Telephone: 280-1219

Class Meetings. M W F 1:30-2:20 in Humanities Center, Room 316

Office Hours. M Tu W Th 2:30-3:20

or by appointment

This course is a study of the formal analysis of reasoning employing the state-of-the-art tools of modern symbolic logic. We will translate arguments stated in a natural language (in this case, English) into symbolic form and then use the methods of symbolic logic to determine whether those arguments are valid or invalid. As the course progresses, we will employ successively more sophisticated tools of analysis. First, we will use sentential logic to assess the validity and invalidity of arguments at the level of sentences. Next, we will employ the more finely tuned tools of monadic predicate logic to demonstrate the validity of some arguments that appear invalid when analyzed with the coarser instruments of sentential logic. Finally, we will attain further precision of analysis by employing the tools of general predicate logic, also known as first-order logic with identity.

There are at least three good reasons for a philosophy student to study symbolic logic. (1) Modern symbolic logic is the most powerful and sophisticated tool that we have for analyzing reasoning. For this reason, those who want to improve their reasoning skills would be well advised to study symbolic logic. (2) Modern symbolic logic is perhaps the most important theoretical tool of twentieth century Anglo-American philosophy. Thus anyone who wants to understand contemporary English-language philosophy needs to have a solid grounding in the elements of symbolic logic. (3) Since at least the time of Leibniz, philosophers have sought to analyze natural-language reasoning in a symbolic, quasi-algebraic way so that disputes about the validity of an argument could be resolved by stating the argument formally and checking its steps mechanically. Modern symbolic logic is the closest we have come to completing this search. Along the way, logicians have sometimes had to sacrifice accuracy in the translation of natural language arguments for the sake of obtaining inference rules that permit us to check arguments’ validity mechanically. This raises the interesting philosophical question of whether modern symbolic logic accurately captures our notion of a valid argument, or whether it strays from this notion in order to attain formal rigor. We will discuss this question and others related to it in class and you will have the opportunity to write essay questions on this subject on the class tests.

Graeme Forbes, Modern Logic: A Text in Elementary Symbolic Logic (Oxford UP)

Three class tests and one final examination, worth 15% each (60%)

• Class tests are tentatively scheduled for Sept. 21, Oct. 9, Nov. 13
• Final examination is scheduled for Friday, Dec. 18, 10:00-11:40 am

Approximately eight to ten quizzes, each graded on a 20-point scale (30%)

• Quizzes will not be announced in advance, and cannot be made up without a documented excuse

Participation in class discussions (10%)

1. The class tests will be designed in part to test your skills at employing the tools of symbolic logic. Typical tests will thus include questions requiring you to translate English-language sentences into the language of symbolic logic, demonstrate the invalidity of an argument by constructing a counterexample to it, and demonstrate the validity of an argument by constructing a formal proof of it. But in keeping with the twofold aim of the course, most tests will also ask you to discuss philosophical questions about the success or failure of modern symbolic logic in analyzing natural-language reasoning. Thus most tests will also include one essay question about some aspect of this philosophical project. Possible topics for these essay questions will be discussed in class in advance of each test.
2. You have two options with respect to the final examination, namely the default option (a) and the alternative (b).

1. The default option is to write a traditional final exam on Friday morning, Dec. 18. This exam will come in two parts, the first of which will be identical in most respects to a class test on first-order logic with identity (Forbes, Chapters 7-8). The second half will be a philosophical essay question that will ask you (more or less) to assess the overall success or failure of the project of modern symbolic logic.
2. The alternative is a take-home exam that will take the form of a short paper (approximately 1000 words) on one of the extensions or alternatives to first-order logic that Forbes discusses: modal logic (Chapter 9), intuitionistic logic (Chapter 10), and fuzzy logic (Chapter 11). Details about this alternative will be discussed in class sometime after the third class test in November, but you should feel free to ask me about it in advance, if you like.

1. Both regular class attendance and regular practice of your logical skills on homework problems are important to success in this course. In the interest of treating you like adults, however, I am not going to check up on you directly by taking attendance or collecting homework. Instead, we will have quizzes on a regular, roughly weekly basis. These quizzes will encourage you to attend class because they will not be announced in advance and they cannot be made up. You can be excused for having missed a quiz, however, if you provide written evidence of circumstances beyond your control that prevented you from writing the quiz. They will also encourage you to do the homework problems that are assigned along with the readings because the questions on the quizzes will often be taken directly from the homework for the previous class.
2. Logic is not a subject that lends itself to discussion to the same extent that most other topics of philosophy courses do. Nevertheless, class participation is still required in this course. The reason for this is that you will master the skills of symbolic logic more rapidly and more perfectly if you regularly talk through how to approach logical problems step-by-step with others. When we take up a problem in class, I will usually either ask for a volunteer to lead us through it or call on someone directly to do so. You don’t have to have all the answers in order to speak up – in fact, it’s often better if you don’t. All you need to do is to be willing to give it a shot.

