- 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
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