Gödel's Incompleteness Theorems

Juliette Kennedy (Autor)

Buch | Softcover

75 Seiten

2022
Cambridge University Press (Verlag)
978-1-108-98699-1 (ISBN)

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This Element takes a deep dive into Gödel's 1931 paper giving the first presentation of the Incompleteness Theorems, opening up completely passages in it that might possibly puzzle the student, such as the mysterious footnote 48a. It considers the main ingredients of Gödel's proof: arithmetization, strong representability, and the Fixed Point Theorem in a layered fashion, returning to their various aspects: semantic, syntactic, computational, philosophical and mathematical, as the topic arises. It samples some of the most important proofs of the Incompleteness Theorems, e.g. due to Kuratowski, Smullyan and Robinson, as well as newer proofs, also of other independent statements, due to H. Friedman, Weiermann and Paris-Harrington. It examines the question whether the incompleteness of e.g. Peano Arithmetic gives immediately the undecidability of the Entscheidungsproblem, as Kripke has recently argued. It considers set-theoretical incompleteness, and finally considers some of the philosophical consequences considered in the literature.

Introduction; 1. The first version of the proof; 2. Gödel's 'intuitionistically acceptable' second proof of the First Incompleteness Theorem; 3. The unprovability of consistency; 4. Löb conditions and adequacy; 5. Other proofs of the First and Second Theorems; 6. Mathematical Incompleteness; 7. Set Theoretical Incompleteness; 8. Further philosophical consequences of the Incompleteness Theorems.

Erscheinungsdatum	05.04.2022
Reihe/Serie	Elements in Philosophy and Logic
Zusatzinfo	Worked examples or Exercises
Verlagsort	Cambridge
Sprache	englisch
Maße	151 x 229 mm
Gewicht	150 g
Themenwelt	Geisteswissenschaften ► Philosophie ► Logik
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	1-108-98699-4 / 1108986994
ISBN-13	978-1-108-98699-1 / 9781108986991
Zustand	Neuware