Lectures on Universal Logic

The lectures deal with the questions of logical universality in the sense of an universal logic system.

Is there one universal logic (i.e. a logic that can be applied in all contexts, even inconsistent ones)? Why should we think so? If there are several universal logics which one is the best, most suitable, most natural? If the universal logic involves restrictions on some logical principles valid in FOL how can we recapture them in harmless contexts? Can an universal logic identify object- and meta-language? Can an universal logic render naive semantics and set theory without engendering triviality?


Lecture 1 - Why Universal Logic? (29.10.2020)

Lecture 2 - Routley's Ultralogic Programme (05.11.2020)

Lecture 3 - Routley's Ultralogic in Action (12.11.2020)

Lecture 4 - Brady's Universal Logic Programme (19.11.2020)

Lecture 5 - The Logic DJdQ. Outline & Proof Theory (26.11.2020)

Lecture 6 - The Logic DJdQ. Semantic Foundations (03.12.2020)

Lecture 7 - The Problem of TND in Universal Logic (10.12.2020)

Lecture 8 - Brady's Theory of Classes and Sets (17.12.2020)

Lecture 9 - Semantic Closure in Universal Logic (07.01.2021)

Lecture 10 - Adaptive Logics as Universal Logics (14.01.2021)

Lecture 11 - A Universal Natural Deduction System (21.01.2021)

Lecture 12 - Universal Logic and the Church-Turing-Thesis (28.01.2021)




Manuel Bremer, 2020.