and women think and act critically, creatively and humanely." I expect nothing less. Whether it be in the classroom, in written assignments, and in your preparation for class, I expect you to think and act critically, creatively and humanely.
Attendance: Given the active nature of the course, regular attendance is mandatory. Attendance and participation are a major part of your overall grade (10-15%) and every absence counts. If you must miss a class, please inform me before the class begins so I can restructure the session if necessary. A quick email is sufficient. If you miss more three times, it will begin impact your grade significantly.
Classroom conduct: No cellphones! (or text messaging, pagers, blackberry, PDAs, etc. UNLESS they are being used for taking notes, recording discussions, etc).
The readings and/or assignments noted on the calendar below should be completed before the class begins. These are the readings we will be discussing in class, so if you haven't read the material, you won't have anything to add to the discussion.
Information Technology: I do use blackboard occasionally. There is a copy of this syllabus available, and I will be updating assignments over the course of the semester. In case of conflict or confusion regarding due dates or scheduled readings, between the website and this document, the website always takes precedence.
Special Accommodation: If you are in need of special accommodation, please see me at least 48 hours before the event for which you would need accommodation. I can be very flexible if approached in a timely manner. Making changes after the fact is difficult if not impossible.
Evaluative Criteria
Exams: There will probably be 2 'full' tests and 2 'mini' tests, as well as a final. I've split off a couple of topics for testing on their own via these 'mini' tests in order to clarify what is tested when. The final, however, will be cumulative. If everything goes according to plan, there will be nothing on the final upon which you have not been tested. (Incidentally - parse the previous sentence for extra credit. What must occur to make that sentence false?)
| Assignment | Value |
| Homework | 15% |
| Test 1 | 15% |
| Test 2 | 15% |
| Test 3 | 15% |
| Final | 30% |
| Attendance and Participation | 10% |
Assignments are subject to change according to the flow of the class. In particular, I may replace a paper with a midterm, or a paper with a presentation, or vice versa. Ratios will, however, remain more or less the same: a majority of your grade depends on your final exam and final paper.
OnLine Homework McGraw-Hill just added their Online Learning Center at http://www.mhhe.com/bergmann5e. It should include additional resources for practice as well as the answer key. I haven't been able to access it yet, so I can't testify to its usability.
Tentative Calendar
| Week 1: Introduction |
| Aug 25 | |
| Aug 27 | 1.3, 1.4, 1.5 |
| Aug 29 | 1.6: 1,3,5,6 |
| Week 2: Propositional Syntax |
| Sept 1 | No Class - Labor Day |
| Sept 3 | 2.1: 1,3,5; 2.2: 1,3 2.3 |
| Sept 5 | 2.4: 3,4,5 |
| Week 3: Propositional Semantics |
| Sept 8 | 3.1 and 3.2 (5) |
| Sept 10 | 3.3 1, 2; 3.4 1, 2, & 4 |
| Sept 12 | 3.5 1, 2, 3 & 5 |
| Week 4: |
| Sept 15 | 3.6 1, 2, & 3 / Review |
| Sept 17 | Exam |
| Sept 19 | Truth-Trees introduced. Read 4.1 & 4.2 |
| Week 5: Prop. Truth Trees |
| Sept 22 | 4.2-4.3 |
| Sept 24 | 4.4 1, 4.5 1,2 & 4 |
| Sept 26 | 4.6 1 & 2 |
| Week 6: Propositional Derivation |
| Sept 29 | Mini-Exam on Truth Trees. Derivations introduced. |
| Oct 1 | 5.1.1-5.1.4, read 5.2 |
| Oct 3 | READ 5.3. 5.3 1 & 2 |
| Week 7: Midterm |
| Oct 6 | 5.3 3 & 4 |
| Oct 8 | 5.3 5-7 |
| Oct 10 | 5.3 8 |
| Week 8: SD+ |
| Oct 13 | Fall Break |
| Oct 15 | 5.4 1,2,3 |
| Oct 17 | 5.4 4 & 5 READ 6.1 |
| Week 9: Metatheory! / Predicate Symbolization |
| Oct 20 | 6.2-6.4 |
| Oct 22 | 7.1-7.3 (1-3) (Symbolization without Quantifiers) |
| Oct 24 | 7.4-7.5 (Quantifiers) |
| Week 10: Predicate Syntax |
| Oct 27 | 7.6 & 7.7 (Math / C.S. / Philosophy Majors: 7.8 & 7.9) |
| Oct 29 | 8.1 & 8.2 |
| Oct 31 | 8.1 1-3; 8.2 1-3 |
| Week 11: Predicate Semantics |
| Nov 3 | 8.3 1-3; 8.4 1-3 |
| Nov 5 | 8.5 1-5 (Math / C.S. / Philosophy Majors: 8.6 & 8.7) |
| Nov 7 | Exam on Predicate Symbolization & Semantics |
| Week 12: Predicate Derivations |
| Nov 10 | 10.1 |
| Nov 12 | 10.2 1-3 |
| Nov 14 | 10.2 4-5 |
| Week 13: Predicate Derivations |
| Nov 17 | 10.2 6 & 7 |
| Nov 19 | 10.3 1 & 2 |
| Nov 21 | 10.3 3 |
| Week 14: Predicate Semantics |
| Nov 24 | Mini-Exam on Predicate Derivations |
| Nov 26 | Thanksgiving |
| Nov 28 | Thanksgiving |
| Week 15: Predicate Trees? |
| Dec 1 | 9.1-9.2 |
| Dec 3 | 9.3 1-4 |
| Dec 5 | Review / Metatheory |
|
Dr. Peter Bradley
