- 613 名前:現代数学の系譜 雑談 [2021/05/27(木) 22:28:22.15 ID:dKVKdotp.net]
- >>521
HOL ”METAPHYSICS”だよ〜ん。 HOLは、数学独占じゃない!!(^^; tedsider.org/teaching/higher_order_20/higher_order_20.html SEMINAR ON HIGHER ORDER METAPHYSICS Rutgers Philosophy Department, 106 Somerset St, 5th floor, Fridays, 9:50-12:50, Spring 2020 Ted Sider, Room 526, office hours TBA and by appointment Syllabus Handout: philosophy of logic and second-order logic tedsider.org/teaching/higher_order_20/HO_CC_second_order_logic.pdf Handout: paradoxes and set theory tedsider.org/teaching/higher_order_20/HO_crash_course_paradoxes.pdf Handout: type theory and lambda abstraction tedsider.org/teaching/higher_order_20/HO_CC_type_theory_lambda_abstraction.pdf Handout: Boolos tedsider.org/teaching/higher_order_20/HO_Boolos.pdf Handout: Prior tedsider.org/teaching/higher_order_20/HO_Prior.pdf Handout: Rayo and Yablo tedsider.org/teaching/higher_order_20/HO_Rayo_Yablo.pdf tedsider.org/teaching/higher_order_20/higher_order_crash_course.pdf Crash course on higher-order logic* Theodore Sider August 14, 2020 Contents 1 Introduction 2 2 Importance of syntax to logic 3 2.1 Syntax in formal languages ..5 3 First- versus second-order logic 7 3.1 Syntax ... 7 3.2 Formal logic and logical consequence ..9 3.3 Semantics ...10 3.4 Proof theory ... 12 3.5 Metalogic ...16 3.5.1 Completeness ..16 3.5.2 Compactness ..17 3.6 Metamathematics ... 20 3.6.1 Skolem’s paradox ..21 3.6.2 Nonstandard models of arithmetic .21 3.6.3 Schematic and nonschematic axiomatizations .23 4 Paradoxes 26 4.1 Abstract mathematics and set-theoretic foundations . 26 4.2 Russell’s paradox ...28 4.3 Axiomatic set theory and ZF .. 30 4.4 Other paradoxes, other solutions ..34 5.1 Third-order logic and beyond ..37 5.2 Higher-order logic and types .. 38 略 以上
|

|