Mathematical Logic as Based on the Theory of Types

  title={Mathematical Logic as Based on the Theory of Types},
  author={Bertrand Russell},
  journal={American Journal of Mathematics},
  • B. Russell
  • Published 1 July 1908
  • Philosophy
  • American Journal of Mathematics

Exploring Predicativity

Prominent constructive theories of sets such as Martin-L¨of type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased

Some remarks about Dependent Type Theory

  • Computer Science
  • 2021
One main theme of this work is the importance of notations in mathematics and computer science: new questions were asked and solved only because of the use of AUTOMATH notation, itself a variation of λ-notation introduced by A. Church for representing functions.


  • W. Dean
  • Philosophy
    The Review of Symbolic Logic
  • 2020
A generalization of the Arithmetized Completeness Theorem is presented whereby Russell’s paradox, a variant of Mirimanoff's paradox, the Liar, and the Grelling–Nelson paradox may be uniformly transformed into incompleteness theorems.

Wittgenstein’s Tractatus Logico-Philosophicus and a Hierarchical Approach to Solving Logical Paradoxes

  • V. Ladov
  • Philosophy
    Filosofija. Sociologija
  • 2019
The hierarchical approach to the solution of logical paradoxes is considered in the article. The foundations and main theses of the hierarchical approach are analysed through consideration of

In Praise of Impredicativity: A Contribution to the Formalization of Meta-Programming

  • François Bry
  • Computer Science
    Theory and Practice of Logic Programming
  • 2019
Reflective Predicate Logic is defined, a conservative extension of first-order logic, which provides a simple formalization of meta-programming.

Quantification and Paradox


Predicativity and Feferman

Predicativity is a notable example of fruitful interaction between philosophy and mathematical logic. It originated at the beginning of the 20th century from methodological and philosophical

All There Is: On the Semantics of Quantification over Absolutely Everything

All There Is: On the Semantics of Quantification over Absolutely Everything is a treatise on semantics over absolutely everything.

Logic Programming and Nonmonotonic Reasoning

  • Tran Cao Son
  • Computer Science
    Lecture Notes in Computer Science
  • 2017
A novel feature of this competition edition is the re-introduction of a Model&Solve track, complementing the usual System track with problem domains where participants need to provide dedicated encodings and solving means.

On the number of types

In this paper, I investigate type theories (TTs) from several perspectives. First, I present and elaborate the philosophical and technical motivations for these theories. I then offer a formal