We give an overview of recent results in ordinal analysis. Therefore,we discuss the different frameworks used in mathematical proof-theory, namely subsystem of analysis including reversemathematics, Kripke–Platek set theory, explicitmathematics, theories of inductive definitions,constructive set theory, and Martin-Löfs typetheory.
We give a reading of binary necessity statements of the form “ϕ is necessary for ψ” in terms of proofs. This reading is based on the idea of interpreting such statements as “Every proof of ψ uses ϕ”.
This article provides the proof-theoretic analysis of the transfinitely iterated fixed point theories $\widehat{ID}_\alpha and \widehat{ID}_{ the exact proof-theoretic ordinals of these systems are presented.
We give a survey on truth theories for applicative theories. It comprises Frege structures, universes for Frege structures, and a theory of supervaluation. We present the proof-theoretic results for these theories and show their syntactical expressive power. In particular, we present as a novelty a syntactical interpretation of ID1 in a applicative truth theory based on supervaluation.
Two hundred years after his death, Kant remains one of the most important modern philosophers. The Prolegomena is the ideal introduction to Kant's unique account of the nature human knowledge, according to which we actively shape the world as we know it. -/- This new edition of Kant's own summary of his philosophy is designed specially for students. Guenter Zoeller assumes no prior knowledge of the Prolegomena and provides an extensive and comprehensive introduction which explores Kant's life, the origin and (...) reception of the Prolegomena, the organization of the work, its principal arguments, and its philosophical significance. This edition also includes detailed notes to aid student understanding, as well as a chronology, a glossary and an annotated bibliography. (shrink)
