PHIL 422, Secs. 1001/1002: MW 11:30am-12:45pm/1pm-2:15pm ONLINE

University of Nevada, Las Vegas

Fall 2020

Professor: James Woodbridge

email:

Course Webpage: http://jwood.faculty.unlv.edu/unlv/Phil422F20.htm

Office: CDC 426

Office Hours: Th via Zoom--TIME TBD

Dept. Phone: 895-3433

This is a course on basic metalogic (with some mathematical preliminaries to start). Metalogic is the study of facts about and properties of logical systems as a whole (as opposed to learning to use a particular logic system, e.g., to construct proofs within that system, as you did in PHIL 114). These metalogical facts determinate the scope and limits of formal theorizing, that is, what it is and is not possible to accomplish with a formal system (e.g., what can and cannot be determined by purely formal processing or what can be modeled formally). As this is a Philosophy class, there will be a number of concepts and distinctions you must learn and be able to explain, along with the techniques you need to master for doing problems and proofs. One of the central issues we will focus on is the distinction between the syntactic features of a certain kind of formal system and the system's semantic features. We will learn how in certain formal system these features line up exactly, and we will prove that they do for a particular formal system we will work with. Topics we will cover along the way will include the basic syntax of a formal language, interpretations and models of sentences from that formal language, the truth-functional expressive completeness of various sets of logical operators, and the soundness, completeness, compactness, and undecidability of First-Order Logic.

The Learning Goals for this course are an extension of the Philosophy Department's general goal to have students exhibit facility in the theory and practice of argumentation, reasoning, and critical thinking. These include the following.

1. Mastering the practice of reasoning well, including

A. The ability to construct clear and concise summarizations and assessments of the reasoning in complex passages by

i) Extracting their conclusions

ii) Distilling the lines of reasoning in support of those conclusions

iii) Evaluating how well such reasoning supports those conclusions.

B. The ability to construct cogent arguments for conclusions and to express the reasoning involved in a coherent and convincing manner.

2. Demonstrating knowledge of, and competence with, the theory of argumentation and logic through the ability to:

A. Describe different approaches to logical theory, and to articulate their aims and scope.

B. Define and apply central concepts and techniques of logical theory.

C. Describe major results of logical theory.

D. Sketch how to arrive at those results.

**II. REQUIRED CLASS MATERIALS**

**Books:**

There is no textbook you need to purchase for this course.

Readings will mainly come from free online postings of handouts I will distribute, plus some chapters from Paul Teller's *A Modern Formal Logic Primer*, available online for free. I will post the course handouts and Teller chapters on the course Webpage.

**III. ONLINE CLASS FORMAT**

The online class meetings will consist mostly of lectures explaining concepts and distinctions, demonstrations of problem-solving and proof techniques, and sample exercises. On Mondays by 11:30am I will make available a prerecorded lecture for both sections that you will need to watch by Tuesday night (to count as having attended). On Wednesdays I will give live virtual lectures at the originally scheduled times for both sections. The live meetings are intended to give you an opportunity to ask questions about the material covered in the readings and the prerecorded lecture and to ask to see particular problems from homework assignments done. All the lectures/meetings will be recorded and available for re-watching/reviewing at later times.

**IV. CLASS REQUIREMENTS AND GRADING SCHEME**

__Requirements__
.............................................__Percent of Final Grade
__

Participation.................................................................5%

Homework...................................................................20%

First Test......................................................................15%

Second Test..................................................................20%

Third Test.....................................................................20%

Final Exam...................................................................20%

__Homework__—This requirement covers completion of and performance on the homework assignments. The homework provides practice with the techniques presented during the course lectures, so *it is crucial that you keep up with the assignments*. There will be an assignment due every week. No late assignments will be accepted.

__The First Test__—There will be a timed, scheduled test distributed online in mid-late September. The test questions will cover concepts and definitions and include problems like those on the homework assignments and in the readings, and the proofs done in the course lectures.

__The Second Test__—There will be a second timed, scheduled test distributed online in mid October. Again, the test questions will consist of problems like those on the homework assignments and proofs done during the course lectures.

__The Third Test__—There will be a third timed, scheduled test distributed online in mid November. Again, the test questions will consist of problems like those on the homework assignments and proofs done during course lectures.

__The Final Exam__—There will be a timed, scheduled final exam distributed online during Exam Week. The final will essentially be cumulative, but it will emphasize the material since the Third Test. The exam questions will include problems similar to the homework and course lecture proofs, as well as some pertaining to concepts.

The course units and topic covered in them are as follows.

0. Mathematical Preliminaries

Introduction to the notation and basic aspects of set theory, and an explanation of mathematical induction, including the distinction between1. Artificial Formal Language (FOL) BasicsstrongMI andweakMI. (1 week)

Review of basic syntax (Lexicon and Formation Rules) and semantics (e.g., "translational" or intensional interpretations, intuitive models, truth-tables) for the language of First-Order Logic. (2 weeks)2. General Semantics and Model Theory

Extensional interpretations, models, contingency, consistency, semantic proofs, logical truth/falsity, entailments/enfailments, inconsistency, semantic equivalents (4 weeks)3. Deductive Apparatus

Tree system rules, theorems/anti-theorems/neutrals, compatibility/incompatibility, establishment/non-establishment, coupled/uncoupled sentences (3 weeks)4. Metalogic

Mathematical induction (for real), soundness, completeness, König's Lemma, compactness, undecidability (4 weeks)