Make-up Tests. If you miss an exam or a class test due to reasons beyond your control, then you can arrange to take a make-up exam or test by contacting the instructor as soon as possible, and no more than 24 hours after the scheduled time of the exam or test. In order to obtain permission to take a make-up test or exam, you need to provide documentary proof of the circumstances that prevented you from writing the exam or test at the scheduled time within 5 business days of the scheduled time. If you fail to contact the instructor within 24 hours or to provide evidence of what prevented you from taking the test within 5 business days, then you will receive a grade of zero for that test or exam.

Academic Honesty. If you present the words or thoughts of another person as if they were your own, you are guilty of plagiarism. This is true whether or not you intended to pass off the words or thoughts in question as your own. You are also guilty of plagiarism if you present the same work for credit in two different university courses. Plagiarism is an extremely serious academic offense. Penalties for plagiarism can range from getting a zero on the assignment in question through getting an F in the course to being expelled from the university. Plagiarism is also relatively easy for the experienced instructor to spot, so it is difficult to get away with. Given the severe penalties you may incur as a result of plagiarism and the high risk of getting caught, it is wise to do all in your power to avoid committing plagiarism knowingly or unknowingly.

Appropriateness. Does your essay satisfy each of the requirements specified in the handout you received in class? Will it be obvious to the reader how your essay satisfies each of those requirements?

Clarity of exposition and argument. How clearly have you explained the relevant readings? How clearly have you expressed your critical evaluation of the arguments contained in the readings? Have you clearly stated the reasons behind your evaluations?

Critical understanding of the material. Have you demonstrated a detailed, thorough understanding of the relevant readings? Is there any important part or aspect of an argument that you have not considered? Do your accounts of the arguments make sense in light of what you know about the larger context in which they are set (i.e. the book or article as a whole)?

Fairness to the authors' arguments. Are your interpretations of the authors’ arguments charitable? Have you done your best to interpret them as good, strong arguments? If you think a certain argument is badly flawed, have you supplied an argument to support that evaluation?

Coherence of your explanations and arguments. Does your essay make sense as a whole? Does your introduction make clear what your essay is trying to accomplish? Is it clear how each part of your essay serves the overall goal which you set out in your introduction? At each stage of the essay, is it easy to tell what you are saying and how that fits in with what you have already said? Are there any conflicts between things you say at different points in the essay? Do your arguments flow logically from your premises to your conclusions?

Ability to anticipate objections to your point of view. Have you considered how the authors of the articles you discuss (or someone else who read your essay and disagreed with you) might respond to your arguments? Are your arguments open to any obvious objections? Have you committed any glaring errors of reasoning? Are any of the assumptions you make obviously false?

Documentation of works cited. Have you noted where you refer to the work of writers other than yourself? Have you included page numbers in parentheses in the text of your essay to mark where you refer to works on the course syllabus? Have you included full endnotes or footnotes to mark where you refer to works other than those on the course syllabus? Have you included a bibliography listing all the bibliographical information about books you refer to which are not on the course syllabus?

F "Failure – no credit"

• Extreme lack of clarity or coherence of expression or thought.
• Disregard for the objectives and requirements of the assignment.
• Absent or irrelevant use of the relevant course readings.
• Submission of another’s words or thoughts as if they were your own, whether in the form of plagiarism or failure to acknowledge the source of an idea or expression.

D "Work of inferior quality, but passing"

• Unclear or incoherent expression or argument.
• Failure to satisfy the requirements of the assignment.
• Inadequate understanding of the relevant course readings.
• Inadequate acknowledgment or citation of the sources of your expressions or ideas.

C "Satisfactory work"

• Basic clarity and coherence of expression and argument.
• Satisfaction of the assignment’s basic requirements.
• Adequate understanding of the views expressed in the relevant course readings and the arguments provided in support of those views.
• Clear, coherent expression of an evaluation of the views and arguments expressed in the relevant course readings.
• Minimally appropriate acknowledgment and citation of the sources of your expressions and ideas.

B "Noteworthy level of performance"

• Above average clarity and coherence of expression and argument.
• Clear, logical organization of the essay’s introduction, body, and conclusion.
• Clear, detailed, accurate understanding of the views expressed in the relevant course readings and the arguments offered in support of those views.
• Adequate attempt to provide argumentative support for your evaluation of the views and arguments expressed in the relevant course readings.

A "Outstanding achievement and an unusual degree of intellectual initiative"

• Excellent clarity and coherence of expression and argument.
• Clear, cogent, logical argumentative support for your evaluation of the views and arguments expressed in the relevant course readings.
• Originality of interpretation, explanation, argumentation, or ideas.

F - extremely infrequent class attendance

- little or no participation in class discussions

D - infrequent class attendance

- limited participation in class discussions

C - regular class attendance

- limited participation in class discussions

B - regular class attendance

- regular participation in class discussions

A - regular class attendance

- regular participation in class discussions

- frequent thoughtful, insightful, or provocative contributions to class discussions