Logic

 

Classes taught:

  • Natural Deduction (FOL ...)

  • Modal Logic 

  • Deontic Logic

  • Metalogic

  • Temporal Logic

  • Inductive Reasoning

  • Paraconsistent Logic

  • Second Order Logic

  • 3-Valued Logic

  • Set Theory

  • Relevant Logic

  • Epistemic Logic

  • The Infinite

  • Dialectics in Kant and Hegel

  • Montague Grammar

  • The Law of Non-Contradiction

  • Gödel's Incompleteness Theorems

  • Frege, Grundlagen der Arithmetik

 

Teaching materials:

 

Published Work:

An Introduction to Paraconsistent Logics.
Bern/New York/Frankfurt a.M. (Lang), 2005.

Table of Content

Universality in Set Theories. A Study in Formal Ontology.Frankfurt a.M. (Ontos), 2010.

Table of Content

 

 

Some Reviews:

 

Some Talks:

Somebody posing with a semantics book
in front of Frege's house in Jena

 

General Research/Fields of Interest:

Philosophical Logic, Metalogic and Its Applications
So called "philosophical logics" (mainly modal logics) are a primary tool of conceptual analysis and model building. The work of conceptual clarification or  model building, nowadays ascribed to the philosopher, has to use these logics as tools. The relation between various systems (say of modalities like necessity) and our different preconceptions of the modalities is one field of special importance, as is the ongoing development of such (modal) logics and corresponding meta-logical work. Another related philosophical application of logic I am interested in is the relation between meta-logical results established for formal systems and the question of the limits of the human mind. Church`s Thesis could be understood as a bridge between meta-logic and the philosophy of mind (see these slides on this questions, or the paper). In general issues of computability and complexity link logic and the cognitive sciences (cf. my fields of interest in the cognitive sciences).
Paraconsistency and Dialetheism
Since philosophy traditionally claims to make universal claims (about truth, language or knowledge) the questions of universality and closure are central if this traditional claim (of a version of transcendental philosophy) is not to be given up. I do not think philosophy should give up this self-understanding. So philosophy has to deal with the paradoxes of semantic closure and universality. My work in paraconsistency (see the book An Introduction to Paraconsistent Logics and the lectures on paraconsistency) tries to find a way to secure semantic closure without sacrificing too much of our standard logical approach. Continuing work deals with the problem of new paradoxes within paraconsistent logic (see the papers on asserting contradictions and on hypercontradictions) and the recent developments of paraconsistent logic and its applications. A topic related to universality are the foundations of set theory as set theory is generally used in meta-logical modelling and set theory itself has its own problem of universality (ranging from the paradoxes involving the universal set to the difficult ontological status of the set theoretic universe). My book Universality in Set Theories addresses some of these issues.

 

© Manuel Bremer