Phil. 160 Deductive Logic II

PHIL. 160
Weekly Schedule of
Topics and Readings

Spring Semester 2012

Prof. Dowden

Week 1: Survey of What Is Ahead: Standard and Nonstandard Logics, Semantics and Proofs, Meta-theory, Gödel's Theorems, Church-Turing Undecidability, Modal Logic.

Reading: Browse "A Very Brief History of Mathematical Logic". "Very Brief Survey of the Main Nonclassical Logics". Definitions of "logically correct". Pages 1-11 of Sider's Logic for Philosophy.

Weeks 2-3: Propositional Logic: Syntax, Semantics, Axioms, and Meta-Logic.

Reading: "Review of Propositional Logic".

Reading: Pages 12-24 of Sider chapter 1. "Propositional Logic" by Wilfrid Hodges [patience required for the slow loading time]. Chapter 2 of Sider; merely browse sections 2.5 and 2.9 on sequent proofs and Henkin's completeness proof.

Weeks 3-4: Beyond Standard Propositional Logic: Expressive Completeness, Polish Notation, Three-Valued Logics by Lukasiewicz, Kleene and Priest. 4-Valued Paraconsistent Logic. Fuzzy Logic. Supervaluations.

Reading: "Introduction to 3-Valued Logic".

Reading: Chapter 3.

Weeks 5-6: Predicate Logic: Syntax, Semantics, Axioms, and Meta-Logic.

Reading: Chapter 4.

Weeks 7-9: Identity, Functions, the Unsolvability of the Halting Problem, the Church-Turing Undecidability Theorem for Predicate Calculus, Tarki's Undefinability Theorem for Truth in Predicate Calculus, Robinson Arithmetic, and Gödel's Incompleteness Theorems.

Reading: Chapter 5, pages 107-113. "Halting and Undecidability," "Proof of Gödel's First Incompleteness Theorem," "Proof of Gödel's Second Incompleteness Theorem," "Gödel and the Nature of Mathematical Truth, " "History of Logic" and "Logic for Calculus".
Midterm on Thursday of week 8.

Week 10: Beyond Standard Predicate Logic: Binary Quantifiers, Second-Order Logic, Free Logic.

Reading: Chapter 5, pages 113-132, skipping sections 5.3 and 5.5.

Weeks 11-12: Standard Modal Logics and Kripke Models.

Reading: "Kripke's Modal Logic" in SacCT. Chapter 6.

Week 13-15: Beyond Standard Modal Logic to Deontic, Epistemic, Tense, and Intuitionistic Logic.

Reading: Chapter 7.

The above schedule of course topics may be changed somewhat as we progress through the semester, but these changes, if any, are not expected to affect the scheduled due dates for the homeworks and tests.

back to the main syllabus

PHILOSOPHY DEPARTMENT / PROF. DOWDEN / CSUS
Updated: April 25, 2012


PHIL. 160 Weekly Schedule of Topics and Readings Spring Semester 2012 Prof. Dowden


	Week 1: Survey of What Is Ahead: Standard and Nonstandard Logics, Semantics and Proofs, Meta-theory, Gödel's Theorems, Church-Turing Undecidability, Modal Logic. Reading: Browse "A Very Brief History of Mathematical Logic". "Very Brief Survey of the Main Nonclassical Logics". Definitions of "logically correct". Pages 1-11 of Sider's Logic for Philosophy. Weeks 2-3: Propositional Logic: Syntax, Semantics, Axioms, and Meta-Logic. Reading: "Review of Propositional Logic". Reading: Pages 12-24 of Sider chapter 1. "Propositional Logic" by Wilfrid Hodges [patience required for the slow loading time]. Chapter 2 of Sider; merely browse sections 2.5 and 2.9 on sequent proofs and Henkin's completeness proof. Weeks 3-4: Beyond Standard Propositional Logic: Expressive Completeness, Polish Notation, Three-Valued Logics by Lukasiewicz, Kleene and Priest. 4-Valued Paraconsistent Logic. Fuzzy Logic. Supervaluations. Reading: "Introduction to 3-Valued Logic". Reading: Chapter 3. Weeks 5-6: Predicate Logic: Syntax, Semantics, Axioms, and Meta-Logic. Reading: Chapter 4. Weeks 7-9: Identity, Functions, the Unsolvability of the Halting Problem, the Church-Turing Undecidability Theorem for Predicate Calculus, Tarki's Undefinability Theorem for Truth in Predicate Calculus, Robinson Arithmetic, and Gödel's Incompleteness Theorems. Reading: Chapter 5, pages 107-113. "Halting and Undecidability," "Proof of Gödel's First Incompleteness Theorem," "Proof of Gödel's Second Incompleteness Theorem," "Gödel and the Nature of Mathematical Truth, " "History of Logic" and "Logic for Calculus". Midterm on Thursday of week 8. Week 10: Beyond Standard Predicate Logic: Binary Quantifiers, Second-Order Logic, Free Logic. Reading: Chapter 5, pages 113-132, skipping sections 5.3 and 5.5. Weeks 11-12: Standard Modal Logics and Kripke Models. Reading: "Kripke's Modal Logic" in SacCT. Chapter 6. Week 13-15: Beyond Standard Modal Logic to Deontic, Epistemic, Tense, and Intuitionistic Logic. Reading: Chapter 7. The above schedule of course topics may be changed somewhat as we progress through the semester, but these changes, if any, are not expected to affect the scheduled due dates for the homeworks and tests. back to the main syllabus PHILOSOPHY DEPARTMENT / PROF. DOWDEN / CSUS Updated: April 25, 2012