• Corpus ID: 125710420

Collected Works, Volume I, Publications 1929-1936

  title={Collected Works, Volume I, Publications 1929-1936},
  author={Solomon Feferman and John W. Dawson and Stephen Cole Kleene and Gregory H. Moore and Robert Solovay},

Brain. Conscious and Unconscious Mechanisms of Cognition, Emotions, and Language

Conscious and unconscious brain mechanisms, including cognition, emotions and language, are considered in this review, and dynamic logic is modeled by dynamic logic, evolving from vague and unconscious representations toward crisp and conscious thoughts.

Learning in brain and machine—complexity, Gödel, Aristotle

This article discusses combinatorial complexity of learning algorithms, which means that learning problems of average complexity require more learning examples and more computer operations than all of the interactions of all elementary particles in the entire life of the Universe.

Mathematical continua & the intuitive idea of continuity

The construction of an axiomatic system can help to defend arithmetical continuity, which is omnipresent in modern mathematics; yet, it is fraught with difficulties in relation to the infinite.

What puzzle are you in?

Nature is a tapestry of puzzles, and solving them is a central source of joy in research. Despite their complexity, nature’s puzzles can be classified in the same way as puzzles humans invented for

HYPER-REF: A General Model of Reference for First-Order Logic and First-Order Arithmetic

Abstract In this article I present HYPER-REF, a model to determine the referent of any given expression in First-Order Logic (FOL). I also explain how this model can be used to determine the referent

Betting on Conspiracy Theories: Kurt Godel and ‘The Leibniz Cover-Up’

My contribution to this 2021 symposium on “Alternative Realities, Conspiracy Theory, and the Constitutional and Democratic Order” will explore a little-known conspiracy theory: The Leibniz

Mathematical Incompleteness Results in First-Order Peano Arithmetic: A Revisionist View of the Early History

  • Saul Kripke
  • Philosophy, Mathematics
    History and Philosophy of Logic
  • 2021
In the Handbook of Mathematical Logic, the Paris-Harrington variant of Ramsey's theorem is celebrated as the first result of a long ‘search’ for a purely mathematical incompleteness result in

The Collapse of the Hilbert Program: A Variation on the G\"odelian Theme

The Hilbert program was actually a specific approach for proving consistency. Quantifiers were supposed to be replaced by ε-terms. εxA(x) was supposed to denote a witness to ∃xA(x), arbitrary if

From Intuitionism to Many-Valued Logics through Kripke Models

  • S. Salehi
  • Philosophy
    Logic, Epistemology, and the Unity of Science
  • 2021
Alternative proofs for intuitionistic Propositional Logic are provided by using models of Kripke by providing some results on the inter-definability of propositional connectives in this logic.