Logic & Proofs

(80-210)

Instructor: Wilfried Sieg

Teaching Assistant: Tyler Gibson

Discussion Sections:Office Hours:

Fr 11:00-11:50Mon 4:00-5:00

Fr 1:00-1:50By appointment

Baker Hall 150Baker Hall 135G

This is a brand-new course, though it appears under an old course number and has been offered four times. Naturally, it is still an introduction to logic!

Issues: The broad informal question we are going to address is this: How can one analyze the structure of rational discourse or, more specifically, the logicalstructure of argumentation? To answer this question, we have to take four distinct steps:

(i)uncover the logical form of statements;

(ii)define the correctness or soundness of logical steps;

(iii)formulate sound inference rules appropriate for the logical forms;

(iv)design strategies for logical argumentation using the inference rules.

We will do this for two different analyses of “logical form,” namely, one provided by Sentential Logic and one provided by Quantificational Logic (also called Predicate or First-order Logic). The latter framework is rich and far-reaching; it also can serve as a paradigm for further extensions.

Material: After an informal Introduction (Module 1), the material is presented in two big Parts, dealing with the two types of logical analyses mentioned above. In Sentential Logic statements (expressed by declarative sentences that are either true or false) are the atoms of discourse; these atoms can be joined into compound statements by using logical connectives like ‘and,’ ‘or,’ ‘if …, then …’, and ‘not.’ This constitutes an important part of logical argumentation, but it is only a proper part. Even such an obvious and classical logical step as the inference from ‘All philosophers are wise’ and ‘Socrates is a philosopher’ to ‘Socrates is wise’ cannot be taken in sentential logic. For that, and much more, the framework of Quantificational Logic is needed. In both cases we are going to take the steps (i) – (iv) indicated above. This will provide you with the tools for, and the practice of, analyzing and constructing arguments.

Presentation: All material is presented on-line – with quizzes and exercises; some of the exercises have to be done with pen and paper. There will be some additional readings of a more historical sort, complementing the systematic on-line presentation. The most sophisticated framework for on-line exercises is provided by the Carnegie Proof Lab (briefly, CPL), in which you are asked to construct logical arguments.

The course delivery system is called JCourse; its development was begun in the Department of Philosophy several years ago, but it is now part of the Open Learning Initiative (OLI), which is supported by a grant from the Hewlett Foundation. OLI is developing also courses in Economics, Statistics, Biology, Chemistry, and Causal & Statistical Reasoning.

The on-line presentation is supplemented in our weekly meetings by collaborative reviews, the opportunity for discussing substantive issues, and also for critical responses to the on-line material. As to the latter, we are very eager to hear where you have difficulties, where an additional example might be helpful, and so on.

Requirements: (I) working through the on-line material, which includes completing quizzes and on-line exercises, in particular proof constructions in CPL; (II) pen & paper work, i.e., some additional exercises; (III) a mid-term concerning sentential logic; (IV) a final concerning predicate logic; (V) attendance of and participation in the weekly meetings.

Grades will be based on (I) – (V) in the proportion 35:15:15:25:10. As to (IV), the weekly meetings are extremely important, and attending them is one of your real obligations.

Structure of weekly meetings: Our meetings will be divided roughly into two segments. In the first segment, twenty minutes or so, we review the material systematically and may discuss some additional issues of interest. The second segment will be devoted to brief presentations by you, to questions you have, on the one hand, and to your critical responses to the on-line presentation, on the other hand.

Remarks: I also urge you to make use of my office hours; if you have any problems with the course material, do come. You can also make an appointment with me by a phone call (286-8565) or an e-note (). For problems with the software or also other issues, please contact our software developer or the Teaching Assistant for this class .

Policies: We encourage collaboration and intensive discussion, but all submitted work must be your individual work.

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